Ansys Ls Dyna Crash Biomechanics

Concussions

Use of Brain Biomechanical Models for Monitoring Impact Exposure

Marzieh Hajiaghamemar,5 Matthew B. Panzer,6 Remy Willinger,7

MICHAEL D. GILCHRIST,8 SVEIN KLEIVEN,9 and JOEL D. STITZEL10 Dublin 4, Ireland; 9Division of Neuronic Engineering, KTH Royal Institute of Technology, Ha¨ lsova¨ gen 11C, 141 57 Huddinge, (Received 6 May 2022; accepted 22 June 2022; published online 22 July 2022) Associate Editor Stefan M. Duma oversaw the review of this article.

Abstract—Head acceleration measurement sensors are now widely deployed in the field to monitor head kinematic exposure in contact sports. The wealth of impact kinematics data provides valuable, yet challenging, opportunities to study the biomechanical basis of mild traumatic brain injury (mTBI) and subconcussive kinematic exposure. Head impact kinematics are translated into brain mechanical responses through physics-based computational simulations using val- idated brain models to study the mechanisms of injury. First, this article reviews representative legacy and contemporary brain biomechanical models primarily used for blunt impact simulation. Then, it summarizes perspectives regarding the development and validation of these models, and discusses how simulation results can be interpreted to facilitate injury risk assessment and head acceleration exposure monitoring in the context of contact sports. Recommendations and consensus statements are presented on the use of validated brain models in conjunction with kinematic sensor data to understand the biomechanics of mTBI and subconcussion.

Mainly, there is general consensus that validated brain models have strong potential to improve injury prediction and interpretation of subconcussive kinematic exposure over global head kinematics alone. Nevertheless, a major road- block to this capability is the lack of sufficient data encompassing different sports, sex, age and other factors.

The authors recommend further integration of sensor data and simulations with modern data science techniques to generate large datasets of exposures and predicted brain responses along with associated clinical findings. These efforts are anticipated to help better understand the biome- chanical basis of mTBI and improve the effectiveness in monitoring kinematic exposure in contact sports for risk and injury mitigation purposes.

Keywords—Brain biomechanics, Concussion, Subconcus- sion, Impact kinematics, Instrumentation, Finite element model.

Imperial College

cal Engineering, Worcester Polytechnic Institute, Worcester, MA, Biomedical Engineering, Wake Forest School of Medicine, Winston-

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0090-6964/22/1100-1389/0  2022 The Author(s) under exclusive licence to Biomedical Engineering Society

This Work Was Part Of The Consensus Head Accel-

eration Measurement Practices (CHAMP) project. The

Objective Of Champ Was To Develop Consensus Best

practices for the gathering, reporting, and analysis of head acceleration measurement data in sport. Subject matter experts were recruited to draft a series of papers on various aspects of the issue. As described in detail in a companion paper (Arbogast et al. 2022),9 each team

March 24–25, 2022 At The Children’S Hospital Of

Philadelphia.

Regarding Brain Computational Modeling Were Dis-

cussed, revised as necessary, and ultimately approved

By More Than 80% Of The Vote At The Conference:

1.

To Improve Injury Prediction And Interpret Kine-

matic exposure over global head kinematics alone.

They Provide The Ability To Interrogate Physics-

based tissue level response, estimate risk of injury,

And Offer Insight Into Injury Specifics Such As

location and extent of structural damage. 2.

Subjects’

morphological and demographic information. 3.

Data Related To The Metric Used For Model Predic-

tions (e.g. deformation, strain, stress), correlating

Against Real-World Data, And Then Where Possible,

comparing to responses from existing models. It is

Validation Quality When New Experimental Data Or

analytic strategies become available. 4.

Science Techniques To Efficiently Process Large

amounts of sensor data. 5.

The Modeling Community Advocates For A Curated

open-access database repository to facilitate shar- ing of real-world data such as subject-specific head kinematics, injury diagnoses, and other associated

Addition, Simulation Results From Existing Models

using idealized kinematic profiles should be shared as a benchmark for cross-model examination.

This Paper Intends To Recommend Best Practices

related to using physics-based, computational finite element (FE) models of the human brain for predicting intracranial biomechanical responses and subsequent interpretation of sustained head impact kinematics.

Topics of model development, validation, simulation, result interpretation, and limitations are discussed.

Consen-

sus-derived best practices are presented. Wherever possible, all of these topics are taken in the context of interpreting intracranial biomechanical responses from

Instrumentation-Based Measurements Of Head Impact

kinematics in contact sports.

The Purpose Of Developing A Human Brain Biome-

chanical model (hereafter ‘brain model’) is to accu- rately represent brain biomechanics in silico. This allows estimating brain responses in real-world kine- matic events through computer simulations that are otherwise difficult or impossible to measure directly.

Most brain models are developed using physics-based finite element (FE) method, which is a modern engi-

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neering tool widely used across industry and academia. The solution of the mechanical response of a complex FE model is resolved within a discretized mesh con- sisting of a collection of simple-shaped elements. Here, several critical aspects of FE model development are addressed, including mesh development, assignment of material properties, and defining boundary conditions.

Several high-quality brain models are now available

For Estimating Brain Responses During Blunt Head

kinematics. Some comparisons of these models include model validations,32,82 evaluation of predicted brain

Generating High-Quality Meshes Of The Brain Is

usually the first hurdle in model development. This is critical for representing the complex brain anatomy and providing accurate element-level response predic- tions. In the literature, 8-noded hexahedral meshes are usually preferred to represent the brain,63 which often incorporate an o-grid or ‘‘butterfly’’ pattern to repre- sent rounded surfaces (Fig. 1a). Together with selec- tively reduced integration and hourglass control, linear hexahedral elements provide sufficient accuracy and efficiency using explicit time integration in LS-Dyna (Ansys, Canonsburg, PA)54,62,80,99,114,122,135,144,155,166 or ABAQUS (Dassault Syste` mes, France)149,172 solvers (Fig. 1b). Higher order tetrahedral elements are also possible for meshing the brain,117 but they can suffer in

Efficiency.63 Brain Models With Various Numbers Of

elements ranging from five thousand to three million have been reported (Fig. 1a). The effects of element

Number On Predicting Brain Strains Have Also Been

quantified.63,170 Thin shell elements have been used to represent the falx and tentorium that are important to support the brain in rotational motion. Other com- ponents include ventricles that are sometimes approx- imated as fluid elements or low-shear solids and skull- to-brain membranes that are usually overlaid to near- by solid elements.

After meshing, material properties are assigned to each element to represent brain anatomical structures.

Constitutive Model Assumptions And Parameters Are

often periodically updated as new experimental data

Become

available.

Visco-Hyperelas-

tic54,62,99,135,144,149,155,172 material properties have been

Commonly Used (Fig. 1C). Typically, The Brain Is

assumed to have a density close to water, and is nearly incompressible with the bulk modulus many orders of magnitude greater than the shear modulus (GPa vs.

kPa). This combination of material characteristics is

Intracranial

pressure gradients during translational head motion.

In Addition To The Brain Parenchyma, Membrane

structures including the falx, tentorium, dura, arach- noid, and pia if included are usually defined as elastic

Figure 1.

A brief overview of a number of selected brain models (see text for model acronyms). (a) All hexahedral meshes with various element numbers of the models (in logarithmic scale; WHIM shows the maximum number available170), (b) solvers used by the various models, (c) material model with more using nonlinear with viscoelasticity, and (d) brain-skull interface with the majority adopting tied or nodal sharing conditions.

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materials. Due to the rather large variation in material property characterization of the brain,23,168 it is com-

Parameters To Improve Model Validation While Bal-

ancing numerical stability and efficiency for practical use.

Ditions Between The Brain And Skull, And Among

internal brain structures remains a challenge because these areas lack abundant experimental data to sup- port modeling choices. A common practice is to use

Shar-

ing,54,62,80,114,122,135,144,155,166,172 as used in the majority of models (Fig. 1d). A tangential-sliding-only interface condition is also possible, allowing sliding motion between the skull and brain.99,149 Similar to brain material property assignment, it is also common to select and optimize brain-skull boundary conditions to satisfy model validation. Nevertheless, there remains concern that a tied brain–skull boundary condition is not a perfect anatomical representation,183 even if it

May Produce Reasonable Model Validation Against

cadaveric data deep to the brain.72 There has been limited investigation on the relative motion between the brain-skull interface and the resulting strain at the

Outer Surface Of Brain Models.122

It is noteworthy that new capabilities are continu- ally adopted to improve a model’s sophistication and predictive power. The stiffening effect of blood vessels,

Which Are Small In Volume Percentage But Have A

stiffness value orders of magnitude higher than the brain, has been studied by incorporating the cerebral vasculature network.76,165,173,174 White matter fiber tracts have also been modeled either through material definition59,136,171 or explicitly embedded in the brain to study axon loadings.102,155,178 Fluid–solid interac- tion between brain and cerebrospinal fluid (CSF) has also been investigated,38,181 which is an alternative to assigning low shear modulus fluids to the CSF. Lastly, brain models with detailed meshes with millions of elements are also available, offering an improved look at brain anatomy such as gyri and sulci or direct cor-

More Contemporary Ones At The Global Organ Level,

their unique features and applications, ordered by the year each developer group first published their initial versions. This list is not inclusive of every brain model ever developed and was compiled by the authors. It

Aims To Avoid Endorsement Of Any Model Over Any

other.

Model

(WSUHM) was developed based on earlier versions in 1993134 and 1995.179 It was one of the first models used to study concussions in American football.167 Pressure and shear stress were predicted across the brain in 12 National Football League (NFL) impacts involving 24 players, with 9 players diagnosed with concussion. The study found intracranial pressure to be more strongly correlated with translational acceleration than rota- tional acceleration. In addition, large shear stress in the brainstem and thalamus was identified. These are areas

That Are Often Damaged In Traumatic Brain Injury

(TBI), particularly in conjunction with diffuse axonal injury (DAI), and are also relevant in concussion. The study showed shear stress in the upper brainstem can better predict concussion than pressure, translational acceleration, rotational acceleration and Head Injury Criterion (HIC).150 Later, the model was used to pre- dict strain distribution in the brain in 28 NFL colli- sions (22 concussions).151 It was shown that midbrain

Strain And Strain Rate Correlated With Memory And

cognitive deficits and removal from play. FEHM) has been used to determine injury metrics for predicting the risk of concussion, subdural hematoma (SDH) and skull fractures. It originated from work in 1997.88 This visco-elastic brain model has been applied to the replication of 28 NFL collisions153 and 125 real world head trauma31 to derive brain tolerance limits. A

Sufehm-Box Pipeline Has Been Made Available For

end users for assessment of head protection systems in the automotive,56,126 motorcycle,17,145 and bike and equestrian helmet industries.15,30,71 SUFEHM is part of ‘‘Certimoov.com’’ helmet rating and used for front car crash safety assessment within EuroNCAP. A deep learning version of the model was developed for helmet applications.16 An anisotropic version with visco-hy- perelastic material for white matter from diffusion tensor imaging (DTI) data has been developed.24,25 This was validated135 and used to derive prediction for

Skull Fracture137 And Mild Tbi.138 The Prediction

capability of multiple metrics including maximum ax-

Damage Metric (Csdm), Etc. Showed Axonal Strain

prediction capability.

Kniska Ho¨ Gskolan Royal Institute Of Technology)

models exist. An early version with visco-hyperelastic brain material properties was used to simulate 58 NFL collisions and to determine the mechanical parameter for better concussion prediction.98 Later, Giordano

Material

properties for white matter to test the prediction

Accuracy Of Mps, Mas, Csdm, Hic And Bric. They

found that they are all significant predictors of con-

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cussion based on logistic regression. The model was

Also Used For Multiscale Modeling Of Tbi26 And To

incorporate white matter mechanical anisotropy and assess its effects on the predictions.57,58 Another ver- sion incorporating several pairs of bridging veins has shown large strains in these veins under head rotations, suggesting that large rotational accelerations can pro-

A Smoothed Voxel Kth Version Was Also Developed

from MRI,75,77,78 which was validated by segmentation accuracy, element quality and brain motion. It showed that maximal strain was concentrated in the depth of sulci during rotational loading, similar to reported locations of DAI.77 Therefore, it was suggested that the inclusion of sulci may be considered for future FE head models.

The Adapt Model105,124 (A Detailed And Person-

alizable Head Model with Axons for Injury Prediction) is the latest from the KTH group. It is an anatomically detailed model with conforming meshes of sulci and

Adapt Model Is Equipped With A Hierarchical Image

registration-based personalization pipeline that allows fast generation of detailed subject-specific models for

Almost Any Brains That Have Significant Anatomical

differences comparing with the baseline.104 The per- formance of the head model is evaluated by comparing model predictions with experimental data of brain– skull relative motion, brain strain, and intracranial

Pressure. The Adapt Model Has Been Used In A Sub-

ject-specific multiscale analysis of concussion.124 (UCDBTM)79 has been used to study falls and sport- ing injuries, to evaluate helmet performance and to establish threshold metrics of concussion.35,89,128 It was shown that the model can predict the location of contusions in two reconstructed falls.35 Recent work has used this model to explore relationship between strain in white matter regions of interest and DTI abnormalities in 8 reconstructed TBI cases.127 A sig-

Nificant Relationship Was Found Between Radial And

mean diffusivity in fornix and shear strain in this re-

Gion. The Model Was Updated In 2020149 With An

important feature being a low coefficient of friction between scalp and skull (0.06), which is based on dy-

Was Developed By Researchers At Nhtsa.143 Loading

data from experiments on animals (114 experiments in total) were used to determine thresholds for strain, pressure and relative brain/skull displacement, which

With Improved Anatomy And More Elements To Better

preserve anatomical details (~ 46 k vs ~ 8 k elements). This model was calibrated for predicting the risk of DAI only. SIMon was used in later studies to develop

Head Model Was Developed By Researchers At Toyota

Central Research and Development labs.95 This model included various tissues, including scalp, skull, CSF, brain and meninges. In a recent version of the model, the brain, CSF and skull were connected with shared nodes, in contrast to a tied contact in the older version, to address computational instability issues81 and later an anisotropic material model was incorporated for the brain.10 This model was used to develop brain injury criteria based on rotational kinematics of the head

(Ric And Prhic).94 The Thums Is Available In

several anthropometries.

Ghbmc 50Th Percentile Male Model Developed By An

international consortium.114 It has been used to predict

Brain Tissue Response In Automotive And Sporting

impacts.40,46,103,139,142 The GHBMC model has been used to develop brain injury criteria, BrIC and UBrIC,

Brain

strain.46,47,142 It was later used to determine correla-

Tions Between Fifteen Kinematics-Based Head Injury

criteria and strain in brain tissue in occupant and pedestrian crash tests.45 This study showed strong correlation between rotational kinematics and brain tissue strain. As with THUMS, several other sizes ex- ist, including but not limited to the 5th percentile fe-

Male And The 95Th Percentile Male. The Ghbmc

model pedestrian model is approved for use with Euro NCAP in silico test guidelines for pedestrian protection which involve the calculation of TBI risk.

The Worcester Head Injury Model (Whim) Has

been used to study concussion in sports.12,86,115 An early version was used to study concussed ice hockey

Diffusion Imaging Scans.115 The Model Was Used To

predict strain and strain rate in the corpus callosum of the players, using acceleration data from instrumented helmets. They showed that both strain and strain rate in the corpus callosum correlated with changes in dif- fusion tensor imaging parameters of the corpus callo-

To Study The Reconstructed Nfl Concussion Dataset

using machine learning.21,160 White matter anisotropy

Based On Whole-Brain Tractography From The Same

subject used to develop the model was later incorpo- rated through the Holzapfel Gasser-Ogden constitutive

Model (Anisotropic Whim V1.0).171 This Model Also

serves as the basis for deep learning models for (near) real-time regional or whole-brain responses.55,158,159,161 The model was recently further upgraded (anisotropic

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WHIM V2.1) to reach strain mesh convergence170 and to include the cerebral vasculature network and brain heterogenous material properties from magnetic reso- nance elastography.173,174 This model offers insight into strains of the cerebral vascular network in typical concussive impacts in sports and severe impacts in car crashes.

Cerebrum, Cerebellum, And Brain Stem With Special

attention paid to similarity and interoperability with imaging atlases. The boundary conditions, including falx cerebri and tentorium cerebelli, are modeled in a matter to allow sliding. The CSF layer is tied to the brain and the boundary between the CSF and skull is defined to allow relative motion. The brain interacts with normal forces and against the skull and the falx and tentorium affecting its motion. The model includes gyri and sulci and was developed from an atlas of the

(Mni) Space By Converting Mri Voxels Into Hexahe-

dral elements. This model was used to create and ex- plore computational metrics of injury118 and has been used to explore pre to post season imaging changes in football players.91,92,120,129 Recently, this model was used to explore and report a large variety of whole-

Brain And More Targeted Injury Metrics Focused On

tensile, shear and compressive strains,118 where strain- based injury metrics outperformed kinematic metrics

Head Was Developed Using An Image-Based Meshing

method to incorporate fine details of the brain anat- omy, including the sulci. By using this model, it has been shown that maximal strain and strain rate are concentrated in the depth of sulci in sporting colli- sions.54,186 The sulcal depths are the locations where

Encephalopathy

(CTE), has been found in athletes subjected to repeti- tive head kinematics. An analysis of the diffusion imaging of a large cohort of TBI patients also showed that white matter abnormalities are concentrated in sulci, providing converging evidence for the predic- tions of the model. This model has been used to eval-

Uate New Helmet Technologies That Are Designed To

manage the rotational motion of the head.2,93,140 Re-

Details Of The Venous System Mapped From 7T Qsm

(quantitative susceptibility mapping) image of the same subject.37 This model was shown to be able to predict the location of small deposits of venous blood, known as microbleeds and a marker for axonal injury in mild TBI, seen in the SWI (susceptibility weighted imaging) scan of a rugby player following a head col- lision.

Bridge Between Fe Modeling And Imaging By Devel-

oping a method to explicitly represent axonal fiber tractography,49,50 a technique now adopted by others. It has been used to study impacts in football as well as

This

embedded axon technique was later incorporated into primate brain models to study interspecies scaling156

Identified That Global Maximum Axonal Strain Mea-

sured in the embedded axons was the best predictor of injury for all species and TBI severities studied, with global MPS-95 as a suitable alternative metric.157 Further, the UVA-Axon model has been used to study the functional changes that occur from TBI by evalu- ating the loss of functional network efficiency from

Morphing

(RBM) technique to automatically generate subject- specific FE brain models through registration to pre-

Serve Both External And Internal Neuroanatomical

characteristics.61 A unique aspect of the model was that brain material properties were optimized to ensure the model is biofidelic across a wide-range of kinematic conditions using human volunteer magnetic elastog-

Cadaver Sonomicrometry Data.4 The Optimized Model

was then validated against additional sonomicrometry data and the final tissue properties were validated against independent tissue experimental data.

Most Of These Models Represent A Generic Subject,

typically that of a 50th percentile male head. It is known that a larger brain will produce higher strains

Input.62,100,105,109,156

Therefore, caution must be used when applying generic models to a specific subject, especially for females and youth subjects, where greater differences in brain morphology relative to the generic model are expected.

Conversely, additional work is necessary to develop advanced modeling and/or simulation strategies that will compensate for brain response differences due to morphological variations to improve subject speci-

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ficity.105,109 A recent study identified that the size of the head and brain, tragion-to-top distance, as well as

Head Length And Width Are The Anatomic Components

that most significantly influence head geometric vari-

Validation Is A Process Where The Response Of The

model is compared to independently measured exper- imental data under the same applied loading condi- tions.

Against

experimental data to establish the necessary confidence in prediction accuracy of the response variable of interest.7 Early brain models were validated against

Human

cadaveric impacts.125,147 However, brain pressure is not thought to be a mechanism relevant to brain tissue shear responses due to the assumed near incompress- ibility of the brain.99,116 In fact, brain pressure is di- rectly related to the mass (volume/density) and shape of the brain when subjecting the head to linear accel- eration.19,176 Therefore, a model only ‘‘validated’’ against pressure is not sufficient for predicting large brain deformation generated from shearing of brain tissue.

To probe the brain’s shearing deformation, relative

Brain-Skull Displacements Were Measured In Human

cadaveric heads. An earlier technique used high-speed X-ray that employed neutral density targets (NDTs) made from radio-opaque materials. They are sparsely implanted in the brains of human cadaveric head-neck specimens.39,72,73 The specimens are subjected to im- pact, and 2D in-plane marker motion is tracked. The use of a second X-ray system orthogonal to the pri- mary X-ray source enables the visualization of out-of-

Plane Marker Motion, Permitting Measurement Of 3D

brain motion.73 The X-ray method requires a line-of- sight between the emitter, specimen, and camera to obtain a clear image, which can potentially limit the mounting hardware and the direction of loading for the tested specimen.

Sonomicrometry Has Also Been Used To Measure

dynamic 3D displacements of brain3,4 via trilateration and Kalman filtering.5 Because displacement is mea- sured sonically rather than visually, this technique does

Not Limit The External Mounting Hardware Or The

direction of specimen loading. Nevertheless, the mea- surement sampling rate is limited by the number of transmitting crystals. Finally, dynamic ultrasound has also been used to study peripheral brain motion.113 Limitations with this technique are the penetration depth of ultrasound waves, 2D tracking of motion, and the substantial disruption of the brain-skull boundary condition due to the craniectomy.

To validate a brain model, head kinematics are first prescribed for simulation. A common practice to assess model biofidelity is to compare model predicted rela- tive brain-skull displacement trajectories with those

From Experiments. The Degree Of Model-Experiment

agreement is then evaluated independently for each

Displacement Component Before An Average Score Is

calculated. If model-predicted displacements closely match with those from the experiment, then the model can be thought to be well validated against the avail- able data. These assertions are subject to the limita- tions associated with experimental error, differences between human cadavers and live subjects, differences in anatomy between the experimental subjects and the

Models, And The Biomechanical Variation Naturally

occurring in the population.172 Complete agreement with all experimental data is unlikely in practice. There are also efforts using marker-based displace- ments to derive brain strains for validation.172,184,185 Essentially, the strategy is to assess the aggregated consistency between model and experiment in terms of

Marker Displacement Components Among Multiple

markers as a whole. The magnitude of these ‘‘averaged strains’’ are shown to be consistent with model pre- dicted whole or averaged brain strains, suggesting that

Strain

responses.172,185 Nevertheless, there is potential for

Displacement Measurement Error To Propagate Into

sparse marker-based strains.177 In addition, the aver- aged strains may not have the spatial resolution to inform strain accuracy at the element level because the number of markers is limited, and they cannot be too

In

practice.

Hypothetically,

nonetheless, the averaged strains would converge to

More Localized Counterparts When More Embedded

markers are available.

Sparse

markers may preclude validation for strain prediction at the element level, regardless of the approach.177

Human Volunteers May Mitigate Some Of The Limita-

tions, as they provide voxel-wise strains.11 However, their ‘‘effective’’ spatial resolution is similarly limited by spacing between tag lines and imaging planes.22,101 In addition, they are limited to impact severities far below injury, and extrapolation of data to injurious

Levels May Be Flawed Given The Brain Non-Linear

responses. Nevertheless, peak rotational kinematics of these measurements (244–370 rad/s2) are on the same order relative to the 25th percentile sub-concussive rotational acceleration peak magnitudes (531–682 rad/ s2).132,168 Therefore, these data have been increasingly used to validate brain models at low impact magni-

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tudes,48,86,154,172 which may offer insight into brain biomechanics relevant to subconcussive kinematics.

The Cadaveric And In Vivo Brain Biomechanics Data

are all valuable in assessing the response of a brain model. However, a ‘‘gold-standard’’ strain field to validate a model for injury-level deformation predic- tion with typical FE element-level resolution in live

Such As Cora52 Are Commonly Used During Valida-

tion, but the specific use of these types of rating methods are not consistent across the field. In addition, the quality assessment may not be effective, as different versions of the same model can produce significantly

Given These Considerations, We Recommend A Com-

prehensive validation approach against representative high- and mid-rate cadaveric experiments with varying impact direction, kinematic magnitude, and duration.

For brain models intended to simulate low severity kinematics common in contact sports, additional val- idations against in vivo brain strains are also recom- mended,168 especially given the potential relevance of

Subconcussive Kinematics To The Onset Of Concus-

sion.133,141 A comprehensive validation across a wide range of loading conditions is expected to maximize the confidence in deriving tissue-based injury met- rics.118 For all validations, it is important that the model be scaled to match with the test subject’s head dimension, and ideally, the brain dimensions if such

Finally, It Is Important To Recognize That As New

experimental data4,39,65 and analytic strategies172,185

Models Should Be Reevaluated From Time To Time To

maintain or improve the level of confidence in kine- matic simulation.

After Model Development And Validation, A Brain

model is ready for kinematic simulation. Typically, this is completed using a commercial FE solver,1,110 al- though open-source alternatives such as FEBio111 also exist. Most commercial codes can use explicit time integration schemes with parallel processing.

There are a host of numerical challenges that brain models face primarily due to the rapid loading to soft biological tissues. As previously described in Sect. 3, a

Typical Material Model For Brain Tissue Is Nearly

incompressible, which leads to a Poisson’s ratio close

A Consequence, This

requires special numerical techniques to alleviate the numerical issues related to volume and shear lock- ing.29,63 In addition, for typical brain models utilizing under-integrated hexahedral meshes, the elements can exhibit hourglassing, which are non-physical, spurious

Packages Allow Brain Modeling To Be Numerically

accurate and stable. Nevertheless, modeling such a compliant, nonlinear and viscous material remains a challenge.

Should Account For Dynamics, The Ability To Model

nonlinear viscoelastic materials (e.g., visco-hyperelas- tic), reduced integration with hourglass control or other elements free of locking. Furthermore, parallel computing capabilities, hexahedral based meshes and coordinate system transformations (i.e., body fixed vs ground fixed) are encouraged. Note that while wear- able kinematic sensors may have the ability to measure repeated sub-concussive impacts with accuracy, there are currently no widely accepted methods for quanti- fying the history-dependent tissue damage that results

Aspect Needing Attention. Conceptually, An Impact

transfers force to the head via contact with the helmet or ground. However, most sensor systems report linear and rotational accelerations instead of force or pres- sure. For impacts relevant to contact sports, the skull is usually assumed to be rigid because skull deforma- tion is expected to be negligible. Therefore, skull mo- tion is fully described by the linear acceleration and angular acceleration/velocity, such that impact loca-

Tion And Direction Become Irrelevant For Modeling

purposes. This allows the kinematics to be commonly prescribed in terms of 6 degrees of freedom (DOF) of head acceleration (three for linear and three for rota- tional), or equivalently velocity, to the rigid body skull at the head center of gravity (CG). The head CG is the location where accelerometers are mounted in crash test dummies, and is often the location where wearable sensors measurements are transformed.

With The Assumption Of Near Incompressibility Of

the brain, linear acceleration induces little strain.14,87,98

As A Consequence, 3Dof Head Rotational Kinematics

provide the majority of the information necessary to drive models for strain estimation. Linear acceleration does influence brain strain in the critical brainstem region when there is a large component in the inferior- superior direction,96,97,161 which should not be ignored in real-world applications. Even if pure linear acceler- ation produces limited strain, it can lead to injury.

Therefore, mechanical variables sensitive to linear acceleration such as stress may also be considered as an alternative.

Sensors

should also be handled with care because they may not

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use a standardized orientation or naming methodol-

Physical

accelerometer and gyroscope readings embedded in a

Mouthguard Situated On The Teeth To The Estimated

head CG of the athlete. However, other sensor systems export data directly from the sensors without trans- formations. The burden then lies on the modeler to transform the data properly before kinematic simula- tion. Our group recommends sensor manufacturers to standardize their data export protocol. One reference for this may be the J211 coordinate system adopted in the automotive and military area.131 Another alterna- tive is to follow that used in the medical imaging community, where the y and z positive directions are reversed relative to those in J211. In either case, it is necessary to define and use anatomical axes.

Wearable Sensors Measure The Motion Of The Skull

while the brain motion lags behind the skull. This phenomenon and the time-dependent deviatoric (i.e., time lag) material behavior of the brain tissue causes the brain to continue to deform in response to head impact in some cases even after significant skull motion ends.4,83 In some cases, this ‘post-impact’ brain tissue deformation can be larger than that experienced during the impact duration when the main skull motion oc- curs and the sensor data is collected. This post-impact brain deformation is also shown to be dependent on the brain geometry and is more significant in larger brains.107 Current head kinematic sensor systems col- lect data for approximately 50–200 ms which contain pre-trigger and post-trigger times and the trigger time point is typically considered when the resultant linear acceleration exceeds a threshold value. When dealing with data near the lower end of 50 ms, the simulation input can end, while the brain tissue may continue to

Encompass A Longer Time Window Than The Impact

duration and check for significant brain strains ‘post-

Impact’. A Recent Study Recommends A 20 Ms Pre-

trigger and 70 ms post-trigger duration for a proper capture of brain deformation during the full kinemat- ics.107,174 From a simulation perspective, another study

Recommends At Least ~ 20 Ms Additional Simulation

time (with zero acceleration) for the deep brain regions to reach peak strain.83 .

While Great Strides Have Been Made Over The Past

half century to improve the sophistication and biofi- delity of head injury models,112,162 relatively less attention has been paid to improve simulation effi- ciency. Direct impact simulations using a validated brain model may be the most accurate, but substantial

For Real-Time Monitoring And Assessment. This Is

important and especially relevant to contact sports, as each player typically sustains dozens to hundreds of impacts in a play season and there is growing concern

On The Cumulative Effects From Many Subconcussive

kinematics on the onset of concussion. To achieve rapid estimation of brain response, sev- eral approaches have been pursued. One method is to develop generalized kinematic-based tissue deforma- tion hypersurface through parametric simulations.47,68 This allows brain strain to be quickly elucidated from kinematics. However, the idealized acceleration pulses used for simulation may not capture details of realistic accelerations. Another limitation is that they typically estimate MPS of the whole brain; thus, losing the de-

Spatial

distribution.

Alternative

approach is a pre-computed brain response atlas based on simulations of idealized rotational pulses using

Discretized Parameters Of Head Impact (I.E., Peak

magnitude and duration, rotational axis azimuth and elevation angles). Although this method allows ele- ment-wise brain strains to be efficiently interpolated or extrapolated,84 accuracy may suffer when kinematics

Recent Deep Learning-Based Approaches Avoid These

limitations, as they retain high accuracy without the need to simplify the brain model, response output, or kinematic input. These models use kinematic profiles directly16,55,158 or extracted features164 as input, and employ thousands of direct model simulations based on realistic kinematic profiles to generate training data.

Upon convergence, the trained deep learning models can instantly estimate detailed strains55,164 or maxi- mum stress of the brain and injury risk directly.16 Recently, a transformer and a separate convolutional neural network have been developed to rapidly esti-

With R2 > 0.99).159

Given these results, deep learning models may have the potential to allow monitoring detailed brain strains

From Many Head Impacts And For A Large Number Of

athletes in diverse contact sports teams. With high accuracy relative to direct model simulation, deep learning models could also promote model sharing by effectively shielding the details of FE model construc- tion from end users. This may be especially helpful when it is not practical to share the biomechanical model, including the mesh elements and nodes, itself.

An Added Benefit Is That They Do Not Need Any Spe-

cialized FE code or sophisticated computing hardware, and computation time is drastically reduced. Never- theless, a large number of training samples are neces- sary to yield a desired accuracy, which would demand

Society

Use of Brain Biomechanical Models for Monitoring Impact Exposure

1397

a enormous initial cost of simulation. This could be mitigated by transfer learning (i.e., reusing network weights instead of random initialization) to reduce the samples required, even when the technique is applied to a different brain model or impact type (e.g., auto-

Brain Response Sensitivity To Impact Kinematics

Errors in kinematics are typically assessed by the percentage of peak magnitudes of linear and rotational acceleration and rotational velocity.108 A potential limitation is that this approach is unable to assess the significance of other important kinematic features on the resulting brain responses, such as direction of rotation,4,96,97,152 area of the brain that experiences high strains or stresses,98,115 temporal variation,14,169 variation by direction or orientation of brain tis- sue,26,57,59,86,154 and even digital filters that are known to affect strain magnitude and distribution.90 We are in the adolescent stage of exploring these variations, with many promising findings that are helping researchers better understand the biomechanics they are encoun- tering in the field. Determining how kinematic errors affect brain response may seem straightforward, e.g., by comparing the simulated brain responses to refer- ence data using a validated brain model. Nevertheless,

There Are Several Considerations Related To Model

result interpretation in the context of head impact simulation using kinematic data measured from head

Has Been Achieved Regarding The Model Development

and biofidelity, there are many metrics that are com-

Quantifying Head Kinematic Severity. The Aphorism

‘‘All models are wrong, but some are useful’’ is often attributed to the statistician George Box,18 and surely applies to FE modeling of the brain, one of the most complex human anatomical structures.

A main objective for the creation and use of brain models is to better interpret head kinematics in the context of injury risk. This involves calculation of FE based metrics for subsequent quantification of impact exposure, risk estimation, or other activities. Fre- quently, these results are used to relate to contextual

And Outcomes Information. Contextual Information

here is defined as information which may be useful to coaches, athletes, parents, regulatory bodies, equip- ment designers, etc. Outcome information generally refers to clinically and scientifically useful information relating to maximizing benefit and reducing risk. This can be neurocognitive,154 imaging,28,115,129,163 or bio- marker data,64 etc. There is long-term potential for FE brain model results to improve our understanding of pre- and post-exposure changes of various clinical biomarkers, and better utilize head kinematics to pre- dict clinically relevant outcomes typically interpreted by the engineer, physician, athletic trainer, public health scientist, etc.

In A Sense The Fe Modeling Community Is At The

early stages of understanding and utilizing the tissue- level metrics that can be computed using brain models. They represent an example of the pareto principle—the majority of the value can be achieved with less effort,

And The Remaining Value Will Require Pushing The

boundaries of thought and expertise, is the purview of researchers, and holds the promise for better capturing

Nuance And Serving As A Better Context Or Outcome

discriminator. These activities are expected to lead to a better fundamental understanding of the biomechanics of kinematic exposure and acute or chronic injury.

Considering That There Is Known Asymmetry In The

brain both anatomically and functionally,36 the brain changes structurally with age,33 and is a networked system that is structurally and functionally complex,20 no FE modeling approach totally represents the anat- omy or function of the brain completely. Further, no FE model allows tissue-level interpretation of even the most basic functional, biochemical, or molecular out-

Comes Observed In Neurotrauma Models. Most Biome-

chanics researchers studying the brain focus on trying to approximate the mechanical response of the par-

And

boundary condition data. The outcomes of these sim- ulations are complex, but metrics are used to simplify the simulated outcomes to allow quality analyses to be performed.

There Are Basic Metrics Commonly Adopted In Brain

models, beginning with simple strain measurements.121 Peak maximum principal strain and stress are some of

The Earliest Explored Metrics From A Test And Fe

modeling standpoint.73,98 The history and experience

With Modern, Fe-Based Approaches Has Rapidly Ex-

panded over the past couple of decades, allowing for a slew of other metrics.

Scalar Values May Come From One Element Of The

brain at one specific time in the simulation, often the time of peak maximum principal strain and strain rate

Or Their Product, At Any Point During The Simula-

tion.27,87,115,172 Most FE models provide this scalar value. Nevertheless, the peak or highest strain in an FE brain may be spurious. Therefore, this measure may

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