ffsshhttiikk 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
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
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
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
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
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
- Model Validation: Compare with experimental data
- Parameter Sensitivity: Test parameter ranges
- Noise: Include realistic noise models
- Spatial Resolution: Consider imaging limitations
- Multiple Comparisons: Correct for fMRI analysis
Common Patterns
# 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
- Biophysical neuron modeling
- Synaptic plasticity mechanisms
- Neural signal processing
- Brain imaging analysis
- Cognitive paradigm analysis