Abstract
Recent mouse brain injury experiments examine diffuse axonal injury resulting from accelerative head rotations. Evaluating brain deformation during these events would provide valuable information on tissue level thresholds for brain injury, but there are many challenges to imaging the brain’s mechanical response during dynamic loading events, such as a blunt head impact. To address this shortcoming, we present an experimentally validated computational biomechanics model of the mouse brain that predicts tissue deformation, given the motion of the mouse head during laboratory experiments. First, we developed a finite element model of the mouse brain that computes tissue strains, given the same head rotations as previously conducted in situ hemicephalic mouse brain experiments. Second, we calibrated the model using a single brain segment, and then validated the model based on the spatial and temporal strain responses of other regions. The result is a computational tool that will provide researchers with the ability to predict brain tissue strains that occur during mouse laboratory experiments, and to link the experiments to the resulting neuropathology, such as diffuse axonal injury.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- MPS:
-
Maximum principal strain
- \(E_{xx}\) :
-
Normal strain in the X direction
- \(E_{yy}\) :
-
Normal strain in the Y direction
- \(E_{xy}\) :
-
Shear strain in the X–Y direction
- \({\mathbf{E}}\) :
-
Green–Lagrange strain tensor
References
Aggarwal M, Zhang J, Miller MI et al (2009) Magnetic resonance imaging and micro-computed tomography combined atlas of developing and adult mouse brains for stereotaxic surgery. Neuroscience 162:1339–1350. https://doi.org/10.1016/j.neuroscience.2009.05.070
Alshareef A, Wu T, Giudice JS, Panzer MB (2021) Toward subject-specific evaluation: methods of evaluating finite element brain models using experimental high-rate rotational brain motion. Biomech Model Mechanobiol 20:2301–2317. https://doi.org/10.1007/s10237-021-01508-7
Bernal R, Pullarkat PA, Melo F (2007) Mechanical properties of axons. Phys Rev Lett 99:6–9. https://doi.org/10.1103/PhysRevLett.99.018301
Bigot M, Chauveau F, Beuf O, Lambert SA (2018) Magnetic resonance elastography of rodent brain. Front Neurol 9:1–8. https://doi.org/10.3389/fneur.2018.01010
Bradfield C, Voo L, Drewry D et al (2023) Dynamic strain fields of the mouse brain during rotation. Biomech Model Mechanobiol. https://doi.org/10.1007/s10237-023-01781-8
Budday S, Sommer G, Holzapfel GA et al (2017) Viscoelastic parameter identification of human brain tissue. J Mech Behav Biomed Mater 74:463–476. https://doi.org/10.1016/j.jmbbm.2017.07.014
Burcaw LM, Fieremans E, Novikov DS (2015) Mesoscopic structure of neuronal tracts from time-dependent diffusion. Neuroimage 114:18–37. https://doi.org/10.1016/j.neuroimage.2015.03.061
Caeyenberghs K, Leemans A, Geurts M et al (2011) Correlations between white matter integrity and motor function in traumatic brain injury patients. Neurorehabil Neural Repair 25:492–502. https://doi.org/10.1177/1545968310394870
Chen YC, Mao H, Yang KH et al (2014) A modified controlled cortical impact technique to model mild traumatic brain injury mechanics in mice. Front Neurol 5:1–14. https://doi.org/10.3389/fneur.2014.00100
Dennerll TJ, Joshi HC, Steel VL et al (1988) Tension and compression in the cytoskeleton of PC-12 neurites II: quantitative measurements. J Cell Biol 107:665–674. https://doi.org/10.1083/jcb.107.2.665
Ekmark-Lewén S, Flygt J, Kiwanuka O et al (2013) Traumatic axonal injury in the mouse is accompanied by a dynamic inflammatory response, astroglial reactivity and complex behavioral changes. J Neuroinflammation 10:1–19. https://doi.org/10.1186/1742-2094-10-44
Field D, Ammouche Y, Peña JM, Jérusalem A (2021) Machine learning based multiscale calibration of mesoscopic constitutive models for composite materials: application to brain white matter. Comput Mech 67:1629–1643. https://doi.org/10.1007/s00466-021-02009-1
Fijalkowski RJ, Yoganandan N, Zhang J, Pintar FA (2009) A finite element model of region-specific response for mild diffuse brain injury. SAE Tech Pap 2009-Novem, pp 193–213. https://doi.org/10.4271/2009-22-0007
Ganpule S, Daphalapurkar NP, Ramesh KT et al (2017) A three-dimensional computational human head model that captures live human brain dynamics. J Neurotrauma 34:2154–2166. https://doi.org/10.1089/neu.2016.4744
Garimella HT, Kraft RH (2017) Modeling the mechanics of axonal fiber tracts using the embedded finite element method. Int J Numer Method Biomed Eng 33:26–35. https://doi.org/10.1002/cnm.2823
Gefen A, Gefen N, Zhu Q et al (2003) Age-dependent changes in material properties of the brain and braincase of the rat. J Neurotrauma 20:1163–1177. https://doi.org/10.1089/089771503770802853
Gehre C, Gades H, Wernicke P (2009) Objective rating of signals using test and simulation responses. In: Proceedings of the 21ST international technical conference, Stuttgart, Germany, pp 1–8
Giordano C, Kleiven S (2014a) Connecting fractional anisotropy from medical images with mechanical anisotropy of a hyperviscoelastic fibre-reinforced constitutive model for brain tissue. J R Soc Interface. https://doi.org/10.1098/rsif.2013.0914
Giordano C, Kleiven S (2014b) Evaluation of axonal strain as a predictor for mild traumatic brain injuries using finite element modeling. Stapp Car Crash J 58:29–61. https://doi.org/10.4271/2014-22-0002
Jean A, Nyein MK, Zheng JQ et al (2014) An animal-to-human scaling law for blast-induced traumatic brain injury risk assessment. Proc Natl Acad Sci U S A 111:15310–15315. https://doi.org/10.1073/pnas.1415743111
Ji S, Zhao W, Ford JC et al (2015) Group-wise evaluation and comparison of white matter fiber strain and maximum principal strain in sports-related concussion. J Neurotrauma 32:441–454. https://doi.org/10.1089/neu.2013.3268
Kim JH, Song SK (2013) Diffusion tensor imaging of the mouse brainstem and cervical spinal cord. Nat Protoc 8:409–417. https://doi.org/10.1038/nprot.2013.012
Kimpara H, Iwamoto M (2012) Mild traumatic brain injury predictors based on angular accelerations during impacts. Ann Biomed Eng 40:114–126. https://doi.org/10.1007/s10439-011-0414-2
Kleiven S (2007) Predictors for traumatic brain injuries evaluated through accident reconstructions. Stapp Car Crash J 51:81–114. https://doi.org/10.4271/2007-22-0003
Kleiven S (2013) Why most traumatic brain injuries are not caused by linear acceleration but skull fractures are. Front Bioeng Biotechnol 1:1–5. https://doi.org/10.3389/fbioe.2013.00015
Knutsen AK, Gomez AD, Gangolli M et al (2020) In vivo estimates of axonal stretch and 3D brain deformation during mild head impact. Brain Multiphys 1:100015. https://doi.org/10.1016/j.brain.2020.100015
Kraft RH, Mckee PJ, Dagro AM, Grafton ST (2012) Combining the Finite element method with structural connectome-based analysis for modeling neurotrauma: connectome neurotrauma mechanics. PLoS Comput Biol. https://doi.org/10.1371/journal.pcbi.1002619
Kroon D-J (2008) DTI and fiber tracking. In: MATLAB Cent. File Exch. http://www.mathworks.com/matlabcentral/fileexchange/21130-dti-and-fiber-tracking/content/fspecial3.m. Accessed 7 Aug 2015
Lamy M, Baumgartner D, Willinger R et al (2011) Study of mild traumatic brain injuries using experiments and finite element modeling. Ann Adv Automot Med 55:125–135
Lamy M, Baumgartner D, Yoganandan N et al (2013) Experimentally validated three-dimensional finite element model of the rat for mild traumatic brain injury. Med Biol Eng Comput 51:353–365. https://doi.org/10.1007/s11517-012-1004-7
Li X, Zhou Z, Kleiven S (2021) An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain. Biomech Model Mechanobiol 20:403–431. https://doi.org/10.1007/s10237-020-01391-8
Lu L (2019) Biomechanical analysis of open-skull high-rate traumatic brain injury using finite element mouse brain model. Western University, New York
Lu L, Dao M, Kumar P et al (2020) Extraction of mechanical properties of materials through deep learning from instrumented indentation. Proc Natl Acad Sci USA 117:7052–7062. https://doi.org/10.1073/pnas.1922210117
Macmanus DB, Pierrat B, Murphy JG, Gilchrist MD (2016) Mechanical characterization of the P56 mouse brain under large-deformation dynamic indentation. Sci Rep 6:1–9. https://doi.org/10.1038/srep21569
MacManus DB, Pierrat B, Murphy JG, Gilchrist MD (2017) A viscoelastic analysis of the P56 mouse brain under large-deformation dynamic indentation. Acta Biomater 48:309–318. https://doi.org/10.1016/j.actbio.2016.10.029
Mao H, Jin X, Zhang L et al (2010) Finite element analysis of controlled cortical impact-induced cell loss. J Neurotrauma 27:877–888. https://doi.org/10.1089/neu.2008.0616
Matousek J (1998) On the L2-discrepancy for anchored boxes. J Complex 14:527–556
Medana IM, Esiri MM (2003) Axonal damage: a key predictor of outcome in human CNS diseases. Brain 126:515–530. https://doi.org/10.1093/brain/awg061
Miller LE, Urban JE, Stitzel JD (2016) Development and validation of an atlas-based finite element brain model. Biomech Model Mechanobiol 15:1201–1214. https://doi.org/10.1007/s10237-015-0754-1
Miller LE, Urban JE, Stitzel JD (2017) Validation performance comparison for finite element models of the human brain. Comput Methods Biomech Biomed Eng 20:1273–1288. https://doi.org/10.1080/10255842.2017.1340462
Montanino A, Kleiven S (2018) Utilizing a structural mechanics approach to assess the primary effects of injury loads onto the axon and its components. Front Neurol 9:1–12. https://doi.org/10.3389/fneur.2018.00643
Namjoshi DR, Cheng WH, McInnes KA et al (2014) Merging pathology with biomechanics using CHIMERA (closed-head impact model of engineered rotational acceleration): a novel, surgery-free model of traumatic brain injury. Mol Neurodegener 9:218–252
Namjoshi DR, Cheng WH, Bashir A et al (2017) Defining the biomechanical and biological threshold of murine mild traumatic brain injury using CHIMERA (Closed Head Impact Model of Engineered Rotational Acceleration). Exp Neurol 292:80–91. https://doi.org/10.1016/j.expneurol.2017.03.003
Ng LJ, Volman V, Gibbons MM et al (2017) A mechanistic end-to-end concussion model that translates head kinematics to neurologic injury. Front Neurol 8:1–18. https://doi.org/10.3389/fneur.2017.00269
Ogden RW (1973) Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Rubber Chem Technol 46:398–416. https://doi.org/10.5254/1.3542910
Pleasant JM, Carlson SW, Mao H et al (2011) Rate of neurodegeneration in the mouse controlled cortical impact model is influenced by impactor tip shape: implications for mechanistic and therapeutic studies. J Neurotrauma 28:2245–2262. https://doi.org/10.1089/neu.2010.1499
Prange MT, Margulies SS (2002) Regional, directional, and age-dependent properties of the brain undergoing large deformation. J Biomech Eng 124:244–252. https://doi.org/10.1115/1.1449907
Rajagopalan J, Tofangchi A, Saif MTA (2010) Drosophila neurons actively regulate axonal tension in vivo. Biophys J 99:3208–3215. https://doi.org/10.1016/j.bpj.2010.09.029
Sabet AA, Christoforou E, Zatlin B et al (2007) Deformation of the human brain induced by mild angular acceleration. J Biomech 41:863–864. https://doi.org/10.1016/j.jbiomech.2007.09.016
Sahoo D, Deck C, Willinger R (2016) Brain injury tolerance limit based on computation of axonal strain. Accid Anal Prev 92:53–70. https://doi.org/10.1016/j.aap.2016.03.013
Sardinha DS, Vieira RDCA, Paiva WS et al (2019) Behavioral changes and associated factors after diffuse axonal injury. J Trauma Nurs 26:328–339. https://doi.org/10.1097/JTN.0000000000000471
Sauerbeck AD, Fanizzi C, Kim JH et al (2018) ModCHIMERA: a novel murine closed-head model of moderate traumatic brain injury. Sci Rep 8:1–17. https://doi.org/10.1038/s41598-018-25737-6
Scott GG, Margulies SS, Coats B (2016) Utilizing multiple scale models to improve predictions of extra-axial hemorrhage in the immature piglet. Biomech Model Mechanobiol 15:1101–1119. https://doi.org/10.1007/s10237-015-0747-0
Sepehrband F, Clark KA, Ullmann JFP et al (2015) Brain tissue compartment density estimated using diffusion-weighted MRI yields tissue parameters consistent with histology. Hum Brain Mapp 36:3687–3702. https://doi.org/10.1002/hbm.22872
Sobol IM (1976) Uniformly distributed sequences with an additional uniform property. USSR Comput Math Math Phys 16:1332–1337
Stolp HB, Ball G, So PW et al (2018) Voxel-wise comparisons of cellular microstructure and diffusion-MRI in mouse hippocampus using 3D bridging of optically-clear histology with neuroimaging data (3D-BOND). Sci Rep 8:1–12. https://doi.org/10.1038/s41598-018-22295-9
Sullivan S, Eucker SA, Gabrieli D et al (2015) White matter tract-oriented deformation predicts traumatic axonal brain injury and reveals rotational direction-specific vulnerabilities. Biomech Model Mechanobiol 14:877–896. https://doi.org/10.1007/s10237-014-0643-z
Unnikrishnan G, Mao H, Sundaramurthy A et al (2019) A 3-D rat brain model for blast-wave exposure: effects of brain vasculature and material properties. Ann Biomed Eng. https://doi.org/10.1007/s10439-019-02277-2
Upadhyay K, Alshareef A, Knutsen AK et al (2022) Development and validation of subject-specific 3D human head models based on a nonlinear visco-hyperelastic constitutive framework. J R Soc Interface. https://doi.org/10.1098/rsif.2022.0561
Wang G, Zhang YP, Gao Z et al (2018) Pathophysiological and behavioral deficits in developing mice following rotational acceleration-deceleration traumatic brain injury. DMM Dis Model Mech. https://doi.org/10.1242/dmm.030387
Wittek A, Omori K (2003) Parametric study of effects of brain-skull boundary conditions and brain material.pdf. LSME Int J 46:1388–1399
Wright RM, Post A, Hoshizaki B, Ramesh KT (2013) A multiscale computational approach to estimating axonal damage under inertial loading of the head. J Neurotrauma 30:102–118. https://doi.org/10.1089/neu.2012.2418
Wu T, Alshareef A, Giudice JS, Panzer MB (2019a) Explicit modeling of white matter axonal fiber tracts in a finite element brain model. Ann Biomed Eng 47:1908–1922. https://doi.org/10.1007/s10439-019-02239-8
Wu T, Antona-Makoshi J, Alshareef A et al (2019b) Investigation of cross-species scaling methods for traumatic brain injury using finite element analysis. J Neurotrauma 13:1–13. https://doi.org/10.1089/neu.2019.6576
Xiong Y, Mahmood A, Chopp M (2016) Animal models of traumatic brain injury. Nat Rev Neurosci 14:3951995. https://doi.org/10.1038/nrn3407
Yousefsani SA, Farahmand F, Shamloo A (2018) A three-dimensional micromechanical model of brain white matter with histology-informed probabilistic distribution of axonal fibers. J Mech Behav Biomed Mater 88:288–295. https://doi.org/10.1016/j.jmbbm.2018.08.042
Zhou Z, Li X, Kleiven S, Hardy WN (2019) Brain strain from motion of sparse markers. Stapp Car Crash J 63:1–27. https://doi.org/10.4271/2019-22-0001
Zhou Z, Li X, Kleiven S (2020) Evaluation of brain-skull interface modelling approaches on the prediction of acute subdural hematoma in the elderly. J Biomech 105:109787. https://doi.org/10.1016/j.jbiomech.2020.109787
Acknowledgements
We gratefully thank Dr. Susumu Mori at the Johns Hopkins University School of Medicine for providing the mouse brain imaging data (accessed through https://cmrm.med.jhmi.edu/) used for the geometric basis of our finite element model.
Funding
This work was supported in part by the National Health Mission Area of Johns Hopkins University Applied Physics Laboratory and the US National Institute of Neurological Disorder and Stroke (NIH Grant NS05595).
Author information
Authors and Affiliations
Contributions
CB contributed to conceptualization, methodology; formal analysis, investigation, visualization, and writing, (original draft), LV was involved in supervision and writing (original draft), AB contributed to conceptualization, methodology, and formal analysis, and writing (original draft), and KTR contributed to supervision and writing (original draft).
Corresponding author
Ethics declarations
Conflict of interest
Authors have no conflicts of interest to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Bradfield, C., Voo, L., Bhaduri, A. et al. Validation of a computational biomechanical mouse brain model for rotational head acceleration. Biomech Model Mechanobiol 23, 1347–1367 (2024). https://doi.org/10.1007/s10237-024-01843-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-024-01843-5