ネコLGN細胞のスパイクトリガー平均による受容野解析
ネコLGNのX細胞のスパイクトリガー平均(Spike triggered average; STA)による受容野解析をしてみます。データと設定はTheoretical Neuroscienceの演習問題(Chapter 2-3)より (神経活動の元データはP. Kara, P.Reinagel, & R.C. Reid. (2000)より)。
データとコードは https://github.com/takyamamoto/STA-for-catLGNcell で公開しています。動かしたい場合はリポジトリをCloneした後に
sta_catLGN.pyを実行してください。
import numpy as np
import matplotlib.pyplot as plt
import scipy.io
import scipy.ndimage
from matplotlib import gridspec
from tqdm import tqdm
# Load data
data = scipy.io.loadmat('./data/lgn_sta_data/c2p3.mat')
# stim : 16 x 16 images that were presented at the corresponding times.
stim = data['stim'] # (16, 16, 32767)
# counts : vector containing the number of spikes in each 15.6 ms bin.
counts = data['counts']
counts = np.reshape(counts, (-1)) # (32767)
"""
Calculate the spike-triggered average images
for each of the 12 time steps(= 187.2 ms) before each spike
"""
spike_timing = np.where(counts > 0)[0]
num_spikes = np.sum(counts > 0) # number of spikes
num_timesteps = 12
H, W = 16, 16 # height and width of stimulus image
sta = np.zeros((H, W, num_timesteps)) #spike-triggered average
for t in spike_timing:
if t > num_timesteps:
sta += stim[:, :, t-num_timesteps:t]*counts[t]
sta /= num_spikes
#collapse-hide
for T in tqdm(range(num_timesteps)):
if T in [0, num_timesteps-2, num_timesteps-1]:
fig = plt.figure(figsize=(10,3))
fig.suptitle("The receptive field of a cat LGN X cell. (timesteps : "+str(T)+")", fontsize=14)
gs = gridspec.GridSpec(1, 3, width_ratios=[1, 1, 2], height_ratios=[1])
x = np.arange(-W//2, W//2+2, 2)
y = np.arange(-H//2, H//2+2, 2)
ax1 = plt.subplot(gs[0,0])
plt.imshow(sta[:,:,T])
plt.gca().set_aspect('equal')
plt.gca().invert_yaxis()
plt.xlabel('x')
plt.ylabel('y')
ax1.title.set_text('heatmap')
plt.xticks(list(np.arange(0, W+1, 2)-0.5), list(x))
plt.yticks(list(np.arange(0, H+1, 2)-0.5), list(y))
zoom = 3
smoothed_sta = scipy.ndimage.zoom(sta[:,:,T], zoom=zoom) # smoothed
x = np.arange(-W//2*zoom, W//2*zoom)
y = np.arange(-H//2*zoom, H//2*zoom)
X, Y = np.meshgrid(x, y)
ax2 = plt.subplot(gs[0,1])
plt.contour(X, Y, smoothed_sta, 25)
plt.xlabel('x')
ax2.title.set_text('contour')
plt.gca().set_aspect('equal')
ax3 = plt.subplot(gs[0,2], projection='3d')
ax3.plot_surface(X, Y, smoothed_sta, shade=True,
color='grey')
ax3.set_xlabel('x')
ax3.set_ylabel('y')
plt.show()
plt.close()
いずれもcenter-surroundingな受容野を持っているのですが、最後は符号が反転しています。
問題文に
In the averaged images, you should see a central receptive field that reverses sign over time.
とあるので解析を間違えたわけではなさそうですが、ちゃんと理解できていません。
#collapse-hide
# Calculate spatio-temporal receptive field
sum_sta = np.sum(sta, axis=1).T
fig = plt.figure(figsize=(12, 3))
fig.suptitle("The spatio-temporal receptive field of a cat LGN X cell.", fontsize=14)
gs = gridspec.GridSpec(1, 3, width_ratios=[1, 1, 1.5],
height_ratios=[1])
x = np.arange(-H//2, H//2+2, 2)
ax1 = plt.subplot(gs[0,0])
plt.imshow(sum_sta)
plt.gca().set_aspect('equal')
plt.gca().invert_yaxis()
plt.xlabel('x')
plt.ylabel('time steps')
ax1.title.set_text('heatmap')
plt.xticks(list(np.arange(0, W+1, 2)-0.5), list(x))
zoom = 3
smoothed_sum_sta = scipy.ndimage.zoom(sum_sta, zoom=zoom) # smoothed
x = np.arange(-H//2*zoom, H//2*zoom)
t = np.arange(12*zoom)
X, T = np.meshgrid(x, t)
ax2 = plt.subplot(gs[0,1])
plt.contour(X, T, smoothed_sum_sta, 25)
plt.xlabel('x')
ax2.title.set_text('contour')
plt.gca().set_aspect('equal')
ax3 = plt.subplot(gs[0,2], projection='3d')
ax3.plot_surface(X, T, smoothed_sum_sta, shade=True,
color='grey')
ax3.set_xlabel('x')
ax3.set_ylabel('time steps')
plt.show()
plt.close()
Theoretical Neuroscienceの図2.25Cのような図が再現できました。