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

TL;DR

The paper addresses calibrating a coupled electrophysiological–mechanical axon model with six interdependent parameters against experimental stretch-induced CAP data. It deploys a parallel differential evolution strategy with an OpenMP implementation to accelerate fitness evaluations, starting from a simplified single-axon setup and extending to a 27-axon fibre using morphometric sampling and a diameter-weighted CAP aggregation. Key contributions include demonstrating automatic calibration that surpasses manual results for mild to moderate damage, analyzing parameter interactions, and establishing a framework for large-scale nerve damage simulations at the fibre level. The work provides a physics-grounded, scalable approach to modeling stretch-induced axonal deficits and identifies practical paths (GPU acceleration, surrogate models) to handle larger bundles in the future.

Abstract

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 mechanical electrophysiological 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.

Figures (13)

• Figure 1: Double sucrose gap set-up Shi1999.
• Figure 2: CAP amplitudes of six loading cases (presented as a percentage of the pre-strain signal) during a 30min post-stretch period Shi2006.
• Figure 3: The complementary models that simulate the electrophysiological-mechanical coupling: The mechanical model (1) translates the mechanical loads into geometrical and functional changes (2) of the parameters used by the electrophysiological model (3) Jerusalem2014.
• Figure 4: Computation of the fitness value for an arbitrary case.
• Figure 5: Comparison of manual and automatic calibrations of the model. In each plot, the blue lines with squares represent the mild-slow case, green lines with circles the mild-fast case, red lines with diamonds the moderate-slow case, cyan lines with triangles the moderate-fast case, purple lines with upside-down triangles the severe-slow case and, finally, black lines with stars the severe-fast case.