Deformable image registration of heterogeneous human lung incorporatingthe bronchial tree
Adil Al-Mayah,a� Joanne Moseley, Mike Velec, Shannon Hunter, and Kristy BrockRadiation Medicine Program, Princess Margaret Hospital, 610 University Avenue,Toronto, Ontario M5G 2M9, Canada
�Received 20 November 2009; revised 24 June 2010; accepted for publication 8 July 2010;published 6 August 2010�
The advancement of radiation therapy techniques such asSBRT and IMRT requires a precise location of the targetwhile sparing the healthy tissues and avoiding organs at risk.Image guided radiotherapy �IGRT� has addressed this re-quirement by aligning the patient in each treatment session.An essential part of the IGRT technique is image registration.There are two types of image registration, namely, rigid anddeformable. Rigid registration may be sufficient for organsexperiencing little deformation such as the brain. However, itis not suitable for organs with large deformation, such aslungs.
A number of deformable image registration techniqueshave been used including intensity-based and biomechanicalmodels. Although intensity-based models such as B-spline,1
thin plate spline,2 and demons3–5 have accurately modeledthe breathing motion of lungs, registration errors “are proneto appear in regions with low image gradients” as shown byZhong et al.6 in addition to the changing image intensity
caused by blood circulation variation as a result of breathing
4560 Med. Phys. 37 „9…, September 2010 0094-2405/2010/37
motion.7 These points can be addressed using finite elementmodels,6 which “allow more principled control of localizeddeformations.”8
Different finite element models have been developed toinvestigate the effect of lung weight,9 material proper-ties,10–12 and boundary conditions.13–15 These studies mod-eled the lung as a homogeneous material. The lung paren-chyma contains branching tubes of the bronchial tree thathave different material properties from the rest of thetissues.16 As one of the main parts of the lung, bronchial treegeometry and biomechanical properties may affect the defor-mation of the lung.
Tai and Lee17 conducted an experimental study on theeffect of heterogeneity and isotropy on the lung deformation.Samples were taken from different locations, some of whichincluded large airways in the middle of the parenchyma. Itwas found that the mean deformation is not affected by thelarge airway.
Lai-Fook and Kallok18 studied the interaction between the
bronchus, artery, and parenchyma at the local level using a
4561 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4561
2D finite element model with the bronchus adjoining theartery. The airway and its location have a pronounced effecton the deformation of the surrounding tissues. Also, theshape of bronchial tree affects the airway flow resistances.This effect is large in the central airway.
This study investigates the effect of heterogeneity on thedeformation of the lungs by including the bronchial tree.Unlike previous studies,17,18 the complete lung is examinedin order to reach a realistic model that simulates lung’s ge-ometry, material properties, and its interaction with sur-rounding tissues. The lung parenchyma is modeled using hy-perelastic material properties based on experimentalresults.19 The lungs are allowed to slide relative to the chestcavities using frictionless contact surface. Frictionless sur-face is proved to be effective in improving the accuracy ofthe lungs’ model based on a previous investigation conductedby the authors.11 This model will facilitate further investiga-tion of the effect of diseases, radiation toxicity, and compli-
TABLE I. Patients’ data including tumor location anvolume change between inhale and exhale, bronchial
cations. Comparisons between the different material modelsare evaluated using �1� the accuracy of the deformable reg-istration based on bifurcation points, �2� a relative compari-son of each model using all bronchial tree nodes in themodel, and �3� a dosimetric comparison comparing the dosecalculated to the predicted exhale position for each model.The purpose of the relative comparison is to ensure that thelimited number of bifurcation points is not influencing theoutcome of the evaluation �using bronchial tree nodes in themodel simulates having an anatomical point at each position;however, this is only a relative comparison, as the “truth” isnot available for each point�. The purpose of the dosimetriccomparison is to evaluate the clinical impact of the discrep-ancies from the different modeling techniques. The deforma-tion algorithm deforms the inhale position to the exhale po-sition; therefore, the dose that would be delivered to eachpredicted exhale position is compared. This is also a relativecomparison, as the truth is unknown for each position.
e, diaphragm breathing motion in the SI direction,e percentage to lung volume, and comorbid illness.
e pulmonary disease, HTN: Hypertension, MI: Myo-atica, and PVD: Peripheral vascular disease.
le Image
rface FIG. 1. Model development starts by acquiring CT im-ages for both exhale and inhale phases. 3D surfacemeshes are created and used for the projection of theinhale and exhale surfaces to find the boundary condi-tions. The inhale surface mesh of all components,except the bronchial tree, is tetrameshed, leaving thebronchial trees as shell structures. After applying con-tact surface on the lungs, finite element analysis areconducted.
d sizvolum
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4562 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4562
II. MODEL DESCRIPTION AND MATERIALS
II.A. General
Ten nonsmall cell lung cancer patients are investigated inthis study. Patients’ details are listed in Table I including thetumor size and location, diaphragm motion during normalbreathing, volume change between inhale and exhale, vol-ume percentage of the segmented bronchi, and comorbidi-ties. Using four dimensional computed tomography �4DCT�data of ten lung cancer patients, three dimensional �3D� finiteelement models have been developed. Each model consistsof a body, both lungs, bronchial tree of each lung, and tumor.In the literature, a number of techniques have been used tosegment the bronchial tree, namely, knowledge based, regiongrowing, centerline extraction, and mathematical morphol-ogy, as classified by Sluimer et al.,20 where an extensivereview is provided. For the purpose of this preliminary study,the bronchial tree is constructed by setting a contrast thresh-old on the 4DCT images with a value ranging from �700 to�600 HU. Three nodes surface shell elements are used for
TABLE II. Bifurcation points distribution relative to their position to the lungof points within a distance of 5, 10, and 15 mm from the lungs’ edge and b
FIG. 2. Bifurcation points in inhale and exhale images. The error in thelocation of bifurcation points represents the difference in location betweenthe estimated FEM location and the image-based location in the exhalebreathing phase.
Medical Physics, Vol. 37, No. 9, September 2010
the bronchial tree with an average surface area of 1.5 mm2.Volumetric four nodes tetrahedral elements are used for thebody, lungs, and tumor.
II.B. Model development
The model is created by contouring lungs, body, and tu-mor using the 4DCT images. A surface mesh is created foreach component at both the inhale and exhale phases, asshown in Fig. 1.21 Using a finite element preprocessor �HY-
PERMESH, Altair Engineering, Troy, MI,� the bronchial tree iscreated by including its surface mesh inside the lung surfacemesh. The volume of the lung outside the bronchial tree, inaddition to the body and tumor, is tetrameshed, leaving thebronchial tree as a shell structure interconnected to the lungsparenchyma.
A surface based contact model is then applied to eachlung by selecting the face of each tetrahedral element on theexternal boundary of the lung using a finite element package�ABAQUS, v 6.8, Providence, RI�. Similarly, the surface of thetetrahedral elements that create the chest cavity representingthe internal surface of the body is selected. This procedure isperformed for each lung and its corresponding cavity. Avalue of zero friction is assigned for the lung-chest cavityinterface to simulate the lubrication of the pleural liquid.11
II.C. Boundary conditions
The inhale phase of the body and lungs is used as theinitial representation at time zero of the simulation. The ex-hale position is considered the final position of the deforma-tion onto which the lungs and body are deformed from theinhale position. In other words, the boundary conditions ap-plied in the model are the location differences between theinhale and exhale positions of surface nodes of the lungs andbody. These differences are found using the surface projec-tion technique HYPERMORPH �Altair Engineering, Troy, MI�.
e and bronchial tree represented by the average distance and the percentageial tree surface.
4563 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4563
The boundary conditions can be divided into two groups,namely, external and internal. The external boundary condi-tion is the set of displacements derived from the projectionof the body external surface between inhale and exhale po-sitions. The internal set is the displacement applied to the
TABLE III. Average absolute bifurcation error in LR,bronchial tree �Eb� and homogeneous lungs �dimensi
nodes of chest cavities in direct contact with lungs. Since a
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contact surface is applied between the chest cavity and thelung, the boundary conditions are applied indirectly to thelung surface in a form of contact pressure through the sur-rounding nodes of the chest cavities. In order to simulate thiscontact pressure on the lungs and avoid any separation be-
I, and vector values with different elastic moduli ofn mm�.
tween contacting surfaces, the inhale breathing phase is used
4564 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4564
as a primary state subjected to contact pressure that com-presses it to the smaller volume at the exhale phase.
II.D. Material properties
Hyperelastic material properties of the lung parenchymaare applied using experimental test data reported by Zeng etal.19 A nearly incompressible parenchyma is also character-ized by a Poisson’s ratio of 0.4 that provides a minimumregistration error based on previous study conducted by theauthors.11 The body is modeled as linear elastic with a modu-lus of elasticity of 6.0 kPa and Poisson’s ratio of 0.4.
Different values of modulus of elasticity of the airwayhave been reported in the literature including 0.01, 0.12,16,18
0.13,22 and 5.8 MPa.23 Experimental studies on the bronchialtrees that relate the wall thickness to diameter23 andpressure-diameter relationship25 of human airways haveshown a value of modulus of elasticity within the proximityof 0.12 MPa at a transpulmonary pressure of 20 cmH2O.The highest value of modulus of elasticity of 18 MPa isreported for tracheal rings.26 In order to find the effect of
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mechanical properties of the bronchial tree, different valuesof modulus of elasticity are investigated in this study includ-ing 0.01, 0.12, 0.5, 10, and 18 MPa.
II.E. Model accuracy
An average of 40 landmarks in the form of bifurcationpoints are used for the accuracy check of each model. Previ-ously, intraobserver study was conducted at the institutewhere the observer was asked to identify the bifurcationpoints once a week over a period of 4 weeks. The averageerror was less than 1.0 mm in all directions.21
The coordinates of each bifurcation point are located inthe inhale image. The same anatomical point is also locatedin the exhale image, as illustrated in Fig. 2. The differencebetween the coordinates of the point on the inhale and exhaleimages represents the image-based displacement. The sameprocedure is conducted with each bifurcation point using thefinite element model where the displacement of each point iscalculated by finding the difference in location of the pointbetween original and deformed positions. The registration
P10
og0.01 MPa0.12 MPa0.5 MPa10 MPa18 MPa
FIG. 3. The percentage of bifurcation points with abso-lute registration error less than 2.5 mm in the LR direc-tion using different elastic modulus of the bronchial tree�Eb� and compared to the homogeneous model.
P10
og0.01 MPa0.1 MPa0.5 MPa10 MPa18 MPa
FIG. 4. The percentage of bifurcation points with abso-lute registration error less than 2.5 mm in the AP direc-tion using different elastic modulus of the bronchial tree�Eb� and compared to the homogeneous model.
P9
HomEb=Eb=Eb=Eb=Eb=
P9
HomEb=Eb=Eb=Eb=Eb=
4565 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4565
error is the difference between the image-based and finiteelement displacements. Average absolute errors in the LR,AP, and SI directions are reported in this study.
The bifurcation point distribution inside the lung plays animportant role on their validity in representing the lung de-formation. Specifically, the registration errors tend to besmall near the boundary.27 Furthermore, since sliding of thelungs relative to the chest cavity is modeled, the location ofthese points relative to the sliding interface becomes essen-tial. Therefore, the distance between each point and the edgeof the lung in contact with the chest cavity is calculated, aslisted in Table II. It is shown that few points �an averagepercentage of 9.7%� are located within the 5 mm distancefrom the edge and increases to 51.9% as the distance in-creases to 15 mm.
As part of the bronchial tree, the distribution of the bifur-cation points around the bronchial tree can provide a roughestimation of the performance of the segmentation of the tree�Table II� where smaller airways may not be included by thethreshold segmentation. It can be concluded that a significantnumber of bifurcation points �an average of 71.4% of points�
are within the 5 mm distance from the bronchial tree and97% of the points are within a distance of 15 mm from thetree.
II.F. Dose calculations
The clinical impact of the variation in displacement basedon the material properties of the bronchial tree is evaluatedby comparing the dose that would be delivered at the predi-cated exhale position using each deformation map �fromeach of the material properties tested�. As this is a relativecomparison, since the truth at the exhale position of themodel is not known, one of the parameters must be chosen asa reference with which to compare the other values. A valueof 0.12 MPa is chosen as the reference, as it represents themost reported value within the literature. The dose calcula-tions are conducted using a commercially available planningsystem �Pinnacle3 v6.2–8.1, Philips Medical Systems, Madi-son, WI� with a grid resolution of 2.5�2.5�2.5 mm3. Thebronchial tree nodes and their deformation from inhale toexhale are interpolated onto the exhale dose grid from Pin-
P10
og0.01 MPa0.1 MPa0.5 MPa10 MPa18MPa
FIG. 5. The percentage of bifurcation points with abso-lute registration error less than 2.5 mm in the SI direc-tion using different elastic modulus of the bronchial tree�Eb� and compared to the homogeneous model.
7.5
LRAPSI
FIG. 6. Histogram of displacement difference betweenbronchial tree with modulus of elasticity of 18 and 0.01MPa in the LR, AP, and SI directions.
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HomEb=Eb=Eb=Eb=Eb=
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4566 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4566
nacle to obtain the dose at the predicted exhale position.Details of dose calculations using deformable model are pre-sented elsewhere.28
III. RESULTS
III.A. Bifurcation analysis
Using bifurcation points, the accuracy of each model isexamined. The average absolute error of displacement isfound for each patient in LR, AP, and SI directions, in addi-tion to the vector value, as listed in Table III. Heterogeneousmodels with different modulus of elasticity of the bronchialtree �Eb� of 0.01, 0.12, 0.5, 10, and 18 MPa are used in theanalysis and compared to the homogeneous model. It is in-teresting to note that no significant difference is found be-tween the errors using homogenous and heterogeneous mod-els in all directions. The t-test shows an average p value of0.39 with a minimum value of 0.08 found in two cases. Thisis in an agreement with the experimental findings of Tai andLee,17 where mean deformation is not affected by including
FIG. 7. Displacement of the bronchial tree in the SI direction relative to itsposition in the SI direction using modulus of elasticity of the bronchial treeEb tree of 0.5 and 10 MPa, in addition to the displacement difference usingthese two moduli.
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an airway in the sample of the lung. The average vectorvalue of the error in the homogeneous and the model withbronchial tree with stiffness of 0.01, 0.1, and 0.5 MPa isaround 2.66 mm and increased to 2.83 mm for bronchial treewith 18 MPa. This is within the range of accuracy error of3.3�2.1 mm reported by Werner et al.15 using homoge-neous biomechanical modeling of the lungs.
The effect of changing the modulus of elasticity of thebronchial tree on the bifurcation error is also negligible withthe largest difference of 1 mm in patient P6 in the SI direc-tion as the stiffness increases from 0.12 to 0.5 MPa andhigher. This is likely related to the lower role of mechanicalproperties of the bronchial tree on the deformation in com-parison to the role of bronchial geometry.29
The percentage of bifurcation points with an absolute reg-istration error less than the dose grid of 2.5 mm for eachpatient is also calculated in order to find the potential ofincluding the bronchial tree in reducing the registration erroras shown in Figs. 3–5 in the LR, AP, and SI directions,respectively. There is no significant difference between thehomogenous and heterogeneous models. This is an indicationthat the accuracy of the model using the bifurcation pointshas not been affected by including the bronchial tree in themodel.
III.B. Effect of modulus of elasticity on localdeformation
For a clear illustration of the effect of Eb, the extreme Eb
values of 0.01 and 18 MPa are applied to find the displace-ment difference between nodes of the bronchial tree asshown in Fig. 6, where the histogram of the displacementdifference is illustrated for patient P5. Although there is alarge displacement difference as much as 8.5 mm in a fewnodes in the LR direction, most of the bronchial nodes ex-perience an insignificant displacement difference. In a per-centage form for patient P5, 95.2%, 99.9%, and 89.3% of thebronchial nodes have a displacement difference within thedimension of the dose grid, 2.5 mm, in the LR, AP, and SIdirections, respectively. Similarly, considering all patients,
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FIG. 8. Minimum and maximum displacement differ-ences in the LR direction using different modulus ofelasticity of the bronchial trees of 0.01, 0.5, and 18MPa.
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Eb=18
4567 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4567
the average percentage of nodes of the ten patients with dis-placement differences within the grid size are 98.5�2.1,99.3�0.9, and 96.1�3.6 in the LR, AP, and SI directions,respectively.
At the local level, the displacement of all nodes of thebronchial tree is examined in all three directions using dif-ferent values of modulus of elasticity of the bronchial tree�Eb�. The displacement of the bronchial tree nodes with dif-ferent modulus of elasticity �Eb� of 0.5 and 10 MPa in the SIdirection is shown in Fig. 7 for patient P9 where the largestdiaphragm motion is experienced. The displacement differ-ences and the locations of minimum and maximum differ-ences are also illustrated in the figure. As expected, the larg-est displacement is in the bronchial tree near the diaphragmwhich is corresponding to the largest deformation experi-enced by the lung. This displacement decreases near the topof the lung. Similarly, the displacement difference is morepronounced in the part of the lung near the diaphragm. Theextreme positive differences are in the area near the dia-phragm. Few nodes experience negative differences at theentrance of the bronchi into the lung, although the average
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difference at this specific location is near zero. This is likelyrelated to the deformation of the large tube in the radialdirection at the entrance while the smaller tubes near thediaphragm experience more of translation movement thandeformation.
To further investigate the effect of the material propertiesof the bronchial tree on the deformation at the local level, themaximum and minimum differences in displacement in theLR, AP, and SI directions for all patients are illustrated inFigs. 8–10, respectively. The displacement difference ��� isfound by subtracting the displacement of the bronchial nodeswith Eb of 0.01 MPa ��Eb=0.01� from that of the same nodesusing Eb of 0.5 MPa ��Eb=0.5� and by subtracting �Eb=0.5
from �Eb=18.Patients with a minimum breathing volume change be-
tween inhale and exhale exhibit the lowest displacement dif-ferences as the stiffness changes. This is clearly observed inpatients P1, P2, P3, P8, and P10 regardless of the diaphragmmotion. The largest displacement difference is shown in caseof P5 in the LR and SI directions where a large diaphragmmotion is combined with large breathing volume change. Pa-
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FIG. 9. Minimum and maximum displacement differ-ences in the AP direction using different modulus ofelasticity of the bronchial trees of 0.01, 0.5, and 18MPa.
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5 - ∆Eb=0.01- ∆Eb=0.5
FIG. 10. Minimum and maximum displacement differ-ences in the SI direction using different modulus ofelasticity of the bronchial trees of 0.01, 0.5, and 18MPa.
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Eb=18
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4568 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4568
tient P6 exhibits uniform displacement difference in threedirections despite the fact it has large diaphragm motion inthe SI direction. Although, the largest diaphragm motion isexperienced by patient P9, it has a displacement pattern simi-lar to that of P6 but with a lower displacement difference. Itcan be concluded that the most of the extreme displacementdifferences �minimum and maximum� are within the proxim-ity of 2.5 mm gird size especially for the case of Eb changingbetween 0.01 and 0.5 MPa. These differences increase forthe case of the hard bronchi with Eb of 18 MPa. However,most of the nodes experience displacement differenceswithin the dimension of the dose grid as reported earlier�98.5�2.1%, 99.3�0.9%, and 96.1�3.6% in the LR, AP,and SI directions, respectively�.
The effect of the bronchial tree stiffness on the tumordeformation is investigated in patients P1 and P6 based on itsposition relative to the bronchial tree. The tumor in P1 isaway from the bronchi while it is surrounded by the tree inP6, as shown in Fig. 11. Patients P1 and P6 are selected fortheir similar breathing characteristics including the breathingmotion and volume change from inhale to exhale, in additionto the similar tumor size but different tumor motion. Theaverage displacement difference in tumor nodes is measuredbetween the softest �Eb=0.01 MPa� and the hardest �Eb
=18 MPa� bronchial tree. The average difference in P1 is0.2, 0.2, and 0.0 mm in the LR, AP, and SI direction, respec-
P1: Tumor away from bronchi P6: Tumor near bronchi
FIG. 11. Tumor location relative to the bronchial tree.
TABLE IV. The average �SD and maximum differennodes for different moduli �Eb� compared to Eb=0.1
tively, with a maximum difference of 0.3 mm. As for case ofP6, the average differences are �0.3, �0.5, and �0.1 mm inthe LR, AP, and SI directions, respectively, with a maximumabsolute difference of 0.9 mm. Therefore, the tumor sur-rounded by the tree is more affected by the change of bron-chial material. However, the overall difference, and thereforethe difference in the center of mass motion of the tumor, isvery small. This is in agreement with the minor nodal dis-placement difference illustrated earlier.
III.C. Effect of modulus of elasticity on dosedistribution
Since some local displacement differences are observed asa result of changing the modulus of elasticity of the bron-chial tree, dose distribution may also be affected. Therefore,the dose delivered to the bronchial tree at the predicted ex-hale position for each modeled modulus of elasticity is in-vestigated. The results are compared to the dose calculatedwhen a modulus of elasticity of 0.12 MPa is used. The dosedistribution is compared to this modulus of elasticity as it isthe most reported property as indicated in Sec. II D. Theaverage, standard deviation, and maximum dose differencesat each node within in the bronchial tree between the fourmoduli of elasticity and that of 0.12 MPa are listed in TableIV. The average and maximum dose differences are at thelowest level when compared to 0.01 and 0.5 MPa. The aver-age percentages of the bronchial nodes with dose differencegreater than 100 cGy, a potentially clinically significantvalue, are 1.9%, 1.5%, 8.3%, and 9.2% in case of Eb of 0.01,0.5, 10, and 18 MPa, respectively. When increasing this to a200 cGy threshold, the nodes with difference exceeding thisvalue decreases to 0.4%, 0.2%, 3.1%, and 3.7% in case of Eb
of 0.01, 0.5, 10, and 18 MPa, respectively. This is an indica-tion that modulus of elasticity of the bronchial tree has littleeffect on the dose distribution for the modulus of elasticitybetween 0.01 and 0.5 MPa.
breathing dose accumulation of the bronchial treea.
4569 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4569
IV. DISCUSSION
Modeling lungs as homogeneous or heterogeneous mate-rial depends on the scale of deformation. In other words, ifdeformation is required on the scale of alveolus, the hetero-geneous model is required while the homogeneous modelmay be sufficient for the larger scale of deformation.16 Toverify the importance of the bronchial tree on the deforma-tion of the lung, this study is conducted using the full lungand bronchial tree instead of segments of the airway that wasused by Tai and Lee17 and Lai-Fook and Kallok.18
The biomechanics and geometry of the bronchial treehave been the subjects of many research projects. Theseprojects have investigated the bronchial tubethickness,24,30–33 material properties,25,26,34,35 geometry,36 andinteraction with the parenchyma.37,38
The interdependence of the bronchial tree and lung paren-chyma has attracted attention since its introduction by Meadet al.39 The main goal is to estimate the effect of the bron-chial tree on the overall behavior of the lung or vice versa.Hughes et al.36 studied the relationship between the airwaydeformation and rest of the lung. It is reported that the air-way length changed by the cube root of the lung volume. Thechange in length and any distortion are resisted by the paren-chyma with different levels of force depending on thebranching angle of the tree.40 These forces are transferred bythe shear stresses at the interface between the bronchial treeand the parenchyma where the shear modulus of the paren-chyma is the main factor while the Poisson’s ratio of theparenchyma has little effect.37 This gives the parenchyma agreater role than the bronchus in controlling the complianceof the intact bronchi.38
This role of parenchyma on the deformation of the bron-chi may be the reason behind the conclusion made by Tai andLee17 where the large airway has no effect on the mean de-formation of the sample. A similar observation may be foundin Lai-Fook and Kallok18 in the modeling of the adjoiningbronchial and arterial tubes. It is reported that although thetubes are deformed, their deformation is limited within asmall space, as if they are competing to occupy the samespace as stated by Hogg et al.41
In light of these conclusions, the results of this studyshow no significant effect of the bronchial tree on the globaldeformation of the lungs, as shown in the bifurcation pointanalysis. This may be related to the combined effect of re-sponse of the parenchyma to applied deformation, and thebronchi geometrical configurations. The effect of paren-chyma can be seen by its ability to absorb the applied dis-placement within a smaller distance from the diaphragmwhere the largest displacement is applied. This is shown inFig. 12 for patient P9 with a large diaphragm breathing mo-tion of 20 mm. On the other hand, the bronchi geometricalconfiguration, such as bifurcation, can also play a role in thedeformation of the airways as mentioned by Kamm.42 Infact, the mechanics of expanding airways inside the lungs are
“highly dependent on geometry” and not solely dependent on
Medical Physics, Vol. 37, No. 9, September 2010
the elastic properties of the structure.29 Therefore, the bron-chial material properties have little effect on the lung me-chanical properties.
However, on a local level where the nodes of the elementsof the bronchial tree �an average of 38 000 nodes� are con-sidered, there is some difference in the displacement of fewnodes associated with large increase of the modulus of elas-ticity of the tree. This can also be found in the earlier resultsof deformation of the bronchial tree at a very local level asindicated by Lai-Fook and Kallok.18
These local displacement differences may affect the dosedistribution since few nodes experienced displacement dif-ference larger than the dose grid of 2.5 mm. Since the per-centage of these nodes with large difference is very low, thedose distribution is not affected by the modulus of elasticityof the bronchial tree.
Building on these results and experimental investigationreported in the literature, it can be concluded that the bron-chial tree has little effect on the overall deformation of thelungs and, consequently, dose distribution. However, in orderto minimize the local deformation differences experiencedby few nodes, a realistic value of modulus of elasticity of thebronchial tree is needed. Although a large range of modulusof elasticity values are investigated in this study �0.01–18MPa�, the most reported value for the bronchial tree is withinthe proximity of 0.12 MPa,16,18,22,24,25 while the highest valueof 18 is reported for the tracheal rings.26
V. CONCLUSIONS
Effect of heterogeneity of the lungs is investigated byincluding the bronchial tree attached to the parenchyma. Thelungs, including the internal tree and tumor, are allowed toslide relative to the chest cavities by applying frictionlesssurfaces. The effect of modulus of elasticity of the bronchialtree on the deformation is examined using five values of
FIG. 12. Lung deformation from inhale to exhale for P9. The deformation ismore confined to the area near diaphragm �dimensions in cm�.
modulus of elasticity: 0.01, 0.12, 0.5, 10, and 18 MPa.
4570 Al-Mayah et al.: Deformable image registration of heterogeneous human lung 4570
Using bifurcation points for the model accuracy evalua-tion, the bronchial tree has no global effect on the modelaccuracy, regardless of the modulus of elasticity used for thebronchial tree. However, the modulus of elasticity affects thedeformation of the bronchial tree on the local level whichcan be reflected on the dose distribution on the tree. There-fore, dose distribution is calculated using different values ofmodulus of elasticity.
As the most reported value of modulus of elasticity of thetree, 0.12 MPa is used to compare the dose distribution onthe tree to other values modulus of elasticity of 0.01, 0.5, 10,and 18 MPa. In contrast to the tree with 10 and 18 MPa, arelatively larger dose difference is found in trees with modu-lus of elasticity between 0.01 and 0.5 MPa.
In general, the gross approximation of homogeneity of thelungs is sufficient for deformable image registration purpose.However, if more detailed local analysis at a smaller scale isrequired, the heterogeneity may play a significant role in theinvestigation.
ACKNOWLEDGMENTS
The authors would like to thank Andrea Bezjak, the AddieMacNaughton Chair in Thoracic Radiation Oncology, andKevin Franks for their assistance in obtaining the patientdata. This work was supported by the National Cancer Insti-tute of Canada-Terry Fox Foundation and NIH Grant No.1R01CA124714-01A2. Dr. Brock is supported as a CancerCare Ontario Research Chair.
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