The provided MATLAB code is a computational model aiming to simulate the biophysical effects of extracellular electrical stimulation on neurons, particularly focusing on the membrane potential responses under various conditions. ### Biological Basis #### 1. **Extracellular Electrical Stimulation:** - **Definition:** Extracellular stimulation involves applying an electric field to a neuron from the outside, influencing its membrane potential. - **Goal of the Model:** The code aims to predict how different parameters affect the membrane potential changes when neurons are stimulated externally. The focus is on transverse modes of stimulation, examining current density boundary conditions. #### 2. **Neuron and Membrane Properties:** - **Membrane Potential (`V_M`):** This is a critical biophysical property of neurons, representing the voltage difference across the neuronal membrane. The model calculates changes in this potential due to stimulation. - **Membrane Resistance (`RM`) and Capacitance (`CM`):** These parameters characterize the neuron's membrane. Resistance and capacitance are key determinants of how neurons integrate and respond to electrical stimuli. The code uses specific conductance and capacitance values to simulate realistic neuronal responses. #### 3. **Geometric Parameters:** - **Axon Model (`a`, `b`, `d`):** The code uses cylindrical geometry to represent a neuron with an inner radius (`a`), an outer radius (`b`), and a thickness (`d`). These parameters are essential for calculating the resistive properties of both extracellular (`r_e`) and intracellular (`r_i`) spaces. #### 4. **Resistive Properties:** - **Intracellular (`rho_i`) and Extracellular (`rho_e`) Resistivity:** These resistivities influence the current flow through the surrounding tissue and inside the axon, reflecting different conductive properties of the neuronal environment and cytoplasm. #### 5. **Current Density and Stimulation Parameters:** - **Current Density (`JA`):** Represents the stimulus intensity applied in the extracellular space, influencing the degree to which the membrane potential is altered. - **Spatial Variability (`gz`):** Gaussian distribution is used to represent the spatial spread of the applied current around the neuron, emphasizing how the localized application influences the neuron’s potential. ### Analytical Predictions vs. Simulations: - The code is intended to compare the theoretical predictions based on analytic expressions with simulated results to validate the model's accuracy. The figures referenced indicate different aspects of the membrane potential as functions of stimulation parameters, such as the ratio of `d/a`, current frequency (`w`), and geometric scaling of `b/σ`. ### Conclusion: The code embodies the complexity of modeling electrical stimulation in neural tissues by incorporating multiple biological parameters, reflecting how neurons respond to external currents. It highlights the importance of membrane properties, tissue conductivity, and geometry in understanding the outcomes of neuromodulation strategies, potentially applicable for neural engineering fields like neuroprosthetics and therapeutic stimulation.