The provided code snippet is related to a computational neuroscience model that simulates neural mass dynamics, particularly focusing on K-complexes and slow wave activities (SWA) in cortical brain activity. The key aspects of the biological basis modeled by this code include: ### Biological Phenomena 1. **K-Complexes and Slow Wave Activity (SWA):** - The study of K-complexes and SWA is crucial for understanding sleep physiology. K-complexes are large amplitude waves that occur during non-REM sleep, often associated with the transition between different sleep stages. SWA represents the low-frequency oscillations seen during deep sleep, particularly in the N3 stage of non-REM sleep. 2. **Neural Mass Model:** - The model used here is a neural mass model. Such models are simplified representations of brain activity that describe averaged dynamics of large populations of neurons. They are particularly useful for simulating global brain activity such as oscillations and waves seen in sleep stages. ### Key Parameters 1. **Sigma_e and g_KNa:** - The `sigma_e` parameter represents excitability within the cortical network. Alterations in this parameter can simulate different levels of neural excitation which is pertinent for studying the transitions between sleep stages. - The `g_KNa` parameter is related to the conductance of sodium-activated potassium currents. This current is crucial for regulating neuronal excitability and contributes to the resting membrane potential and repolarization phase of action potentials. Variability in `g_KNa` can influence the dynamics of sleep-related oscillations. 2. **dphi:** - Although set to zero in the provided parameters, `dphi` is often used to represent phase shifts or delays in the propagation of neural signals. This can be important for understanding the synchronization of neural activity patterning in different cortical regions. ### Stimulation Protocol 1. **Stimulation Modes:** - The parameter `var_stim` includes specifications for external stimulation. This encompasses: - Mode of stimulation (`0`: none, `1`: semi-periodic, `2`: phase-dependent). - Parameters defining the strength, duration, and timing of stimulus application, imitating external perturbations like auditory stimuli which are known to elicit K-complexes during sleep. 2. **Simulation Runs:** - The repeated simulations (`N = 15`) indicate a parameter sweep over various stimulation strengths, reflecting attempts to understand how varying input intensities influence the generation and properties of K-complexes and slow wave activities. In summary, this code snippet is effectively modeling the dynamics of sleep-related brain activity through a neural mass model. It examines how different parameters related to excitability and ionic conductance impact the generation of K-complexes and SWA, coupled with externally applied stimuli representative of auditorium inputs that may modify these brain states. These aspects are essential for exploring how the brain transitions through different sleep phases and how external stimulation might influence these transitions.