Research ArticleReconstruction of Intima and Adventitia Models intoa State Undeformed by a Catheter by Using CT IVUS andBiplane X-Ray Angiogram Images
Jinwon Son and Young Choi
School of Mechanical Engineering Chung-Ang University 221 Heukseok-dong Dongjak-gu Seoul 156-756 Republic of Korea
Correspondence should be addressed to Young Choi yychoicauackr
Received 28 October 2016 Accepted 6 December 2016 Published 5 January 2017
Academic Editor Xiaopeng Zhao
Copyright copy 2017 J Son and Y Choi This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The number of studies on blood flow analysis using fluid-structure interaction (FSI) analysis is increasingThough a 3D blood vesselmodel that includes intima and adventitia is required for FSI analysis there are difficulties in generating it using only one type ofmedical imaging In this paper we propose a 3D modeling method for accurate FSI analysis An intravascular ultrasound (IVUS)image is used with biplane X-ray angiogram images to calculate the position and orientation of the blood vessel However theseimages show that the blood vessel is deformed by the catheter inserted into the blood vessel for IVUS imaging To eliminate suchdeformation a CT image was added and the twomodels were registered First a 3Dmodel of the undeformed intima was generatedusing a CT image In the second stage a model of intima and adventitia deformed by the catheter was generated by combining theIVUS image and the X-ray angiogram images A 3D model of intima and adventitia with the deformation caused by insertion ofthe catheter eliminated was generated by matching these 3D blood vessel models in different states In addition a 3D blood vesselmodel including bifurcation was generated using the proposed method
1 Introduction
Thanks to the advances in computing and analysis tech-niques studies on circulatory diseases using CFD (compu-tational fluid dynamics) analysis are now using FSI (fluid-structure interaction) analysis that can take into account themovement of blood vessel walls [1ndash4] As opposed to CFDanalysis that requires only a 3D model of intima a 3D modelcontaining information about the blood vessel thickness isrequired to analyze the blood flow inside the blood vesseland the forces applied to the blood vessel wall using FSIanalysis [5ndash9] However there are difficulties in generatinga 3D model of blood vessel that includes both the intima andadventitia using only a single type of medical image owingto the characteristics of the imaging techniques To achievethis many studies have proposed 3D modeling methods ofblood vessels that include intima and adventitia by combiningdifferent imaging techniques or by making assumptionsThe representative imaging techniques used for such blood
vessel modeling methods are CT (computed tomography)and IVUS (intravascular ultrasound)
Though the shape of a blood vessel intima can be easilyobtained using a CT image no information can be obtainedabout the blood vessel adventitia In addition owing to thelow accuracy of CT images the blood vessel intima modelgenerated using a CT image will have an uneven surfaceAntiga has proposed a method of calculating the centerlineof the blood vessel model to resolve the problem of the bloodvessel model generated using such a CT image [10 11] A3D blood vessel model generated using a CT image wasautomatically corrected using the centerline of the 3D bloodvessel model and a 3D blood vessel model that includes theintima and adventitia was generated with the assumption thatthe thickness of a blood vessel wall is proportional to theinner diameter
An IVUS image is an image that shows the cross sectionof a blood vessel by inserting a microminiaturized ultrasonicinstrument into the blood vessel As an IVUS image is
HindawiComputational and Mathematical Methods in MedicineVolume 2017 Article ID 9807617 13 pageshttpsdoiorg10115520179807617
2 Computational and Mathematical Methods in Medicine
(a) (b)
Figure 1 (a) Shape of blood vessel before catheter insertion (b) Shape of blood vessel after catheter insertion [19]
taken around a blood vessel a lot more detailed informationabout the blood vessel can be obtained than that with aCT image In addition because an ultrasonic wave is usedit has the advantage that the information about the bloodvessel adventitia can also be obtained However an IVUSimage only shows the cross section of a blood vessel withoutshowing the position and direction at which the IVUS imageis taken Whale has proposed a sequential triangulationmethod that calculates the position and orientation of anIVUS image using biplane X-ray angiogram images [12ndash17] The 3D path along which IVUS images were takenwas generated using biplane X-ray angiogram images andthe positions and orientations of these IVUS images werecalculated using only the geometric shape of this path
However the catheter inserted to take the IVUS imageheavily deforms the blood vessel as shown in Figure 1Accordingly the IVUS image and the biplane X-rayangiogram images taken with the catheter inserted show theinformation about the blood vessel deformed by the catheterinsertion In addition the blood vessel model generated bycombining these images will also be in a deformed state
The initial state of the blood vessel has a great effect onthe analysis result of the blood vessel model Accordinglyin this study we propose a 3D modeling method of intimaand adventitia with the deformation caused by insertion of acatheter eliminated for accurate FSI analysis
2 Overview
Figure 2 shows the overall flow of the 3D blood vesselmodeling method proposed in this study
This method can be largely divided into three stagesFirst a 3D model of the undeformed intima is generated
using a CT image CT images only require a contrast mediumto be administered and thus do not have any deformationcaused by insertion of a catheter
Then a 3D intima and adventitia model in a statedeformed by a catheter is generated by combining IVUS and
CT image
Undeformedintimal model
Centerline
of intima
Deformedintimaladventitial model
Centerline
of intima of adventitia
Transformation
of intima of adventitia
Registration
IVUS image 3D catheter path
X-ray angiogram image
Cross section Cross section Cross section
Cross section Cross section
Undeformed 3D blood vessel model
Figure 2 Overview of the proposed blood vessel modelingmethod
biplane X-ray angiogram images As explained earlier IVUSimages and biplane X-ray angiogram images show informa-tion about the blood vessel in a state deformed by insertionof a catheter
The last stage involves converting the 3D model of thedeformed intima and adventitia into a 3D model of theundeformed intima and adventitia through registration
The last stage involves converting the 3D model of thedeformed intima and adventitia into a 3D model of theundeformed intima and adventitia through registration Forthis the cross sections of the 3D models are extracted andregistered First as the intimae exist in different states thedeformed intima is registered with the undeformed intima
Computational and Mathematical Methods in Medicine 3
An artificial blood vessel model IVUS image
CT image
angiogram imagesBiplane X-ray
(a) (b)
Figure 3 (a) Blood vessel replica (b) CT IVUS and biplane X-ray angiogram images of the replica
The cross sections of the undeformed intima and adventitiaare calculated by applying the registration result to the crosssection of the deformed adventitia
A blood vessel replica was produced as shown inFigure 3(a) to facilitate acquisition of the medical imagesrequired for the method proposed in this paper A siliconetube was used as the replica blood vessel and gelatin was usedto fix it and to enable it to be deformed when a catheter wasinserted Figure 3(b) shows the CT IVUS and biplane X-rayimages taken using the blood vessel replica
3 Reconstruction of UndeformedIntima Model
ACT image can be obtained without inserting a catheter intothe blood vessel by administering a contrastmediumand thusshows the undeformed shape of the blood vessel Howeveras it only shows the contrast medium passing through theblood vessel no information about the adventitia of the bloodvessel can be acquired Accordingly we intended to utilizethe overall shape of the blood vessel without the catheter-induced deformation by using such characteristics of CTimages For this a 3D intimamodel with no catheter-induceddeformation was generated using the CT image of the bloodvessel replica
A CT image consists of voxel data produced by stackingtomograms of a human body To generate a 3D blood vesselmodel a process of extracting the polygon data correspond-ing to the blood vessel from the voxel data is required Togenerate the polygon data of the blood vessel from the voxeldata the isosurfaces that have the same intensity value asthat of the section corresponding to the blood vessel were
Figure 4 Generated 3D undeformed intima model of replica
extracted from each tomogram A polygon model of theblood vessel was generated by stacking these isosurfaces andapproximating the NURB surfaces Figure 4 shows the 3Dmodel of the undeformed intima generated using the CTimage of the blood vessel replica
4 Reconstruction of Deformed Intima andAdventitia Model
41 Extraction of the Blood Vessel Intima and Adventitia CrossSections in a Deformed State An IVUS image shows theinside of a blood vessel in greater detail than a CT image asit is obtained by imaging the inside of the blood vessel withan ultrasonic device inserted into the blood vessel Moreoverit provides information about the shape of the blood vesseladventitia Figure 5 shows the cross sections of blood vesselintima and adventitia extracted from an IVUS image
4 Computational and Mathematical Methods in Medicine
1
2
3
Figure 5 IVUS image of blood vessel
Figure 6 Segmented intima and adventitia contours from IVUSimage
As an IVUS image does not include color values but haspoints with gray scale values there are difficulties in automat-ically extracting the areas corresponding to the intima andthe adventitia of a blood vessel Accordingly in this studywe checked the IVUS image and manually segmented thesections corresponding to the intima and adventitia of theblood vessel respectively as shown in Figure 6
42 Restoration of 3D Catheter Path Though an IVUS imagecontains information about cross section of a blood vesselthe position and orientation at which the image was acquiredare unknown Accordingly to generate a 3D blood vesselmodel using the cross sections of the blood vessel intima andadventitia extracted earlier from an IVUS image the positionand orientation where the IVUS image has been actuallytaken should be conjectured using other medical imaging
techniques For this biplane X-ray angiogram images wereused in this study
When taking IVUS images the path along which theIVUS images are to be taken is secured by inserting acatheter in advance to place an IVUS ultrasonic device at theplace where the imaging is to be started When the IVUSultrasonic device arrives at the desired position it followsthe catheter and acquires images of the blood vessel crosssections with the path of the IVUS images matching the pathof the catheter To obtain the catheter path X-ray angiogramswere taken from different directions immediately before theIVUS ultrasonic device was pulled back to take images The3D catheter path was generated as shown in Figure 7 usingthe two 2D catheter paths extracted from the biplane X-rayangiogram images
43 Calculation of IVUS Image Position and OrientationWhen IVUS images are acquired the IVUS ultrasonic devicemoves out of the catheter at a constant speed using the IVUSpullback device Accordingly if the 3D catheter path restoredusing the biplane X-ray angiogram images is divided intoas many parts as the number of the IVUS images using thesame interval the positions where the IVUS images havebeen acquired can be easily calculated However as the IVUSultrasonic device rotates around the catheter when it travelsaround a bent blood vessel the IVUS image acquired at thistime is in a rotated state
Whale has proposed the sequential triangulation methodthat can determine the twist angles of IVUS images usingthe characteristics of such IVUS images With this methodthe orientations of IVUS images were calculated using onlythe geometric shape of the catheter restored in 3D A 3Dcatheter path was divided into small pieces assuming that itis comprised of innumerable joints and links The positionsand orientations of IVUS images were determined as shownin Figure 8 using the 3 consecutive points on the 3D pathdivided into smaller pieces The orientation of each IVUS
Computational and Mathematical Methods in Medicine 5
(a) (b)
Figure 7 (a) Biplane X-ray angiogram images of IVUS catheter (b) Restored IVUS catheter path in 3D space
Frame 0 Frame 1 Frame 2 Frame 3Frame 4
P0
P1
P2
P3
P4
P5
n0
n1n2
n3
Figure 8 Sequential triangulation method [15]
image is determined by the plane made of the 3 consecutivepoints existing on the catheter P is the position of each pointand S which is the position of an IVUS image is the centerof the two points as shown in the following [12ndash17]
S119894 = (P119894 + P119894+1)2
S119894+1 = (P119894+1 + P119894+2)2 (1)
Also the tangent vector t at P is calculated as follows
t119894 = P119894+1 minus P119894t119894+1 = P119894+2 minus P119894+1
(2)
The normal vector n which is each of the 119910-axis direc-tions of the 2D IVUS images was calculated by calcu-
lating the outer products of the two neighboring tangentvectors t
n = t119894 times t119894+1 (3)
Through such a method the position and orientationwhere an IVUS image was taken were determined fromthe 3D path of the catheter Figure 9(a) shows the result ofapplying the position and orientation calculated using thesequential triangulation method to the cross sections of theblood vessel intima and adventitia extracted from a 2D IVUSimage and Figure 9(b) shows the polygon model generatedusing the points in 3D space As these models were generatedby combining the IVUS and biplane X-ray angiogram imagestaken in a state deformed by a catheter they are the bloodvessel intima and adventitia models deformed by insertion ofa catheter
5 Computation of Undeformed Intima andAdventitia Model by Registration
In this chapter we intend to compute a 3D intima andadventitia model without the catheter-induced deformationTo achieve this the 3D model of deformed intima andadventitia generated by combining the IVUS and biplane X-ray angiogram imageswas registeredwith the 3Dmodel of theundeformed intima generated using aCT image As these two3D models do not only exist on different coordinate systemsbut also have different scales there are difficulties in directlyregistering these 3D models Accordingly in this study we
6 Computational and Mathematical Methods in Medicine
Contoursof intima 3D catheter path
Deformed intima model
Deformed adventitia model
(a) (b)
Figure 9 (a) A series of deformed intima cross sections (b) A polygon model of deformed intima and adventitia model
propose a method of determining the corresponding relationbetween the two 3D blood vessel models to extract the crosssections at the corresponding positions and matching them
51 Calculation of Centerline and Extraction of Cross SectionTo define a plane required for extraction of 2D cross sectionsfrom the 3D blood vessel intimamodel in a tube form one 3Dpoint and normal vector are required For this the centerlinethat could well express the shape of the blood vessel shouldbe calculated
In the study carried out by Luca the centerline existingbetween twopointswithin amodel in a tube formwas definedto be the line farthermost from the boundary Accordinglythe centerline of an object Ω existing in a 3D space can beexpressed as the pathC = C(s) between two points P1 and P2which minimizes
Ecenterline (C) = intL=Cminus1(P1)
0=Cminus1(P0)F (C (s)) 119889119904 (4)
For this the Delaunay triangulation of the object Ω wascalculated throughwhich themaximum spheres inscribed inthe blood vessel model were calculated The centerline of the3D blood vessel model was extracted using the center pointsof these spheres
52 Correspondence Definition between 3D Blood Vessel Mod-els and Extraction of Cross Sections To register two bloodvessel models in different states correspondence between thetwomodels should be defined first For this the centerlines ofthe two intima models calculated earlier were used Becausethe CT IVUS and biplane X-ray angiogram images wereall obtained by imaging the same section of the bloodvessel replica the 3D blood vessel models generated earliermodel the same section of the blood vessel though they arein different states Accordingly the corresponding relation
between these two intima models was defined by dividingthe center curves of these two intima models into the samenumber of lines using the same interval and the crosssections of the 3D models were extracted at the definedpositions
53 Registering between Cross Sections in Different States Inthis study we intend to generate a 3D intima and adven-titia model from which the catheter-induced deformationis removed through registration Accordingly we attemptedto convert the cross sections of the deformed intima andadventitia extracted earlier into the cross sections of theundeformed intima and adventitia For this the cross sectionsof the deformed intima and adventitia were registered withthe cross sections of the undeformed intima
Registration is the calculation of the coordinate transfor-mation that can minimize the distance between two pointsets Accordingly registration in this study is to calculate thetranslation (119909 119910) rotation (120579) and scale (119904) that minimizesthe distance between the two point sets (X target point cloudY source point cloud) which compose the 2D blood vesselcross sections In this study the coordinate transformationmatrix T0 that minimizes the distance between the two pointsets X and Y was calculated using the optimization methodafter setting these 4 elements as the variables In additionto make a result linear to the rotation value of the previousframe when registering cross sections the value closest to therotation value 120579 of the previous frame was calculated
T0 = min (sum dist (XY1015840)) (5)
whereY1015840 = T (119909 119910 120579 119904)Y (6)
To achieve this the multiminimizer function of theGNU Scientific Library was used [18] Figure 10 shows theregistration result of the two intima cross sections
Computational and Mathematical Methods in Medicine 7
Deformed intima
Registration
Undeformed intima
Figure 10 Registration between undeformed and deformed intima contours using the proposed method
60y = minus3E minus 09x5 + 2E minus 06x4 minus 00005x3 + 00344x2 + 07059x minus 10207
Figure 11 Trend line of rotation angle result
The 119909 119910 120579 and 119904 calculated through the registrationbetween intima cross sections are the values at which thedeformed intima cross section changes to the undeformedintima cross section Accordingly the calculated 119909 119910 120579 and 119904were equally applied to change the deformed adventitia crosssection to the undeformed adventitia cross section Figure 11shows the rotation values of all the cross sections registeredusing the optimization method To more linearly transformsuch rotation values the trend linewas calculated using all therotation values and the rotation value of each cross sectionwas corrected to the trend line value
54 Generation of an Undeformed Intima and AdventitiaModel The cross sections of the undeformed intima andadventitia were calculated through a process similar to thatabove To finally generate a model in an undeformed stateusing such cross sections the cross sections should be locatedat the proper positions and in proper orientation For thisthe centerline extracted from the 3D model of the intimanot deformed by a catheter which was generated from a CTimage was used A 3D blood vessel polygon model whichincluded the intima and adventitia as shown in Figure 12was generated by placing the calculated cross sections ofthe undeformed intima and adventitia on the undeformedcenterline
6 Bifurcated Blood Vessel Model
In fact human blood vessels are not comprised of singleblood vessels but a combination of blood vessels with many
Figure 12 Generated 3D blood vessel model including intima andadventitia
branches Accordingly to actually model the blood vessel ofa patient not a single blood vessel model but a 3D bloodvessel model that includes branches should be generatedAccordingly a 3D blood vessel model including branches notdeformed by a catheter was generated using the proposedblood vessel modeling method in this chapter For this ablood vessel replica including branches was produced asshown in Figure 13 Different from the case of a single bloodvessel this replicawas produced by creating a 3Dmodel usingthe CT images of an actual patient and producing a moldusing a 3D printer A blood vessel replica of the desired formwas produced by injecting silicon into this mold For thisreplica gelatin was again used to fix the blood vessel tube
The CT IVUS and biplane X-ray angiogram images weretaken using the produced blood vessel replica as per the caseof a single blood vessel As the replica includes branches theIVUS images and the X-ray angiogram images of each bloodvessel branch were taken Figure 14 shows themedical imagestaken using the blood vessel replica
61 Generation of a 3D Intima Model Including Branches NotDeformed by a Catheter and Extraction of Cross Sections In
8 Computational and Mathematical Methods in Medicine
Figure 13 Replica of blood vessel
CT IVUS
X-ray angiogram
Figure 14 CT biplane X-ray angiogram and IVUS images of replica
the case of the blood vessel that includes branches a 3Dmodel of the intima not deformed by a catheter was alsogenerated using the CT image as per the single blood vesselFigure 15 shows the 3D model of the intima not deformed bya catheter which was generated using a CT image
To extract the cross sections of the 3D intima models thecenterline of each branch was calculated using a 3D Voronoidiagram Figure 16 shows the centerline of each branch andthe cross sections extracted using them
62 Generation of a 3DModel of the Intima andAdventitia NotDeformed by aCatheterThat Includes Branches and Extractionof Cross Sections To generate a blood vessel model thatincludes branches the IVUS images of all the blood vesselbranches should be taken to obtain data about the intimaand adventitia of each blood vessel branch In addition tocalculate the position and orientation of the IVUS imageof each branch when the IVUS image of each blood vesselbranch is taken the inserted catheter should be photographedfrom different directions Accordingly as the blood vesselreplica used in this study had two blood vessel branches 2
(a) (b)
Figure 15 (a) Bifurcated artificial blood vesselmodel (b)Generatedundeformed 3D intima model
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
2 Computational and Mathematical Methods in Medicine
(a) (b)
Figure 1 (a) Shape of blood vessel before catheter insertion (b) Shape of blood vessel after catheter insertion [19]
taken around a blood vessel a lot more detailed informationabout the blood vessel can be obtained than that with aCT image In addition because an ultrasonic wave is usedit has the advantage that the information about the bloodvessel adventitia can also be obtained However an IVUSimage only shows the cross section of a blood vessel withoutshowing the position and direction at which the IVUS imageis taken Whale has proposed a sequential triangulationmethod that calculates the position and orientation of anIVUS image using biplane X-ray angiogram images [12ndash17] The 3D path along which IVUS images were takenwas generated using biplane X-ray angiogram images andthe positions and orientations of these IVUS images werecalculated using only the geometric shape of this path
However the catheter inserted to take the IVUS imageheavily deforms the blood vessel as shown in Figure 1Accordingly the IVUS image and the biplane X-rayangiogram images taken with the catheter inserted show theinformation about the blood vessel deformed by the catheterinsertion In addition the blood vessel model generated bycombining these images will also be in a deformed state
The initial state of the blood vessel has a great effect onthe analysis result of the blood vessel model Accordinglyin this study we propose a 3D modeling method of intimaand adventitia with the deformation caused by insertion of acatheter eliminated for accurate FSI analysis
2 Overview
Figure 2 shows the overall flow of the 3D blood vesselmodeling method proposed in this study
This method can be largely divided into three stagesFirst a 3D model of the undeformed intima is generated
using a CT image CT images only require a contrast mediumto be administered and thus do not have any deformationcaused by insertion of a catheter
Then a 3D intima and adventitia model in a statedeformed by a catheter is generated by combining IVUS and
CT image
Undeformedintimal model
Centerline
of intima
Deformedintimaladventitial model
Centerline
of intima of adventitia
Transformation
of intima of adventitia
Registration
IVUS image 3D catheter path
X-ray angiogram image
Cross section Cross section Cross section
Cross section Cross section
Undeformed 3D blood vessel model
Figure 2 Overview of the proposed blood vessel modelingmethod
biplane X-ray angiogram images As explained earlier IVUSimages and biplane X-ray angiogram images show informa-tion about the blood vessel in a state deformed by insertionof a catheter
The last stage involves converting the 3D model of thedeformed intima and adventitia into a 3D model of theundeformed intima and adventitia through registration
The last stage involves converting the 3D model of thedeformed intima and adventitia into a 3D model of theundeformed intima and adventitia through registration Forthis the cross sections of the 3D models are extracted andregistered First as the intimae exist in different states thedeformed intima is registered with the undeformed intima
Computational and Mathematical Methods in Medicine 3
An artificial blood vessel model IVUS image
CT image
angiogram imagesBiplane X-ray
(a) (b)
Figure 3 (a) Blood vessel replica (b) CT IVUS and biplane X-ray angiogram images of the replica
The cross sections of the undeformed intima and adventitiaare calculated by applying the registration result to the crosssection of the deformed adventitia
A blood vessel replica was produced as shown inFigure 3(a) to facilitate acquisition of the medical imagesrequired for the method proposed in this paper A siliconetube was used as the replica blood vessel and gelatin was usedto fix it and to enable it to be deformed when a catheter wasinserted Figure 3(b) shows the CT IVUS and biplane X-rayimages taken using the blood vessel replica
3 Reconstruction of UndeformedIntima Model
ACT image can be obtained without inserting a catheter intothe blood vessel by administering a contrastmediumand thusshows the undeformed shape of the blood vessel Howeveras it only shows the contrast medium passing through theblood vessel no information about the adventitia of the bloodvessel can be acquired Accordingly we intended to utilizethe overall shape of the blood vessel without the catheter-induced deformation by using such characteristics of CTimages For this a 3D intimamodel with no catheter-induceddeformation was generated using the CT image of the bloodvessel replica
A CT image consists of voxel data produced by stackingtomograms of a human body To generate a 3D blood vesselmodel a process of extracting the polygon data correspond-ing to the blood vessel from the voxel data is required Togenerate the polygon data of the blood vessel from the voxeldata the isosurfaces that have the same intensity value asthat of the section corresponding to the blood vessel were
Figure 4 Generated 3D undeformed intima model of replica
extracted from each tomogram A polygon model of theblood vessel was generated by stacking these isosurfaces andapproximating the NURB surfaces Figure 4 shows the 3Dmodel of the undeformed intima generated using the CTimage of the blood vessel replica
4 Reconstruction of Deformed Intima andAdventitia Model
41 Extraction of the Blood Vessel Intima and Adventitia CrossSections in a Deformed State An IVUS image shows theinside of a blood vessel in greater detail than a CT image asit is obtained by imaging the inside of the blood vessel withan ultrasonic device inserted into the blood vessel Moreoverit provides information about the shape of the blood vesseladventitia Figure 5 shows the cross sections of blood vesselintima and adventitia extracted from an IVUS image
4 Computational and Mathematical Methods in Medicine
1
2
3
Figure 5 IVUS image of blood vessel
Figure 6 Segmented intima and adventitia contours from IVUSimage
As an IVUS image does not include color values but haspoints with gray scale values there are difficulties in automat-ically extracting the areas corresponding to the intima andthe adventitia of a blood vessel Accordingly in this studywe checked the IVUS image and manually segmented thesections corresponding to the intima and adventitia of theblood vessel respectively as shown in Figure 6
42 Restoration of 3D Catheter Path Though an IVUS imagecontains information about cross section of a blood vesselthe position and orientation at which the image was acquiredare unknown Accordingly to generate a 3D blood vesselmodel using the cross sections of the blood vessel intima andadventitia extracted earlier from an IVUS image the positionand orientation where the IVUS image has been actuallytaken should be conjectured using other medical imaging
techniques For this biplane X-ray angiogram images wereused in this study
When taking IVUS images the path along which theIVUS images are to be taken is secured by inserting acatheter in advance to place an IVUS ultrasonic device at theplace where the imaging is to be started When the IVUSultrasonic device arrives at the desired position it followsthe catheter and acquires images of the blood vessel crosssections with the path of the IVUS images matching the pathof the catheter To obtain the catheter path X-ray angiogramswere taken from different directions immediately before theIVUS ultrasonic device was pulled back to take images The3D catheter path was generated as shown in Figure 7 usingthe two 2D catheter paths extracted from the biplane X-rayangiogram images
43 Calculation of IVUS Image Position and OrientationWhen IVUS images are acquired the IVUS ultrasonic devicemoves out of the catheter at a constant speed using the IVUSpullback device Accordingly if the 3D catheter path restoredusing the biplane X-ray angiogram images is divided intoas many parts as the number of the IVUS images using thesame interval the positions where the IVUS images havebeen acquired can be easily calculated However as the IVUSultrasonic device rotates around the catheter when it travelsaround a bent blood vessel the IVUS image acquired at thistime is in a rotated state
Whale has proposed the sequential triangulation methodthat can determine the twist angles of IVUS images usingthe characteristics of such IVUS images With this methodthe orientations of IVUS images were calculated using onlythe geometric shape of the catheter restored in 3D A 3Dcatheter path was divided into small pieces assuming that itis comprised of innumerable joints and links The positionsand orientations of IVUS images were determined as shownin Figure 8 using the 3 consecutive points on the 3D pathdivided into smaller pieces The orientation of each IVUS
Computational and Mathematical Methods in Medicine 5
(a) (b)
Figure 7 (a) Biplane X-ray angiogram images of IVUS catheter (b) Restored IVUS catheter path in 3D space
Frame 0 Frame 1 Frame 2 Frame 3Frame 4
P0
P1
P2
P3
P4
P5
n0
n1n2
n3
Figure 8 Sequential triangulation method [15]
image is determined by the plane made of the 3 consecutivepoints existing on the catheter P is the position of each pointand S which is the position of an IVUS image is the centerof the two points as shown in the following [12ndash17]
S119894 = (P119894 + P119894+1)2
S119894+1 = (P119894+1 + P119894+2)2 (1)
Also the tangent vector t at P is calculated as follows
t119894 = P119894+1 minus P119894t119894+1 = P119894+2 minus P119894+1
(2)
The normal vector n which is each of the 119910-axis direc-tions of the 2D IVUS images was calculated by calcu-
lating the outer products of the two neighboring tangentvectors t
n = t119894 times t119894+1 (3)
Through such a method the position and orientationwhere an IVUS image was taken were determined fromthe 3D path of the catheter Figure 9(a) shows the result ofapplying the position and orientation calculated using thesequential triangulation method to the cross sections of theblood vessel intima and adventitia extracted from a 2D IVUSimage and Figure 9(b) shows the polygon model generatedusing the points in 3D space As these models were generatedby combining the IVUS and biplane X-ray angiogram imagestaken in a state deformed by a catheter they are the bloodvessel intima and adventitia models deformed by insertion ofa catheter
5 Computation of Undeformed Intima andAdventitia Model by Registration
In this chapter we intend to compute a 3D intima andadventitia model without the catheter-induced deformationTo achieve this the 3D model of deformed intima andadventitia generated by combining the IVUS and biplane X-ray angiogram imageswas registeredwith the 3Dmodel of theundeformed intima generated using aCT image As these two3D models do not only exist on different coordinate systemsbut also have different scales there are difficulties in directlyregistering these 3D models Accordingly in this study we
6 Computational and Mathematical Methods in Medicine
Contoursof intima 3D catheter path
Deformed intima model
Deformed adventitia model
(a) (b)
Figure 9 (a) A series of deformed intima cross sections (b) A polygon model of deformed intima and adventitia model
propose a method of determining the corresponding relationbetween the two 3D blood vessel models to extract the crosssections at the corresponding positions and matching them
51 Calculation of Centerline and Extraction of Cross SectionTo define a plane required for extraction of 2D cross sectionsfrom the 3D blood vessel intimamodel in a tube form one 3Dpoint and normal vector are required For this the centerlinethat could well express the shape of the blood vessel shouldbe calculated
In the study carried out by Luca the centerline existingbetween twopointswithin amodel in a tube formwas definedto be the line farthermost from the boundary Accordinglythe centerline of an object Ω existing in a 3D space can beexpressed as the pathC = C(s) between two points P1 and P2which minimizes
Ecenterline (C) = intL=Cminus1(P1)
0=Cminus1(P0)F (C (s)) 119889119904 (4)
For this the Delaunay triangulation of the object Ω wascalculated throughwhich themaximum spheres inscribed inthe blood vessel model were calculated The centerline of the3D blood vessel model was extracted using the center pointsof these spheres
52 Correspondence Definition between 3D Blood Vessel Mod-els and Extraction of Cross Sections To register two bloodvessel models in different states correspondence between thetwomodels should be defined first For this the centerlines ofthe two intima models calculated earlier were used Becausethe CT IVUS and biplane X-ray angiogram images wereall obtained by imaging the same section of the bloodvessel replica the 3D blood vessel models generated earliermodel the same section of the blood vessel though they arein different states Accordingly the corresponding relation
between these two intima models was defined by dividingthe center curves of these two intima models into the samenumber of lines using the same interval and the crosssections of the 3D models were extracted at the definedpositions
53 Registering between Cross Sections in Different States Inthis study we intend to generate a 3D intima and adven-titia model from which the catheter-induced deformationis removed through registration Accordingly we attemptedto convert the cross sections of the deformed intima andadventitia extracted earlier into the cross sections of theundeformed intima and adventitia For this the cross sectionsof the deformed intima and adventitia were registered withthe cross sections of the undeformed intima
Registration is the calculation of the coordinate transfor-mation that can minimize the distance between two pointsets Accordingly registration in this study is to calculate thetranslation (119909 119910) rotation (120579) and scale (119904) that minimizesthe distance between the two point sets (X target point cloudY source point cloud) which compose the 2D blood vesselcross sections In this study the coordinate transformationmatrix T0 that minimizes the distance between the two pointsets X and Y was calculated using the optimization methodafter setting these 4 elements as the variables In additionto make a result linear to the rotation value of the previousframe when registering cross sections the value closest to therotation value 120579 of the previous frame was calculated
T0 = min (sum dist (XY1015840)) (5)
whereY1015840 = T (119909 119910 120579 119904)Y (6)
To achieve this the multiminimizer function of theGNU Scientific Library was used [18] Figure 10 shows theregistration result of the two intima cross sections
Computational and Mathematical Methods in Medicine 7
Deformed intima
Registration
Undeformed intima
Figure 10 Registration between undeformed and deformed intima contours using the proposed method
60y = minus3E minus 09x5 + 2E minus 06x4 minus 00005x3 + 00344x2 + 07059x minus 10207
Figure 11 Trend line of rotation angle result
The 119909 119910 120579 and 119904 calculated through the registrationbetween intima cross sections are the values at which thedeformed intima cross section changes to the undeformedintima cross section Accordingly the calculated 119909 119910 120579 and 119904were equally applied to change the deformed adventitia crosssection to the undeformed adventitia cross section Figure 11shows the rotation values of all the cross sections registeredusing the optimization method To more linearly transformsuch rotation values the trend linewas calculated using all therotation values and the rotation value of each cross sectionwas corrected to the trend line value
54 Generation of an Undeformed Intima and AdventitiaModel The cross sections of the undeformed intima andadventitia were calculated through a process similar to thatabove To finally generate a model in an undeformed stateusing such cross sections the cross sections should be locatedat the proper positions and in proper orientation For thisthe centerline extracted from the 3D model of the intimanot deformed by a catheter which was generated from a CTimage was used A 3D blood vessel polygon model whichincluded the intima and adventitia as shown in Figure 12was generated by placing the calculated cross sections ofthe undeformed intima and adventitia on the undeformedcenterline
6 Bifurcated Blood Vessel Model
In fact human blood vessels are not comprised of singleblood vessels but a combination of blood vessels with many
Figure 12 Generated 3D blood vessel model including intima andadventitia
branches Accordingly to actually model the blood vessel ofa patient not a single blood vessel model but a 3D bloodvessel model that includes branches should be generatedAccordingly a 3D blood vessel model including branches notdeformed by a catheter was generated using the proposedblood vessel modeling method in this chapter For this ablood vessel replica including branches was produced asshown in Figure 13 Different from the case of a single bloodvessel this replicawas produced by creating a 3Dmodel usingthe CT images of an actual patient and producing a moldusing a 3D printer A blood vessel replica of the desired formwas produced by injecting silicon into this mold For thisreplica gelatin was again used to fix the blood vessel tube
The CT IVUS and biplane X-ray angiogram images weretaken using the produced blood vessel replica as per the caseof a single blood vessel As the replica includes branches theIVUS images and the X-ray angiogram images of each bloodvessel branch were taken Figure 14 shows themedical imagestaken using the blood vessel replica
61 Generation of a 3D Intima Model Including Branches NotDeformed by a Catheter and Extraction of Cross Sections In
8 Computational and Mathematical Methods in Medicine
Figure 13 Replica of blood vessel
CT IVUS
X-ray angiogram
Figure 14 CT biplane X-ray angiogram and IVUS images of replica
the case of the blood vessel that includes branches a 3Dmodel of the intima not deformed by a catheter was alsogenerated using the CT image as per the single blood vesselFigure 15 shows the 3D model of the intima not deformed bya catheter which was generated using a CT image
To extract the cross sections of the 3D intima models thecenterline of each branch was calculated using a 3D Voronoidiagram Figure 16 shows the centerline of each branch andthe cross sections extracted using them
62 Generation of a 3DModel of the Intima andAdventitia NotDeformed by aCatheterThat Includes Branches and Extractionof Cross Sections To generate a blood vessel model thatincludes branches the IVUS images of all the blood vesselbranches should be taken to obtain data about the intimaand adventitia of each blood vessel branch In addition tocalculate the position and orientation of the IVUS imageof each branch when the IVUS image of each blood vesselbranch is taken the inserted catheter should be photographedfrom different directions Accordingly as the blood vesselreplica used in this study had two blood vessel branches 2
(a) (b)
Figure 15 (a) Bifurcated artificial blood vesselmodel (b)Generatedundeformed 3D intima model
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
Computational and Mathematical Methods in Medicine 3
An artificial blood vessel model IVUS image
CT image
angiogram imagesBiplane X-ray
(a) (b)
Figure 3 (a) Blood vessel replica (b) CT IVUS and biplane X-ray angiogram images of the replica
The cross sections of the undeformed intima and adventitiaare calculated by applying the registration result to the crosssection of the deformed adventitia
A blood vessel replica was produced as shown inFigure 3(a) to facilitate acquisition of the medical imagesrequired for the method proposed in this paper A siliconetube was used as the replica blood vessel and gelatin was usedto fix it and to enable it to be deformed when a catheter wasinserted Figure 3(b) shows the CT IVUS and biplane X-rayimages taken using the blood vessel replica
3 Reconstruction of UndeformedIntima Model
ACT image can be obtained without inserting a catheter intothe blood vessel by administering a contrastmediumand thusshows the undeformed shape of the blood vessel Howeveras it only shows the contrast medium passing through theblood vessel no information about the adventitia of the bloodvessel can be acquired Accordingly we intended to utilizethe overall shape of the blood vessel without the catheter-induced deformation by using such characteristics of CTimages For this a 3D intimamodel with no catheter-induceddeformation was generated using the CT image of the bloodvessel replica
A CT image consists of voxel data produced by stackingtomograms of a human body To generate a 3D blood vesselmodel a process of extracting the polygon data correspond-ing to the blood vessel from the voxel data is required Togenerate the polygon data of the blood vessel from the voxeldata the isosurfaces that have the same intensity value asthat of the section corresponding to the blood vessel were
Figure 4 Generated 3D undeformed intima model of replica
extracted from each tomogram A polygon model of theblood vessel was generated by stacking these isosurfaces andapproximating the NURB surfaces Figure 4 shows the 3Dmodel of the undeformed intima generated using the CTimage of the blood vessel replica
4 Reconstruction of Deformed Intima andAdventitia Model
41 Extraction of the Blood Vessel Intima and Adventitia CrossSections in a Deformed State An IVUS image shows theinside of a blood vessel in greater detail than a CT image asit is obtained by imaging the inside of the blood vessel withan ultrasonic device inserted into the blood vessel Moreoverit provides information about the shape of the blood vesseladventitia Figure 5 shows the cross sections of blood vesselintima and adventitia extracted from an IVUS image
4 Computational and Mathematical Methods in Medicine
1
2
3
Figure 5 IVUS image of blood vessel
Figure 6 Segmented intima and adventitia contours from IVUSimage
As an IVUS image does not include color values but haspoints with gray scale values there are difficulties in automat-ically extracting the areas corresponding to the intima andthe adventitia of a blood vessel Accordingly in this studywe checked the IVUS image and manually segmented thesections corresponding to the intima and adventitia of theblood vessel respectively as shown in Figure 6
42 Restoration of 3D Catheter Path Though an IVUS imagecontains information about cross section of a blood vesselthe position and orientation at which the image was acquiredare unknown Accordingly to generate a 3D blood vesselmodel using the cross sections of the blood vessel intima andadventitia extracted earlier from an IVUS image the positionand orientation where the IVUS image has been actuallytaken should be conjectured using other medical imaging
techniques For this biplane X-ray angiogram images wereused in this study
When taking IVUS images the path along which theIVUS images are to be taken is secured by inserting acatheter in advance to place an IVUS ultrasonic device at theplace where the imaging is to be started When the IVUSultrasonic device arrives at the desired position it followsthe catheter and acquires images of the blood vessel crosssections with the path of the IVUS images matching the pathof the catheter To obtain the catheter path X-ray angiogramswere taken from different directions immediately before theIVUS ultrasonic device was pulled back to take images The3D catheter path was generated as shown in Figure 7 usingthe two 2D catheter paths extracted from the biplane X-rayangiogram images
43 Calculation of IVUS Image Position and OrientationWhen IVUS images are acquired the IVUS ultrasonic devicemoves out of the catheter at a constant speed using the IVUSpullback device Accordingly if the 3D catheter path restoredusing the biplane X-ray angiogram images is divided intoas many parts as the number of the IVUS images using thesame interval the positions where the IVUS images havebeen acquired can be easily calculated However as the IVUSultrasonic device rotates around the catheter when it travelsaround a bent blood vessel the IVUS image acquired at thistime is in a rotated state
Whale has proposed the sequential triangulation methodthat can determine the twist angles of IVUS images usingthe characteristics of such IVUS images With this methodthe orientations of IVUS images were calculated using onlythe geometric shape of the catheter restored in 3D A 3Dcatheter path was divided into small pieces assuming that itis comprised of innumerable joints and links The positionsand orientations of IVUS images were determined as shownin Figure 8 using the 3 consecutive points on the 3D pathdivided into smaller pieces The orientation of each IVUS
Computational and Mathematical Methods in Medicine 5
(a) (b)
Figure 7 (a) Biplane X-ray angiogram images of IVUS catheter (b) Restored IVUS catheter path in 3D space
Frame 0 Frame 1 Frame 2 Frame 3Frame 4
P0
P1
P2
P3
P4
P5
n0
n1n2
n3
Figure 8 Sequential triangulation method [15]
image is determined by the plane made of the 3 consecutivepoints existing on the catheter P is the position of each pointand S which is the position of an IVUS image is the centerof the two points as shown in the following [12ndash17]
S119894 = (P119894 + P119894+1)2
S119894+1 = (P119894+1 + P119894+2)2 (1)
Also the tangent vector t at P is calculated as follows
t119894 = P119894+1 minus P119894t119894+1 = P119894+2 minus P119894+1
(2)
The normal vector n which is each of the 119910-axis direc-tions of the 2D IVUS images was calculated by calcu-
lating the outer products of the two neighboring tangentvectors t
n = t119894 times t119894+1 (3)
Through such a method the position and orientationwhere an IVUS image was taken were determined fromthe 3D path of the catheter Figure 9(a) shows the result ofapplying the position and orientation calculated using thesequential triangulation method to the cross sections of theblood vessel intima and adventitia extracted from a 2D IVUSimage and Figure 9(b) shows the polygon model generatedusing the points in 3D space As these models were generatedby combining the IVUS and biplane X-ray angiogram imagestaken in a state deformed by a catheter they are the bloodvessel intima and adventitia models deformed by insertion ofa catheter
5 Computation of Undeformed Intima andAdventitia Model by Registration
In this chapter we intend to compute a 3D intima andadventitia model without the catheter-induced deformationTo achieve this the 3D model of deformed intima andadventitia generated by combining the IVUS and biplane X-ray angiogram imageswas registeredwith the 3Dmodel of theundeformed intima generated using aCT image As these two3D models do not only exist on different coordinate systemsbut also have different scales there are difficulties in directlyregistering these 3D models Accordingly in this study we
6 Computational and Mathematical Methods in Medicine
Contoursof intima 3D catheter path
Deformed intima model
Deformed adventitia model
(a) (b)
Figure 9 (a) A series of deformed intima cross sections (b) A polygon model of deformed intima and adventitia model
propose a method of determining the corresponding relationbetween the two 3D blood vessel models to extract the crosssections at the corresponding positions and matching them
51 Calculation of Centerline and Extraction of Cross SectionTo define a plane required for extraction of 2D cross sectionsfrom the 3D blood vessel intimamodel in a tube form one 3Dpoint and normal vector are required For this the centerlinethat could well express the shape of the blood vessel shouldbe calculated
In the study carried out by Luca the centerline existingbetween twopointswithin amodel in a tube formwas definedto be the line farthermost from the boundary Accordinglythe centerline of an object Ω existing in a 3D space can beexpressed as the pathC = C(s) between two points P1 and P2which minimizes
Ecenterline (C) = intL=Cminus1(P1)
0=Cminus1(P0)F (C (s)) 119889119904 (4)
For this the Delaunay triangulation of the object Ω wascalculated throughwhich themaximum spheres inscribed inthe blood vessel model were calculated The centerline of the3D blood vessel model was extracted using the center pointsof these spheres
52 Correspondence Definition between 3D Blood Vessel Mod-els and Extraction of Cross Sections To register two bloodvessel models in different states correspondence between thetwomodels should be defined first For this the centerlines ofthe two intima models calculated earlier were used Becausethe CT IVUS and biplane X-ray angiogram images wereall obtained by imaging the same section of the bloodvessel replica the 3D blood vessel models generated earliermodel the same section of the blood vessel though they arein different states Accordingly the corresponding relation
between these two intima models was defined by dividingthe center curves of these two intima models into the samenumber of lines using the same interval and the crosssections of the 3D models were extracted at the definedpositions
53 Registering between Cross Sections in Different States Inthis study we intend to generate a 3D intima and adven-titia model from which the catheter-induced deformationis removed through registration Accordingly we attemptedto convert the cross sections of the deformed intima andadventitia extracted earlier into the cross sections of theundeformed intima and adventitia For this the cross sectionsof the deformed intima and adventitia were registered withthe cross sections of the undeformed intima
Registration is the calculation of the coordinate transfor-mation that can minimize the distance between two pointsets Accordingly registration in this study is to calculate thetranslation (119909 119910) rotation (120579) and scale (119904) that minimizesthe distance between the two point sets (X target point cloudY source point cloud) which compose the 2D blood vesselcross sections In this study the coordinate transformationmatrix T0 that minimizes the distance between the two pointsets X and Y was calculated using the optimization methodafter setting these 4 elements as the variables In additionto make a result linear to the rotation value of the previousframe when registering cross sections the value closest to therotation value 120579 of the previous frame was calculated
T0 = min (sum dist (XY1015840)) (5)
whereY1015840 = T (119909 119910 120579 119904)Y (6)
To achieve this the multiminimizer function of theGNU Scientific Library was used [18] Figure 10 shows theregistration result of the two intima cross sections
Computational and Mathematical Methods in Medicine 7
Deformed intima
Registration
Undeformed intima
Figure 10 Registration between undeformed and deformed intima contours using the proposed method
60y = minus3E minus 09x5 + 2E minus 06x4 minus 00005x3 + 00344x2 + 07059x minus 10207
Figure 11 Trend line of rotation angle result
The 119909 119910 120579 and 119904 calculated through the registrationbetween intima cross sections are the values at which thedeformed intima cross section changes to the undeformedintima cross section Accordingly the calculated 119909 119910 120579 and 119904were equally applied to change the deformed adventitia crosssection to the undeformed adventitia cross section Figure 11shows the rotation values of all the cross sections registeredusing the optimization method To more linearly transformsuch rotation values the trend linewas calculated using all therotation values and the rotation value of each cross sectionwas corrected to the trend line value
54 Generation of an Undeformed Intima and AdventitiaModel The cross sections of the undeformed intima andadventitia were calculated through a process similar to thatabove To finally generate a model in an undeformed stateusing such cross sections the cross sections should be locatedat the proper positions and in proper orientation For thisthe centerline extracted from the 3D model of the intimanot deformed by a catheter which was generated from a CTimage was used A 3D blood vessel polygon model whichincluded the intima and adventitia as shown in Figure 12was generated by placing the calculated cross sections ofthe undeformed intima and adventitia on the undeformedcenterline
6 Bifurcated Blood Vessel Model
In fact human blood vessels are not comprised of singleblood vessels but a combination of blood vessels with many
Figure 12 Generated 3D blood vessel model including intima andadventitia
branches Accordingly to actually model the blood vessel ofa patient not a single blood vessel model but a 3D bloodvessel model that includes branches should be generatedAccordingly a 3D blood vessel model including branches notdeformed by a catheter was generated using the proposedblood vessel modeling method in this chapter For this ablood vessel replica including branches was produced asshown in Figure 13 Different from the case of a single bloodvessel this replicawas produced by creating a 3Dmodel usingthe CT images of an actual patient and producing a moldusing a 3D printer A blood vessel replica of the desired formwas produced by injecting silicon into this mold For thisreplica gelatin was again used to fix the blood vessel tube
The CT IVUS and biplane X-ray angiogram images weretaken using the produced blood vessel replica as per the caseof a single blood vessel As the replica includes branches theIVUS images and the X-ray angiogram images of each bloodvessel branch were taken Figure 14 shows themedical imagestaken using the blood vessel replica
61 Generation of a 3D Intima Model Including Branches NotDeformed by a Catheter and Extraction of Cross Sections In
8 Computational and Mathematical Methods in Medicine
Figure 13 Replica of blood vessel
CT IVUS
X-ray angiogram
Figure 14 CT biplane X-ray angiogram and IVUS images of replica
the case of the blood vessel that includes branches a 3Dmodel of the intima not deformed by a catheter was alsogenerated using the CT image as per the single blood vesselFigure 15 shows the 3D model of the intima not deformed bya catheter which was generated using a CT image
To extract the cross sections of the 3D intima models thecenterline of each branch was calculated using a 3D Voronoidiagram Figure 16 shows the centerline of each branch andthe cross sections extracted using them
62 Generation of a 3DModel of the Intima andAdventitia NotDeformed by aCatheterThat Includes Branches and Extractionof Cross Sections To generate a blood vessel model thatincludes branches the IVUS images of all the blood vesselbranches should be taken to obtain data about the intimaand adventitia of each blood vessel branch In addition tocalculate the position and orientation of the IVUS imageof each branch when the IVUS image of each blood vesselbranch is taken the inserted catheter should be photographedfrom different directions Accordingly as the blood vesselreplica used in this study had two blood vessel branches 2
(a) (b)
Figure 15 (a) Bifurcated artificial blood vesselmodel (b)Generatedundeformed 3D intima model
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
4 Computational and Mathematical Methods in Medicine
1
2
3
Figure 5 IVUS image of blood vessel
Figure 6 Segmented intima and adventitia contours from IVUSimage
As an IVUS image does not include color values but haspoints with gray scale values there are difficulties in automat-ically extracting the areas corresponding to the intima andthe adventitia of a blood vessel Accordingly in this studywe checked the IVUS image and manually segmented thesections corresponding to the intima and adventitia of theblood vessel respectively as shown in Figure 6
42 Restoration of 3D Catheter Path Though an IVUS imagecontains information about cross section of a blood vesselthe position and orientation at which the image was acquiredare unknown Accordingly to generate a 3D blood vesselmodel using the cross sections of the blood vessel intima andadventitia extracted earlier from an IVUS image the positionand orientation where the IVUS image has been actuallytaken should be conjectured using other medical imaging
techniques For this biplane X-ray angiogram images wereused in this study
When taking IVUS images the path along which theIVUS images are to be taken is secured by inserting acatheter in advance to place an IVUS ultrasonic device at theplace where the imaging is to be started When the IVUSultrasonic device arrives at the desired position it followsthe catheter and acquires images of the blood vessel crosssections with the path of the IVUS images matching the pathof the catheter To obtain the catheter path X-ray angiogramswere taken from different directions immediately before theIVUS ultrasonic device was pulled back to take images The3D catheter path was generated as shown in Figure 7 usingthe two 2D catheter paths extracted from the biplane X-rayangiogram images
43 Calculation of IVUS Image Position and OrientationWhen IVUS images are acquired the IVUS ultrasonic devicemoves out of the catheter at a constant speed using the IVUSpullback device Accordingly if the 3D catheter path restoredusing the biplane X-ray angiogram images is divided intoas many parts as the number of the IVUS images using thesame interval the positions where the IVUS images havebeen acquired can be easily calculated However as the IVUSultrasonic device rotates around the catheter when it travelsaround a bent blood vessel the IVUS image acquired at thistime is in a rotated state
Whale has proposed the sequential triangulation methodthat can determine the twist angles of IVUS images usingthe characteristics of such IVUS images With this methodthe orientations of IVUS images were calculated using onlythe geometric shape of the catheter restored in 3D A 3Dcatheter path was divided into small pieces assuming that itis comprised of innumerable joints and links The positionsand orientations of IVUS images were determined as shownin Figure 8 using the 3 consecutive points on the 3D pathdivided into smaller pieces The orientation of each IVUS
Computational and Mathematical Methods in Medicine 5
(a) (b)
Figure 7 (a) Biplane X-ray angiogram images of IVUS catheter (b) Restored IVUS catheter path in 3D space
Frame 0 Frame 1 Frame 2 Frame 3Frame 4
P0
P1
P2
P3
P4
P5
n0
n1n2
n3
Figure 8 Sequential triangulation method [15]
image is determined by the plane made of the 3 consecutivepoints existing on the catheter P is the position of each pointand S which is the position of an IVUS image is the centerof the two points as shown in the following [12ndash17]
S119894 = (P119894 + P119894+1)2
S119894+1 = (P119894+1 + P119894+2)2 (1)
Also the tangent vector t at P is calculated as follows
t119894 = P119894+1 minus P119894t119894+1 = P119894+2 minus P119894+1
(2)
The normal vector n which is each of the 119910-axis direc-tions of the 2D IVUS images was calculated by calcu-
lating the outer products of the two neighboring tangentvectors t
n = t119894 times t119894+1 (3)
Through such a method the position and orientationwhere an IVUS image was taken were determined fromthe 3D path of the catheter Figure 9(a) shows the result ofapplying the position and orientation calculated using thesequential triangulation method to the cross sections of theblood vessel intima and adventitia extracted from a 2D IVUSimage and Figure 9(b) shows the polygon model generatedusing the points in 3D space As these models were generatedby combining the IVUS and biplane X-ray angiogram imagestaken in a state deformed by a catheter they are the bloodvessel intima and adventitia models deformed by insertion ofa catheter
5 Computation of Undeformed Intima andAdventitia Model by Registration
In this chapter we intend to compute a 3D intima andadventitia model without the catheter-induced deformationTo achieve this the 3D model of deformed intima andadventitia generated by combining the IVUS and biplane X-ray angiogram imageswas registeredwith the 3Dmodel of theundeformed intima generated using aCT image As these two3D models do not only exist on different coordinate systemsbut also have different scales there are difficulties in directlyregistering these 3D models Accordingly in this study we
6 Computational and Mathematical Methods in Medicine
Contoursof intima 3D catheter path
Deformed intima model
Deformed adventitia model
(a) (b)
Figure 9 (a) A series of deformed intima cross sections (b) A polygon model of deformed intima and adventitia model
propose a method of determining the corresponding relationbetween the two 3D blood vessel models to extract the crosssections at the corresponding positions and matching them
51 Calculation of Centerline and Extraction of Cross SectionTo define a plane required for extraction of 2D cross sectionsfrom the 3D blood vessel intimamodel in a tube form one 3Dpoint and normal vector are required For this the centerlinethat could well express the shape of the blood vessel shouldbe calculated
In the study carried out by Luca the centerline existingbetween twopointswithin amodel in a tube formwas definedto be the line farthermost from the boundary Accordinglythe centerline of an object Ω existing in a 3D space can beexpressed as the pathC = C(s) between two points P1 and P2which minimizes
Ecenterline (C) = intL=Cminus1(P1)
0=Cminus1(P0)F (C (s)) 119889119904 (4)
For this the Delaunay triangulation of the object Ω wascalculated throughwhich themaximum spheres inscribed inthe blood vessel model were calculated The centerline of the3D blood vessel model was extracted using the center pointsof these spheres
52 Correspondence Definition between 3D Blood Vessel Mod-els and Extraction of Cross Sections To register two bloodvessel models in different states correspondence between thetwomodels should be defined first For this the centerlines ofthe two intima models calculated earlier were used Becausethe CT IVUS and biplane X-ray angiogram images wereall obtained by imaging the same section of the bloodvessel replica the 3D blood vessel models generated earliermodel the same section of the blood vessel though they arein different states Accordingly the corresponding relation
between these two intima models was defined by dividingthe center curves of these two intima models into the samenumber of lines using the same interval and the crosssections of the 3D models were extracted at the definedpositions
53 Registering between Cross Sections in Different States Inthis study we intend to generate a 3D intima and adven-titia model from which the catheter-induced deformationis removed through registration Accordingly we attemptedto convert the cross sections of the deformed intima andadventitia extracted earlier into the cross sections of theundeformed intima and adventitia For this the cross sectionsof the deformed intima and adventitia were registered withthe cross sections of the undeformed intima
Registration is the calculation of the coordinate transfor-mation that can minimize the distance between two pointsets Accordingly registration in this study is to calculate thetranslation (119909 119910) rotation (120579) and scale (119904) that minimizesthe distance between the two point sets (X target point cloudY source point cloud) which compose the 2D blood vesselcross sections In this study the coordinate transformationmatrix T0 that minimizes the distance between the two pointsets X and Y was calculated using the optimization methodafter setting these 4 elements as the variables In additionto make a result linear to the rotation value of the previousframe when registering cross sections the value closest to therotation value 120579 of the previous frame was calculated
T0 = min (sum dist (XY1015840)) (5)
whereY1015840 = T (119909 119910 120579 119904)Y (6)
To achieve this the multiminimizer function of theGNU Scientific Library was used [18] Figure 10 shows theregistration result of the two intima cross sections
Computational and Mathematical Methods in Medicine 7
Deformed intima
Registration
Undeformed intima
Figure 10 Registration between undeformed and deformed intima contours using the proposed method
60y = minus3E minus 09x5 + 2E minus 06x4 minus 00005x3 + 00344x2 + 07059x minus 10207
Figure 11 Trend line of rotation angle result
The 119909 119910 120579 and 119904 calculated through the registrationbetween intima cross sections are the values at which thedeformed intima cross section changes to the undeformedintima cross section Accordingly the calculated 119909 119910 120579 and 119904were equally applied to change the deformed adventitia crosssection to the undeformed adventitia cross section Figure 11shows the rotation values of all the cross sections registeredusing the optimization method To more linearly transformsuch rotation values the trend linewas calculated using all therotation values and the rotation value of each cross sectionwas corrected to the trend line value
54 Generation of an Undeformed Intima and AdventitiaModel The cross sections of the undeformed intima andadventitia were calculated through a process similar to thatabove To finally generate a model in an undeformed stateusing such cross sections the cross sections should be locatedat the proper positions and in proper orientation For thisthe centerline extracted from the 3D model of the intimanot deformed by a catheter which was generated from a CTimage was used A 3D blood vessel polygon model whichincluded the intima and adventitia as shown in Figure 12was generated by placing the calculated cross sections ofthe undeformed intima and adventitia on the undeformedcenterline
6 Bifurcated Blood Vessel Model
In fact human blood vessels are not comprised of singleblood vessels but a combination of blood vessels with many
Figure 12 Generated 3D blood vessel model including intima andadventitia
branches Accordingly to actually model the blood vessel ofa patient not a single blood vessel model but a 3D bloodvessel model that includes branches should be generatedAccordingly a 3D blood vessel model including branches notdeformed by a catheter was generated using the proposedblood vessel modeling method in this chapter For this ablood vessel replica including branches was produced asshown in Figure 13 Different from the case of a single bloodvessel this replicawas produced by creating a 3Dmodel usingthe CT images of an actual patient and producing a moldusing a 3D printer A blood vessel replica of the desired formwas produced by injecting silicon into this mold For thisreplica gelatin was again used to fix the blood vessel tube
The CT IVUS and biplane X-ray angiogram images weretaken using the produced blood vessel replica as per the caseof a single blood vessel As the replica includes branches theIVUS images and the X-ray angiogram images of each bloodvessel branch were taken Figure 14 shows themedical imagestaken using the blood vessel replica
61 Generation of a 3D Intima Model Including Branches NotDeformed by a Catheter and Extraction of Cross Sections In
8 Computational and Mathematical Methods in Medicine
Figure 13 Replica of blood vessel
CT IVUS
X-ray angiogram
Figure 14 CT biplane X-ray angiogram and IVUS images of replica
the case of the blood vessel that includes branches a 3Dmodel of the intima not deformed by a catheter was alsogenerated using the CT image as per the single blood vesselFigure 15 shows the 3D model of the intima not deformed bya catheter which was generated using a CT image
To extract the cross sections of the 3D intima models thecenterline of each branch was calculated using a 3D Voronoidiagram Figure 16 shows the centerline of each branch andthe cross sections extracted using them
62 Generation of a 3DModel of the Intima andAdventitia NotDeformed by aCatheterThat Includes Branches and Extractionof Cross Sections To generate a blood vessel model thatincludes branches the IVUS images of all the blood vesselbranches should be taken to obtain data about the intimaand adventitia of each blood vessel branch In addition tocalculate the position and orientation of the IVUS imageof each branch when the IVUS image of each blood vesselbranch is taken the inserted catheter should be photographedfrom different directions Accordingly as the blood vesselreplica used in this study had two blood vessel branches 2
(a) (b)
Figure 15 (a) Bifurcated artificial blood vesselmodel (b)Generatedundeformed 3D intima model
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
Computational and Mathematical Methods in Medicine 5
(a) (b)
Figure 7 (a) Biplane X-ray angiogram images of IVUS catheter (b) Restored IVUS catheter path in 3D space
Frame 0 Frame 1 Frame 2 Frame 3Frame 4
P0
P1
P2
P3
P4
P5
n0
n1n2
n3
Figure 8 Sequential triangulation method [15]
image is determined by the plane made of the 3 consecutivepoints existing on the catheter P is the position of each pointand S which is the position of an IVUS image is the centerof the two points as shown in the following [12ndash17]
S119894 = (P119894 + P119894+1)2
S119894+1 = (P119894+1 + P119894+2)2 (1)
Also the tangent vector t at P is calculated as follows
t119894 = P119894+1 minus P119894t119894+1 = P119894+2 minus P119894+1
(2)
The normal vector n which is each of the 119910-axis direc-tions of the 2D IVUS images was calculated by calcu-
lating the outer products of the two neighboring tangentvectors t
n = t119894 times t119894+1 (3)
Through such a method the position and orientationwhere an IVUS image was taken were determined fromthe 3D path of the catheter Figure 9(a) shows the result ofapplying the position and orientation calculated using thesequential triangulation method to the cross sections of theblood vessel intima and adventitia extracted from a 2D IVUSimage and Figure 9(b) shows the polygon model generatedusing the points in 3D space As these models were generatedby combining the IVUS and biplane X-ray angiogram imagestaken in a state deformed by a catheter they are the bloodvessel intima and adventitia models deformed by insertion ofa catheter
5 Computation of Undeformed Intima andAdventitia Model by Registration
In this chapter we intend to compute a 3D intima andadventitia model without the catheter-induced deformationTo achieve this the 3D model of deformed intima andadventitia generated by combining the IVUS and biplane X-ray angiogram imageswas registeredwith the 3Dmodel of theundeformed intima generated using aCT image As these two3D models do not only exist on different coordinate systemsbut also have different scales there are difficulties in directlyregistering these 3D models Accordingly in this study we
6 Computational and Mathematical Methods in Medicine
Contoursof intima 3D catheter path
Deformed intima model
Deformed adventitia model
(a) (b)
Figure 9 (a) A series of deformed intima cross sections (b) A polygon model of deformed intima and adventitia model
propose a method of determining the corresponding relationbetween the two 3D blood vessel models to extract the crosssections at the corresponding positions and matching them
51 Calculation of Centerline and Extraction of Cross SectionTo define a plane required for extraction of 2D cross sectionsfrom the 3D blood vessel intimamodel in a tube form one 3Dpoint and normal vector are required For this the centerlinethat could well express the shape of the blood vessel shouldbe calculated
In the study carried out by Luca the centerline existingbetween twopointswithin amodel in a tube formwas definedto be the line farthermost from the boundary Accordinglythe centerline of an object Ω existing in a 3D space can beexpressed as the pathC = C(s) between two points P1 and P2which minimizes
Ecenterline (C) = intL=Cminus1(P1)
0=Cminus1(P0)F (C (s)) 119889119904 (4)
For this the Delaunay triangulation of the object Ω wascalculated throughwhich themaximum spheres inscribed inthe blood vessel model were calculated The centerline of the3D blood vessel model was extracted using the center pointsof these spheres
52 Correspondence Definition between 3D Blood Vessel Mod-els and Extraction of Cross Sections To register two bloodvessel models in different states correspondence between thetwomodels should be defined first For this the centerlines ofthe two intima models calculated earlier were used Becausethe CT IVUS and biplane X-ray angiogram images wereall obtained by imaging the same section of the bloodvessel replica the 3D blood vessel models generated earliermodel the same section of the blood vessel though they arein different states Accordingly the corresponding relation
between these two intima models was defined by dividingthe center curves of these two intima models into the samenumber of lines using the same interval and the crosssections of the 3D models were extracted at the definedpositions
53 Registering between Cross Sections in Different States Inthis study we intend to generate a 3D intima and adven-titia model from which the catheter-induced deformationis removed through registration Accordingly we attemptedto convert the cross sections of the deformed intima andadventitia extracted earlier into the cross sections of theundeformed intima and adventitia For this the cross sectionsof the deformed intima and adventitia were registered withthe cross sections of the undeformed intima
Registration is the calculation of the coordinate transfor-mation that can minimize the distance between two pointsets Accordingly registration in this study is to calculate thetranslation (119909 119910) rotation (120579) and scale (119904) that minimizesthe distance between the two point sets (X target point cloudY source point cloud) which compose the 2D blood vesselcross sections In this study the coordinate transformationmatrix T0 that minimizes the distance between the two pointsets X and Y was calculated using the optimization methodafter setting these 4 elements as the variables In additionto make a result linear to the rotation value of the previousframe when registering cross sections the value closest to therotation value 120579 of the previous frame was calculated
T0 = min (sum dist (XY1015840)) (5)
whereY1015840 = T (119909 119910 120579 119904)Y (6)
To achieve this the multiminimizer function of theGNU Scientific Library was used [18] Figure 10 shows theregistration result of the two intima cross sections
Computational and Mathematical Methods in Medicine 7
Deformed intima
Registration
Undeformed intima
Figure 10 Registration between undeformed and deformed intima contours using the proposed method
60y = minus3E minus 09x5 + 2E minus 06x4 minus 00005x3 + 00344x2 + 07059x minus 10207
Figure 11 Trend line of rotation angle result
The 119909 119910 120579 and 119904 calculated through the registrationbetween intima cross sections are the values at which thedeformed intima cross section changes to the undeformedintima cross section Accordingly the calculated 119909 119910 120579 and 119904were equally applied to change the deformed adventitia crosssection to the undeformed adventitia cross section Figure 11shows the rotation values of all the cross sections registeredusing the optimization method To more linearly transformsuch rotation values the trend linewas calculated using all therotation values and the rotation value of each cross sectionwas corrected to the trend line value
54 Generation of an Undeformed Intima and AdventitiaModel The cross sections of the undeformed intima andadventitia were calculated through a process similar to thatabove To finally generate a model in an undeformed stateusing such cross sections the cross sections should be locatedat the proper positions and in proper orientation For thisthe centerline extracted from the 3D model of the intimanot deformed by a catheter which was generated from a CTimage was used A 3D blood vessel polygon model whichincluded the intima and adventitia as shown in Figure 12was generated by placing the calculated cross sections ofthe undeformed intima and adventitia on the undeformedcenterline
6 Bifurcated Blood Vessel Model
In fact human blood vessels are not comprised of singleblood vessels but a combination of blood vessels with many
Figure 12 Generated 3D blood vessel model including intima andadventitia
branches Accordingly to actually model the blood vessel ofa patient not a single blood vessel model but a 3D bloodvessel model that includes branches should be generatedAccordingly a 3D blood vessel model including branches notdeformed by a catheter was generated using the proposedblood vessel modeling method in this chapter For this ablood vessel replica including branches was produced asshown in Figure 13 Different from the case of a single bloodvessel this replicawas produced by creating a 3Dmodel usingthe CT images of an actual patient and producing a moldusing a 3D printer A blood vessel replica of the desired formwas produced by injecting silicon into this mold For thisreplica gelatin was again used to fix the blood vessel tube
The CT IVUS and biplane X-ray angiogram images weretaken using the produced blood vessel replica as per the caseof a single blood vessel As the replica includes branches theIVUS images and the X-ray angiogram images of each bloodvessel branch were taken Figure 14 shows themedical imagestaken using the blood vessel replica
61 Generation of a 3D Intima Model Including Branches NotDeformed by a Catheter and Extraction of Cross Sections In
8 Computational and Mathematical Methods in Medicine
Figure 13 Replica of blood vessel
CT IVUS
X-ray angiogram
Figure 14 CT biplane X-ray angiogram and IVUS images of replica
the case of the blood vessel that includes branches a 3Dmodel of the intima not deformed by a catheter was alsogenerated using the CT image as per the single blood vesselFigure 15 shows the 3D model of the intima not deformed bya catheter which was generated using a CT image
To extract the cross sections of the 3D intima models thecenterline of each branch was calculated using a 3D Voronoidiagram Figure 16 shows the centerline of each branch andthe cross sections extracted using them
62 Generation of a 3DModel of the Intima andAdventitia NotDeformed by aCatheterThat Includes Branches and Extractionof Cross Sections To generate a blood vessel model thatincludes branches the IVUS images of all the blood vesselbranches should be taken to obtain data about the intimaand adventitia of each blood vessel branch In addition tocalculate the position and orientation of the IVUS imageof each branch when the IVUS image of each blood vesselbranch is taken the inserted catheter should be photographedfrom different directions Accordingly as the blood vesselreplica used in this study had two blood vessel branches 2
(a) (b)
Figure 15 (a) Bifurcated artificial blood vesselmodel (b)Generatedundeformed 3D intima model
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
6 Computational and Mathematical Methods in Medicine
Contoursof intima 3D catheter path
Deformed intima model
Deformed adventitia model
(a) (b)
Figure 9 (a) A series of deformed intima cross sections (b) A polygon model of deformed intima and adventitia model
propose a method of determining the corresponding relationbetween the two 3D blood vessel models to extract the crosssections at the corresponding positions and matching them
51 Calculation of Centerline and Extraction of Cross SectionTo define a plane required for extraction of 2D cross sectionsfrom the 3D blood vessel intimamodel in a tube form one 3Dpoint and normal vector are required For this the centerlinethat could well express the shape of the blood vessel shouldbe calculated
In the study carried out by Luca the centerline existingbetween twopointswithin amodel in a tube formwas definedto be the line farthermost from the boundary Accordinglythe centerline of an object Ω existing in a 3D space can beexpressed as the pathC = C(s) between two points P1 and P2which minimizes
Ecenterline (C) = intL=Cminus1(P1)
0=Cminus1(P0)F (C (s)) 119889119904 (4)
For this the Delaunay triangulation of the object Ω wascalculated throughwhich themaximum spheres inscribed inthe blood vessel model were calculated The centerline of the3D blood vessel model was extracted using the center pointsof these spheres
52 Correspondence Definition between 3D Blood Vessel Mod-els and Extraction of Cross Sections To register two bloodvessel models in different states correspondence between thetwomodels should be defined first For this the centerlines ofthe two intima models calculated earlier were used Becausethe CT IVUS and biplane X-ray angiogram images wereall obtained by imaging the same section of the bloodvessel replica the 3D blood vessel models generated earliermodel the same section of the blood vessel though they arein different states Accordingly the corresponding relation
between these two intima models was defined by dividingthe center curves of these two intima models into the samenumber of lines using the same interval and the crosssections of the 3D models were extracted at the definedpositions
53 Registering between Cross Sections in Different States Inthis study we intend to generate a 3D intima and adven-titia model from which the catheter-induced deformationis removed through registration Accordingly we attemptedto convert the cross sections of the deformed intima andadventitia extracted earlier into the cross sections of theundeformed intima and adventitia For this the cross sectionsof the deformed intima and adventitia were registered withthe cross sections of the undeformed intima
Registration is the calculation of the coordinate transfor-mation that can minimize the distance between two pointsets Accordingly registration in this study is to calculate thetranslation (119909 119910) rotation (120579) and scale (119904) that minimizesthe distance between the two point sets (X target point cloudY source point cloud) which compose the 2D blood vesselcross sections In this study the coordinate transformationmatrix T0 that minimizes the distance between the two pointsets X and Y was calculated using the optimization methodafter setting these 4 elements as the variables In additionto make a result linear to the rotation value of the previousframe when registering cross sections the value closest to therotation value 120579 of the previous frame was calculated
T0 = min (sum dist (XY1015840)) (5)
whereY1015840 = T (119909 119910 120579 119904)Y (6)
To achieve this the multiminimizer function of theGNU Scientific Library was used [18] Figure 10 shows theregistration result of the two intima cross sections
Computational and Mathematical Methods in Medicine 7
Deformed intima
Registration
Undeformed intima
Figure 10 Registration between undeformed and deformed intima contours using the proposed method
60y = minus3E minus 09x5 + 2E minus 06x4 minus 00005x3 + 00344x2 + 07059x minus 10207
Figure 11 Trend line of rotation angle result
The 119909 119910 120579 and 119904 calculated through the registrationbetween intima cross sections are the values at which thedeformed intima cross section changes to the undeformedintima cross section Accordingly the calculated 119909 119910 120579 and 119904were equally applied to change the deformed adventitia crosssection to the undeformed adventitia cross section Figure 11shows the rotation values of all the cross sections registeredusing the optimization method To more linearly transformsuch rotation values the trend linewas calculated using all therotation values and the rotation value of each cross sectionwas corrected to the trend line value
54 Generation of an Undeformed Intima and AdventitiaModel The cross sections of the undeformed intima andadventitia were calculated through a process similar to thatabove To finally generate a model in an undeformed stateusing such cross sections the cross sections should be locatedat the proper positions and in proper orientation For thisthe centerline extracted from the 3D model of the intimanot deformed by a catheter which was generated from a CTimage was used A 3D blood vessel polygon model whichincluded the intima and adventitia as shown in Figure 12was generated by placing the calculated cross sections ofthe undeformed intima and adventitia on the undeformedcenterline
6 Bifurcated Blood Vessel Model
In fact human blood vessels are not comprised of singleblood vessels but a combination of blood vessels with many
Figure 12 Generated 3D blood vessel model including intima andadventitia
branches Accordingly to actually model the blood vessel ofa patient not a single blood vessel model but a 3D bloodvessel model that includes branches should be generatedAccordingly a 3D blood vessel model including branches notdeformed by a catheter was generated using the proposedblood vessel modeling method in this chapter For this ablood vessel replica including branches was produced asshown in Figure 13 Different from the case of a single bloodvessel this replicawas produced by creating a 3Dmodel usingthe CT images of an actual patient and producing a moldusing a 3D printer A blood vessel replica of the desired formwas produced by injecting silicon into this mold For thisreplica gelatin was again used to fix the blood vessel tube
The CT IVUS and biplane X-ray angiogram images weretaken using the produced blood vessel replica as per the caseof a single blood vessel As the replica includes branches theIVUS images and the X-ray angiogram images of each bloodvessel branch were taken Figure 14 shows themedical imagestaken using the blood vessel replica
61 Generation of a 3D Intima Model Including Branches NotDeformed by a Catheter and Extraction of Cross Sections In
8 Computational and Mathematical Methods in Medicine
Figure 13 Replica of blood vessel
CT IVUS
X-ray angiogram
Figure 14 CT biplane X-ray angiogram and IVUS images of replica
the case of the blood vessel that includes branches a 3Dmodel of the intima not deformed by a catheter was alsogenerated using the CT image as per the single blood vesselFigure 15 shows the 3D model of the intima not deformed bya catheter which was generated using a CT image
To extract the cross sections of the 3D intima models thecenterline of each branch was calculated using a 3D Voronoidiagram Figure 16 shows the centerline of each branch andthe cross sections extracted using them
62 Generation of a 3DModel of the Intima andAdventitia NotDeformed by aCatheterThat Includes Branches and Extractionof Cross Sections To generate a blood vessel model thatincludes branches the IVUS images of all the blood vesselbranches should be taken to obtain data about the intimaand adventitia of each blood vessel branch In addition tocalculate the position and orientation of the IVUS imageof each branch when the IVUS image of each blood vesselbranch is taken the inserted catheter should be photographedfrom different directions Accordingly as the blood vesselreplica used in this study had two blood vessel branches 2
(a) (b)
Figure 15 (a) Bifurcated artificial blood vesselmodel (b)Generatedundeformed 3D intima model
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
60y = minus3E minus 09x5 + 2E minus 06x4 minus 00005x3 + 00344x2 + 07059x minus 10207
Figure 11 Trend line of rotation angle result
The 119909 119910 120579 and 119904 calculated through the registrationbetween intima cross sections are the values at which thedeformed intima cross section changes to the undeformedintima cross section Accordingly the calculated 119909 119910 120579 and 119904were equally applied to change the deformed adventitia crosssection to the undeformed adventitia cross section Figure 11shows the rotation values of all the cross sections registeredusing the optimization method To more linearly transformsuch rotation values the trend linewas calculated using all therotation values and the rotation value of each cross sectionwas corrected to the trend line value
54 Generation of an Undeformed Intima and AdventitiaModel The cross sections of the undeformed intima andadventitia were calculated through a process similar to thatabove To finally generate a model in an undeformed stateusing such cross sections the cross sections should be locatedat the proper positions and in proper orientation For thisthe centerline extracted from the 3D model of the intimanot deformed by a catheter which was generated from a CTimage was used A 3D blood vessel polygon model whichincluded the intima and adventitia as shown in Figure 12was generated by placing the calculated cross sections ofthe undeformed intima and adventitia on the undeformedcenterline
6 Bifurcated Blood Vessel Model
In fact human blood vessels are not comprised of singleblood vessels but a combination of blood vessels with many
Figure 12 Generated 3D blood vessel model including intima andadventitia
branches Accordingly to actually model the blood vessel ofa patient not a single blood vessel model but a 3D bloodvessel model that includes branches should be generatedAccordingly a 3D blood vessel model including branches notdeformed by a catheter was generated using the proposedblood vessel modeling method in this chapter For this ablood vessel replica including branches was produced asshown in Figure 13 Different from the case of a single bloodvessel this replicawas produced by creating a 3Dmodel usingthe CT images of an actual patient and producing a moldusing a 3D printer A blood vessel replica of the desired formwas produced by injecting silicon into this mold For thisreplica gelatin was again used to fix the blood vessel tube
The CT IVUS and biplane X-ray angiogram images weretaken using the produced blood vessel replica as per the caseof a single blood vessel As the replica includes branches theIVUS images and the X-ray angiogram images of each bloodvessel branch were taken Figure 14 shows themedical imagestaken using the blood vessel replica
61 Generation of a 3D Intima Model Including Branches NotDeformed by a Catheter and Extraction of Cross Sections In
8 Computational and Mathematical Methods in Medicine
Figure 13 Replica of blood vessel
CT IVUS
X-ray angiogram
Figure 14 CT biplane X-ray angiogram and IVUS images of replica
the case of the blood vessel that includes branches a 3Dmodel of the intima not deformed by a catheter was alsogenerated using the CT image as per the single blood vesselFigure 15 shows the 3D model of the intima not deformed bya catheter which was generated using a CT image
To extract the cross sections of the 3D intima models thecenterline of each branch was calculated using a 3D Voronoidiagram Figure 16 shows the centerline of each branch andthe cross sections extracted using them
62 Generation of a 3DModel of the Intima andAdventitia NotDeformed by aCatheterThat Includes Branches and Extractionof Cross Sections To generate a blood vessel model thatincludes branches the IVUS images of all the blood vesselbranches should be taken to obtain data about the intimaand adventitia of each blood vessel branch In addition tocalculate the position and orientation of the IVUS imageof each branch when the IVUS image of each blood vesselbranch is taken the inserted catheter should be photographedfrom different directions Accordingly as the blood vesselreplica used in this study had two blood vessel branches 2
(a) (b)
Figure 15 (a) Bifurcated artificial blood vesselmodel (b)Generatedundeformed 3D intima model
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
8 Computational and Mathematical Methods in Medicine
Figure 13 Replica of blood vessel
CT IVUS
X-ray angiogram
Figure 14 CT biplane X-ray angiogram and IVUS images of replica
the case of the blood vessel that includes branches a 3Dmodel of the intima not deformed by a catheter was alsogenerated using the CT image as per the single blood vesselFigure 15 shows the 3D model of the intima not deformed bya catheter which was generated using a CT image
To extract the cross sections of the 3D intima models thecenterline of each branch was calculated using a 3D Voronoidiagram Figure 16 shows the centerline of each branch andthe cross sections extracted using them
62 Generation of a 3DModel of the Intima andAdventitia NotDeformed by aCatheterThat Includes Branches and Extractionof Cross Sections To generate a blood vessel model thatincludes branches the IVUS images of all the blood vesselbranches should be taken to obtain data about the intimaand adventitia of each blood vessel branch In addition tocalculate the position and orientation of the IVUS imageof each branch when the IVUS image of each blood vesselbranch is taken the inserted catheter should be photographedfrom different directions Accordingly as the blood vesselreplica used in this study had two blood vessel branches 2
(a) (b)
Figure 15 (a) Bifurcated artificial blood vesselmodel (b)Generatedundeformed 3D intima model
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
Computational and Mathematical Methods in Medicine 9
(a) (b) (c)
Figure 16 (a) Undeformed intima model (b) Centerlines of each branch (c) Extracted cross sections using each centerline
Reconstructed catheter path
Leftside
Rightside
Biplane X-ray angiogram images
Figure 17 Reconstructed 3D catheter path of each branch
sets of biplane X-ray angiogram images were acquired byphotographing the catheter inserted into each blood vesselbranch twice from different directions which were used togenerate two 3D paths of the catheter as shown in Figure 17
In addition to acquire the detailed shape of the bloodvessel the two sets of IVUS images obtained by imaging eachblood vessel branch were used In the case that branches areincluded as in the case of the CT images the IVUS images
also show the sections where the blood vessel is bifurcatedas shown in Figure 18 When the cross sections in the IVUSimages were registered with the cross sections extracted fromthe CT images the cross sections of the relevant intimaand adventitia were all extracted from the IVUS imagesso that the branched sections can be accurately matchedFurthermore evenwhen the shapes of the blood vessel intimaand adventitia on the other side are not perfectly obtained
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
10 Computational and Mathematical Methods in Medicine
Figure 18 Segmented intima and adventitia contours from IVUS image at bifurcation
Reconstructedcatheter path IVUS image Deformed
adventitia modelDeformed
intima model
Leftside
Rightside
Figure 19 Reconstructed deformed 3D intima and adventitia models of each branch
the shapes of the intima and adventitia were extracted byoverlapping them as shown in Figure 18
A 3D model of the intima and adventitia not deformedby the catheter inserted was generated as shown in Figure 19by applying the result of the sequential triangulation method
using each 3D catheter path to each cross section of the intimaand adventitia extracted from the IVUS images
63 Computation of a 3D Model of the Intima and AdventitiaIncluding Branches with the Deformation Caused by the
Computational and Mathematical Methods in Medicine 11
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
Catheter Eliminated through Registration In the case of ablood vessel that includes bifurcation a 3D model of intimaand adventitia deformed by a catheter is generated in theform of a single blood vessel for each branch and thecross sections are also found to be similar to the case ofa single blood vessel Accordingly to carry out registra-tion using these cross sections the intima cross sectionsextracted from each branch in the undeformed intimamodelwhich had been generated through the CT images earlierwere used directly The cross sections of the undeformedintima and adventitia were calculated by registering the crosssections of the deformed intima and adventitia with thecross sections of the undeformed intima that included thesebranch points Figure 20 shows the result of registrationbetween the cross sections of the undeformed and deformedintima at a branch point It can be seen that even whenbranch points are included cross sections can be properlymatched using the proposed registration method in thisstudy
The rotation values of the registered cross sections werecorrected to enable the rotation variations of the cross sec-tions to be linear using the trend line equations of the rotationvalues of the cross sections when all the cross sectionsof the right and left blood vessel branches are registeredAfter transforming the cross sections of the intima andadventitia in a deformed state into the cross sections of theintima and adventitia in an undeformed state through such aregistration process all the cross sections were placed on thecenterline extracted from the 3D model in an undeformedstate as shown in Figure 21(a) A model of the intima andthe adventitia that included a branch point was generated asshown in Figure 21(b) using all the points corresponding tothe left and right blood vessel branches which were used togenerate a 3D blood vessel model that included intima andadventitia
7 Conclusion and Discussion
In this paper we have proposed a method for generating a3D model of intima and adventitia for accurate FSI analysis
that eliminates the deformation caused by insertion of acatheterThemethod of combining IVUS images and biplaneX-ray angiogram images is widely used for generation of 3Dblood vessel models and generates a 3D model of the intimaand adventitia that is deformed by the inserted catheter Toeliminate such deformation a 3Dmodel of the intimawithoutcatheter-induced deformation was additionally generatedfrom CT images and these two models were registered toeliminate the catheter-induced deformation
In the registration the 3D models were not directly reg-istered but the cross sections of each model were registeredThe cross sections of the deformed intima were registeredwith the cross sections of the undeformed intima and thecross sections of the undeformed adventitia were convertedby applying the registration result to the cross sections of thedeformed adventitia A 3D blood vessel model that includedthe undeformed intima and adventitia was finally generatedby placing the cross sections of the undeformed intima andadventitia calculated through such a process on the centerlineextracted from the undeformed intima model
The method of modeling a 3D blood vessel proposedin this study has various limitations To determine theposition and direction of the intima and adventitia crosssections extracted from IVUS images these cross sectionswere registered with the cross sections of the intima extractedfrom CT images The values of movement (119909 119910) rotation(120579) and scale (119904) calculated through the registration betweenthe two intima cross sections were equally applied to thecross sections of the adventitia extracted from IVUS imagesHowever such a method calculates an ideal result withoutconsidering the material properties of the blood vessel In thecase of an actual blood vessel the intima and the adventitiawill not equally deform because of the material propertiesof the blood vessel wall In addition for a patient withatherosclerosis the blood vessel wall will not be isotropicowing to the plague existing on the blood vessel wallAccordingly the intima and adventitia model calculatedusing the method proposed in this study contains sucherrors
Another limitation is that it is difficult to accuratelyevaluate the accuracy of the blood vessel model generatedthrough the proposed method This is because the onlymedical image through which the information about bloodvessel adventitia can be obtained is IVUS image
If OCT (Optical Coherence Tomography) that can pho-tograph lumenmore clearly than IVUS is used to further thisstudy more accurate information about blood vessel intimacan be obtained However as OCT uses light there are dif-ficulties in obtaining accurate information about adventitiaunlike IVUS that uses ultrasound Accordingly more precise3D blood vessel models are expected to be generated by usingOCT to obtain intima data and IVUS to obtain adventitiadata
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
12 Computational and Mathematical Methods in Medicine
(a) (b) (c)
Figure 21 (a) Intima and adventitia point sets placed on undeformed centerline (b) Computed undeformed intima and adventitia model(c) Three-dimensional blood vessel model including intima and adventitia
Acknowledgments
This research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT andFuture Planning (NRF-2012R1A2A2A01047366 and NRF-2015R1D1A1A01060486)
References
[1] K Dumont J Vierendeels R Kaminsky G Van Nooten PVerdonck and D Bluestein ldquoComparison of the hemodynamicand thrombogenic performance of two bileaflet mechanicalheart valves using a CFDFSI modelrdquo Journal of BiomechanicalEngineering vol 129 no 4 pp 558ndash565 2007
[2] P Reymond P Crosetto S Deparis A Quarteroni and NStergiopulos ldquoPhysiological simulation of blood flow in theaorta comparison of hemodynamic indices as predicted by 3-D FSI 3-D rigid wall and 1-D modelsrdquoMedical Engineering andPhysics vol 35 no 6 pp 784ndash791 2013
[3] X Huang C Yang J Zheng et al ldquoHigher critical plaque wallstress in patients who died of coronary artery disease comparedwith those who died of other causes a 3D FSI study based on exvivo MRI of coronary plaquesrdquo Journal of Biomechanics vol 47no 2 pp 432ndash437 2014
[4] H A PakravanM S Saidi and B Firoozabadi ldquoFSI simulationof a healthy coronary bifurcation for studying the mechanicalstimuli of endothelial cells under different physiological condi-tionsrdquo Journal of Mechanics in Medicine and Biology vol 15 no5 Article ID 1550089 28 pages 2015
[5] A Valenciaa F Munoza S Arayaa R Riverab and E BravobldquoComparison between computational fluid dynamics fluidndashstructure interaction and computational structural dynamicspredictions of flow-induced wall mechanics in an anatomically
realistic cerebral aneurysm modelrdquo International Journal ofComputational Fluid Dynamics vol 23 no 9 pp 649ndash6662009
[6] J Knight S Baumuller V Kurtcuoglu et al ldquoLong-term follow-up computed tomography and computational fluid dynamicsof theCabrol procedurerdquo Journal ofThoracic andCardiovascularSurgery vol 139 no 6 pp 1602ndash1608 2010
[7] Y Qian J L Liu K Itatani K Miyaji and M Umezu ldquoCom-putational hemodynamic analysis in congenital heart diseasesimulation of the Norwood procedurerdquo Annals of BiomedicalEngineering vol 38 no 7 pp 2302ndash2313 2010
[8] K M Tse P Chiu H P Lee and P Ho ldquoInvestigation of hemo-dynamics in the development of dissecting aneurysm withinpatient-specific dissecting aneurismal aortas using computa-tional fluid dynamics (CFD) simulationsrdquo Journal of Biome-chanics vol 44 no 5 pp 827ndash836 2011
[9] W Lee H S Ryou S Kim J W Nam W S Lee and S WCho ldquoStudy of hemodynamic parameters to predict coronaryartery disease using assumed healthy arterial modelsrdquo Journalof Mechanical Science and Technology vol 29 no 3 pp 1319ndash1325 2015
[10] L Antiga Patient-SpecificModeling of Geometry and Blood Flowin Large Arteries Politecnico di Milano Milan Italy 2002
[11] L Antiga B Ene-Iordache and A Remuzzi ldquoComputationalgeometry for patient-specific reconstruction and meshing ofblood vessels fromMRandCT angiographyrdquo IEEE Transactionson Medical Imaging vol 22 no 5 pp 674ndash684 2003
[12] A Wahle H Oswald and E Fleck ldquoNew 3-D attributeddata model for archiving and interchanging of coronary vesselsystemsrdquo in Computers in Cardiology 1993
[13] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoQuantitative volume analysis of coronary vesselsystems by 3-D reconstruction from biplane angiogramsrdquo in
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
Computational and Mathematical Methods in Medicine 13
Proceedings of the IEEE Nuclear Science Symposium amp MedicalImaging Conference pp 1217ndash1221 November 1994
[14] A Wahle E Wellnhofer I Mugaragu H U Sauer H Oswaldand E Fleck ldquoAssessment of diffuse coronary artery disease byquantitative analysis of coronary morphology based upon 3-dreconstruction from biplane angiogramsrdquo IEEE Transactions onMedical Imaging vol 14 no 2 pp 230ndash241 1995
[15] A Wahle G P M Prause S C DeJong and M Sonka ldquo3-D fusion of biplane angiography and intravascular ultrasoundfor accurate visualization and volumetryrdquo in Medical ImageComputing and Computer-Assisted InterventionmdashMICCAI rsquo98First International Conference Cambridge MA USA October11ndash13 1998 Proceedings vol 1496 of Lecture Notes in ComputerScience pp 146ndash155 Springer Berlin Germany 1998
[16] A Wahle ldquoGeometrically correct 3-D reconstruction of intra-vascular ultrasound images by fusionwith biplane angiography-methods and validationrdquo IEEE Transactions on Medical Imag-ing vol 18 no 8 pp 686ndash699 1999
[17] A Wahle S C Mitchell M E Olszewski R M Long and MSonka ldquoAccurate visualization and quantification of coronaryvasculature by 3-D4-D fusion from biplane angiography andintravascular ultrasoundrdquo in Proceedings of the Biomonitoringand Endoscopy Technologies Proceedings of SPIE pp 144ndash155Amsterdam Netherlands July 2001
[18] B Gough GNU Scientific Library Reference Manual NetworkTheory Ltd Godalming UK 2009
[19] P Schoenhagen S E Nissen and E Murat IVUS Made EasyInforma Health Care 2005
