Influence of FE model variability in predicting brain motion and intracranial pressure changes in head impact simulations

TL;DR: The results indicate that, despite the fundamental differences between these six model formulations, the comparisons with the experimentally measured pressures and relative displacements were largely consistent and in good agreement and may prove useful for those attempting to model real life accident scenarios.

Abstract: In order to create a useful computational tool that will aid in the understanding and perhaps prevention of head injury, it is important to know the quantitative influence of the constitutive properties, geometry and model formulations of the intracranial contents upon the mechanics of a head impact event. The University College Dublin Brain Trauma Model (UCDBTM) [1] has been refined and validated against a series of cadaver tests and the influence of different model formulations has been investigated. In total six different model configurations were constructed: (i) the baseline model, (ii) a refined baseline model which explicitly differentiates between grey and white neural tissue, (iii) a model with three elements through the thickness of the cerebrospinal fluid (CSF) layer, (iv) a model simulating a sliding boundary, (v) a projection mesh model (which also distinguishes between neural tissue) and (vi) a morphed model. These models have been compared against cadaver tests of Trosseille [2] an...

Summary

Introduction

• Traumatic head impact injuries occur when the human skull and brain are rapidly subjected to intolerable levels of energy.
• Motor-vehicle crashes are the most common cause of brain injury.
• In particular, a FE model that describes in detail the complex geometry and the multiple material compositions of the brain can be used to calculate internal stress, strain and pressure at all locations and at any given instant during an impact [12] .
• Shugar [16] developed a 3D model of the skull in 1975 and described its method of construction and limitations.
• Both suffered somewhat with problems in creating a well-conditioned element mesh.

Construction of the FE variations 1. Baseline Model

• The baseline model includes the cerebrum, cerebellum and brainstem, intracranial membranes (falx and tentorium), pia, cerebrospinal fluid layer (CSF), dura, a varying thickness three-layered skull (cortical and trabecular bone layers), scalp and the facial bone.
• 7,318 hexahedral elements represent the brain and 2,874 hexahedral elements represent the CSF layer with one element through the thickness.

2. Sliding Boundary Model

• A model was built with a sliding boundary between the pia and the CSF layer.
• The algorithm allows no separation of the contacting pia and CSF layers and thus prevents the formation of a gap at the CSF-cerebrum interface.
• Considering the effect of fibrous trabaculae and the fluid nature of the CSF, material properties assumed for the solid elements which were used for the CSF were the bulk modulus of water and a very low shear modulus.
• The CSF which exists between the falx and the brain, and between the tentorium and cerebrum/cerebellum was also included using the same type of fluid-structure contact algorithm.

3. Grey-White-Ventricular Matter Model (GWV Model)

• The physiological accuracy of the baseline UCDBTM was refined by explicitly distinguishing between grey matter, white matter and the ventricles.
• Hexahedral meshing along the boundaries of such regions would require an unnecessary mesh development effort and the distinction between these types of neural tissue was conveniently made by modifying the baseline finite element mesh in such a way that elements were assigned material properties appropriate to these corresponding regions of the cerebrum.
• Each element then performed a global search to find the MRI voxels in its vicinity, and then performed a more detailed local search to discover exactly what elements were contained within its volume.
• Figure 2 shows how this algorithm operates schematically.
• Any hexahedron element, which is the only type of solid element used in the UCDBTM, can be decomposed into tetrahedrons.

4. 3-element CSF Model

• Instead, a model was developed to consist of three elements through the CSF layer, the outer nodes being tied to the skull and brain.
• In this way the 'no-slip' condition of fluid mechanics could be met.
• Because of the small size of the associated elements, it was decided to use a slightly deeper fluid element model which was developed previously [1] .
• Problems arose when attempts were made to define an Eulerian boundary condition at the foramen.
• This causes there to be a very large number of separate amplitude curves to be defined for the ABAQUS input deck.

5. Projection Mesh Model

• As the mesh density of the circle is increased, the internal angle of these elements approaches 180 degrees.
• These and adjacent elements will be ill-conditioned and this is particularly problematic for analyses where the outer regions are of greatest interest and where numerical accuracy is required to be highest.
• An alternative mesh generation scheme, referred to as the projection mesh method, does not involve this distortion of a square mesh.
• These projected lines, in turn, define the edges of rows of quadrilateral elements (hexahedral in 3D).
• Because of the definite change in mesh structure at the boundary of the square, the quality of the elements in the projection region will not degrade further, regardless of how refined the mesh density is made.

Tentorium (shell elements)

• Brain Skull (rigid in this paper) CSF layer with 3 elements through its thickness.
• This technique of meshing curved objects using multiple blocks is commonly used.
• Normal curves to be constructed from edges of original swept mesh, at a distance user picks -must be sufficient to give room for inner block, and maintain even mesh density as much as possible, also known as Rule 1.
• A further advantage of the projection mesh model is that its element density can be increased to any desired level without loss of element quality; a corresponding increase in element density of the baseline model would reduce the mesh quality at the outer sides of the brain.
• Longer duration impact events (falls, pedestrian and RTAs) do not require meshes of such high element density.

6. Morphed Model

• It was of interest to see how the pressure and displacements of the FE model would change if a different intracranial space (other than that of the visible male's) was modelled.
• Creation of another entire head FE model, even with knowledge of where the decomposition sections should be [1] , was deemed outside the scope of this work.
• This has the basis that a plate with isotropic properties (eg. Steel) can be morphed to fit a homologous shape (a shape that can be formed from the original without joining, crossing or tearing of the original shape) by means of applying forces and constraints to 'bend' the plate to the new desired shape.
• Vectors were constructed by picking points on the coarse grid and their matching landmark point on the new skull ), until every point on the coarse grid had a displacement vector associated with it.
• A static displacement analysis, using all of these displacement vectors as input, was then carried out on this coarse grid (giving it isotropic properties) and the results were read into MSC/Patran [40] .

Constitutive Property Assignment

• The baseline model was previously validated against the pressure information of the cadaver test of Nahum and has been discussed previously [1] .
• It was noted before that changes in intracranial properties affected different simulation results using this model by different.
• The material properties used in this present paper are presented in Table 2 .

1. Predictions of Intracranial Pressure During Impact

• The baseline and five variant FE models were used to simulate Trosseille's cadaver impact test [2] .
• The mechanics of this experiment were more complicated than the cadaver test of Nahum [33] , which had been used previously to validate the baseline model [1] .
• This impact situation was conveniently simulated with the present finite element models by applying the six time varying components of the linear and angular velocity measured experimentally to the FE models (up to 35 ms of the recorded data).
• EQUATION Figures 9 and 10 compare the experimental and simulated frontal and occipital pressures while Figure 11 compares the pressure at the lateral ventricle (baseline and GWV models only).
• The sliding model exhibits a similar frontal pressure, but this is most likely due to the contact formulation in this area.

2. Predictions of Brain Displacement During Impact

• Experimental data from recent cadaver head impact experiments of Hardy and Kleiven provided vectorised information on the motion of different regions of the brain during impact [3, 46] .
• In Hardy's experiment, two sets of neutral density targets with approximately the same density as brain were inserted in two vertical columns into the brain.
• By assuming that the CG of the FE model was coincident with that of the cadaver head, the kinematics of the FE head would be exactly the same as those of the cadaver head for any given impact [12] .
• The displacements were measured in a coordinate system fixed to the head as shown in Figure 12 , which shows the comparison between the experimental relative displacements (projected onto the X-Z plane) and those predicted numerically by the UCDBTM.
• For ease of viewing, results in Figure 12 show only the results of the GWV model.

Conclusions

• The baseline UCDBTM has previously been validated against the pressure data of Nahum.
• These six variant models were compared against two cadaveric tests: one to measure the variation of intracranial pressure during impact and the second to measure the motion of the brain relative to the skull during impact.
• The most notable difference was observed when comparing the sliding boundary model's pressure response, though this is more likely to be due to the penalty contact formulation used.
• Again little evident difference was noted when the models were compared against the relative motion data.

Figures

Figure 2: The basis upon which the purpose-written MATLAB program works involves two steps to assign specific material properties to the elements of the cerebrum. The MRI voxels and finite elements within the FE model are registered to occupy the same space. Each element identifies which voxels are contained within its six faces. By an appropriate choice of threshold values of voxel intensities, the element is assigned the constitutive properties for grey, white or ventricular matter, although the MATLAB program can assign intermediate properties to each element uniquely.

Figure 8: Steps used to make the morphed model. A coarse grid (b) was constructed on the original model (a). A Discrete field of displacement vectors were then applied to every node of this coarse grid (half of which are visible in (c)), and this field was converted into a continuous field in order to create (d). The morphed model is of Van Lierde and Vander Sloten [42] while the original model is of the visible male [32].

Figure 11: Comparison of experimental and simulated pressures at the lateral ventricle for the baseline and the GWV model. Pressure is measured at the same element for both models.

Figure 3: Tetrahedron vertices. The volume of a tetrahedron with vertices at a, b, c and d is positive when calculated using a, b and c in an anti-clockwise fashion.

Table 1: Comparison of projection mesh model with baseline mesh model in terms of individual hexahedron element quality. Note that for the baseline model, the proportionate increase of high edge angled elements would increase with increasing mesh density.

Figure 7: Comparison of element quality in projection mesh model (left) with baseline model (right). Note the large internal angles in the outer elements of the baseline model as compared to those in the projection mesh model.

Figure 10: Comparison of remaining 3 models’ pressure response versus the Trosseille experimental data.

Figure 16: Comparison of the simulated relative displacements against the data of Hardy et. al. [3] for the GWV model. Displacements here are in the local Z direction. The impact direction being in the Frankfort x-direction, the magnitudes of motion in the z direction are smaller than in the x.

Figure 15: Comparison of the simulated relative displacements against the data of Hardy et. al. [3] for the GWV model. Displacements here are in the local X direction. The accuracy of the more inferior markers (1-4, 7-10) is poorer than those of the superior markers (5, 6, 11 and 12), where more simulated brain motion takes place.

Figure 9: Experimentally measured [2] and simulated predictions of frontal pressure. D34 and C28 represent the names of the experimental frontal and occipital pressure responses, respectively.

Figure 4: Detail of CSF layer when three elements were placed through the thickness rather than one. The size of the resulting elements between the skull and the intracranial membranes required the use of adaptive meshing.

Figure 14: Still from GWV model at 26ms during Hardy impact simulation (time chosen to match that of the first peak motion seen in the experimental motion shown in Figure 15). Image shows a fringe plot of the relative displacements (in metres) of brain elements with respect to the skull. The greatest relative motion is towards the interior of the cerebrum, while the outside region moves essentially in unison with the skull.

Figure 13: Close up on path taken by NDT 6 in experiment (black solid line) and path taken by the closest equivalent node in the simulation (grey dashed line). The solid black box indicates the starting position for the experimental data while the open black box is the initial position of the adjacent node.

Table 2: Material properties used in the analyses. For some analyses the CSF layer required a small value for stiffness in shear in order for the test to run to completion.

Figure 5: The swept mesh method (a) is simple to implement but will not be numerically well-conditioned if only quadrilateral elements are used. The projection mesh method involves two meshing steps but combines good element quality throughout the resulting mesh with the complete use of quadrilateral (b) and hexahedral elements (c). Images courtesy of the TrueGrid homepage [38].

Figure 6: How to change or convert a swept mesh into a projection mesh.

Figure 1: Overview of baseline finite element model (whole head, left; brain, right) , i.e., baseline UCDBTM.

Figure 12: Overview of results comparing predicted and measured brain displacements (relative to the skull). The solid black curves represent the experimental trace of brain motion, while the grey dashed curves show the simulated results. The direction of motion is qualitatively predicted and, in the case of the superior markers, accurate magnitudes of direction are also predicted.

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Title Influence of FE model variability in predicting brain motion and intracranial pressure
changes in head impact simulations
Authors(s) Horgan, T. J.; Gilchrist, M. D.
Publication date 2004-08
Publication information International Journal of Crashworthiness, 9 (4): 401-418
Publisher Informa UK (Taylor & Francis)
Item record/more information http://hdl.handle.net/10197/4687
Publisher's statement This is an electronic version of an article published in International Journal of
Crashworthiness (2004) 9(4): 401-418. International Journal of Crashworthiness is available
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Influence of FE model variability in predicting brain motion
and intracranial pressure changes in head impact
simulations
Timothy J. Horgan
1
Michael D. Gilchrist
1,*
1
Department of Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland
* Corresponding author: Michael.Gilchrist@ucd.ie
Abstract
In order to create a useful computational tool that will aid in the understanding and perhaps
prevention of head injury, it is important to know the quantitative influence of the
constitutive properties, geometry and finite element formulations of the intracranial contents
upon the mechanics of a head impact event. The University College Dublin Brain Trauma
Model (UCDBTM) [1] has been refined and validated against a series of cadaver tests and the
influence of different finite element formulations has been investigated. In total six different
model configurations were constructed: (i) the baseline model, (ii) a refined baseline model
which explicitly differentiates between grey and white neural tissue, (iii) a model with three
elements through the thickness of the cerebrospinal fluid (CSF) layer, (iv) a model simulating
a sliding boundary, (v) a projection mesh model (which also distinguishes between neural
tissue) and (vi) a morphed model. These models have been compared against a cadaver test
of Trosseille [2] and of Hardy [3]. The results indicate that, despite the fundamental
differences between these six model formulations, the comparisons with the experimentally
measured pressures and relative displacements were largely consistent and in good
agreement. These results may prove useful for those attempting to model real life accident
scenarios, especially when the time to construct a patient specific model using traditional
mesh generation approaches is taken into account.
Introduction
Traumatic head impact injuries occur when the human skull and brain are rapidly subjected
to intolerable levels of energy. There exist many causes of neurotrauma; accidents, falls,
assaults and injuries occurring during occupational, recreational and sporting activities. The
relative ratio of these causes differ worldwide. While RTAs tend to be the leading cause of
injury related death, falls tend to be the leading cause of non-fatal hospitalisation [5, 4]. In
Ireland, falls are the single greatest cause of hospital admissions for both males and females
across most age groups, with head injuries occurring in approximately a quarter of all fall
admissions [5]. In the United States, traumatic brain injury results in over 50 thousand
fatalities and nearly one million injuries each year. Motor-vehicle crashes are the most
common cause of brain injury. Since the introduction of automotive restraint systems such as
airbags used in conjunction with seat belts, many forms of injury have been reduced,
including brain injury. However, it has not been eliminated as an automotive-related injury
and head injuries continue to be sustained by cyclists, pedestrians and motorcyclists.
Much of what is known about brain injury mechanisms in living humans has been as a result
of experimental studies. Tests have included physical models, human cadavers and both
anaesthetised and cadaveric animals. Experiments conducted on living humans have defined

the response of the head to non-injurious impact [6]. Human cadaver experiments have the
advantage of accurate anatomy, but the limitation of not properly representing the physiology
of the living human (although attempts have been made to simulate vascular lesions by
pressurising the vascular system prior to impacting cadaver heads). On the other hand the
anaesthetised animal is a living subject but differs anatomically from the human. Highly
sophisticated experimental techniques have been developed in the course of animal-based
head injury studies. Although the anatomical differences are least in the non-human primate,
the smaller size of the monkey skull and brain introduce problems of dimensional scaling
when attempting to relate associated results to the living human. Experiments have been
conducted on physical models of the brain and have included measurements of strain. These
were recorded by measuring the distortion of an impregnated grid or by using photoelastic
techniques, in accelerated gel-filled containers (eg. [7], [8]).
Ward and Thompson [9] suggested that the relative motion between the brain and skull could
explain many types of brain injury such as intracerebral haematomas, which are principally
due to rupture of bridging veins. Since the skull and brain are of different densities and the
cerebrospinal fluid (CSF) surrounds the brain, the brain can move relative to the skull during
a blunt impact event causing contusions, intracerebral bruises and contrecoup lesions [10].
Bandak [11] categorized this type of “Relative Motion Brain Injury” as a class of focal
injuries caused by the tangential motion of the brain relative to the skull, resulting in some
classes of focal contusions or blood vessel rupture.
Brain movement within an externally loaded skull poses a complex three-dimensional
dynamic boundary value problem. With the rapid advances in computer technology,
sophisticated computer models of the head can provide useful information in the
investigation of neurotrauma due to impact. The internal biomechanical responses of the
brain cannot be completely measured by experimental techniques without introducing large
complexity and/or cost, and so finite element (FE) models may be used to study impact
events. Moreover, they reduce the need to conduct a large number of experimental tests. In
particular, a FE model that describes in detail the complex geometry and the multiple
material compositions of the brain can be used to calculate internal stress, strain and pressure
at all locations and at any given instant during an impact [12]. Results from such a model can
be used to relate the severity and extent of pathophysiological changes and/or structural
failure to the magnitudes and directions of input mechanical variables. These models, if
validated rigorously, can be used to design countermeasures to mitigate brain injuries in the
future.
Only 3D FE models of the human head are suitable for simulating most impact and inertial
load analyses. Due to the low shear resistance and large bulk modulus of the intracranial
contents, material exchange between regions is likely to occur (CSF, foramen magnum etc.),
when the head is subjected to large deformations. This can only be described using 3D
models [13]. However, 2D models are useful for parametric studies of controlled planar
motions. Also, 2D models simplify the inclusion of geometrical details compared to a
corresponding 3D model (for example [14, 15]). Many attempts have been made over the
past thirty years to model the human head in three dimensions by finite element analysis.
Shugar [16] developed a 3D model of the skull in 1975 and described its method of
construction and limitations. Hosey and Liu [17] constructed a model which included all the
main anatomical features of the head, albeit in a coarse mesh. The model was subjected to a
sagittal impact and it was found that pressure varied linearly across the model, with positive
pressure at the coup side, and negative pressure at the contre-coup, with a point of zero

pressure over the anterior of the foramen magnum. Ward [18] constructed a physically
accurate brain model which included the membranes and the CSF. The skull was not included
and instead was modeled by a boundary condition. Major findings were that the internal folds
of the dura influenced the response and he postulated that high normal stresses cause serious
brain injury, and that combined tension and shear stresses produce subarachnoid
haemorrhage. Ruan [19] constructed a detailed 3D model of the head which is still being used
a decade later. The model was subjected to frontal, side, and occipital impacts. He found that
viscoelasticity had no significance on the pressure response in short duration frontal impacts,
and that impactor velocity had more effect than impactor mass. DiMasi [20] created a model
which included a skull and brain with simplified shape. That work concluded that there exists
higher shear strain for windshield impact compared with A-pillar impact. Khalil and Viano
[21] and Voo et al., [22] have reviewed these older models. More recently, Claessens [23]
constructed a model and used it for parametric tests. Zhou [24] showed that differentiation
between gray and white matter and inclusion of the ventricles (the regions were constructed
manually slice by slice in his model) are necessary to match regions of high shear stress to
locations of DAI. This model was later updated and further tested by Al-Bsharat [25]. Kang
et al. [26] constructed a 3D model of the head and validated it against the three cadaver tests
of Nahum [33], Trosseille [2] and Yoganandan [27] and included a fracture criterion in their
model. This model was further tested against motorcycle accident cases. These and some
others have been reviewed by [28]. Kleiven [13] constructed a 3D model and related injury to
both brain and head size. Zhang et al. [12] at Wayne State University have constructed what
is currently the highest density mesh which also has a detailed facial structure. Of all the
aforementioned models, only those of Al-Bsharat [25], Kleiven [13] and Zhang [12] have
been compared to the relative displacement data of Hardy [3].
With regard to the particular methods used to construct the various finite element models,
Bandak [29] and Krabbel et al. [30] developed procedures for generating a detailed FE model
of the human skull from CT scan images. Both suffered somewhat with problems in creating
a well-conditioned element mesh. Kumaresan et al. [31] used the upper limits of the
landmark coordinates of the external geometry of a dummy head and divided the head into 33
layers in the horizontal plane. Horgan and Gilchrist [1] showed a number of sections through
the contours of the intracranial space and suggested how these may be used to create other FE
models of the head.
The present authors have recently constructed [1] a new 3D FE representation of the human
head complex, shown in Figure 1, using anatomical data from [32]. The model contains both
shell and solid elements, all of which are hexahedral and not tetrahedral. When constructing
the model, emphasis was placed on element quality and ease of mesh generation, as this has
proved to be a difficulty in other models. The model was validated against the pressure
response of Nahum’s [33] cadaveric impact test. A parametric study was also performed on
the material properties of the intracranial contents for the same cadaver test. It was found that
the short-term shear modulus of the brain and the bulk modulus of the CSF had the greatest
effect on the pressure response. The effect of skull topology, CSF depth and overall model
weight were also investigated and it was found that careful consideration of each is required
when attempting to predict the intracranial pressure response.
Clearly, significant effort in using 3D FE models to simulate head impact injury has taken
place in the past three decades. None of these models represent the true physiological and
anatomical details of the head. All involve various simplifying assumptions concerning
geometry, boundary and loading conditions, constitutive properties and element formulations.

For example, should linear or higher order shell or solid elements be used, is it necessary to
consider the influence of the scalp, face or pia in predicting the occurrence of an injury, or
how can the CSF be modelled most simply? To date, no research effort has attempted to
establish the consequences of such widely different levels of simplification. Similarly, no in-
depth comparison has yet been made of the predictions obtained by a number of these
different models when simulating even the simplest of impact cases. This paper attempts to
address this knowledge deficit: variations of the baseline UCDBTM are analysed and the
different predictions compared against experimental measurements of intracranial pressure
and brain motion. The results of this investigation serve to clarify the degree of complexity
required in 3D FE models when simulating brain trauma.
Construction of the FE variations
1. Baseline Model
This model has been described in detail elsewhere [1] and is shown in Figure 1. The baseline
model includes the cerebrum, cerebellum and brainstem, intracranial membranes (falx and
tentorium), pia, cerebrospinal fluid layer (CSF), dura, a varying thickness three-layered skull
(cortical and trabecular bone layers), scalp and the facial bone. 7,318 hexahedral elements
represent the brain and 2,874 hexahedral elements represent the CSF layer with one element
through the thickness.
Figure 1: Overview of baseline finite element model (whole head, left; brain, right) , i.e., baseline
UCDBTM.
2. Sliding Boundary Model
A model was built with a sliding boundary between the pia and the CSF layer. The algorithm
allows no separation of the contacting pia and CSF layers and thus prevents the formation of
a gap at the CSF-cerebrum interface. Considering the effect of fibrous trabaculae and the
fluid nature of the CSF, material properties assumed for the solid elements which were used
for the CSF were the bulk modulus of water and a very low shear modulus. For all the sliding
interfaces a friction coefficient of 0.2 was used, as proposed by Miller et al. [34]. The CSF
which exists between the falx and the brain, and between the tentorium and
cerebrum/cerebellum was also included using the same type of fluid-structure contact
algorithm.

Frequently asked questions

Q1. What is the reason for the skull deformations?

Due to the low shear resistance and large bulk modulus of the intracranial contents, material exchange between regions is likely to occur (CSF, foramen magnum etc.), when the head is subjected to large deformations. 

Q2. What have the authors contributed in "Influence of fe model variability in predicting brain motion and intracranial pressure changes in head impact simulations" ?

In total six different model configurations were constructed: ( i ) the baseline model, ( ii ) a refined baseline model which explicitly differentiates between grey and white neural tissue, ( iii ) a model with three elements through the thickness of the cerebrospinal fluid ( CSF ) layer, ( iv ) a model simulating a sliding boundary, ( v ) a projection mesh model ( which also distinguishes between neural tissue ) and ( vi ) a morphed model. 

Q3. What is the implications for future modelling activity?

The implications for future modelling activity is that the very large mesh densities that are required to properly simulate the propagation of compressive waves of ballistic impacts using explicit finite element solvers (elements of order 50µm in size [39]) will most likely be developed via projection mesh methods. 

Q4. Why do the elements in the projection mesh degrade?

Because of the definite change in mesh structure at the boundary of the square, the quality of the elements in the projection region will not degrade further, regardless of how refined the mesh density is made. 

Q5. What was the assumption of a rigid skull?

The assumption of a rigid skull was necessary in order to satisfy the rigid body criteria used to obtain the six acceleration components. 

Q6. What is the role of computer models in the investigation of neurotrauma?

With the rapid advances in computer technology, sophisticated computer models of the head can provide useful information in the investigation of neurotrauma due to impact. 

Q7. What were the pressures measured in the subarachnoid space and in the ventricular?

Miniature pressure transducers were placed in the subarachnoid space and in the ventricular system to measure intracranial and ventricular pressures. 

Q8. What was the emphasis on when constructing the model?

When constructing the model, emphasis was placed on element quality and ease of mesh generation, as this has proved to be a difficulty in other models. 

Q9. What is the advantage of cadaver experiments?

Human cadaver experiments have the advantage of accurate anatomy, but the limitation of not properly representing the physiology of the living human (although attempts have been made to simulate vascular lesions by pressurising the vascular system prior to impacting cadaver heads). 

Q10. What is the effect of the deformation of a regular square grid?

If a regular square grid is deformed in such a way as to form a circle (Figure 5), it would produce 4 elements, corresponding to the four corners of the block, which are highly distorted. 

Q11. What was the process of calculating the CSF layer?

In this formulation, the CSF layer was continually smoothed during the impact simulations, moving the nodes to maintain element quality while mapping the solution from the old mesh positions to the new optimised ones. 

Q12. What was the UCDBTM used to determine the relative displacement of the cadaver head?

These position vectors were then converted into a moving coordinate system so as to determine the relative displacement of the targets with respect to the skull. 

Q13. Where did the mesh be used to update and improve the quality of the elements?

In the regions of the brain stem and where the midbrain transitions to the temporal lobe, further methods (not reported here) were used to update and improve the element quality while retaining the ability for the user to choose the refinement level.