Continuum mechanical modeling of axonal growth

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

Continuum mechanical modeling of axonal growth

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

A new strain rate dependent continuum framework for Mg alloys

Magnesium (Mg) alloys have recently been put under the spotlight for their specific strength, the highest among structural metals. Although the mechanical behavior of Mg alloys at quasi-static strain rates has been extensively modelled in the recent years, high strain rate studies have been much scarcer. This is mainly due to the rate dependent (RD) mechanical response of their hexagonal close-packed (hcp) crystalline structure. As a result, existing RD models do not account for the differentiated rate sensitivities of each slip and twin systems. Instead, the rate dependency is often conceived as a numerical artefact utilised to smooth the elasto-plastic transition and facilitate the scheme convergence. We thus propose a novel efficient RD crystal plasticity model for hcp metals, applied here to a rolled Mg AZ31 alloy sheet at room temperature. The constitutive RD equations are solved at each time step by either a Newton-Raphson based implicit scheme or an explicit scheme modified so as to ensure convergence independently of the stochastic bursts of slip systems inherent to such approach. Most of the model parameters are taken from the previously calibrated RI model of Fernandez et al. (2011), except for the new RD variables (strain rate sensitivity coefficients and reference shear strain rates), taken from the literature when available, or chosen so as to fulfill full compatibility with the the RI model under quasi-static conditions. The model is validated against uniaxial compression tests at high strain rate (10^3 s^-1), in the rolling and normal directions. The results reveal the ability of the model to simulate the mechanical behavior of Mg AZ31 alloy under a very large range of loading rates. To the best of the knowledge of the authors, the proposed model is the first RD continuum model for hcp metals involving physically accurate slip and twin system rate sensitivities, while ensuring convergence

Model calibration using a parallel differential evolution algorithm in computational neuroscience: Simulation of stretch induced nerve deficit

Neuronal damage, in the form of both brain and spinal cord injuries, is one of the major causes of disability and death in young adults worldwide. One way to assess the direct damage occurring after a mechanical insult is the simulation of the neuronal cells functional deficits following the mechanical event. In this study, we use a coupled electrophysiological-mechanical model with several free parameters that are required to be calibrated against experimental results. The calibration is carried out by means of an evolutionary algorithm (differential evolution, DE) that needs to evaluate each configuration of parameters on six different damage cases, each of them taking several minutes to compute. To minimise the simulation time of the parameter tuning for the DE, the stretch of one unique fixed-diameter axon with a simplified triggering process is used to speed up the calculations. The model is then leveraged for the parameter optimization of the more realistic bundle of independent axons, an impractical configuration to run on a single processor computer. To this end, we have developed a parallel implementation based on OpenMP that runs on a multi-processor taking advantage of all the available computational power. The parallel DE algorithm obtains good results, outperforming the best effort achieved by published manual calibration, in a fraction of the time. While not being able to fully capture the experimental results, the resulting nerve model provides a complex averaging framework for nerve damage simulation able to simulate gradual axonal functional alteration in a bundle

Intensive Care [1E]

Presentation of a renal Dialysis Machine to Intensive Care by a GMH representative. GMH Holdens donated $33 333 towards the new machine. The remaining$6000 dollars needed to buy the machine was raised by ICU staff through their participation in drug trial schemes.LtoR: 1. Dr Sandra Peake [Medical Director - 1E]2. Diane Thorton [1E - C.N.C]3. Geoff Weatheley [GMH Public relations manager ]4. Dr Marco Giardini [A/Site manager]negative folder - 18.9 presentations [1

3D finite element formulation for mechanical-electrophysiological coupling in axonopathy

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 focussed 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

Cyclone Effects on the Structure and Production of a Tropical Upland Rainforest: Implications for Life-History Tradeoffs

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