Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differentiated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specifically, the direct relations between brain and spinal cord tissue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanisticbased damage criteria, simulated function-based damage criteria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus providing a link between mechanical trauma and subsequent functional deficits.
Axonal growth is a complex phenomenon in which many intra-and extra-cellular signals collaborate simultaneously. Two different compartments can be identified in the growing axon: the growth cone, the leading tip that guides and steers the axon, and the axonal shaft, connecting the soma to the growth cone. The complex relations between both compartments and how their interaction leads the axon to its final synaptic target remain a topic of intense scrutiny. Here, we present a continuum and computational model for the development of the axonal shaft. Two different regions are considered: the axoplasm, filled with microtubules, and the surrounding cortical membrane, consisting mainly of F-actin, Myosin II motor proteins and the membrane. Based on the theory of morphoelasticity, the deformation gradient is decomposed into anelastic and viscoelastic parts. The former corresponds to either a growth tensor for the axoplasm, or a composition of growth and contractile tensors for the cortical membrane. The biophysical evolution for the anelastic parts is obtained at the constitutive level, in which the polymerization and depolymerization of microtubules and F-actin drive the growth, while the contractility is due to the pulling exerted by the Myosin II on the F-actin and depends on the stress. The coupling between cytoskeletal dynamics and mechanics is naturally derived from the equilibrium equations. The framework is exploited in two representative scenarios in which an external force is applied to the axonal shaft either along the axis or off the axis. In the first case three states are found: growth, collapse and stall. In the second case, axonal turning is observed. This framework is suitable to investigate the complex relationship between the local mechanical state, the cytoskeletal polymerization/depolymerization rates, and the contractility of the cortical membrane in axonal guidance.
With the growing body of research on traumatic brain injury and spinal cord injury, computational neuroscience has recently focused its modeling efforts on neuronal functional deficits following mechanical loading. However, in most of these efforts, cell damage is generally only characterized by purely mechanistic criteria, functions of quantities such as stress, strain or their corresponding rates. The modeling of functional deficits in neurites as a consequence of macroscopic mechanical insults has been rarely explored. In particular, a quantitative mechanically based model of electrophysiological impairment in neuronal cells, Neurite, has only very recently been proposed. In this paper, we present the implementation details of this model: a finite difference parallel program for simulating electrical signal propagation along neurites under mechanical loading. Following the application of a macroscopic strain at a given strain rate produced by a mechanical insult, Neurite is able to simulate the resulting neuronal electrical signal propagation, and thus the corresponding functional deficits. The simulation of the coupled mechanical and electrophysiological behaviors requires computational expensive calculations that increase in complexity as the network of the simulated cells grows. The solvers implemented in Neurite—explicit and implicit—were therefore parallelized using graphics processing units in order to reduce the burden of the simulation costs of large scale scenarios. Cable Theory and Hodgkin-Huxley models were implemented to account for the electrophysiological passive and active regions of a neurite, respectively, whereas a coupled mechanical model accounting for the neurite mechanical behavior within its surrounding medium was adopted as a link between electrophysiology and mechanics. This paper provides the details of the parallel implementation of Neurite, along with three different application examples: a long myelinated axon, a segmented dendritic tree, and a damaged axon. The capabilities of the program to deal with large scale scenarios, segmented neuronal structures, and functional deficits under mechanical loading are specifically highlighted.
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