2.1.

Subjects

Thirty-one stroke patients enrolled from the Chinese Medicine Rehabilitation Center of Beijing Rehabilitation Hospital Affiliated to Capital Medical University participated in this study. The inclusion criteria were as follows: (1) MRI or CT confirmation of the first unilateral stroke, (2) age: 30 to 80 years, (3) modified Ashworth score $\le 2$ points, (4) Glasgow coma ccale $\text{score}\ge 8$, and (5) ability to maintain the sitting position for at least 6 min. The exclusion criteria were as follows: (1) previous experience with mental illness or taking antipsychotic medication or (2) having any of the following conditions: congestive heart failure, respiratory failure, deep vein thrombosis of the lower extremities, malignant progressive hypertension, active liver disease, or severe liver or kidney insufficiency. FMA was used to evaluate the patient’s motor function. According to the FMA scores, stroke patients were divided into two groups: Mild (15 patients, $\mathrm{FMA}\ge 85$) and MtS (16 patients, $\mathrm{FMA}<85$). We also recruited 11 healthy people, ranging in age from 48 to 59 years (mean ± SD: $50.91\pm 3.09$), as the control group. All subjects signed an informed consent form and were informed of the basic requirements and procedures prior to the experiment. The Ethics Committee of Beijing Rehabilitation Hospital Affiliated to Capital Medical University reviewed and approved this study. The registration number for the clinical trial is ChiCTR2000040137.

2.2.

Data Collection

We used the ETG-4000 (Hitachi, Japan), a 22-channel NIRS imaging device, to measure the hemodynamic signals in the motor cortex from subjects in the RS. The NIRS cap consisted of 7 detectors and 8 emitters (light sources), making up 22 channels. The distance between the detector and emitter was 30 mm, and the brain region below each channel (i.e., midpoint between detector and emitter) was the main detection area for the channel. Referring to the 10/20 electrode placement system, Cz was used as the anchor point for placing the NIRS cap, and the lower edge of the NIRS cap was parallel to the coronal axis (Fig. 1). According to previous studies, this source-detector placement covers the motor-related cortex area, including the premotor cortex, the supplementary motor cortex, and the primary motor cortex.^32–35 The experiment was conducted in a dark, quiet setting. To reduce movement artifacts, participants were instructed to close their eyes, remain conscious, and refrain from moving their bodies throughout the experiment. With a sampling rate of 10 Hz, NIRS data were obtained for 6 min.³⁶

Fig. 1

NIRS-measured brain area schematic diagram.

2.3.

Data Processing

By measuring the attenuation variations of near infrared light at two wavelengths (695 and 830 nm), ETG-4000 used the modified Beer-Lambert law to calculate two cerebral hemodynamic signals: the concentration changes of oxygenated hemoglobin ($\mathrm{\Delta }[{\mathrm{HbO}}_2]$) and deoxygenated hemoglobin ($\mathrm{\Delta }[\mathrm{Hb}]$). The hemodynamic signals were pre-processed in Matlab. The pre-processing involved the following steps: (1) detecting and correcting motion artifacts with the standard deviation and spline interpolation method, (2) removing frequency noise and low-frequency baseline drift with a second order band-pass Butterworth filter (0.01 to 0.1 Hz),³⁷ (3) reducing the superficial interference with the common average reference spatial filtering,^38,39 and (4) excluding the first and last 5 s of data to ensure a stable signal. Most subjects had 350-s of data for subsequent brain network analyses, whereas nine participants used 180-s of data for brain network analyses due to residual artifacts. Compared with $\mathrm{\Delta }[\mathrm{Hb}]$, $\mathrm{\Delta }[{\mathrm{HbO}}_2]$ has a higher signal-to-noise ratio and a higher correlation with the blood oxygen concentration dependence signal.⁴⁰ Thus, only the ${\mathrm{HbO}}_2$ data were analyzed in this paper, and the corresponding results of Hb are shown in the Supplementary Material.

2.4.

Correlation Matrix and Graph Construction

We used the 22 NIRS channels as network nodes and calculated Pearson correlation coefficients between each pair of channels to obtain a correlation coefficient matrix of $22\times 22$. Fisher’s Z transformation was used to convert the correlation matrix into a Z-value matrix to improve the normality.⁴¹ The matrix’s diagonal value was set to zero. Finally, the Z-value matrix was converted into the corresponding binary matrix by sparseness with different thresholds. All analyses were carried out over a range of thresholds because there is no “correct” threshold.⁴² We selected the threshold ranges of 0.3 to 0.7 with a step size of 0.01 to rarefy the network. 0.3 was chosen to exclude the low-level correlation in topology, and 0.7 was chosen to reduce the data splitting.⁴³ The absolute values of Z-scores in the matrix were sorted from smallest to largest, and those with absolute values greater than the threshold were set to 1 in the corresponding binary matrix, and the others were set to 0. For example, when the threshold was set as 0.4, the first 60% absolute values of Z were set to 1 in the corresponding binary matrix, and the others were set to 0. A value of 1 indicated that two channels were connected, that is, an edge existed between these two channels. Constructing graphs in this manner guaranteed the comparison of different groups’ topological properties under the same connection number.

2.5.

Small-World Properties

To analyze the motor network characteristic, we used the brain connectivity toolbox to calculate the following small-world properties of each binary network:⁴⁴ clustering coefficient ($C$), characteristic path length ($L$), transitivity ($T$), local efficiency ($LE$), global efficiency (GE), normalized clustering coefficient ($\gamma$), normalized characteristic path length ($\lambda$), and small-worldness ($\delta$).

A node’s clustering coefficient ($C_i$) represents the degree of connectivity between the node and its neighbors. The network’s clustering coefficient ($C$) is the average of all node clustering coefficients [Eq. (1)], and it reflects the entire network’s degree of local clustering and segregation; it is given as

The characteristic path length ($L$) is the average of all shortest paths between pairs of nodes [Eq. (2)] and reflects the overall routing efficiency and integration of the network. A shorter $L$ indicates faster information propagation. $L$ is calculated as

The global efficiency (GE) reflects the network’s global transmission capacity, which is the average of efficiencies between nodes and is calculated as

The local efficiency ($LE$) is the mean efficiency of the subgraph $G_i$, which consists of all of the neighboring nodes for each node and is calculated as

Transitivity ($T$) is the ratio of triangles (closed triples) to triples (three nodes that have connections) in the network. It is given as

To check whether the motor network had a small-world characteristic, its clustering coefficient and characteristic path length were compared with those from a random network with a similar node number and degree distribution. In general, we expected the small-world network to have ratios of $\gamma >1$, $\lambda \approx 1$, and $\delta >1$

To overcome the threshold influence on statistical analyses and modeling, we calculated the area between the topological property curve and the $X$-axis by the numerical integration method to get the area under the curve (AUC).⁴⁵ The AUC can provide an aggregated scalar that is not affected by the choice of a single threshold⁴⁶ and is sensitive to the network topology change.^47,48 We compared the AUC indicators between groups, analyzed the correlation between patients’ FMA and AUCs of topology properties, and used the AUC indicators as features in SVM.

2.6.

Relation Between Network Properties and Patients’ Motor Function

To explore the relationship between patients’ motor function and the motor network properties, we calculated the Partial correlations between patients’ FMA and the AUCs of topology properties with age and gender as control variables.

2.7.

SVM Classification

We used SVM to classify Mild patients, MtS patients, and Healthy controls in Python. SVM is a supervised machine learning algorithm. Through the selection of function subsets and corresponding discriminant functions, the actual risk of the SVM classifier is minimized according to the structural risk minimization criterion. SVM’s optimal decision plane is dependent only on the position and number of support vectors, which can perform well in the case of small samples. Essentially, SVM is a two-group classifier. It is possible to use one-versus-rest (OVR) or one-versus-one strategies for multigroup classification.

We used the AUCs of eight topological properties as alternative characteristics and used the recursive feature elimination method to select the features. The performance of SVM was validated using a nested cross-validation (CV) process with an outer and an inner loop. In the outer loop, we used leave-one-out CV, with one subject as the test sample and the remaining subjects as the training samples that were input to the inner loop. In the inner loop, we used 10-fold CV and used grid search to optimize the optimal model parameters. Specifically, all possible parameter combinations were enumerated by the grid search, and each parameter combination was trained 10 times. Then we selected the parameter combination with the best performance in the inner loop and applied it to the model evaluation in the outer loop. The OVR approach was used for the multigroup classification, and we calculated the sensitivity and specificity of each classifier.

2.8.

Statistical Analyses

The analysis of variance (ANOVA) with age and gender as covariables and group (Healthy, Mild, and MtS) as the between-subject factor was used to examine the differences in network topological properties among groups. Then posthoc T-tests (LSD correction) were performed for multiple comparisons. The Shapiro-Wilk test was used to determine whether the data had a normal distribution, and the Levene test was used to determine whether the variance was homogeneous. Statistical Package for the Social Sciences (SPSS) was used for statistical analyses, and the level of statistical significance was set to 0.05.

3.1.

Clinical Results

In this study, stroke patients were at $1.2\pm 1.04$ months after a stroke. As shown in Table 1, there was no significant difference in gender among the three groups, but there was a significant difference in age between groups. In the later analyses, we took both age and gender as control variables to eliminate their influence on the results. Lesion side and time after stroke onset were not significantly different between the Mild and MtS groups, and the FMA score was evidently lower for the MtS group than the Mild group (Table 1).

Table 1

Subject characteristics.

3.2.

Small-World Properties

The hemodynamic signals at a typical channel from one Healthy subject, one Mild patient, and one MtS patient are shown in Fig. 2. $\mathrm{\Delta }[{\mathrm{HbO}}_2]$ was used for calculating the motor network’s small-world properties. The trends of the motor network’s small-world properties for the three subject groups are depicted in Fig. 3. The majority of node pairs had connections when the threshold was low. When the threshold increased, some connections were lost, which led to a $C$ decrease. Therefore, connections between node pairs had to go through more nodes, resulting in the $L$ increase. The number of closed triples, as well as the local and global information transmission efficiency, decreased. High clustering ($\gamma >1$), small characteristic path ($\lambda \approx 1$), and small-world characteristics ($\delta >1$) were observed in all three groups.

Fig. 2

Time course of $\mathrm{\Delta }[{\mathrm{HbO}}_2]$ and $\mathrm{\Delta }[\mathrm{Hb}]$ at a typical channel (Ch13) from one Healthy subject (a), one Mild patient (b), and one MtS patient (c).

Fig. 3

Mean $C$ (a), $L$ (b), LE (c), GE (d), $T$ (e), $\gamma$ (f), $\lambda$ (g), and $\delta$ (h) for the three groups under each threshold. The shaded part indicates the standard error (SEM). The black, blue, and red small triangles represent significant differences between Healthy and Mild groups, Mild and MtS groups, and Healthy and MtS groups.

(p < 0.05, FDR correction) under this threshold, respectively.

Our first goal was to study the patients’ motor network reorganization. Thus, we examined how the three groups’ network properties differed from each other. As shown in Fig. 3, $C$, $LE$, and $T$ for the Mild group were lower than those for the MtS group and larger than those for the Healthy group. This was observed across a wide range of thresholds. At certain thresholds, GE for the Mild group was larger than that for the MtS group and lower than that for the healthy group. $L$, $\gamma$, and $\delta$ were greater in both the mild and MtS groups than in the healthy group under some thresholds. There was almost no intergroup difference in $\lambda$ among the three groups.

ANOVA with age and gender as covariables revealed that the group effect was significant for the AUCs of $C(p={1\mathrm{e}}^{-13})$, $L(p={7\mathrm{e}}^{-3})$, $LE(p={2\mathrm{e}}^{-7})$, $\mathrm{GE}(p={3\mathrm{e}}^{-4})$, $T(p={2\mathrm{e}}^{-9})$, and $\gamma (p=0.019)$. Then, we performed posthoc T-tests to analyze AUC differences between groups, and the results are shown in Fig. 4.

Fig. 4

AUC indicators of the small-world properties for the three groups, * indicates p < 0.05, ** indicates p < 0.01, and *** indicates p < 0.001 (LSD correction).

3.3.

Relation Between Network Properties and Patients’ Motor Function

With age and gender as control variables, we conducted Partial correlation analyses between patients’ FMA and the AUCs of eight network properties. The results displayed that AUCs of $C$, $LE$, and $T$ had a significant negative correlation with FMA, whereas the AUC of GE had a significant positive correlation with FMA (Fig. 5).

Fig. 5

Scatterplots of significant correlations between FMA and $C$-AUC (a), $LE$-AUC (b), $T$-AUC (c), and GE-AUC (d).

3.4.

SVM Classification

We used AUCs of all topological properties as alternative characteristics, and the results of feature selection showed that $C$ (weight = 0.232) presented the highest distinguishing ability, followed by $LE$ (weight = 0.222), $T$ (weight = 0.162), $L$ (weight = 0.120), GE (weight = 0.110), $\gamma$ (weight = 0.103), $\delta$ (weight = 0.038), and $\lambda$ (weight = 0.013) in sequence. The established SVM model achieved the highest accuracy of 85.7% for classifying the three groups of subjects using the first six network properties’ AUCs as features. The receiver operator characteristic (ROC) curves of the SVM models are shown in Fig. 6(b). The AUCs of ROC curves of SVM1 (Healthy to others); SVM2 (Mild to others) and SVM3 (MtS to others) were 98%, 89%, and 97%, respectively; the sensitivities of SVM1, SVM2, and SVM3 were 81.8%, 93.3%, and 81.3%, respectively; and the specificities of SVM1, SVM2, and SVM3 were 100%, 88%, and 95.8%, respectively. The small-world properties demonstrated high sensitivity and specificity for Healthy, Mild, and MtS subjects.

Fig. 6

(a) The confusion matrix of the classification result and (b) the ROC curves of the three SVM models.