The provided code is a computational model aimed at exploring the electrical properties of the extracellular environment around neurons, focusing specifically on the electrical resistance between an electrode and spatial locations within neural tissue. This is often relevant in the context of electrophysiological recordings or neuromodulation research. Below are the key biological concepts encapsulated by the code: ### Biological Context #### Electrode and Tissue Interaction - **Electrode Size (`elecRad`)**: The model considers a point electrode in a tissue medium, with a given size in micrometers (20 µm). This is representative of electrodes used in invasive neural recordings or stimulation. #### Extracellular Medium - **Extracellular Resistivity (`rho`)**: This parameter represents the resistive properties of the extracellular space. It is a critical factor in determining how electrical signals propagate through the neural tissue. #### Geometric Considerations - **Radial and Vertical Distances**: The code calculates the geodesic between an electrode and points in the surrounding tissue, taking into account lateral (x) and vertical (z) displacements. This simulates different positions relative to the electrode, reflecting the three-dimensional configuration of the brain's extracellular space. ### Modeling Objective The model aims to characterise the spatial variation in the extracellular resistance (\(Rx_{xtra}\)) by calculating how it attenuates with distance from the electrode. This can be understood as a means to predict the effectiveness or reach of an electrical signal emitted or recorded by an electrode implanted in neural tissue. ### Mathematical Representation - **The Geodesic Function (`geo`)**: The model uses a mathematical formula to represent the spatial dependency of electrode-tissue interactions. This formula includes the electrode size and the spatial dimensions, providing insight into the resistive properties of the surrounding space relative to electrode position. ### Visualization - **Graphical Output**: The code generates plots showing how the electrical resistance changes with radial distance from the electrode at various heights. This could help in visualizing the spatial dynamics of electrical field propagation in the neural tissue. ### Relevance to Electrophysiology The findings of this kind of modeling can inform the design and placement of electrodes for neural recordings to ensure optimal signal quality and resolution, or for stimulation to ensure effective targeting of neuronal populations. Understanding how resistance changes spatially is crucial for interpreting electrophysiological data and improving neurotechnological interfaces. This code provides insight into the theoretical underpinning of extracellular recordings and interventions, essential for interpreting the biophysical interactions between electrodes and neural tissues.