The provided code models the diffusion of calcium ions (Ca²⁺) within a three-dimensional neural structure. This approach is aligned with computational neuroscience's goal to quantitatively study neuronal dynamics and signaling. Here are the biological aspects captured by this code:
Calcium Dynamics:
The key species modeled is calcium (denoted as ca in the code), which plays a critical role in neuronal signaling, synaptic plasticity, and intracellular processes. The diffusion of calcium is simulated within the specified region, represented by the domain which might correspond to a section of a neural cell such as a dendrite or axonal segment.
Diffusion Process:
Calcium diffusion is governed by Fick's laws, and in this model, it's implemented through the specified diffusion constant D. This parameter is crucial for mimicking how calcium spreads through the intracellular space of neurons.
Spatial and Temporal Domains:
The model defines a specific three-dimensional space (start_x, stop_x, start_y, stop_y, start_z, stop_z) in which the calcium concentration changes over time (tstop). This setup allows for the simulation of calcium movement over a short time period (20 ms in this case), capturing the transient nature of calcium signaling in cells.
Source of Calcium:
An initial concentration of calcium is provided within a defined spatial region by init_concentration. This represents the biological scenario where calcium concentration is higher near the source, such as near sites of calcium influx like voltage-gated calcium channels.
Computational Validation:
The code aims to validate the diffusion model by comparing the simulated calcium concentrations against an analytic solution (solution_from_domain) that accounts for the diffusion from a finite region in an infinite domain. Errors in approximation are evaluated by checking the relative error between the simulated and expected concentrations at various distances from the center of the source.
Overall, this code addresses the need to understand calcium dynamics in neural computations and biological processes by modeling and validating calcium diffusion in a simplified three-dimensional neural structure. This simulation approach helps researchers explore how alterations in diffusion parameters might affect neural signaling and cellular functions.