NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering 346 (2019) 1025-1050, DOI: 10.1016/j.cma.2018.09.006
All documents in ORBi are protected by a user license.
mechanical-electrophysiological coupling; finite element method; neuronal membrane; axonal injury; Hodgkin-Huxley; Cable Theory
Abstract :
[en] Traumatic injuries to the central nervous system (brain and spinal cord) have recently been put under the spotlight because of their devastating socio-economical cost. At the cellular scale, recent research efforts have focused on primary injuries by making use of models aimed at simulating mechanical deformation induced axonal electrophysiological functional deficits. The
overwhelming majority of these models only consider axonal stretching as a loading mode, while other modes of deformation such as crushing or mixed modes|highly relevant in spinal cord injury|are left unmodelled. To this end, we propose here a novel 3D finite element framework coupling mechanics and electrophysiology by considering the electrophysiological Hodgkin-
Huxley and Cable Theory models as surface boundary conditions introduced directly in the weak form, hence eliminating the need to geometrically account for the membrane in its electrophysiological contribution. After validation against numerical and experimental results, the approach is leveraged to model an idealised axonal dislocation injury. The results show that the sole consideration of induced longitudinal stretch following transverse loading of a
node of Ranvier is not necessarily enough to capture the extent of axonal electrophysiological
deficit and that the non-axisymmetric loading of the node participates to a larger extent to the subsequent damage. On the contrary, a similar transverse loading of internodal regions was not shown to significantly worsen with the additional consideration of the non-axisymmetric
loading mode.
M.T.K., M.B. and A.J. acknowledge funding from the European Union's Seventh Framework Programme (FP7 20072013) ERC Grant Agreement No.306587. H.Y. would like to acknowledge China Regenerative Medicine Limited (CRMI) for funding and the EPSRC DTP (Award no. 1514540) for F.B.'s studentship.
Funders :
UE - Union Européenne [BE] EPSRC - Engineering and Physical Sciences Research Council [GB] CE - Commission Européenne [BE]
Goriely, A., Geers, M.G.D., Holzapfel, G.A., Jayamohan, J., Jérusalem, A., Sivaloganathan, S., Squier, W., van Dommelen, J.A.W., Waters, S., Kuhl, E., Mechanics of the brain: perspectives, challenges, and opportunities. Biomech. Model. Mechanobiol. 14:5 (2015), 931–965.
Bar-Kochba, E., Scimone, M.T., Estrada, J.B., Franck, C., Strain and rate-dependent neuronal injury in a 3D in vitro compression model of traumatic brain injury. Sci. Rep., 6, 2016, 30550.
Chen, Y.C., Smith, D.H., Meaney, D.F., In-vitro approaches for studying blast-induced traumatic brain injury. J. Neurotrauma 26:6 (2009), 861–876.
Magou, G.C., Pfister, B.J., Berlin, J.R., Effect of acute stretch injury on action potential and network activity of rat neocortical neurons in culture. Brain Res. 1624 (2015), 525–535.
Magou, G.C., Guo, Y., Choudhury, M., Chen, L., Hususan, N., Masotti, S., Pfister, B.J., Engineering a high throughput axon injury system. J. Neurotrauma 28:11 (2011), 2203–2218.
Sun, W., Fu, Y., Shi, Y., Cheng, J.-X., Cao, P., Shi, R., Paranodal myelin damage after acute stretch in guinea pig spinal cord. J. Neurotrauma 29:3 (2012), 611–619.
Shi, R., Whitebone, J., Conduction deficits and membrane disruption of spinal cord axons as a function of magnitude and rate of strain. J. Neurophysiol. 95 (2006), 3384–3390.
Greer, J.E., Povlishock, J.T., Jacobs, K.M., Electrophysiological abnormalities in both axotomized and nonaxotomized pyramidal neurons following mild traumatic brain injury. J. Neurosci. 32:19 (2012), 6682–6687.
Ouyang, H., Sun, W., Fu, Y., Li, J., Cheng, J.-X., Nauman, E., Shi, R., Compression induces acute demyelination and potassium channel exposure in spinal cord. J. Neurotrauma 27:6 (2010), 1109–1120.
Wang, J.A., Lin, W., Morris, T., Banderali, U., Juranka, P.F., Morris, C.E., Membrane trauma and Na+ leak from Nav1.6 channels. Am. J. Physiol. Cell Physiol. 297:4 (2009), C823–C834.
Ouyang, H., Galle, B., Li, J., Nauman, E., Shi, R., Biomechanics of spinal cord injury: a multimodal investigation using ex vivo guinea pig spinal cord white matter. J. Neurotrauma 25:1 (2008), 19–29.
Pfister, B.J., Bonislawski, D.P., Smith, D.H., Cohen, A.S., Stretch-grown axons retain the ability to transmit active electrical signals. FEBS Lett. 580:14 (2006), 3525–3531.
Kang, W.H., Cao, W., Graudejus, O., Patel, T.P., Wagner, S., Meaney, D.F., Morrison, B.r., Alterations in hippocampal network activity after in vitro traumatic brain injury. J. Neurotrauma 32:13 (2015), 1011–1019.
Kang, W.H., Morrison, B., Predicting changes in cortical electrophysiological function after in vitro traumatic brain injury. Biomech. Model. Mechanobiol. 14:5 (2015), 1033–1044.
Babbs, C.F., Shi, R., Subtle paranodal injury slows impulse conduction in mathematical model of myelinated axons. PLoS One 8:7 (2013), 1–11.
Boucher, P.A., Joós, B., Morris, C.E., Coupled left-shift of Nav channels: Modeling the Na+-loading and dysfunctional excitability of damaged axons. J. Comput. Neurosci. 33:2 (2012), 301–319.
Volman, V., Ng, L.J., Primary paranode demyelination modulates slowly developing axonal depolarization in a model of axonal injury. J. Comput. Neurosci. 37:3 (2014), 439–457.
Suchyna, T.M., Markin, V.S., Sachs, F., Biophysics and structure of the patch and the gigaseal. Biophys. J. 97:3 (2009), 738–747.
Jérusalem, A., García-Grajales, J.A., Merchán-Pérez, A., Peña, J.M., A computational model coupling mechanics and electrophysiology in spinal cord injury. Biomech. Model. Mechanobiol. 13:4 (2014), 883–896.
Drapaca, C.S., An electromechanical model of neuronal dynamics using Hamilton's principle. Front. Cell. Neurosci., 9, 2015, 271.
Cinelli, I., Destrade, M., Duffy, M., McHugh, P., Electro-mechanical response of a 3D nerve bundle model to mechanical loads leading to ixonal injury. Int. J. Numer. Methods Biomed. Eng., 34, 2017 e2942.
Simulia, Abaqus 6.10, 2010.
Geuzaine, C., Remacle, J.F., Gmsh: A 3D finite element mesh generator with built-in pre- and post-processing facilities. Internat. J. Numer. Methods Engrg. 79:11 (2009), 1309–1331.
Wu, L., Tjahjanto, D., Becker, G., Makradi, A., Jérusalem, A., Noels, L., A micro-meso-model of intra-laminar fracture in fiber-reinforced composites based on a discontinuous Galerkin/cohesive zone method. Eng. Fract. Mech. 104 (2013), 162–183.
Cheng, G., Kong, R.-h., Zhang, L.M., Zhang, J.N., Mitochondria in traumatic brain injury and mitochondrial-targeted multipotential therapeutic strategies. Br. J. Pharmacol. 167 (2012), 699–719.
García-Grajales, J.A., Rucabado, G., García-Dopico, A., Peña, J., Jérusalem, A., Neurite, a finite difference large scale parallel program for the simulation of electrical signal propagation in neurites under mechanical loading. PLoS One 10:2 (2015), 1–22.
Jow, F., He, L., Kramer, A., Hinson, J., Bowlby, M.R., Dunlop, J., Wang, K.W., Validation of DRG-like F11 cells for evaluation of KCNQ/M-channel modulators. Assay Drug Dev. Technol. 4:1 (2006), 49–56.
Fan, S.F., Shen, K.F., Scheideler, M.A., Crain, S.M., F11 neuroblastoma x DRG neuron hybrid cells express inhibitory/.l- and 6-opioid receptors which increase voltage-dependent K + currents upon activation. Brain Res. 590 (1992), 329–333.
F. Bianchi, J.H. George, M. Malboubi, A. Jerusalem, M.S. Thompson, H. Ye, Engineering a uniaxial substrate-stretching device for simultaneous electrophysiology and imaging of strained peripheral neurons (unpublished).
Malboubi, M., Gu, Y., Jiang, K., Characterization of surface properties of glass micropipettes using SEM stereoscopic technique. Microelectron. Eng. 88:8 (2011), 2666–2670.
Loverde, J., Pfister, B., Developmental axon stretch stimulates neuron growth while maintaining normal electrical activity, intracellular calcium flux, and somatic morphology. Front. Cell. Neurosci., 9, 2015, 308.
Hodgkin, A., Huxley, A., A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117 (1952), 500–544.
Smith, D.H., Wolf, J.A., Lusardi, T.A., Lee, V.M., Meaney, D.F., High tolerance and delayed elastic response of cultured axons to dynamic stretch injury. J. Neurosci. 19:11 (1999), 4263–4269.
Koch, C., Biophysics of Computation. 1999, Oxford University Press.
