Open-source numerical simulation tool for two-dimensional neural fields involving finite axonal transmission speed

Abstract : This work aims to provide an open source and cross-platform simulation tool that integrates numerically integral-differential equations in a two-dimensional quadratic spatial domain with periodic boundary conditions and finite axonal transmission speed inducing space-dependent delays.. The term I denotes the external stimulus, K is the synaptic connectivity kernel and S is the firing rate. Finite axonal transmission speed c induces space-dependent delays. Conventional implementations of two-dimensional integration with space-dependent delays are rather slow due to the missing convolution in the integral. It has been shown in a previous work that this unfortunate property can be overcome by introducing a spatio-temporal kernel, rendering the integral into a spatial integral and an integral over delays. Four major aspects accelerate the integration speed: (a) the underlying numerical method is expedited with a fast Fourier transform in space (b) the simulator writes and executes its own code based on interface selections to efficiently calculate and display only the user-defined features (c) the displayed matrix is put onto the running system's graphics processing unit for hardware acceleration of the visualization (d) reduced rate of GPU uploads optimized for visual perception. The simulator gives the user full control of the variables by permitting free choice of all variables through a text-based interface. Two dimensional field matrices can be displayed in rich detail in a three-dimensional plot. The visualization of field data is easily modified by a keypress, performing functions such as moving, rotating, zooming and changing colors and axis limits. Images and videos can be saved and simulations can be paused and resumed using the keyboard. The software is open-source and written in Python.