非官方中文翻译 本页译自 MNE-Python 官方文档： 查看英文原文 ↗。 文档版权归 MNE Developers 所有（BSD-3-Clause）。

使用电流源密度（CSD）变换 EEG 数据

本脚本展示如何使用 CSD [1] [2] [3] [4]。CSD 对传感器信号取空间拉普拉斯（x 与 y 方向的导数），作用相当于 MEG 中的平面梯度计。计算这些空间导数可减小点扩散；CSD 变换后的数据地形图更锐利、更清晰，从而减轻容积传导的负面影响。

# Authors: Alex Rockhill <aprockhill@mailbox.org>
#
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.

import matplotlib.pyplot as plt
import numpy as np

import mne
from mne.datasets import sample

print(__doc__)

data_path = sample.data_path()

加载示例受试者数据

meg_path = data_path / "MEG" / "sample"
raw = mne.io.read_raw_fif(meg_path / "sample_audvis_raw.fif")
raw = raw.pick(picks=["eeg", "eog", "ecg", "stim"], exclude="bads").load_data()
events = mne.find_events(raw)
raw.set_eeg_reference(projection=True).apply_proj()

Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_raw.fif...
    Read a total of 3 projection items:
        PCA-v1 (1 x 102)  idle
        PCA-v2 (1 x 102)  idle
        PCA-v3 (1 x 102)  idle
    Range : 25800 ... 192599 =     42.956 ...   320.670 secs
Ready.
Reading 0 ... 166799  =      0.000 ...   277.714 secs...
Finding events on: STI 014
320 events found on stim channel STI 014
Event IDs: [ 1  2  3  4  5 32]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...

	General
	Filename(s)	sample_audvis_raw.fif
	MNE object type	Raw
	Measurement date	2002-12-03 at 19:01:10 UTC
	Participant	Unknown
	Experimenter	MEG
	Acquisition
	Duration	00:04:38 (HH:MM:SS)
	Sampling frequency	600.61 Hz
	Time points	166,800
	Channels
	EEG	59
	EOG	1
	Stimulus	9
	Head & sensor digitization	146 points
	Filters
	Highpass	0.10 Hz
	Lowpass	172.18 Hz
	Projections	Average EEG reference (on)

绘制原始数据与 CSD 变换后的原始数据：

raw_csd = mne.preprocessing.compute_current_source_density(raw)
raw.plot()
raw_csd.plot()

• 
• 

Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm

同时查看功率谱密度：

raw.compute_psd().plot(picks="data", exclude="bads", amplitude=False)
raw_csd.compute_psd().plot(picks="data", exclude="bads", amplitude=False)

• 
• 

Effective window size : 3.410 (s)
Plotting power spectral density (dB=True).
Effective window size : 3.410 (s)
Plotting power spectral density (dB=True).

CSD 也可用于诱发（平均）数据。这里先分段并平均，以便演示。

event_id = {
    "auditory/left": 1,
    "auditory/right": 2,
    "visual/left": 3,
    "visual/right": 4,
    "smiley": 5,
    "button": 32,
}
epochs = mne.Epochs(raw, events, event_id=event_id, tmin=-0.2, tmax=0.5, preload=True)
evoked = epochs["auditory"].average()

Not setting metadata
320 matching events found
Setting baseline interval to [-0.19979521315838786, 0.0] s
Applying baseline correction (mode: mean)
Created an SSP operator (subspace dimension = 1)
1 projection items activated
Using data from preloaded Raw for 320 events and 421 original time points ...
0 bad epochs dropped

先看 CSD 如何影响头皮地形图：

times = np.array([-0.1, 0.0, 0.05, 0.1, 0.15])
evoked_csd = mne.preprocessing.compute_current_source_density(evoked)
evoked.plot_joint(title="Average Reference", show=False)
evoked_csd.plot_joint(title="Current Source Density")

• 
• 

Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Projections have already been applied. Setting proj attribute to True.
Projections have already been applied. Setting proj attribute to True.

CSD 有 stiffness 与 lambda2 参数，分别影响平滑程度与样条灵活性。看看它们如何影响解：

fig, ax = plt.subplots(4, 4, layout="constrained")
fig.set_size_inches(10, 10)
for i, lambda2 in enumerate([0, 1e-7, 1e-5, 1e-3]):
    for j, m in enumerate([5, 4, 3, 2]):
        this_evoked_csd = mne.preprocessing.compute_current_source_density(
            evoked, stiffness=m, lambda2=lambda2
        )
        this_evoked_csd.plot_topomap(
            0.1, axes=ax[i, j], contours=4, time_unit="s", colorbar=False, show=False
        )
        ax[i, j].set_title(f"stiffness={m}\nλ²={lambda2}")

Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm
Fitted sphere radius:         91.2 mm
Origin head coordinates:      -4.2 16.4 51.8 mm
Origin device coordinates:    1.5 18.2 -10.1 mm

参考文献

[1]

F. Perrin, O. Bertrand, and J. Pernier. Scalp Current Density Mapping: Value and Estimation from Potential Data. IEEE Transactions on Biomedical Engineering, BME-34(4):283–288, 1987. doi:10.1109/TBME.1987.326089.

[2]

François M. Perrin, Jacques Pernier, Olivier M. Bertrand, and Jean Franćois Echallier. Spherical splines for scalp potential and current density mapping. Electroencephalography and Clinical Neurophysiology, 72(2):184–187, 1989. doi:10.1016/0013-4694(89)90180-6.

[3]

Mike X. Cohen. Analyzing Neural Time Series Data: Theory and Practice. MIT Press, 2014.

[4]

Jürgen Kayser and Craig E. Tenke. On the benefits of using surface Laplacian (Current Source Density) methodology in electrophysiology. International journal of psychophysiology : official journal of the International Organization of Psychophysiology, 97(3):171–173, 2015. doi:10.1016/j.ijpsycho.2015.06.001.