The provided code models the electrical properties of axons in a neural system, focusing on calculating the threshold current needed to achieve a specific level of depolarization (axon threshold) in nerve fibers, given their depth and diameter. This is grounded in the principles of neurophysiology, particularly concerning how axons respond to extracellular electrical stimulation. ### Biological Basis: 1. **Axon Structure and Properties:** - **Axon Radius and Diameter:** The radius and diameter of axons are crucial because the ease with which an axon can be stimulated or depolarized is partly determined by its size. The code calculates the axon radius from the given diameter, affecting further parameters like membrane resistance and axial resistance. - **Specific Membrane and Axial Resistance:** These parameters (Rm and Ra) are intrinsic to the axon and determine how voltage is distributed along it. Membrane resistance relates to the axon's ability to resist current flow across its membrane, while axial resistance represents the resistance to current flow along the axon's length. 2. **Extracellular Stimulation:** - **Electrode Placement:** The model positions an anode and a cathode at specific locations relative to the axon. The simulation calculates the distances from these electrodes to any given point on the axon, which is critical for determining the resulting electric fields. - **Extracellular Potential (Ve):** The model calculates the potential outside the membrane due to the applied electrical stimuli from these electrodes. The extracellular field influences the intracellular potential, which in turn affects whether the axon reaches the depolarization threshold. 3. **Depolarization Threshold:** - **dVmt (Depolarization Threshold Voltage):** This is a critical parameter representing the membrane potential change required to initiate an action potential. The model uses this threshold to determine the current needed to depolarize the axon sufficiently. - **dVi (Intracellular Potential Difference):** The function calculates how the external field affects the intracellular potential along the axon, using a method (`Visolve`) that incorporates the axon's electrical properties. 4. **Electrical Circuit Model:** - The axon is conceptually likened to an electrical circuit with distributed properties (resistances and potentials). This analogy allows the use of mathematical tools to predict how electrical currents will flow and how voltages will change in response to external stimuli, critical for understanding neural excitability and conduction. ### Model Objective: The primary objective of this model is to predict the electrical threshold (current intensity `Is`) necessary to induce action potentials in axons, depending on their geometric (depth and diameter) and biophysical (resistance properties) characteristics. This is relevant for both understanding natural neural processes and designing effective neural stimulation therapies or experiments, such as those used in deep brain stimulation or transcranial magnetic stimulation.