http://www.diva-portal.org Postprint This is the accepted version of a paper published in . This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination. Citation for the original published paper (version of record): Li, X., von Holst, H. (2015) Finite element modeling of decompressive craniectomy (DC) and its clinical validation ADVANCES IN BIOMEDICAL SCIENCE AND ENGINEERING, 2(1): 1-9 Access to the published version may require subscription. N.B. When citing this work, cite the original published paper. Permanent link to this version: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-250746
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http://www.diva-portal.org
Postprint
This is the accepted version of a paper published in . This paper has been peer-reviewed butdoes not include the final publisher proof-corrections or journal pagination.
Citation for the original published paper (version of record):
Li, X., von Holst, H. (2015)Finite element modeling of decompressive craniectomy (DC) and its clinical validationADVANCES IN BIOMEDICAL SCIENCE AND ENGINEERING, 2(1): 1-9
Access to the published version may require subscription.
N.B. When citing this work, cite the original published paper.
Permanent link to this version:http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-250746
ADVANCES IN BIOMEDICAL SCIENCE AND ENGINEERINGISSN(Print): 2377-035X ISSN(Online): 2377-0376
DOI: 10.15764/ABSE.2015.01001Volume 2, Number 1, March 2015
ADVANCES IN BIOMEDICAL SCIENCE AND ENGINEERING
Finite Element Modeling of DecompressiveCraniectomy (DC) and its Clinical ValidationXiaogai Li1*, Hans von Holst21 Division of Neuronic Engineering, School of technology and Health, Royal Institute of Technology (KTH), Stockholm, Sweden2 Section of Neurosurgery, Division of Clinical Neuroscience, Karolinska Institutet, Stockholm, Sweden
Abstract:Decompressive craniectomy (DC) is a reliable neurosurgical approach to reduce a pathologically increasedintracranial pressure after neurological diseases such as severe traumatic brain injury (TBI) and stroke.The procedure has substantially reduced the mortality rate but at the expense of increased neurologicalcognitive impairments. Finite Element (FE) modeling in the past decades has become an important toolto develop innovative treatment strategies in various areas of the clinical neuroscience field. The aim ofthis study was to develop patient-specific FE models to simulate DC surgery and validate the modelsagainst patients’ clinical data. The FE models were created based on the Computed Tomography (CT)images of six patients treated with DC. Brain tissue was modeled as poroelastic material. To validatethe model prediction, the motion of brain surface at the DC area from the simulation was compared withthe measured values from medical images which were derived from image registration. The results fromthe computational simulations gave a reliable prediction of brain surface motion at DC area for all thesix patients evaluated. Both the deformation pattern and the quantitative values of the brain surfacedisplacement from the model simulation were found in good agreement with measured values from medicalimages. The developed FE model and its validation in this study is a prerequisite for future investigationsaiming at finding optimal treatment for a specific patient which hopefully will significantly improve patients’outcome.
Clinical assessment in neurological diseases is a reliable and important evaluation when it comes to define theclinical condition of a patient. Imaging technologies such as Computerized Tomography (CT), Magnetic ResonanceTomography (MR) and Positron Emission Tomography (PET) make it possible to improve not only the clinicalassessment but also the clinical practice. In the foreseeable future it is expected that new image technologies focusingon specific targets will see the light and which further improve the clinical knowledge in a number of neurologicaldiseases.
Decompressive craniectomy (DC) involves removing part of the skull bone to allow the swollen brain expand
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outside the skull [1, 2] to achieve a reduction of the increased intracranial pressure (ICP). Although a number ofstudies have demonstrated a good long-term functional recovery after DC with reducing the mortality rate, this ishowever at the expense of an increasing number of patients with severe neurological cognitive impairments [2–4].Axonal stretching has to some extent been suggested to contribute to this unfavorable outcome [1]. Also, quantitativedata from recent computerized simulations seem to give evidence that the mechanical stretching of brain tissue mayinterfere with normal metabolism [5]. Thus, the debate on its overall effectiveness remains and complete consensushas not been fully achieved among clinicians. Nevertheless, for patients with the most severe traumatic brain injury(TBI) and stroke, except for general and neurological intensive care treatment, DC is the ultimate choice of treatmentto reduce the ICP caused by cerebral swelling [6, 7]. The technical aspects of the surgical procedure are critical to theoverall effectiveness. To date a number of technical improvements have been made to the surgical procedure, yetmany surgical technical problems remain unanswered [8, 9]. The application of advanced computational modelsof the human brain tissue integrating structural and functional information from CT and MR may to some extentimprove our knowledge of clinical practice for this type of neurosurgical approach.
Computerized simulations used in experimental investigations have significantly contributed to better understand theconsequences of trauma through reconstructive simulations of accidents. The introduction of simulation technologyhas also played an important role supporting clinical neuroscience. Among those should be mentioned the FiniteElement (FE) method or modeling. The FE modeling is a numerical method which has the capacity to analyze largerand complex geometrical structures of the skull and brain tissue by dividing it into small and simple geometricalstructures called elements. The use of FE modeling has been tremendously to develop innovative treatment strategiesin various areas of clinical neuroscience field such as to predict the gravity effect on brain edema [10] and braindeformation during neurosurgery [11–14] and tumor resection [15]. In a recent paper, we have developed patientspecific FE models to simulate DC surgery for patients following TBI and stroke. The results showed that doingDC procedure at a non-injured area of the head may have the potential to reduce axonal stretching at the injuredbrain tissue [16]. A prerequisite to successful applications in clinical practice is a true and realistic validation of anaccurate simulation from existing image technologies. Until now there is lack of studies involving modeling andsimulation of DC surgery to support decision-making in clinical surgical field.
The aim of the present study was to develop computational FE model to simulate the response of the DC surgeryand its validation against clinical data of six patients treated with DC.
2. MATERIAL AND METHODS
2.1 Patient Information
Six patients with clinical deterioration following TBI in one patient (MC) and stroke in other five patients wereadmitted to the neurosurgical department for DC treatment. CT image was performed and evaluated before and afterthe DC (Figure 1).
2.2 Finite Element Model Development
The FE mesh was based on the geometrical reconstructions of CT images at pre-craniectomy period. These imagedata has been used in a previous study [5]. Cranial and lateral ventricles were segmented using a threshold method[17]. 3D triangular surface mesh was then generated based on the segmented images. The image processing andsurface model generation were performed in open source software Slice 3D [18]. The surfaces of the model served
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Finite Element Modeling of Decompressive Craniectomy (DC) and its Clinical Validation
Figure 1. Representative axial slices from the CT images of the six patients evaluated both before (upper row) and after thedecompressive craniectomy (lower row).
as an input to a commercial software Hexotic from which all hexahedron elements were generated based on anoctree-algorithm [19]. Dura mater was created as a thin membrane that encloses the cranial surfaces with a thicknessof 0.5 mm. The final generated FE mesh includes cranial, lateral ventricles, dura mater and falx (Figure 2). Thecranial volumes of the generated FE brain were defined to 1369, 1080, 1563, 1538, 1393, 1269 ml respectively forthe six patients.
Figure 2. Generated FE mesh of the patients exemplified by the results from one patient (MC). The semi-transparent surfaceshows the surfaces of the generated FE mesh (left) together with the FE mesh (right). The FE meshes for other patientsinclude similar internal brain structures which were created based on the specific patient’s CT images.
2.3 Poroelastic Modeling of Brain Tissue
Brain tissue was modeled as a poroelastic material consisting of an elastic solid skeleton composed of neurons andneuroglia and permeated by interstitial fluid. The governing poroelastic equations for a fully saturated pore fluid floware described as following.
For fluid phase,
Sε
∂ p∂ t
+−→∇(− k
µ
−→∇ (p+ρ f gD)) =−α
∂
∂ tεb +Qs (1)
where Sε is the specific storage term, g is gravitational acceleration, κ is permeability, µ is fluid viscosity, p is the3
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fluid pressure, D is the elevation/vertical axis along which gravity acts and εb is the volumetric strain of the solidskeleton.
The deformation of brain tissue was governed by the following equilibrium equation:
−G∇2ui−
G(1−2v)
∂uk
∂xixk=−α
∂ p∂xi− ∂ (ρavegD)
∂xi(2)
where Φ represents the porosity, ρave = ρ f Φ + ρt (1-Φ), where ρ f is the CSF density, ρt is the tissue skeletondensity, u is the displacement of the solid skeleton, G is the shear modulus, ν is the Poisson’s ratio an α is theBiot-Willis coefficient.
Brain tissue parameters were adopted from studies [13] giving reasonable fit to the experiment under similar loadingrates to that during neurosurgery. The Young’s modulus and Poisson’s ratio are E=2010 Pa, ν=0.45, respectively, andtissue permeability κ = 1.4×10−14 m2. Falx was modeled as shell elements with 1.5 mm thickness, and E = 31.5×106,ν=0.45 [20]. In most previous studies of brain tissue deformation during neurosurgery [13, 15, 20, 21], dura materwas not explicitly modeled in the FE models. In this model dura mater was modeled as 0.5 mm thick membrane. Theimplementation was performed using the software COMSOL Multiphysics 4.0a (COMSOL, Sweden).
2.4 Computerized Simulation of DC
During DC surgery, part of the skull bone was removed which exposes the dura mater surface directly to theatmosphere pressure. The increased intracranial pressure inside the cranial space then pushes the swelling brainoutside the cavity. In the model, the part of the surface representing the craniectomy defect was set to be free tomove while other parts of the cranial surface were assumed to be fixed representing the constraint from the skull. Thecraniectomy area was determined from the post-operative CT images for a specific patient.
For the fluid phase, the outer surface of the cranial vault was assumed to be impermeable. Fluid pressure at thelateral ventricle wall was designated to 10 mmHg. Similarly, as performed in a previous study [10], the mass effect ofthe injured tissue was modeled as fluid source Qs according to Eq (1). The domain of injured tissue was obtained bymanually delineating the injured brain area from the CT images. For some patients the injured areas were difficult toidentify from pre-operative image, but more visible from post-operative images. To resolve this problem, we selectedthe injured domain from post-operative image, which then was mapped to the pre-operative state. This was done byusing the dense displacement field obtained from nonlinear image registration that represents the changes from post-to pre-operative brain structure. The value of Qs was obtained via an optimization procedure until the interstitial fluidpressure was high enough to push the brain outwards to a certain extent according to the post-operative image fora specific patient. The total displacement of three points at the DC area was used in the objective function duringoptimization.
2.5 Baseline Value of Displacement for Validation
The baseline value of brain surface displacement was obtained from the pre- and post-craniectomy images usingDiffemorphic Demons (DD) registration. The procedures are illustrated in Figure 3. First, the cranial and lateralventricles from both the pre- and post-craniectomy CT images were segmented using a threshold method [17].A representative slice is presented to illustrate the registration results. Before DD registration, there is a largediscrepancy between the overlayed images around both the craniectomy area and the ventricles. After DD registration,the discrepancy is nearly invisible indicating a good alignment, and that the structural change of brain tissue occurring
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Finite Element Modeling of Decompressive Craniectomy (DC) and its Clinical Validation
between different stages was accurately captured. From the DD registration, a three dimensional displacement vectorfield was obtained. Especially, the displacement of the DC area was used to compare with the FE model prediction.
Figure 3. Illustration of the procedures to obtain displacement field from image registration exemplified by the results from onepatient (MC). A representative slice of the segmented images is shown by overlaying the pre- and post-craniectomyimage. Left pictures shows before registration and the picture in the middle shows after registration (middle). Fromthe registration, displacement vector field is obtained for the whole domain. The picture on the right shows the totaldisplacement field of the cranial surface. The picture was created using software ParaView V 3.10.
3. RESULTS
The bulging deformation of the brain tissue at DC area was reproduced by the computational analysis (Figure 4,left column). As the brain motion is related to the stretching of axons at the DC area, the predicted displacementfrom patient models was compared with those measured from medical images obtained from image registration.To quantitatively compare the simulated values with the measured ones, seven points at the DC areas were chosen(Figure 4). Care was taken to ensure that the comparison was made at the same point of the brain tissue between thesimulation and the measured values.
The black circles are the measured data from medical images while the red circles represent the values from thecomputerized simulation. The circles from left to right represent the seven points evaluated. The displacement in xdirection ux(from left to right), y direction uy(from posterior to anterior), z direction uz(from inferior to superior) andtotal displacement (u total) are evaluated.
u total =√
u2x +u2
y +u2z (3)
In general the displacement in x direction is more pronounced than in y and z direction since the brain tends toexpand outwards. Note that for some patients, uxare negative while for others are positive due to the fact that DCwas performed at different sides of the brain. For points at the center of the DC area, the displacement is largerthan the points close to the skull edge. Patient VM showed the most pronounced tissue swelling with maximumdisplacement reached about 18 mm (Figure 4, row 2). Patient NJ presented a minor swelling at the DC area withmaximum displacement about 4 mm (Figure 4, row 6). When calculating the displacement in y direction all measuredand simulated values were congruent in all patients. The same holds true in all patients also for the displacementcalculated in z directions. A similar picture of good validation between measured and simulated values were found inthe total displacement analysis (Figure 4, far right).
To better appreciate the comparison between model predictions and basic truth values measured from images, thequantitative values of the total displacement are listed in Table 1. The results indicate that for some patient, the error
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Figure 4. Total displacement or motion of brain tissue measured in the DC area, the color scale legend is in unit of meter (3Dpictures far left). The displacements of seven points at the DC area at the illustrated positions are plotted. From row1 to 6 are results for patient MC, VM, HJ, LR, MD and NJ, respectively. The graphs from left to right representindividual displacements along the x, y and z direction and the total displacement (far right).
Table 1. The quantitative values of measured (Meas) and simulated (Sim) total displacement (millimeter) of the seven pointsevaluated which corresponds to the plot in Figure 3.
Patient ID P1 P2 P3 P4 P5 P6 P7
MC Meas 10.62 13.25 12.18 6.75 4.83 14.74 12.53
Sim 6.66 12.37 12.88 6.65 5.07 13.13 11.06
VM Meas 3.52 14.84 13.55 10.59 13.50 16.27 15.54
Sim 9.00 17.31 16.60 5.88 9.71 17.63 16.20
HJ Meas 15.73 15.30 13.80 11.06 13.84 16.87 14.56
Sim 14.30 16.37 14.48 9.95 12.56 14.12 10.60
LR Meas 8.79 12.71 10.59 9.87 7.40 13.11 11.55
Sim 7.82 12.28 11.45 6.90 7.50 12.21 11.70
MD Meas 7.54 12.43 13.14 11.91 7.04 12.53 12.05
Sim 5.36 13.89 14.24 10.24 6.38 14.23 9.12
NJ Meas 1.58 2.69 4.30 2.83 0.98 4.22 4.72
Sim 1.46 2.95 3.34 1.18 0.00 1.77 3.13
is within 1 mm in most of the evaluated points (MC, LR, MD). For the other patients a larger difference was found insome tissue points, however, all are less than 5.5 mm. The model recaptures up to 90.3% of the tissue motion forpatient LR.
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Finite Element Modeling of Decompressive Craniectomy (DC) and its Clinical Validation
4. DISCUSSIONS
The development of advanced computational, or numerical, methods for modeling of the human skull and braintissue has contributed to our better knowledge in clinical neuroscience when it comes to fundamental researchknowledge [22–24] of the human brain and the reconstructions of TBI accidents [25, 26]. Also, the computerizedsimulations have lately been introduced for interdisciplinary neuroengineering and clinical applications [5, 27–30]resulting in the application of basic research results into clinical applications [31, 32].
The major limitation today in using computerized simulation for application in clinical neuroscience is the lackof required adaptation of the numerical methods and modeling to the clinical health care. Thus, before advancedcomputerized simulation can be translated for routine clinical applications it is of fundamental significance that thesesimulations are truly suitable and reliable. This approach can only be performed by the interdisciplinary collaborationbetween neuroengineering and clinicians when it comes to the validation of computerized technology with enoughpatient data received from existing CT and MR images.
In the present study we have developed a computational FE model to predict the response of DC surgery andvalidated with patient CT images before and after DC. The results from the simulation showed good reliability. Ingeneral, the computational simulations showed a reasonable prediction of brain tissue displacement for all the sixpatients evaluated. However, there is a larger difference at certain points evaluated and which was expected becauseof the inhomogeneous characteristics of the edematous tissue at the DC area. In the FE model, however, the edema atthis area was modeled as homogenous tissue swelling. Nevertheless, in general the numerical modeling was found tobe sufficiently reliable to provide an approximation of the brain surface movement during DC surgery. The reliabilitymeans that data from the computerized simulations have a chance to enhance our knowledge about the consequencesof DC in each individual case. The new knowledge obtained from computerized simulation may thus give a hintof what happens in the brain tissue already before the neurosurgical approach with regards to alteration of strainlevels in the nerve fibers surrounded by cytotoxic brain tissue when the intracranial pressure is unacceptably high.With the validated model, other surgical options, such as different DC size, each DC location can be simulated andinvestigated. And this new information can change the clinical treatment towards better outcome for the patients.
Even if there remains further evaluation for routine use of computational simulation in clinical neurosciencepractice, it has come to stay but also to enhance our clinical knowledge in some of the consequences to neurosurgicalprocedures. Before this is realistic the validation of such computational simulations are mandatory.
ACKNOWLEDGMENTS
The present investigation was sponsored from the Karolinska University Hospital and Stockholm County researchfund.
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