The code provided is a computational model designed to simulate the electrophysiological dynamics of neurons within the subthalamic nucleus (STN) and the globus pallidus (GP), which are key structures in the basal ganglia of the brain. This model captures the interaction between these brain regions under different stimulation protocols, reflecting conditions relevant to deep brain stimulation (DBS), which is often used for treating conditions like Parkinson’s disease. ### Biological Basis of the Model #### Subthalamic Nucleus (STN) - **Neurons**: The model includes ten STN neurons arranged in a ring-like structure, capturing local and non-local electrotonic coupling. - **Ionic Currents**: - **Sodium (Na+)** and **Potassium (K+)** currents are modeled using fast and delayed rectifier conductances, providing the basis for action potentials. - **AHP Currents** (`iahp`): Models after-hyperpolarization currents often associated with neuronal excitability. - **T-type Calcium Currents** (`it`): Represents low-threshold calcium currents that contribute to rhythmic burst firing, a feature often seen in STN neurons. - **Gating Variables**: - Variables like `h`, `n`, and `r` represent the inactivation and activation states of ion channels, influencing the timing and duration of action potentials. - Equations governing these variables (e.g., `hinf`, `ninf`) are based on sigmoid functions that model the voltage-dependent probability of ions contributing to neuronal firing. - **Synaptic Currents**: - The STN neurons receive synaptic inputs that are modeled to reflect excitatory post-synaptic potentials (EPSPs), which are crucial for modulating neuronal activity. #### Globus Pallidus (GP) - **Neurons**: Another set of ten neurons is included to represent the GP, which interacts closely with the STN. - **Currents and Gating Variables**: Similar to the STN neurons, GP neurons also account for sodium, potassium, and calcium currents (`inag`, `ikg`, `icag`), modulated by specific activation and inactivation dynamics (`hg`, `ng`, `rg`). #### Stimulation Protocol - **Electrode Stimulation**: The model simulates stimulation protocols applied through electrodes near the 5th and 7th STN neurons. Parameters like `w1` and `w2` define local and non-local spread of stimulation signals, simulating the effects of varying DBS strategies. - **Delayed Effects**: The model uses delay differential equations to simulate the effects of stimuli over time and how these translate into observable local field potentials (LFPs), particularly relevant for understanding the feedback and oscillatory behavior in the neuronal circuits. #### Local Field Potentials (LFPs) - **Measurement**: LFPs (`Lfp5`, `Lfp7`) are computed to represent the extracellular recordings near specific neurons, capturing collective neuronal activity patterns. These LFPs are instrumental in understanding the impact of DBS on neuronal synchronization and information transmission in brain tissue. ### Summary This model integrates complex biophysical features of ion channels, synaptic transmission, and external electrical stimulation to provide insights into the functioning of the STN and GP, along with their interactions. The inclusion of stimulation protocols simulates DBS effects, offering a framework to study therapeutic interventions for movement disorders and the underlying basal ganglia network activity.