# Biological Basis of the Computational Model This code models the neural dynamics of a thalamocortical network with specific focus on the interplay between different brain regions in the context of Parkinson's disease. The primary regions involved include the Subthalamic Nucleus (STN), Globus Pallidus (GP), and Thalamocortical (TC) components, which are critical in understanding the pathophysiology of Parkinson's and the effects of Deep Brain Stimulation (DBS). ## Biological Components Modeled ### 1. **Subthalamic Nucleus (STN)** - **Currents and Ions:** The STN model involves several ionic currents including leak current (\(I_{l}\)), sodium current (\(I_{Na}\)), potassium current (\(I_{K}\)), AHP (afterhyperpolarization) current (\(I_{AHP}\)), calcium currents (\(I_{Ca}\)), and high-threshold calcium current (\(I_{T}\)). - **Gating Variables:** These currents are modulated by voltage-dependent gating variables (e.g., \(h\), \(n\), \(r\)), which control the activation and inactivation of ion channels. - **Synaptic Inputs:** The model includes synaptic currents (\(I_{syn}\)), which represent synaptic connections and interactions within the STN and from other neurons. ### 2. **Globus Pallidus (GP)** - **Currents and Ions:** The GP neurons are described with sodium (\(I_{Na}\)), potassium (\(I_{K}\)), AHP (\(I_{AHP}\)), and calcium (\(I_{Ca}\)) currents, accounting for the dynamics within the GP. - **Gating Variables:** Similar to the STN, the activation and inactivation of ion channels are guided by gating variables (e.g., \(N_g, H_g, R_g\)). - **Synaptic Inputs:** Includes modeling of synaptic inhibition similar to STN, as well as inter-nuclear connections. ### 3. **GPI and TC Neurons** - **Currents and Ions:** Both Globus Pallidus Interna (GPI) and TC neurons are modeled similarly, including sodium, potassium, and calcium currents with their respective gating dynamics. - **Synaptic Modulation:** TC neurons receive cortical inputs that are periodic, which is essential to simulate rhythmic cortical activity and its effect on the thalamocortical network. ### 4. **Deep Brain Stimulation (DBS)** - The model integrates a DBS input as a periodic external force applied to the neuronal dynamics. This component is crucial for examining the therapeutic effects of DBS on the neural dynamics typical in Parkinson's disease pathology. ## Biological Relevance This model helps to simulate and understand the complex interactions between the STN, GP, and TC during Parkinson's disease pathophysiology. By introducing DBS, the model aims to reflect how this therapeutic intervention can modulate neuronal firing patterns, thereby potentially alleviating symptoms of Parkinson's. The gating variables and ionic currents modeled here capture the essential electrophysiological properties of neurons, which are critical for accounting for the abnormal neuronal oscillations observed in Parkinson's disease. Understanding these detailed interactions may provide insight into how different types of neural activity are generated and how they can be manipulated through interventions like DBS. In summary, this model offers a computational approach to simulate the intricate biological processes underlying basal ganglia and thalamocortical interactions in the diseased state, with an emphasis on neuromodulation techniques.