Numerical simulation of a neuron under blast load using viscoelastic material models

Document Type : Article


1 Department of Aerospace Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

2 Division of Biomedical Engineering, Department of Life Science Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran


Traumatic brain injury is caused by physical brain injury. A computational model for considering the response of a neuronal cell under blast loading is presented. The neuronal cell consists of four components including the nucleus, cytoplasm, membrane, and also the network of microtubules with different arrays including crossing, stellate as well as random orientations. The effect of the sub-cellular components, specifically the network of microtubules, on a Traumatic Brain Injury’s consequences was studied as a novel and state-of-the-art innovation. Nucleus, cytoplasm, and membrane are assumed viscoelastic, while the network of microtubules follows elastic behavior. Finite element methods and fluid-structure interactions are considered to solve the coupled equations of the solid and the fluid. The results show that the presence of a network of microtubules, regardless of the types of arrays, reduces the total displacement of the cell as well as the von Mises stress. The membrane von Mises stress decreases 50 percent from 30 to 15 Pascal in presence of the network of the microtubules. Results of this research could be used in different fields including treatment of some diseases and pathological conditions such as kidney stones, sports injuries, traumatic astronauts, and ultimately prevention and treatment of traumatic brain injuries.


1. Bernick, K.B. "Cell biomechanics of the central nervous system", Thesis, Massachusetts Institute of Technology, USA (2011).
2. Jerusalem, A. and Dao, M. "Continuum modeling of a neuronal cell under blast loading", Acta Biomater., 8(9), pp. 3360-3371 (2012).
3. Edwards, D.S. and Clasper, J. "Blast injury mechanism", In Blast Injury Science and Engineering, pp. 87-104, Springer (2016).
4. Bernick, K.B., Prevost, T.P., Suresh, S., et al.  Biomechanics of single cortical neurons", Acta Biomater., 7(3), pp. 1210-1219 (2011).
5. Eslaminejad, A., Farid, M.H., Ziejewski, M., et al. "Brain tissue constitutive material models and the finite element analysis of blast-induced traumatic brain injury", Sci. Iran., 25, pp. 3141-3150 (2018).
6. Shams, S., Haddadpour, H., Tuzandejani, H., et al. "Impact crushing behavior of foam-filled paraboloid shells using numerical and experimental methods", Sci. Iran., Trans B, 24(4), pp. 1912-1921 (2017).
7. Ganpule, S., Alai, A., Plougonven, E., et al. "Mechanics of blast loading on the head models in the study of traumatic brain injury using experimental and computational approaches", Biomech. Model Mechan., 12(3), pp. 511-531 (2013).
8. Laksari, K., Assari, S., Seibold, B., et al. "Computational simulation of the mechanical response of brain tissue under blast loading", Biomech. Model Mechan., 14(3), pp. 459-472 (2015).
9. Laksari, K., Sadeghipour, K., and Darvish, K. "Mechanical response of brain tissue under blast loading", J. Mech. Behav. Biomed. Mater., 32, pp. 132-144 (2014).
10. Taylor, P.A., Ludwigsen, J.S., and Ford, C.C. "Investigation of blast-induced traumatic brain injury", Brain Inj., 28(7), pp. 879-895 (2014).
11. Teferra, K., Tan, X.G., Iliopoulos, A., et al. "Effect of human head morphological variability on the mechanical response of blast overpressure loading", Int. J. Numer. Meth. Bio., 34(9), p. e3109 (2018).
12. Ganpule, S., Daphalapurkar, N., Cetingul, M., et al. "Effect of bulk modulus on deformation of the brain under rotational accelerations", Shock Waves, 28(1), pp. 127-139 (2018).
13. Tan, X., Przekwas, A., and Gupta, R. "Computational modeling of blast wave interaction with a human body and assessment of traumatic brain injury", Shock Waves, 27(6), pp. 889-904 (2017).
14. Rodriguez-Millan, M., Tan, L. , Tse, K., et al. "Effect of full helmet systems on human head responses under blast loading", Mater. Design, 117, pp. 58-71 (2017).
15. Finan, J.D. "Biomechanical simulation of traumatic brain injury in the rat", Clin. Biomech., 64, pp. 114- 121 (2019).
16. Palombo, M., Alexander, D.C., and Zhang, H. "A generative model of realistic brain cells with application to numerical simulation of the diffusion-weighted MR signal", NeuroImage, 188, pp. 391-402 (2019).
17. Lu, Y.C., Daphalapurkar, N.P., Knutsen, A.K., et al. "A 3D computational head model under dynamic head rotation and head extension validated using live human brain data, including the falx and the tentorium", Ann. Biomed. Eng., 47(9), pp. 1923-1940 (2019).
18. Ahmadi-Nejad Joushani, H., Vahidi, B., and Sabour, M.H. "Investigating the effects of microtubules in the neuronal cell response to the blast load using  fluidstructure interactions method", Journal of Solid and Fluid Mechanics, 9(3), pp. 13-24 (2019) (in Persian).
19. Sonden, A., Svensson, B., Roman, N., et al. "Laserinduced shock wave endothelial cell injury", Laser Surg. Med., 26(4), pp. 364-375 (2000).
20. Jean, R.P., Chen, C.S., and Spector, A.A. "Finiteelement analysis of the adhesion-cytoskeleton-nucleus mechanotransduction pathway during endothelial cell rounding: axisymmetric model", J. Biomech. Eng., 127(4), pp. 594-600 (2005).
21. Mofrad, M.R. and Kamm, R.D., Cytoskeletal Mechanics: Models and Measurements in Cell Mechanics, Cambridge University Press, UK (2006).
22. O'Connor, C.M., Adams, J.U., and Fairman, J., Essentials of Cell Biology, Cambridge, MA: NPG Education, 1 (2010).
23. Zander, N.E., Piehler, T., Boggs, M.E., et al. "In vitro studies of primary explosive blast loading on neurons", J. Neurosci. Res., 93(9), pp. 1353-1363 (2015).
24. Barreto, S., Clausen, C.H., Perrault, C.M., et al. "A multi-structural single cell model of force-induced interactions of cytoskeletal components", Biomaterials, 34(26), pp. 6119-6126 (2013).
25. Drumheller, D.S., Introduction to Wave Propagation in Nonlinear Fluids and Solids, Cambridge University Press (1998).
26. Meyers, M.A., Dynamic Behavior of Materials, John Wiley & Sons (1994).
27. Kaliske, M. and Rothert, H. "Formulation and implementation of three-dimensional viscoelasticity at small and finite strains", Comput. Mech., 19(3), pp. 228-239 (1997).
28. Felgner, H., Frank, R., Biernat, J., et al. "Domains of neuronal microtubule-associated proteins and flexural rigidity of microtubules", J. Cell Biol., 138(5), pp. 1067-1075 (1997).
29. Prado, G.R., Ross, J.D., DeWeerth, S.P., et al. "Mechanical trauma induces immediate changes in neuronal network activity", J. Neural Eng., 2(4), p.148 (2005).
30. Mathieu, P.S. and Loboa, E.G. "Cytoskeletal and focal adhesion influences on mesenchymal stem cell shape, mechanical properties, and differentiation down osteogenic, adipogenic, and chondrogenic pathways", Tissue Eng. Part B Rev., 18(6), pp. 436-444 (2012).