neuroscience

# Neuroscience ## What I Do I provide comprehensive neuroscience tools including neuronal modeling, synaptic dynamics, neural network analysis, brain imaging quantification, EEG/MEG signal processing, and cognitive assessment for biomedical research applications. ## When to Use Me - Neuronal spiking models - Synaptic plasticity analysis - Brain imaging data analysis - Neural signal processing - Cognitive testing analysis - Neuropharmacology studies ## Core Concepts - **Neuronal Models**: Hodgkin-Huxley, integrate-and-fire - **Synaptic Transmission**: Neurotransmitter release, receptors - **Synaptic Plasticity**: LTP, LTD, STDP - **Neural Networks**: Connectivity, activity patterns - **Brain Imaging**: fMRI, PET, structural analysis - **Neural Signals**: EEG, MEG, LFP analysis - **Cognitive Neuroscience**: Behavioral paradigms - **Neuropharmacology**: Drug-receptor interactions ## Code Examples ### Hodgkin-Huxley Model ```python import numpy as np def alpha_n(V): return 0.01 * (V + 55) / (1 - np.exp(-(V + 55) / 10)) def beta_n(V): return 0.125 * np.exp(-(V + 65) / 80) def alpha_m(V): return 0.1 * (V + 40) / (1 - np.exp(-(V + 40) / 10)) def beta_m(V): return 4 * np.exp(-(V + 65) / 18) def alpha_h(V): return 0.07 * np.exp(-(V + 65) / 20) def beta_h(V): return 1 / (1 + np.exp(-(V + 35) / 10)) def hodgkin_huxley_step(V, n, m, h, dt, I_ext): dn = (alpha_n(V) * (1 - n) - beta_n(V) * n) * dt dm = (alpha_m(V) * (1 - m) - beta_m(V) * m) * dt dh = (alpha_h(V) * (1 - h) - beta_h(V) * h) * dt dV = (I_ext - 36 * n**4 * (V - 12) - 120 * m**3 * h * (V + 115) - 0.3 * (V + 10.613)) * dt return V + dV, n + dn, m + dm, h + dh def simulate_hh(dt=0.01, T=100, I_inj=10): V = -65 n = alpha_n(V) / (alpha_n(V) + beta_n(V)) m = alpha_m(V) / (alpha_m(V) + beta_m(V)) h = alpha_h(V) / (alpha_h(V) + beta_h(V)) t = np.arange(0, T, dt) V_trace = np.zeros_like(t) for i, ti in enumerate(t): V, n, m, h = hodgkin_huxley_step(V, n, m, h, dt, I_inj) V_trace[i] = V return t, V_trace ``` ### Integrate-and-Fire Model ```python class LeakyIntegrateAndFire: def __init__(self, C=1, gL=0.1, EL=-70, Vth=-50, Vreset=-75, tau_ref=2): self.C = C self.gL = gL self.EL = EL self.Vth = Vth self.Vreset = Vreset self.tau_ref = tau_ref self.V = EL def update(self, I, dt): if self.tau_ref > 0: self.tau_ref -= dt return False dV = (-self.gL * (self.V - self.EL) + I) / self.C * dt self.V += dV if self.V >= self.Vth: self.V = self.Vreset self.tau_ref = 2 return True return False def simulate(self, I_func, T, dt): t = np.arange(0, T, dt) spikes = [] V_trace = [] for ti in t: I = I_func(ti) if callable(I_func) else I spiked = self.update(I, dt) if spiked: spikes.append(ti) V_trace.append(self.V) return np.array(t), np.array(V_trace), np.array(spikes) neuron = LeakyIntegrateAndFire() t, V, spikes = neuron.simulate(lambda t: 2.5, 100, 0.1) print(f"Spike count: {len(spikes)}") print(f"Average firing rate: {len(spikes) / 100 * 1000:.1f} Hz") ``` ### Spike Timing Dependent Plasticity ```python def stdp_rule(dt, A_plus=1, tau_plus=20, A_minus=1, tau_minus=20): if dt > 0: return A_plus * np.exp(-dt / tau_plus) else: return -A_minus * np.exp(dt / tau_minus) def update_weights_stdp(weights, pre_spikes, post_spikes, dt, time_window=100): dw = np.zeros_like(weights) for i, t_pre in enumerate(pre_spikes): for j, t_post in enumerate(post_spikes): delta_t = t_post - t_pre if abs(delta_t) <= time_window: dw[i, j] = stdp_rule(delta_t) weights = np.clip(weights + dw, 0, 1) return weights def hebbian_learning(pre_activity, post_activity, learning_rate=0.01): delta_w = learning_rate * np.outer(pre_activity, post_activity) return delta_w def oja's_rule(pre_activity, post_activity, w, alpha=0.001): delta_w = post_activity * (pre_activity - alpha * post_activity * w) return delta_w ``` ### Neural Signal Processing ```python from scipy import signal def bandpower(data, fs, band): f, Pxx = signal.welch(data, fs=fs, nperseg=1024) idx_band = np.logical_and(f >= band[0], f <= band[1]) return np.trapz(Pxx[idx_band], f[idx_band]) def extract_lfp_features(lfp_signal, sampling_rate=1000): theta = bandpower(lfp_signal, sampling_rate, [4, 8]) gamma = bandpower(lfp_signal, sampling_rate, [30, 100]) delta = bandpower(lfp_signal, sampling_rate, [0.5, 4]) return {'theta': theta, 'gamma': gamma, 'delta': delta} def detect_spikes_amplitude(data, threshold=-3): std = np.std(data) mean = np.mean(data) threshold_val = mean + threshold * std spikes = np.where(data > threshold_val)[0] return spikes def coherence_analysis(signal1, signal2, fs=1000): f, Cxy = signal.coherence(signal1, signal2, fs=fs, nperseg=256) return f, Cxy ``` ### fMRI Analysis Basics ```python def spm_hrf(TR, num_volumes): import scipy.stats as stats d = np.arange(0, num_volumes * TR, TR) hrf = stats.gamma.pdf(d, 6) - stats.gamma.pdf(d, 16) / 6 return hrf / np.sum(hrf) def motion_correction(motion_params): corrections = { 'translation_x': motion_params[0], 'translation_y': motion_params[1], 'translation_z': motion_params[2], 'rotation_x': motion_params[3], 'rotation_y': motion_params[4], 'rotation_z': motion_params[5] } return corrections def compute_beta_maps(design_matrix, bold_timeseries): betas = np.linalg.lstsq(design_matrix, bold_timeseries, rcond=None)[0] return betas def roi_timeseries提取(roi_mask, bold_data): n_timepoints = bold_data.shape[3] roi_ts = np.zeros(n_timepoints) for t in range(n_timepoints): roi_ts[t] = np.mean(bold_data[:, :, :, t][roi_mask]) return roi_ts ``` ## Best Practices 1. **Model Validation**: Compare with experimental data 2. **Parameter Sensitivity**: Test parameter ranges 3. **Noise**: Include realistic noise models 4. **Spatial Resolution**: Consider imaging limitations 5. **Multiple Comparisons**: Correct for fMRI analysis ## Common Patterns ```python # Firing rate calculation def firing_rate(spike_times, bin_size, time_range): bins = np.arange(time_range[0], time_range[1] + bin_size, bin_size) counts, _ = np.histogram(spike_times, bins) return counts / bin_size # Information theory measures def mutual_information(rate1, rate2): from sklearn.metrics import mutual_info_score return mutual_info_score(rate1, rate2) # Neural decoding def neural_decoding(patterns, labels): from sklearn.linear_model import LogisticRegression clf = LogisticRegression() clf.fit(patterns, labels) return clf.score(patterns, labels) ``` ## Core Competencies 1. Biophysical neuron modeling 2. Synaptic plasticity mechanisms 3. Neural signal processing 4. Brain imaging analysis 5. Cognitive paradigm analysis