Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=ibij20
Brain Injury
ISSN: 0269-9052 (Print) 1362-301X (Online) Journal homepage: http://www.tandfonline.com/loi/ibij20
Fluid–structure interaction analysis of
cerebrospinal fluid with a comprehensive head
model subject to a rapid acceleration and
deceleration
Milan Toma & Paul D.H. Nguyen
To cite this article: Milan Toma & Paul D.H. Nguyen (2018): Fluid–structure interaction analysis of cerebrospinal fluid with a comprehensive head model subject to a rapid acceleration and deceleration, Brain Injury
To link to this article: https://doi.org/10.1080/02699052.2018.1502470
Published online: 30 Jul 2018.
Submit your article to this journal
imaging or scans. Having a comprehensive head/brain model and using fluid–structure interaction (FSI) simulations enable us to see the exact movement of the cerebrospinal fluid (CSF) under such conditions and to identify the areas of brain most affected. Research Design: The presented work is based on the first FSI model capable of simulating the interaction between the CSF flow and brain. Methods and Procedures: FSI analysis combining smoothed-particle hydrodynamics and high-order finite-element method is used. Main Outcomes and Results: The interaction between the CSF and brain under rapid acceleration and deceleration is demonstrated. The cushioning effect of the fluid and its effect on brain are shown. Conclusions: The capability to locate areas (down to the exact gyri and sulci) of the brain the most affected under given loading conditions, and therefore assess the possible damage to the brain and consequently predict the symptoms, is shown.
Accepted 16 July 2018
KEYWORDS
Fluid–structure interaction; cerebral spinal fluid; comprehensive head model; brain injury; deceleration; acceleration
Introduction
Concussions are the most common type of closed brain injury, or head traumas where the skull is unbreached. Mild closed brain injuries are more difficult to image compared to open brain injuries. Concussions are therefore typically diagnosed symptomatically. Patients may exhibit a range of symptoms, such as headache, photophobia, tinnitus, dizziness, sleepiness, confusion and behavioural changes.
Concussions are thought to be a milder form of diffuse axonal injury (DAI), but DAIs are typically characterized by immediate loss of consciousness. Both injuries, however, can result from acceleration-deceleration mechanisms and result in widespread brain injury. Other types of traumatic brain injuries which may lead to concussions include coup (1) and contrecoup (2) injuries. These injuries occur when a moving object impacts the stationary head or when the moving head strikes a stationary object, respectively. The energy absorbed by the brain results in widespread brain trauma, the degree of which depends on the energy transmitted, the area of contact and the involved area of the cranium (3,4). However, the exact internal processes resulting in brain injuries remain a subject of much debate (5).
Cerebrospinal fluid (CSF) cushions the brain within the skull and serves as a shock absorber for the central nervous system (6). A detailed analysis of the CSF cushioning mechan-ism is useful for the treatment and prevention of brain inju-ries. While the significance of including CSF in the numerical simulations has been shown (7), the current finite-element
studies reported in the literature often lack more detailed anatomical structures (8–11). For example, CSF is commonly presented as existing only outside of the brain, i.e. between the skull and a single, solid mass representing the brain.
The brain has a more complicated structure than what has been described in prior models. CSF fills a system of cavities at the centre of the brain, known as ventricles, and the sub-arachnoid space surrounding the brain and spinal cord (Figure 1) (12). The brain can be structurally divided into the cerebrum, cerebellum and brainstem. The cerebrum is divided into two roughly equal hemispheres connected by the corpus callosum and a shared ventricular system. The brainstem is further divided into the midbrain, pons and medulla oblongata. The model used in this study accurately represents these anatomical features.
The cerebral vasculature, which is omitted in this model, significantly alters brain stiffness. The network of arteries and veins creates a spring-like suspension system that restricts the brain motion (13,14). The omission of the cerebral vascula-ture is a major limitation in this model. However, despite that, the model used in this study represents a leap in head injury modelling by both the complexity and inclusion of the effect of the CSF on potential brain injury.
Specific functions have been correlated with cerebral struc-tures. In 1909, German neurologist Korbinian Brodmann (15) developed the most well-known cytoarchitectural map and divided the cerebrum into approximately 50 areas (16). While the structure–function relationship is still debated,
CONTACTMilan Toma [email protected] Department of Mechanical Engineering, School of Engineering & Computing Sciences, New York Institute of Technology, Old Westbury Campus - HSH116A, Northern Boulevard, Old Westbury, New York 11568-8000, USA.
Color versions of one or more of the figures in the article can be found online atwww.tandfonline.com/ibij.
Brodmann’s map is frequently cited. The Brodmann areas most affected by the acceleration/deceleration loading condi-tions are shown in the results section of this study.
The three published constitutive models representing CSF behaviour are as follows, solid-like, viscoelastic and fluid-like CSF. However, they all are solid material models with differ-ent material properties. The solid-like constitutive model represents CSF as a linear, nearly incompressible elastic solid with a bulk modulus much larger than the shear modulus (17,18). The viscoelastic CSF constitutive model is a linear viscoelastic model with shear relaxation behaviour (9,19). The fluid-like CSF is modelled using elastic solid material with fluid-like constitutive behaviour using an equation of state constitutive model (20). The model used in this study is the first fluid–structure interaction (FSI) model that uses fluid material properties.
In this study, we present FSI analysis of a subject-specific head/brain model exposed to loading conditions associated with impact injuries commonly encountered in sports and motorized vehicular collisions (MVC). We hypothesize that, during rapid acceleration and deceleration, the parietal and temporal lobes will be the most affected areas by the waves developed in the CSF. The acceleration phase is demonstrated inFigure 2where the movements of two fluid particles, A and B, are shown. Fluid particle A will migrate in the negative direction and impact the brain tissue. Fluid particle B will not move significantly and serve to cushion the brain. The limited movement of fluid particle B may be due to its close proximity to the skull.
Methods
Loading conditions
To simulate the crash conditions later prescribed to our com-prehensive head model, the HUMOS2 (HUman MOdel for Safety) (21) is used in the car-crash sled test with a 3-point seatbelt. The sled test is simulated using RADIOSS (Atlair Engineering, Michigan, USA), seeFigure 3. The HUMOS2 is a human numerical model based on a human cadaver and includes the entire skeleton, muscles, organs and ligaments (Figure 3(b)). The deceleration values of the HUMOS2’s head from the sled test are then used to prescribe the velocity, see
Figure 4, to a more comprehensive head model described below.
Head model
The velocity extracted from the above sled test simulation is used to assess the interaction of the CSF and brain/skull.
Figure 5 shows five distinct anatomical structures used in this model. The skull, cerebrum, cerebellum, pituitary gland and brainstem each have unique material properties. The patient-specific model is created from the digital imaging and communications in medicine (DICOM) images based on magnetic resonance imaging (i.e. MRI modality) acquired from an online database (22). The DICOM images are pro-cessed using threshold segmentation in InVesalius (CTI, Brazil). The generated surface is then exported as a raw unstructured triangulated surface file (STL). In the next step, the surface geometry is processed using NetFabb (3FM Consortium, Wakefield MA) to lower the number of triangu-lar elements while increasing the quality of the mesh. The tetrahedral volume mesh is subsequently created using Gmsh (C. Geuzaine and F. Remacle) with 3D Netgen optimization. Anatomical features missing in this model include the skin, spinal cord, meninges and the arachnoid granulation,
Figure 1. Because the CSF flow is relatively slow (0.05– 0.08 m/s) (23), especially when compared to the nearly
Figure 1.The schematic of the CSF in which the brain is submerged. The 3D computational model used is designed based on this schematic.
Figure 2.While the fluid particles (dark blue dots) in the front part of the skull will migrate and affect the brain tissue, the particles in the back of the skull will provide the cushioning effect to the brain without much movement. Therefore, we hypothesize that the parietal and temporal lobes will be the most affected by the wave developed in the CSF due to the rapid acceleration.
instantaneous accident scenario, the fluid can be considered static. Therefore, CSF flow has a negligible impact on the cushioning effect. These assumptions also make the presence of the granulations negligible. While the granulations are not major anatomical feature, they are part of the venous systems. Omission of the vasculature is addressed below.
Computer simulations
As explained above, the model is comprised of five parts. The skull model is assigned rigid material properties with density 1900 kg m−3 (24). Data from studies characterizing the macroscopic physical characteristics of the brain show that it is a viscoelastic material (25). The cerebrum, cerebellum, pituitary gland and brainstem are simulated using a non-linear elastic constitutive material model with varying mate-rial properties based from the literature (26–30). The cere-brum, cerebellum, brainstem and pituitary gland are each composed of a different number of tetrahedral elements, see
Table 1. The stress, from the non-linear elastic constitutive model with damping, is defined as
σ ¼ pI þ 2G: 1 þ ageo devþ b geo dev 2 h i :devþ c cdecò t 0_ τð Þ:e τt cdecdτ;
where G is the shear modulus, dev is the deviatoric strain, geo
dev is the effective deviatoric strain, c is damping coefficient, cdec is damping decay coefficient and a and b are non-linear elasticity parameters.
The CSF was modelled using the smoothed-particle hydro-dynamics (SPH) method with the bulk modulus of 21.9 GPa (9) and density 1000 kg m−3 (31). The number of fluid particles filling the subarachnoid space between the skull and brain, and other cavities, is 94,690. The SPH particles interact with the structural finite elements using a penalty-based contact algorithm. In penalty-penalty-based contact, when a penetration is found, a force proportional to the penetration depth is applied to resist and eliminate penetration. Linear contact spring stiffness is based on the nodal masses that come into contact at the time step size as follows:
k¼ 0:1 m max Δt2
global; Δt2SPHcontact
:
The resulting contact stiffness is independent of the mate-rial constant, so it is well suited for treating contact between fluid and structure. The SPH method is no longer considered as a quick‘last resort’ numerical method, as it may have been at its beginnings and, in the recent years, the SPH method has been used increasingly to simulate the FSI in biomedical applications (32).
The SPH is one of the earliest mesh-free methods and it has been originally developed for modelling astrophysical phenomena in 1977. The SPH, unlike the grid-based methods, can easily handle high velocity impacts due to large deforma-tions and free surfaces. Much effort is still concentrated on problems with the conventional difference and finite-element methods. These problems, to which the conventional numerical methods are difficult to apply, include free surface, deformable boundary, moving interface, large deformation, complex mesh generation, mesh adaptivity and multi-scale resolution. The model presented here, if simulated using conventional methods, would face most of those difficulties.
Figure 3.The HUMOS2 model in its initial configuration (a) and in the sled test (b) to simulate the crash conditions later used to extract the velocities prescribed to the skull of the head model.
Figure 4.The rapid acceleration, denoted by green dot-dashed square, and deceleration, denoted by red dot-dashed square, prescribed to the skull of the head model.
For more detailed discussion on comparison between SPH and conventional numerical methods, see (33).
Fluid motion and boundary interaction calculations were solved with the IMPETUS Afea SPH Solver® (IMPETUS Afea AS, Norway), while large deformations in the solid parts were simultaneously solved with the IMPETUS Afea Solver®. Both the solvers use a commodity GPU for parallel processing. All solid elements were fully integrated, removing the possibility of hourglass modes and element inversion that plagues the classic under-integrated elements. Both fluid and solid domains and their interaction were solved with an explicit integration scheme. All simulations were solved on a standard workstation. Parallel acceleration was achieved with a Tesla K40 GPU with 12 GB of Graphic DDR memory and 2880 CUDA Cores. To confirm that convergence was reached, h-refinement of the finite-element mesh was performed, and the solution was found to yield same results. Our prior pub-lication describes the SPH equations in greater detail (34). Smaller number of particles was used to obtain results within 5% of the values obtained with the higher number of particles. This confirmed that the results are converged. The above stated number of particles, 94 690, is high considering that
the volume of the cavities and subarachnoid space is much smaller than rest of the model.
The SPH method is chosen for this study because tradi-tional FSI techniques can be computatradi-tionally expensive and challenging regarding their parallelization (35). In order to use traditional FSI techniques, geometrical simplifications would need to occur, and the anatomical accuracy would have to be sacrificed.
The use of FSI with SPH is advantageous in this particular study, because unlike in the conventional numerical models it allows us, for the first time, to assess numerically the interaction between CSF flow induced by trauma and brain. None of the existing conventional models simulates the CSF with actual fluid material properties, even the most recent studies still use a simple (n = 1) hyperelastic material model, i.e. solid elements, to simulate the CSF (36). However, that approach can never be able to analyse the effect of the CSF on potential brain injury.
Results
The loads exerted on the brain during the rapid acceleration and deceleration phases deform the brain. Because of this deformation, the volume of the brain decreases while the volume of the rigid skull remains unchanged. Due to this relative volume change, CSF flushes into the skull from the spinal cord and fills in the empty spaces created by the brain deformation. However, our model is a closed system without
Table 1.Number of tetrahedral elements in the model.
Cerebrum Cerebellum Brainstem Pituitary gland
# 96 385 40 808 18 634 310
Figure 5.The depiction of the entire head model with skull, cerebrum, cerebellum, pituitary gland and brainstem, respectively. The subarachnoid space and other cavities are filled with fluid particles (blue dots surrounding the brain model, in the lower right corner). The entire model with half the skull is also shown (lower left). 4 M. TOMA AND P. D. H. NGUYEN
the presence of the spinal cord due to model simplification. Moreover, there is a known disadvantage of SPH where an initial gap is expected between the fluid and object, resulting in an initial fluid compressibility as described in Section 2.3.
Both the brain deformation and the initial fluid compressibility contribute to the formation of empty space depicted inFigure 6.
Figure 6(b) shows that during the rapid acceleration phase, fluid particles flow backward, preventing the brain from impacting the occipital/parietal bone and creating an empty space between the anterior brain and frontal bone. During the rapid deceleration phase, fluid particles flow forward, preventing the brain from impacting the frontal bone and creating an empty space between the posterior brain and the occipital/parietal bones,Figure 6(c). The change from acceleration to deceleration causes the fluid particles to reverse direction. Because the fluid particles move faster than the brain, during the deceleration phase the fluid particles fill in the empty space created in the acceleration phase. This demonstrates the cushioning effect of CSF.
Figure 7 shows the surface pressure resulting from the force of the flowing fluid exerted on the brain surface. The posterior aspects of the gyri (see the schematic inFigure 7) and the occipital/parietal bones experience the greatest surface pressure during the acceleration phase. Conversely, the ante-rior aspects of the gyri and the frontal bone experience the greatest surface pressure during the deceleration phase.
Figure 8shows the effective stress due to brain deformation. During the acceleration phase, the greatest effective stress values are observed in the posterior aspects of the gyri. During the deceleration phase, the greatest effective stress values are observed in the anterior aspects of the gyri. The total affected area with the greatest effective stress is largest at onset of the acceleration phase,
Figure 8(a).
The typical variables used in biomedical fluid mechanics, such wall shear stress, are challenging to derive using SPH. However, SPH does provide different variables with similar meanings. For example, SPH impulse intensity, which is SPH-driven mechanical impulse per unit area in pascal-second, can be interpreted as wall shear stress.
Figure 9shows the SPH impulse intensity at three different time points: peak velocity (a), mid-deceleration (b) and end-deceleration (c). The SPH impulse intensity develops slowly at first, but reaches its maximum values around the peak velo-city. The parietal and upper temporal lobes are the most affected by the fluid particles during their migration to the occipital/parietal bones, i.e. the acceleration phase. At the peak velocity when the fluid particles change direction and start their migration towards the frontal bone, the high SPH impulse intensity values are more visible also in the occipital lobe (a). At the end of the deceleration phase (c), when the fluid particles have reached the frontal lobe, the high SPH impulse intensity values are then visible in the frontal lobe.
Figure 10imposes Brodmann’s map of cytoarchitectonics on Figure 9(a) and shows which functional areas are the most affected at the peak velocity. The areas with more than 10% covered with SPH impulse intensity maxima are 40 (10.1%), 4 (11.7%), 3,2,1 (15.3%) and 52 (21.7%).
Discussion
Using a human numerical model with the displacement/velo-city parameters prescribed in the sled test realistically models conditions seen in a typical MVC or sports injury. These conditions are then applied to a more detailed head model
Figure 6.The fluid particles are visibly concentrated in the back of the head at the end of the rapid acceleration phase (a) and at the front of the head at the end of the rapid deceleration phase (b). The dashed ellipsoids denote the areas where the particle concentration can be observed. The arrows point to the spaces where an empty space is observed after the deformation of the brain and fluid particles migrating with the acceleration/deceleration.
that includes a patient-specific model of the brain and CSF. The FSI analysis is used to simulate the interaction of the brain with CSF in this scenario.
The anatomical features missing in the head model include the skin, arachnoid granulations, spinal cord, vasculature and meninges. Skin is irrelevant for our objectives. The arachnoid
Figure 8.The sagittal view of the effective stress values at the beginning of the acceleration phase (a) and at the end of the deceleration phase (b). The largest area affected is observed at the beginning of the acceleration, while for the rest of the acceleration phase and even during the deceleration phase the maximum areas remain less affected. The cerebellum here is shown with low opacity values to expose the cerebrum. The full brainstem in dorsal view at the peak velocity is also shown (c).
Figure 7.The surface pressure at the beginning of the acceleration (a) and at the end of the deceleration (b) phases. Upper row shows the whole brain with the skull set to low opacity value and the lower row shows the sagittal plane with the skull set to 100% opacity. The posterior and anterior aspects of the gyri (schematic) experience the greatest surface pressure during the acceleration and deceleration phase, respectively.
granulations are negligible due to the relatively slow CSF flow. To make the simulation less computationally expensive, the spinal cord, vasculature and meninges are omitted at this stage but may be considered in future studies. The omission of cerebral vasculature is considered to be a major uncertainty in the proposed predictions and therefore it is to be integrated in the next stage. Subsequently, the displacement of CSF into the spinal subarachnoid space is to be implemented. The final goal is to simulate a closed model of the entire CSF space (37). Natural CSF pulsation may be too slow to affect brain dynamics in high acceleration head injury. However, the
displacement of CSF into the spinal subarachnoid space might occur at much higher wave speeds due to the near incompressibility of the CSF. The plan is to include the complete CSF system dynamics in the future head injury models (12). Another limitation of this study is that the brain is modelled as isotropic. The brain is anisotropic and especially white matter fibre tracts have strong axial stiffness compared to the ability to transmit radial stresses (38). This, too, will be addressed in the future studies.
Moreover, the values from the car-crash simulation are acquired using HUMOS2 model that is different from the head model developed based on the DICOM images. However, many car-crash scenarios occur daily with a high inter-individual variety. Decades ago, the automakers and regulators had to crash over a 100 cars during the design of a single model. These days, computer-aided engineering has largely diminished the need to crash the cars, testing and refining as they go along. The use of HUMOS2 model was chosen to simulate the movement/acceleration that is then prescribed to the more detailed head model with CSF. It is safe to assume that the values acquired this way are realistic. However, this makes the research presented here a single-case study and more individual variations need to be included for statistically more significant results.
The variables commonly used to post-process the results in the biomedical fluid mechanics are somewhat different from those readily available in the SPH method. Extracting wall shear stress values from SPH method is more challenging than when using traditional FSI techniques. However, there are other variables that can be used and offer similar meaning,
Figure 9.The SPH impulse intensity at the peak velocity (a), at the middle of the deceleration phase (b) and at the end of the deceleration (c). The SPH impulse intensity is SPH driven mechanical impulse per unit area. The migration of the fluid particles can be associated with it. The rear half of the brain is the most in contact with the fluid particles exerting pressure on its crevices during the acceleration. This remains unchanged until the fluid particles migrate back to the frontal lobe where then again exert pressure on the brain at the end of the deceleration.
Figure 10.The SPH impulse intensity at the peak velocity (T = 0.025 s) super-imposed with the Brodmann’s map of cytoarchitectonics.
such as the SPH impulse intensity. SPH is used in this study to maintain as much anatomical accuracy as possible. FSI techniques would require more anatomical simplifications.
Figure 10shows the cortical areas affected by the SPH impulse intensity at the peak velocity. The diffuse pattern of SPH impulse intensity maxima may represent the cortical areas most affected by a concussion. Brodmann’s areas with at least 10% coverage of maximal SPH impulse intensity include 40 (10.1%), 4 (11.7%), 1, 2, 3 (15.3%) and 52 (21.7%). Brodmann area 40, the left supra-marginal gyrus, receives input from multiple sensory modalities and supports complex linguistic processes. Lesions here may result Gerstmann syndrome and fluent aphasia, such as Wernicke’s aphasia. Brodmann area 4 is typically associated with motor functions but also plays a supportive role in sensory per-ception. Lesions in the primary motor cortex may result in paralysis and decreased somatic sensation. Brodmann areas 1, 2 and 3 comprise the postcentral gyrus in the parietal lobe and are primarily associated with somatosensory perception. Lesions in the postcentral gyrus may result in cortical sensory impairments, including loss of fine touch and proprioception. Brodmann area 52, the parainsular, is the smallest of the mentioned areas and has the high percentage of SPH impulse intensity maxima coverage. It joins the insula and the temporal lobe.
At the onset of the acceleration phase, Figure 8, midline subcortical structures and the brainstem experience the great-est effective stress. These include the fornix, thalamus, super-ior and infersuper-ior colliculi, cerebral peduncles, postersuper-ior pons and the posterior dorsal medulla oblongata. These structures are more rigid than the rest of the cerebrum, and are related to basic bodily functions such as breathing, heart rate, alert-ness and consciousalert-ness. Damage to the brainstem may affect these functions.
This FSI model and its computational analysis have the cap-ability to locate areas of the brain the most affected under given loading conditions and therefore assess the possible damage to the brain and consequently predict the symptoms. Or, the other way around, when symptoms are known, it can be used to analyse what loading conditions had been exerted on the model. Variety of loading conditions can be easily applied to the model with and without personal protective equipment, e.g. helmets, to assess their effectiveness by comparison.
Declaration of interest
This study was not funded by any grant. No benefits in any form have been or will be received from a commercial party related directly or indirectly to the subject of this manuscript
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
References
1. Morrison AL, King TM, Korell MA, Smialek JE, Troncosso JC. Acceleration deceleration injuries to the brain in blunt force trauma. Am J Forensic Med Pathol. 1998;19:109–12. doi:10.1097/00000433-199806000-00002.
2. Poirier MP. Concussions: assessment, management, and recom-mendations for return to activity. Clin Pediatr Emerg Med. 2003;4:179–85. doi:10.1016/S1522-8401(03)00061-2.
3. Shonauer M, Schisano G, Cimino R, Viola L. Space occupying contusions of cerebral lobes after closed brain injury: considera-tions about 51 cases. J Neurosurg Sci.1979;23:279–88.
4. Bailes JE, Hudson V. Classification of sport-related head trauma: a spectrum of mild to severe injury. J Athletic Training. 2001;36:236–43.
5. Shaw NA. The neurophysiology of concussion. Prog Neurobiol. 2002;67:281–344.
6. Linninger AA, Tangen K, Hsu CY, Frim D. Cerebrospinal fluid mechanics and its coupling to cerebrovascular dynamics. Annu Rev Fluid Mech. 2016;48:219–57. doi: 10.1146/annurev-fluid-122414-034321.
7. Vorwerk J, Clerc M, Burger M, Wolters CH. Comparison of boundary element and finite element approaches to the EEG forward problem. Biomed Eng/Biomedizinische Technik. 2012;57:795–98.
8. Luo Y, Li Z, Chen H. Finite-element study of cerebrospinal fluid in mitigating closed head injuries. J Eng Medicine.2012;226:499– 509. doi:10.1177/0954411912445729.
9. Chafi MS, Dirisala V, Karami G, Ziejewski M. A finite element method parametric study of the dynamic response of the human brain with different cerebrospinal fluid constitutive properties. Proc Institution Mechanical Engineers, H: J Eng Med. 2009;223:1003–19. doi:10.1243/09544119JEIM631.
10. Liang Z, Luo Y. A QCT-based Nonsegmentation finite element head model for studying traumatic brain injury. Appl Bionics Biomech.2015;2015:1–8. doi:10.1155/2015/837585.
11. Bei L, Shijie R, Haiyan L, Shihai C, Lijuan H The effects of different mesh density of the cerebrospinal fluid on the dynamic responses of a 6 years old child finite element head Model in Eighth International Conference on Measuring Technology and Mechatronics Automation (ICMTMA):756–672016.
12. Tangen KM, Hsu CY, Zhu DC, Linninger AA. CNS wide simula-tion of flow resistance and drug transport dur to spinal micro-anatomy. J Biomech. 2015;48(10):2144–54. doi:10.1016/j. jbiomech.2015.02.018.
13. Hsu CY, Schneller B, Alaraj A, Flannery M, Zhou XJ, Linninger AA. Automatic recognition of subject-specific cerebrovascular trees. Magn Resonan Med. 2016;77(1):398–410. doi:10.1002/ mrm.26087.
14. Ghaffari M, Tangen KM, Alaraj A, Du X, Charbel FT, Linninger AA. Large-scale subject-specific cerebral arterial tree modeling using automated parametric mesh generation for blood flow simulation. Comput Biol Med. 2017;91:353–65. doi:10.1016/j. compbiomed.2017.10.028.
15. Brodmann K. Vergleichende Lokalisationslehre der Grosshirnrinde (in German). Leipzig: Johann Ambrosius Barth;1909.
16. Limited TCT Research. Ed. Cortical Functions. Trans Cranial Technologies ldt;2012. Wanchai, Hongkong.
17. Ho J, Kleiven S. Dynamic response of the brain with vasculature: a three dimensional computational study. J Biomech.2007;40:3006– 12. doi:10.1016/j.jbiomech.2007.02.011.
18. Chen Y, Ostoja-Starzewski M. MRI-based finite element modeling of head trauma: spherically focusing shear waves. Acta Mech. 2010;213:155–67. doi:10.1007/s00707-009-0274-0.
19. Watanabe D, Yuge K, Nishimoto T, Murakami S, Takao H. Impact injury analysis of the human head. AutoTechnol. 2007;7:34–37.
20. Madhukar A, Chen Y, Ostoja-Starzewski M. Effect of cerebrosp-inal fluid modelling on spherically convergent shear waves during blunt head trauma. Int J Numer Meth Biomed Engng. 2017. doi:10.1002/cnm.2881.
21. Toma M, Njilie FEA, Ghajari M, Galvaneto U. Assessing motor-cycle crash related head injuries using finite element simulations. Int J Simul Model.2010;9:143–51. doi:10.2507/IJSIMM09(3)3.164. 22. GrabCAD Community. [Accessed 2018 Feb 1]. https://grabcad.
com/library
Neurotrauma.2003;20:1163–77. doi:10.1089/089771503770802853. 29. Kruse SA, Rose GH, Glaser KJ, Manduca A, Felmlee JP, Jack CR Jr,
Ehman RL. Magnetic resonance elastography of the brain. Neuroimage.2008;39:231–37. doi:10.1016/j.neuroimage.2007.08.030. 30. Moore SW, Sheetz MP. Biophysics of substrate interaction: influ-ence on neutral motility, differentiation, and repair. Dev Neurobiol.2011;71:1090–101. doi:10.1002/dneu.20947.
31. Lui AC, Polis TZ, Cicutti NJ. Densities of cerebrospinal fluid and spinal anaesthetic solutions in surgical patients at body tempera-ture. Can J Anaesth.1998;45:297–303. doi:10.1007/BF03012018.
encelophalopathy pathology. Brain. 2017;140(2):333–43. doi:10.1093/brain/aww317.
37. Sweetman B, Xenos M, Zitella L, Linnger AA. Three-dimensional computational prediction of cerebrospinal fluid flow in the human brain. Comput Biol Med.2011;41(2):67–75. doi:10.1016/ j.compbiomed.2010.12.001.
38. Linninger AA, Somayaji MR, Erickson T, Guo X, Penn RD. Computational methods for predicting drug transport in ani-sotropic and heterogeneous brain tissue. J Biomech. 2008;41:2176–87. doi:10.1016/j.jbiomech.2008.04.025.