Many human brain finite element (FE) models lack mesoscopic (~ 1 mm) white matter structures, which may limit their capability in predicting TBI and assessing tissue-based injury metrics such as axonal strain. This study investigated an embedded method to explicitly incorporate white matter axonal fibers into an existing 50th percentile male brain model. The white matter was decomposed into myelinated axon tracts and an isotropic ground substance that had similar material properties to gray matter. The axon tract bundles were derived from a population-based tractography template explicitly modeled using 1-D cable elements. The axonal fibers and ground substance material were implemented using hyper-viscoelastic constitutive models, which were calibrated using white and gray matter brain tissue material testing data available in the literature. Finally, the new axon-based model was extensively validated for brain-skull relative deformation under various loading conditions (n = 17) and showed good biofidelity compared to other brain models. Through these analyses, we demonstrated the applicability of this method for incorporating axonal fiber tracts into an existing FE brain model. The axon-based model will be a useful tool for understanding the mechanisms of TBI, evaluating tissue-based injury metrics, and developing injury mitigation systems.
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Alshareef, A., J. S. Giudice, J. Forman, R. S. Salzar, and M. B. Panzer. A novel method for quantifying human in situ whole brain deformation under rotational loading using sonomicrometry. J. Neurotrauma 35:780–789, 2017.
Arbogast, K. B., and S. S. Margulies. Regional differences in mechanical properties of the porcine central nervous system. SAE Technical Paper, 1997.
Bermejo, M., A. P. Santos, and J. M. Goicolea. Development of practical finite element models for collapse of reinforced concrete structures and experimental validation. Shock Vib. 2017. https://doi.org/10.1155/2017/4636381.
Besl, P. J., and N. D. McKay. Method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Intell. 14(2):239–256, 1992.
Bilston, L. E., Z. Liu, and N. Phan-Thien. Large strain behaviour of brain tissue in shear: some experimental data and differential constitutive model. Biorheology 38:335–345, 2001.
Brands, D. W., P. H. Bovendeerd, G. W. Peters, J. S. Wismans, M. H. Paas, and J. L. van Bree. Comparison of the dynamic behavior of brain tissue and two model materials. SAE Technical Paper, 1999.
Bryan, R., P. S. Mohan, A. Hopkins, F. Galloway, M. Taylor, and P. B. Nair. Statistical modelling of the whole human femur incorporating geometric and material properties. Med. Eng. Phys. 32:57–65, 2010.
Budday, S., R. Nay, R. de Rooij, P. Steinmann, T. Wyrobek, T. C. Ovaert, and E. Kuhl. Mechanical properties of gray and white matter brain tissue by indentation. J. Mech. Behav. Biomed. Mater. 46:318–330, 2015.
Budday, S., G. Sommer, C. Birkl, C. Langkammer, J. Haybaeck, J. Kohnert, M. Bauer, F. Paulsen, P. Steinmann, E. Kuhl, et al. Mechanical characterization of human brain tissue. Acta Biomater. 48:319–340, 2017.
Centers for Disease Control and Prevention. Report to congress on traumatic brain injury in the United States: epidemiology and rehabilitation, 2015.
Chatelin, S., A. Constantinesco, and R. Willinger. Fifty years of brain tissue mechanical testing: from in vitro to in vivo investigations. Biorheology 47:255–276, 2010.
Chatelin, S., C. Deck, and R. Willinger. An anisotropic viscous hyperelastic constitutive law for brain material finite-element modeling. J. Biorheol. 27:26–37, 2013.
Cloots, R. J., J. Van Dommelen, S. Kleiven, and M. Geers. Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads. Biomech. Model. Mechanobiol. 12:137–150, 2013.
Davis, M. L., B. Koya, J. M. Schap, and F. S. Gayzik. Development and full body validation of a 5th percentile female finite element model. SAE Technical Paper, 2016.
Feng, Y., R. J. Okamoto, R. Namani, G. M. Genin, and P. V. Bayly. Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter. J. Mech. Behav. Biomed. Mater. 23:117–132, 2013.
Fish, J. The s-version of the finite element method. Comput. Struct. 43:539–547, 1992.
Fung, Y. Biomechanics: mechanical properties of living tissues. Berlin: Springer Science & Business Media, 2013.
Gabler, L. F., J. R. Crandall, and M. B. Panzer. Assessment of kinematic brain injury metrics for predicting strain responses in diverse automotive impact conditions. Ann. Biomed. Eng. 44(12):3705–3718, 2016.
Gabler, L. F., J. R. Crandall, and M. B. Panzer. Development of a metric for predicting brain strain responses using head kinematics. Ann. Biomed. Eng. 46(7):972–985, 2018.
Gabler, L. F., H. Joodaki, J. R. Crandall, and M. B. Panzer. Development of a single-degree-of-freedom mechanical model for predicting strain-based brain injury responses. J. Biomech. Eng. 140:031002, 2018.
Ganpule, S., N. P. Daphalapurkar, K. T. Ramesh, A. K. Knutsen, D. L. Pham, P. V. Bayly, and J. L. Prince. A three-dimensional computational human head model that captures live human brain dynamics. J. Neurotrauma 34:2154–2166, 2017.
Garimella, H. T., and R. H. Kraft. Modeling the mechanics of axonal fiber tracts using the embedded finite element method. Int. J. Numer. Methods Biomed. Eng. 33:e2823, 2017.
Garo, A., M. Hrapko, J. Van Dommelen, and G. Peters. Towards a reliable characterisation of the mechanical behaviour of brain tissue: the effects of post-mortem time and sample preparation. Biorheology 44:51–58, 2007.
Gasser, T. C., R. W. Ogden, and G. A. Holzapfel. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3:15–35, 2006.
Gehre, C., H. Gades, and P. Wernicke. Objective rating of signals using test and simulation responses. Washington, DC: National Highway Traffic Safety Administration, 2009.
Gennarelli, T. A., L. Thibault, and A. K. Ommaya. Pathophysiologic responses to rotational and translational accelerations of the head. SAE Technical Paper, 1972.
Giordano, C., and S. Kleiven. Evaluation of axonal strain as a predictor for mild traumatic brain injuries using finite element modeling. SAE Technical Paper, 2014.
Giordano, C., and S. Kleiven. Connecting fractional anisotropy from medical images with mechanical anisotropy of a hyperviscoelastic fibre-reinforced constitutive model for brain tissue. J. R. Soc. Interface 11:20130914, 2014.
Giudice, J. S., W. Zeng, T. Wu, A. Alshareef, D. F. Shedd, and M. B. Panzer. An analytical review of the numerical methods used for finite element modeling of traumatic brain injury. Biomed. Eng Ann 2018. https://doi.org/10.1007/s10439-018-02161-5.
Golman, A., A. Wickwire, T. Harrigan, A. Iwaskiw, R. Armiger, and A. Merkle. Hierarchical model validation of the falx cerebri and tentorium cerebelli. In: Proceedings of the forty first international workshop (2013).
Hardy, W. N., C. D. Foster, M. J. Mason, K. H. Yang, A. I. King, and S. Tashman. Investigation of head injury mechanisms using neutral density technology and high-speed biplanar X-ray. SAE Technical Paper, 2001.
Hardy, W. N., M. J. Mason, C. D. Foster, C. S. Shah, J. M. Kopacz, K. H. Yang, A. I. King, J. Bishop, M. Bey, W. Anderst, and S. Tashman. A study of the response of the human cadaver head to impact. Stapp Car Crash J. 51:17–80, 2007.
Holzapfel, G. A., and R. W. Ogden. On the tension–compression switch in soft fibrous solids. Eur. J. Mech. - ASolids 49:561–569, 2015.
Holzapfel, G. A., and R. W. Ogden. On fiber dispersion models: exclusion of compressed fibers and spurious model comparisons. J. Elast. 129:49–68, 2017.
Hrapko, M., J. Van Dommelen, G. Peters, and J. Wismans. The mechanical behaviour of brain tissue: large strain response and constitutive modelling. Biorheology 43:623–636, 2006.
Jin, X., J. B. Lee, L. Y. Leung, L. Zhang, K. H. Yang, and A. I. King. Biomechanical Response of the Bovine Pia-Arachnoid Complex to Tensile Loading at Varying Strain Rates. SAE Technical Paper, 2006.
Jin, X., F. Zhu, H. Mao, M. Shen, and K. H. Yang. A comprehensive experimental study on material properties of human brain tissue. J. Biomech. 46:2795–2801, 2013.
Johnson, C. L., M. D. McGarry, A. A. Gharibans, J. B. Weaver, K. D. Paulsen, H. Wang, W. C. Olivero, B. P. Sutton, and J. G. Georgiadis. Local mechanical properties of white matter structures in the human brain. Neuroimage 79:145–152, 2013.
Jones, D. K., T. R. Knösche, and R. Turner. White matter integrity, fiber count, and other fallacies: the do’s and don’ts of diffusion MRI. Neuroimage 73:239–254, 2013.
Kleiven, S., and W. N. Hardy. Correlation of an FE model of the human head with local brain motion: Consequences for injury prediction. Stapp Car Crash J. 46:123–144, 2002.
Latorre, M., and F. J. Montáns. Stress and strain mapping tensors and general work-conjugacy in large strain continuum mechanics. Appl. Math. Model. 40:3938–3950, 2016.
Lippert, S. A., E. M. Rang, and M. J. Grimm. The high frequency properties of brain tissue. Biorheology 41:681–691, 2004.
Maier-Hein, K., P. Neher, J.-C. Houde, M.-A. Cote, E. Garyfallidis, J. Zhong, M. Chamberland, F.-C. Yeh, Y. C. Lin, Q. Ji, et al. The challenge of mapping the human connectome based on diffusion tractography. Nat Commun. 8(1):1349, 2017.
Mao, H., L. Zhang, B. Jiang, V. V. Genthikatti, X. Jin, F. Zhu, R. Makwana, A. Gill, G. Jandir, A. Singh, and K. H. Yang. Development of a finite element human head model partially validated with thirty five experimental cases. J. Biomech. Eng. 135:111002, 2013.
Meaney, D. F., and D. H. Smith. Biomechanics of concussion. Clin. Sports Med. 30:19–31, 2011.
Miller, L. E., J. E. Urban, and J. D. Stitzel. Development and validation of an atlas-based finite element brain model. Biomech. Model. Mechanobiol. 15:1201–1214, 2016.
Nicolle, S., M. Lounis, and R. Willinger. Shear properties of brain tissue over a frequency range relevant for automotive impact situations: new experimental results. SAE Technical Paper, 2004.
Nilsson, M., J. Lätt, F. St\a ahlberg, D. van Westen, and H. akan Hagslätt. The importance of axonal undulation in diffusion MR measurements: a Monte Carlo simulation study. NMR Biomed. 25:795–805, 2012.
Ning, X., Q. Zhu, Y. Lanir, and S. S. Margulies. A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. J. Biomech. Eng. 128:925–933, 2006.
Park, G., T. Kim, J. Forman, M. B. Panzer, and J. R. Crandall. Prediction of the structural response of the femoral shaft under dynamic loading using subject-specific finite element models. Comput. Methods Biomech. Biomed. Engin. 20:1151–1166, 2017.
Pervin, F., and W. W. Chen. Dynamic mechanical response of bovine gray matter and white matter brain tissues under compression. J. Biomech. 42:731–735, 2009.
Peters, G., J. Meulman, and A. Sauren. The applicability of the time/temperature superposition principle to brain tissue. Biorheology 34:127–138, 1997.
Prange, M. T., and S. S. Margulies. Regional, directional, and age-dependent properties of the brain undergoing large deformation. J. Biomech. Eng. 124:244–252, 2002.
Sahoo, D., C. Deck, and R. Willinger. Development and validation of an advanced anisotropic visco-hyperelastic human brain FE model. J. Mech. Behav. Biomed. Mater. 33:24–42, 2014.
Sahoo, D., C. Deck, and R. Willinger. Brain injury tolerance limit based on computation of axonal strain. Accid. Anal. Prev. 92:53–70, 2016.
Sanchez, E. J., L. F. Gabler, A. B. Good, J. R. Funk, J. R. Crandall, and M. B. Panzer. A reanalysis of football impact reconstructions for head kinematics and finite element modeling. Clin: Biomech, 2018. https://doi.org/10.1016/j.clinbiomech.2018.02.019.
Sanchez, E. J., L. F. Gabler, J. S. McGhee, A. V. Olszko, V. C. Chancey, J. R. Crandall, and M. B. Panzer. Evaluation of head and brain injury risk functions using sub-injurious human volunteer data. J. Neurotrauma 34:2410–2424, 2017.
Shen, F., T. Tay, J. Li, S. Nigen, P. Lee, and H. Chan. Modified Bilston nonlinear viscoelastic model for finite element head injury studies. J. Biomech. Eng. 128:797–801, 2006.
Tabatabaei, S., and S. V. Lomov. Eliminating the volume redundancy of embedded elements and yarn interpenetrations in meso-finite element modelling of textile composites. Comput. Struct. 152:142–154, 2015.
Takhounts, E.G., S.A. Ridella, V. Hasija, R.E. Tannous, J.Q. Campbell, D. Malone, K. Danelson, J.Stitzel, S. Rowson, and S. Duma. Investigation of traumatic brain injuries using the next generation of simulated injury monitor (SIMon) finite element head model. SAE Technical Paper, 2008.
Thibault, K. L., and S. S. Margulies. Age-dependent material properties of the porcine cerebrum: effect on pediatric inertial head injury criteria. J. Biomech. 31:1119–1126, 1998.
Velardi, F., F. Fraternali, and M. Angelillo. Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomech. Model. Mechanobiol. 5:53–61, 2006.
Wright, R. M., A. Post, B. Hoshizaki, and K. T. Ramesh. A multiscale computational approach to estimating axonal damage under inertial loading of the head. J. Neurotrauma 30(2):102–118, 2013.
Yeh, F.-C., S. Panesar, D. Fernandes, A. Meola, M. Yoshino, J. C. Fernandez-Miranda, J. M. Vettel, and T. Verstynen. Population-averaged atlas of the macroscale human structural connectome and its network topology. NeuroImage 178:57–68, 2018.
Zhao, W., B. Choate, and S. Ji. Material properties of the brain in injury-relevant conditions–Experiments and computational modeling. J. Mech. Behav. Biomed. Mater. 80:222–234, 2018.
Zhao, W., and S. Ji. White matter anisotropy for impact simulation and response sampling in traumatic brain injury. J. Neurotrauma 36(2):250–263, 2018.
Diffusion MRI data were provided in part by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. The research presented in this paper was made possible in part by a grant from Football Research, Inc. (FRI). The views expressed are solely those of the authors and do not represent those of FRI or any of its affiliates or funding sources.
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Wu, T., Alshareef, A., Giudice, J.S. et al. Explicit Modeling of White Matter Axonal Fiber Tracts in a Finite Element Brain Model. Ann Biomed Eng 47, 1908–1922 (2019). https://doi.org/10.1007/s10439-019-02239-8