Documentation:FIB book/FE Head and Brain Models

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Finite Element Analysis (FEA) Introduction

Finite Element Analysis (FEA) is a computational modeling approach which allows engineers to predict how structures will respond mechanically when subjected to different conditions. In simple terms, a computer-aided design model defines a volume to be the solution domain. The conditions and properties defined on the outer faces are called boundary conditions. At this point, to solve the boundary value problem, there are a few different numerical methods available. The finite element method revolves around meshing the domain into infinitesimally small, simple subdomains known as elements. Mathematically, this results in simple calculations to approximate the local displacement in each element. The finite element method is dominant “because of its generality and numerical efficiency,” making it favoured by developers of commercial analysis programs[1]. Finite element analysis (FEA) has established itself as an essential instrument for examining skull injuries in injury biomechanics research by providing a way to study fracture patterns alongside tissue deformations and impact forces on the human head [2]. FEA provides detailed and controlled simulations of trauma scenarios that can be repeated easily to improve protective gear development and automotive safety features as well as medical treatments for head injuries unlike older approaches like cadaver studies or crash test dummy assessments[3].

FEA History

Early Use of FEA in Biomechanics

The application of FEA in biomechanics began in the late 1960s and early 1970s[4] as researchers recognized its potential for modelling biological structures, particularly bones. Early studies adapted FEA from structural engineering to analyze stress distribution in human bones in 1972 [5], and it was one of the first to develop a finite element model on the femur. Also, around the same time, Huiskes and Chao[6] expanded FEA's use in orthopedic biomechanics, providing a framework for analyzing implant performance and bone adaptation in 1983[7]. However, early models faced significant challenges due to the limitation of the computational model, which restricted mesh resolution and required simplifying assumptions about bone as a homogeneous, isotropic material[8]. Additionally, accurate material properties were difficult to define, as biological tissues exhibit anisotropic and nonlinear behaviors that early FEA tools struggled to replicate[7]. Nevertheless, these early applications set the stage for increasingly complex bone mechanics simulations, ultimately creating patient-specific skull models for injury analysis.

Evolution of FEA in Skull Injury Biomechanics

Early Applications (1970s–1990s): Static Load Modelling and Simplified Bone Properties

The application of FEA in orthopedic biomechanics began in the 1970s, focusing primarily on bone mechanics and implant design[9]. Rather than modelling dynamic impact scenarios like traumatic brain damage (TBI), early skull biomechanics applications were limited to static load measurement due to a lack of processing capability. During this period, researchers typically modelled bone as a homogeneous, isotropic material, assuming that mechanical properties were uniform throughout the skull[8]. While this simplification allowed for feasible computations, it did not accurately capture human bone tissue's complex heterogeneous and anisotropic situation. Early FEA models were also based on idealized geometries rather than patient specific skull structures, which limited their clinical applicability[6].

Advancements in Skull Biomechanics Modelling (2000s–2010s)

The computational power and medical imaging techniques improved significantly in the 2000s–2010s, and a shift towards a much more realistic skull model in FEA was shown in research. Using computed tomography (CT)-based models was a significant advancement that enabled the researchers to produce 3D skull reconstructions tailored to each patient, allowing more precise injury simulations[10]. As the anisotropic nature of bone is increasingly understood, more sophisticated material property models that take into consideration the directional dependence of bone stiffness and strength have been developed[11]. More accurate stress-strain assessments of skull fractures were made possible by improved meshing techniques, enhancing simulation spatial resolution.

Recent Advances (2020s–Present): AI Integration and High-Fidelity Modelling

In the 2020s, FEA research in skull biomechanics has continued to develop, mainly emphasizing aspect simulations for faster and more accurate injury predictions. Machine learning algorithms are now used to optimize FEA parameters and improve model validation by comparing simulated injuries with real-world clinical data[12]. Moreover, high-resolution 3D modelling using combined MRI and CT imaging has enabled researchers to represent better bone density variations and soft tissue interactions[13]. One of the most significant developments is the incorporation of soft tissue modelling, which makes it possible to analyze the brain and skull interaction in trauma simulations. More advancements in personalized medicine and injury prevention are now possible due to these advancements, which have made FEA a potent tool in sports safety, auto accident testing, and forensic investigations.

A key advancement in skull injury FEA

In skull injury FEA, the advent of nonlinear dynamic models has been one of the most revolutionary developments, especially for high-impact situations like auto accidents and sports injuries[2]. Unlike early static load models, nonlinear simulations allow for time-dependent material behaviour, enabling researchers to study realistic fracture patterns and tissue deformations under dynamic conditions[3]. The Wayne State Head Injury Model (WSHIM), developed in the 1990s, was among the first to utilize dynamic simulations to evaluate skull fractures and brain injuries in automotive crash testing[14].

FEA Current State/Technology

In the past ten years, FEA has advanced substantially owing to faster computers, high-grade medical imaging, and more precisely calibrated computational material models. Modern nonlinear dynamic simulations now account for the time-dependent behaviour of the tissues, which is a clear advancement in the modelling of skull fractures and brain injuries[15]. Current studies suggest that contemporary FEA models are nearly 80 percent more accurate than earlier static models, which is attributable to improvements in the soft and hard tissue material properties, increased mesh refinement, and validation through empirical impact data[16]. Additionally, the use of machine learning and AI in simulation drives enhancement of prediction accuracy, which increases the utility of FEA in forensic analysis, sports medicine, and automotive crash testing[17]. Those challenges aside, replicating real-world conditions of trauma remains elusive, which means refinement of validation techniques and material property selection is still required[18].

FEA Applications

The use of FEA to model human skulls requires expertise and special considerations depending on the scenario. Though many people are trained to use FEA in structural analysis, injury biomechanics is a different story. Unlike many mechanical parts, the head consists of skin, connective tissue, brain tissue, meninges, and of course the brain and the skull. This introduces more complexity and variability in reproducing an injury with FEA. Asgharpour et al. (2014)[19] stress the importance of faithfully representing each anatomical component with the correct density, Young’s modulus, Poisson’s ratio, and more. Yet even after rigorously creating a model, it is shown that “the resulting force in simulations is always over-estimated” with no “constant proportionality factor”[19].

Of course, when using finite element analysis for different injury scenarios, the methods will change. Different scenarios entail different loading conditions and modelling requirements.

Vehicle Collision Scenarios

Firstly, one of the most discussed topics in injury biomechanics is vehicle collisions. Yang et al. (2014)[20] developed a finite element head model specialized for vehicle collisions. The researchers found that most FE head models in published literature were built to measure only a specific aspect of head injury. The goal of this study was to determine the plausibility of creating a head model that could accurately predict a complete set of head responses. MRI and CT scans with high resolution (0.488/1.0 mm for CT and 0.500/4.0 mm for MRI) were used to reconstruct the geometry of the head. In addition, the researchers proposed generating a hexahedral and tetrahedral mesh as opposed to a typically used Delaunay mesh, which resulted in better mesh quality for a complex curved structure like a brain. It is important to note that this study used a 50th percentile Singapore Chinese male and thus is not representative of the entire world’s population.

Key figures not shown due to copyright are used to visualize the validity of the FE model. In one loading condition, the model agrees with PMHS test data, with the main difference being a lower peak and longer impulse duration. Another condition shows the FE function having similar magnitudes and characteristics to the simulation albeit slightly prematurely. When comparing intracranial pressures at four locations, again, generally the main sources of error are overestimated peaks and troughs. In addition, when comparing this FE model to previous studies (not shown), this study’s model is shown to overestimate the maximum principal stresses in the head. To conclude, this model shows good correlations to experimental data but has a tendency to slightly overestimate forces, accelerations, and stresses. The authors assert that this is a positive development, and “in a real collision situation, the FE model can importantly overestimate the brain damage risk.”

Infant Injuries

As one can imagine, creating a finite element head model for an infant requires additional considerations compared to a typical adult. One study[21] hypothesized that combining finite element and material modelling could allow experts to distinguish between accidental and abusive cases of skull fractures. The motivation stemmed from the prevalence of Abusive Head Trauma (AHT, colloquially known as Shaken Baby Syndrome). For some context, AHT occurs when an infant is subjected to rapid acceleration, deceleration, and rotational forces, causing skull fractures, internal swelling and bleeding, and/or spinal cord injuries[22]. It is considered by some to be “a leading cause of traumatic death in children less than two years of age” and suggested to happen as frequently as 14 to 40 per 100,000 children[21].

In response to this, Li et al. constructed FE head models from CT images of infants in a couple of suspected abuse cases. Special attention was paid to the level of ossification (bone formation) of infant skulls, which can even vary month-to-month. Correctly identifying ossification centres is key because newborns’ skulls have a “fiber orientation” where fibers radiate from ossification centres. This leads to the next important measure, which is incorporating directional stiffness. Infant skull bones are orthotropic, meaning material properties differ in different directions. The skull is stiffer along the previously mentioned fiber directions, and as a result, fracture lines will typically exhibit that. As humans age, bones stiffen and become more isotropic, so it is important to model the anisotropy rather than just scaling down values from adult data.

The results of the study reveal that the injuries of the two suspected child abuse victims could be possible due to an accidental fall. As one can imagine, this can be a powerful tool, and it was in fact used to aid the forensic investigation team. A future area of improvement for this model is finding a way to use subject-specific bone properties instead of literature to account for individual variations.

Sports Scenarios

Researchers have used and developed complex 3D FE models since the 90’s due to a rising concern of mild traumatic brain injuries in contact sports. A review on recent development of FE models for head injury simulation highlighted some universal improvements that could be made, such as additional validation through experimental data, material model complexity of soft tissue, and building upon recently built models to effectively improve our knowledge of simulation[23].

A unique study done on hitting a soccer ball with a player’s head developed a novel method that could serve as a precedent for other small-sized objects colliding with human skulls. First, Perkins et al. (2022)[24] developed a hyperelastic model of a soccer ball with separate behaviours for the inner bladder and outer shell and validated the ball’s behaviour with experimental data. Often and rightfully so, a lot of focus is put on the material model of the skull, but this study puts the same amount of effort into the response of a projectile. This practice could be extrapolated to other small projectiles such as sports balls and less-lethal ammunition. In addition, this study accounted for a variable that often gets overlooked - the anticipation by the player of an incoming collision. This was done by introducing an active and a passive neck condition. In vehicle collision models, muscle engagement is often not involved, and more focus is given to seatbelt and airbag restraint instead. In the results and figures of the study, it can be seen that a lack of anticipation greatly increases injury risk and can make the difference between two levels of the Abbreviated Injury Scale (AIS).

Although the FE model was detailed and innovative, ultimately no significant conclusions were drawn from this study due to a couple of key reasons. The FE head model used was a 50th percentile male head model and thus does not account for a wide range of anthropometric head differences for this sport. In addition, it lacked a validated incorporation of the neck and other relevant muscles.

Unique Scenarios

Finally, FEA can be used for more niche and specific areas. One example is blast-related traumatic brain injury: the most prevalent injury for combat personnel in Iraq and Afghanistan[25]. Noticing this, researchers created a FE head model specialized for blast brain injury. Some unique aspects atypical of FE models include a plane-strain approximation and CSF cavitation analysis.

Plane-strain approximation refers to the simplification to a 2D planar stress condition. As a result, this model cannot consider out-of-plane motion of the head and the aerodynamics of the head. Thus, it greatly reduces computational cost while retaining an acceptable degree of accuracy. That being said, it is still a major limitation as “in a 3D environment, the aerodynamics of the head allow for the blast to better flow around the head”[25]. This implies the 2D approximation is conservative.

CSF (cerebrospinal fluid) cavitation is a phenomenon specific to blast-induced traumatic brain injuries. Blast waves create pressure fluctuations within the fluid, which then cause bubbles to collapse and burst, damaging brain tissue. In the past, it was theorized that CSF cavitation was a cause of brain injury in automotive and blast impacts, but it was not clear what conditions were necessary to cause it. In this study, it was confirmed that at significant pressures, CSF cavitation decoupled the brain from the skull and increased brain strain and neural tissue damage. It can also be seen from graphics of the model that CSF cavitation creates localized high-pressure regions, but this only occurred in the most severe blast conditions. Also, CSF cavitation only appears to contribute to a significant increase in peak brain pressure when the impulse/blast duration is large.

Unfortunately, due to the niche application, there is not “a robust set of validation data” to validate the head model, and thus the study and its results are exploratory. This is generally the outcome in any field/topic where finite element analysis is used without prior real-life experimental data.

Limitations

Accuracy of FEA Simulations vs. Real-Life Skull Injuries

Even though Finite Element Analysis (FEA) has significantly advanced the understanding of head injury mechanisms, there are still concerns regarding the accuracy relative to actual trauma outcomes. Ruan et al. (1993)[26] established an early framework by modeling direct head impacts, and the collected data provided invaluable initial insights into the biomechanical responses of cranial structures. In a later study, Wilinger et al. (1999)[27] validated a three-dimensional human head model using two separate experimental impact scenarios, hence demonstrating that FEA can effectively represent and capture general injury trends. However Kleiven (2007)[16] illustrated that even small variations in input model parameters may lead to substantial differences in predicted models and responses, highlighting the challenges of replicating all arbitrary variables in the complexity of traumatic events. These papers indicate that while FEA is an invaluable tool for approximating injury mechanics, it is still in need of further refinement in order to achieve a higher degree of fidelity in replicating real-life conditions.

To improve the predictive power of FEA in skull injury simulations, researchers are actively working to enhance mesh resolution, incorporate more accurate biological tissue material properties, and combine advanced imaging data such as MRI and CT scans to build a much more anatomically precise model. In addition, combining FEA with machine learning algorithms is an emerging approach that helps identify patterns in large datasets of trauma cases to better calibrate and validate models. Researchers are working to standardize impact testing protocols and use real-world biomechanical data collected from cadaveric studies and instrumented helmets to guide and validate simulation results. These advances aim to bridge the gap between simulation predictions and observed clinical outcomes, making FEA more reliable for injury prevention and forensic analysis.

Challenges in Material Property Selection

Accurate bone and soft tissue modelling remains one of the main challenges of FEA. Huiskes (1980)[28] emphasized the importance of including precise material characteristics in the analysis of bone-prosthesis interactions. This incorporates factors such as stress distribution and thermal conductivity, a principle that is directly applicable to cranial biomechanics. Ji et al. (2013)[17] demonstrated that even minor discrepancies in assumed mechanical properties of the bone can result in significant discrepancies in mechanical responses. Moreover, Barbarino et al. (2009)[18] underscored the necessity of detailed both anatomical and material testing in the development and validation of 3D FEA models of the face. All in all, these studies suggest that a more detailed characterization of bone and soft tissue properties is vital for improving the accuracy of FEA models in cranial injury simulations.

Ethical Concerns

The validation of FEA models primarily relies on data acquired from cadaveric specimens, which introduces a range of ethical questions. DeWit and Cronin (2012)[29] used cadaveric spine segments to validate their FEA model, which underscores ethical considerations that are innate in using human tissue for research purposes. Even though cadaveric data provide invaluable insights into the mechanical behaviour of biological tissues, consent-related issues, cultural and religious sensitivity, and the potential for disrespectful handling of human remains must be acknowledged and addressed. As consent is not always well-documented, certain communities may find the usage of cadavers offensive on moral and religious grounds.

Specimen variability and post-mortem changes also raise questions of scientific and ethical relevance. Mechanical properties of cadaveric tissue may differ significantly from living tissue due to factors like hydration loss, embalming, and tissue decomposition. Synthetic models present a promising alternative that may alleviate some ethical concerns, but they often are not able to capture the nuanced properties of living tissues. Synthetic materials lack the anatomical and biomechanical complexity of real human tissue[30]. The challenge remains: to find the balance between ethical issues of model validation and the need for accurate and relevant data.

In a vacuum, finite element analysis is a non-invasive, inoffensive technique, causing researchers to gravitate towards it and other forms of modelling when PMHS are costly or frowned upon. That being said, our literature review confirms that researchers need to be wary of drawing conclusions about head injuries from their FE models. Over-reliance or overconfidence in FE models has adverse effects, with the severity depending on the application. For example, one application discussed earlier was using a model to distinguish accidental and abusive head trauma for infants. In this scenario, a finite element model is powerful since infant PMHS are scarce, and the next best option is animal experimental studies using piglets[21]. Still, controversial discussion will arise regarding how accurately we need to develop FE models as a sole tool in investigating injuries caused by criminal acts. When clinical judgement/observations disagree with biomechanical modelling, how should investigators proceed? The consequences of overlooking dangerous individuals or making wrongful accusations are both grave.

Future Research

Practice Problems

References

  1. ↑ Kurowski, Paul (2022). Finite Element Analysis for Design Engineers. SAE International. ISBN 978-1-4686-0535-8.
  2. ↑ Jump up to: 2.0 2.1 Li X, Sandler H, Kleiven S. The importance of nonlinear tissue modelling in finite element simulations of infant head impacts. Biomech Model Mechanobiol. 2016;16(3):823-840. doi:10.1007/s10237-016-0855-5
  3. ↑ Jump up to: 3.0 3.1 Lindgren N, Henningsen MJ, Jacobsen C, Villa C, Kleiven S, Li X. Prediction of skull fractures in blunt force head traumas using finite element head models. Biomech Model Mechanobiol. 2023;23(1):207-225. doi:10.1007/s10237-023-01768-5
  4. ↑ Ateshian GA, Friedman MH. Integrative biomechanics: A paradigm for clinical applications of fundamental mechanics. J Biomech. 2009;42(10):1444-1451. doi:10.1016/j.jbiomech.2009.04.001
  5. ↑ Parashar SK, Sharma JK. A review on application of finite element modelling in bone biomechanics. Perspect Sci. 2016;8:696-698. doi:10.1016/j.pisc.2016.06.062
  6. ↑ Jump up to: 6.0 6.1 Huiskes R, Chao EYS. A survey of finite element analysis in orthopedic biomechanics: The first decade. J Biomech. 1983;16(6):385-409. doi:10.1016/0021-9290(83)90072-6
  7. ↑ Jump up to: 7.0 7.1 Taylor M, Prendergast PJ. Four decades of finite element analysis of orthopaedic devices: Where are we now and what are the opportunities? J Biomech. 2015;48(5):767-778. doi:10.1016/j.jbiomech.2014.12.019
  8. ↑ Jump up to: 8.0 8.1 Saghaei Z, Hashemi A. Homogeneous material models can overestimate stresses in high tibial osteotomy: A finite element analysis. Proc Inst Mech Eng H. 2023;237(2):224-232. doi:10.1177/09544119221144811
  9. ↑ Roychowdhury A. Application of the finite element method in orthopedic implant design. J Long Term Eff Med Implants. 2009;19(1):55-82. doi:10.1615/jlongtermeffmedimplants.v19.i1.70
  10. ↑ Imai K. Computed tomography-based finite element analysis to assess fracture risk and osteoporosis treatment. World J Exp Med. 2015;5(3):182. doi:10.5493/wjem.v5.i3.182
  11. ↑ Kovács K, Váncsa S, Agócs G, et al. Anisotropy, anatomical region, and additional variables influence Young’s modulus of bone: A systematic review and meta‐analysis. JBMR Plus. 2023;7(12). doi:10.1002/jbm4.10835
  12. ↑ Phellan R, Hachem B, Clin J, Mac‐Thiong J, Duong L. Real‐time biomechanics using the finite element method and machine learning: Review and perspective. Med Phys. 2020;48(1):7-18. doi:10.1002/mp.14602
  13. ↑ Burghardt AJ, Link TM, Majumdar S. High-resolution computed tomography for clinical imaging of bone microarchitecture. Clin Orthop Relat Res. 2011;469(8):2179-2193. doi:10.1007/s11999-010-1766-x
  14. ↑ Zhang L, Yang KH, Dwarampudi R, et al. Recent advances in brain injury research: A new human head model development and validation. SAE Tech Pap Ser. 2001. doi:10.4271/2001-22-0017
  15. ↑ Willinger R, Kang H-S, Diaw B. Three-dimensional human head finite-element model validation against two experimental impacts. Ann Biomed Eng. 1999;27(3):403-410. doi:10.1114/1.165
  16. ↑ Jump up to: 16.0 16.1 Kleiven S. Predictors for traumatic brain injuries evaluated through accident reconstructions. SAE Tech Pap Ser. 2007. doi:10.4271/2007-22-0003
  17. ↑ Jump up to: 17.0 17.1 Ji S, Ghadyani H, Bolander RP, et al. Parametric comparisons of intracranial mechanical responses from three validated finite element models of the human head. Ann Biomed Eng. 2014;42(1):11-24. doi:10.1007/s10439-013-0907-2
  18. ↑ Jump up to: 18.0 18.1 Barbarino GG, Jabareen M, Trzewik J, Nkengne A, Stamatas G, Mazza E. Development and validation of a three-dimensional finite element model of the face. J Biomech Eng. 2009;131(4). doi:10.1115/1.3049857
  19. ↑ Jump up to: 19.0 19.1 Asgharpour Z, Baumgartner D, Willinger R, Graw M, Peldschus S. The validation and application of a finite element human head model for frontal skull fracture analysis. J Mech Behav Biomed Mater. 2013;33:16-23. doi:10.1016/j.jmbbm.2013.02.010
  20. ↑ Yang B, Tse K, Chen N, et al. Development of a finite element head model for the study of impact head injury. Biomed Res Int. 2014;2014:1-14. doi:10.1155/2014/408278
  21. ↑ Jump up to: 21.0 21.1 21.2 Li X, Sandler H, Kleiven S. Infant skull fractures: Accident or abuse? Forensic Sci Int. 2018;294:173-182. doi:10.1016/j.forsciint.2018.11.008
  22. ↑ King WJ, MacKay M, Sirnick A, The Canadian Shaken Baby Study Group. Shaken baby syndrome in Canada: Clinical characteristics and outcomes of hospital cases. CMAJ. 2003;168(2):155-159.
  23. ↑ Dixit P, Liu GR. A review on recent development of finite element models for head injury simulations. Arch Comput Methods Eng. 2017;24(4):979-1031. doi:10.1007/s11831-016-9196-x
  24. ↑ Perkins RA, Bakhtiarydavijani A, Ivanoff AE, et al. Assessment of brain injury biomechanics in soccer heading using finite element analysis. Brain Multiphysics. 2022;3:100052. doi:10.1016/j.brain.2022.100052
  25. ↑ Jump up to: 25.0 25.1 Panzer MB, Myers BS, Capehart BP, Bass CR. Development of a finite element model for blast brain injury and the effects of CSF cavitation. Ann Biomed Eng. 2012;40(7):1530-1544. doi:10.1007/s10439-012-0519-2
  26. ↑ Ruan JS, Khalil TB, King AI. Finite element modeling of direct head impact. SAE Tech Pap Ser. 1993. doi:10.4271/933114
  27. ↑ Willinger R, Kang H-S, Diaw B. Three-dimensional human head finite-element model validation against two experimental impacts. Ann Biomed Eng. 1999;27(3):403-410. doi:10.1114/1.165
  28. ↑ Huiskes R. Some fundamental aspects of human joint replacement: Analyses of stresses and heat conduction in bone-prosthesis structures. Acta Orthop Scand. 1980;51(suppl 185):3-208. doi:10.3109/ort.1980.51.suppl-185.01
  29. ↑ DeWit JA, Cronin DS. Cervical spine segment finite element model for traumatic injury prediction. J Mech Behav Biomed Mater. 2012;10:138-150. doi:10.1016/j.jmbbm.2012.02.015
  30. ↑ Barbarino GG, Jabareen M, Mazza E, Hurschler C, Taylor Z. Mechanical characterization of soft tissues for the development of synthetic facial skins. Skin Res Technol. 2009;15(1):77-89. doi:10.1111/j.1600-0846.2008.00332.x


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