An fNIRS-Based Dynamic Functional Connectivity Analysis Method to Signify Functional Neurodegeneration of Parkinson’s Disease

Parkinson’s disease (PD) is a prevalent brain disorder, and PD diagnosis is crucial for treatment. Existing methods for PD diagnosis are mainly focused on behavior analysis, while the functional neurodegeneration of PD has not been well investigated. This paper proposes a method to signify functional neurodegeneration of PD with dynamic functional connectivity analysis. A functional near-infrared spectroscopy (fNIRS)-based experimental paradigm was designed to capture brain activation from 50 PD patients and 41 age-matched healthy controls in clinical walking tests. Dynamic functional connectivity was constructed with sliding-window correlation analysis, and k-means clustering was applied to generate the key brain connectivity states. Dynamic state features including state occurrence probability, state transition percentage and state statistical features were extracted to quantify the variations of brain functional networks. A support vector machine was trained to classify PD patients and healthy controls. Statistical analysis was conducted to investigate the difference between PD patients and healthy controls as well as the relationship between dynamic state features and the MDS-UPDRS sub-score of gait. The results showed that PD patients had a higher probability of transiting to brain connectivity states with high levels of information transmission compared with healthy controls. The MDS-UPDRS sub-score of gait and the dynamics state features showed a significant correlation. Moreover, the proposed method had better classification performances than the available fNIRS-based methods in terms of accuracy and F1 score. Thus, the proposed method well signified functional neurodegeneration of PD, and the dynamic state features may serve as promising functional biomarkers for PD diagnosis.

statistical features were extracted to quantify the variations of brain functional networks. A support vector machine was trained to classify PD patients and healthy controls. Statistical analysis was conducted to investigate the difference between PD patients and healthy controls as well as the relationship between dynamic state features and the MDS-UPDRS sub-score of gait. The results showed that PD patients had a higher probability of transiting to brain connectivity states with high levels of information transmission compared with healthy controls. The MDS-UPDRS sub-score of gait and the dynamics state features showed a significant correlation. Moreover, the proposed method had better classification performances than the available fNIRS-based methods in terms of accuracy and F1 score. Thus, the proposed method well signified functional neurodegeneration of PD, and the dynamic state features may serve as promising functional biomarkers for PD diagnosis.

I. INTRODUCTION
P ARKINSON'S disease (PD) is a prevalent neurodegenerative disorder [1], [2]. It results from the loss of nerve cells in the basal ganglia, leading to the gradual decline of dopamine [3], [4]. The degeneration of dopamine-containing cells results in the deterioration of motor function and commonly causes gait disorders [5]. The diagnosis of PD is crucial to the development and improvement of treatment plans [6].
Previous studies tried to perform PD diagnosis with clinical rating scales [7]. However, clinical ratings are easily affected by the subjective judgment of raters. Many studies attempted to approach PD diagnosis in the kinematic levels, through diverse devices including accelerometer, video, inertial measurement units, etc [8], [9], [10], [11], [12], [13]. Nevertheless, such devices could not detect the brain functional neurodegeneration and thus have intrinsic constraints to PD diagnosis.
A growing number of studies are attempting to proceed PD diagnosis at the level of brain functions by investigating brain activation features from functional magnetic resonance imaging, electroencephalographic, and diffusion tensor imaging in the resting state [14], [15], [16], [17]. In addition to these modalities, functional near-infrared spectroscopy (fNIRS), an emerging neuroimaging technology, is increasingly applied to explore the brain functional neurodegeneration of PD patients in clinical walking tests [18], [19], [20] for its portability for task-related measurement, convenience to transfer and use, flexibility for experiments and tolerance to movement noises, etc [21], [22]. In [23], [24], [25], [26], and [27], researchers tried to analyze the difference between PD patients and healthy controls in clinical walking tests with mean, standard deviation, mean detrended time series, range, transition acceleration and angle of hemoglobin concentration changes.
Existing methods have been tried to differentiate PD patients and healthy controls with brain activation features, while the functional neurodegeneration of PD has not been thoroughly investigated, especially from the aspect of dynamic functional connectivity in clinical walking tests. Compared with the commonly used resting-state experiment, walking could promote more valuable signals of PD patients since gait disorder is common among PD patients and is considered as one of the primary disabling symptoms [28], [29]. Dynamic functional connectivity considers the temporal variations of brain networks and could capture the meaningful changes during walking [30], [31], [32], [33]. The dynamics of the brain are impacted by PD, which may lead to the deterioration of brain information transmission during walking [34], [35], [36]. Thus, dynamic functional connectivity is promising to signify functional neurodegeneration of PD during walking.
This paper proposed a method to signify functional neurodegeneration of PD with dynamic functional connectivity analysis. Specifically, three key brain connectivity states were derived with dynamic functional connectivity and k-means clustering. Dynamic state features were extracted to quantify the variations of brain functional networks. The results showed that the proposed method well signified functional neurodegeneration of PD.

II. METHOD
The participants and experimental design are introduced first. Then the analysis method is provided to signify the functional neurodegeneration of PD. The capability of our method is demonstrated with the statistical analysis of extracted features and classification performances for PD diagnosis.
A. Participants and Experiment Design 1) Participants: Fifty PD patients and forty-one agematched healthy controls took part in this experiment. Healthy controls have no history of brain disorders. Patients were tested without PD medication. PD patients were considered if they were neurologist-diagnosed with PD and able to perform unassisted walking for 75 s. PD patients were excluded if they were with brain trauma and could not follow the directions of clinical specialists. Table I shows the clinical features of participants. PD patients and healthy controls had similar age, sex, height, and weight. Moreover, PD patients had significantly different MDS-UPDR sub-score of gait compared with healthy controls. Ethics approval of this study was obtained from the Ethics Committee of Tianjin Huanhu Hospital, Tianjin, China, and written consents of all participants were attained. Moreover, the study has been registered in Chinese Clinical Trial Registry (ChiCTR1900022655).
2) Experimental Paradigm and fNIRS Recording: Figure 1 provides the experimental paradigm of clinical walking tests. Participants conducted three walking tests. Each walking test consisted of standing for 30 s, walking for 35 s at a usual pace, standing for 10 s, and rest for 2 minutes.
Each participant wore a portable Huichuang Nirsmart system (Danyang Huichuang Medical Equipment Co., Ltd, China) with 26 optodes to record the fNIRS signals. The fNIRS optodes consisted of 14 sources and 12 detectors, as shown in Figure 2. The optodes were placed at six brain regions: left and right prefrontal cortex (L-PFC and R-PFC), premotor cortex (L-PMC and R-PMC), primary somatosensory cortex (L-S1 and R-S1). Figure 3 provides the framework of the proposed method. The preprocessed fNIRS brain signals were used for the The arrangement of optodes containing 14 sources and 12 detectors. The optodes were put at six brain regions: left and right prefrontal cortex (L-PFC and R-PFC), premotor cortex (L-PMC and R-PMC), primary somatosensory cortex (L-S1 and R-S1), resulting in 30 fNIRS channels. The i-th fNIRS channel is denoted by Ci.

B. Proposed Method
construction of dynamic functional connectivity matrices. The constructed matrices were processed with k-means clustering to generate key recurring brain connectivity states, which were characterized by network properties. Dynamic state features were extracted to quantify the time-varying properties of brain functional networks. Dynamic state features were analyzed and applied to classify patients and healthy controls.
1) Preprocessing: The collected fNIRS brain signals were processed with the following steps: (1) the modified Beer-Lambert law was used to transform the recorded optical intensities into the oxyhemoglobin concentration change (△H bO) [37]. (2) a 0.01-0.2 Hz Butterworth bandpass filter was applied to filter out the physiological noises, such as heartbeats and respiration [38], [39]. (3) a sliding window with standard deviation and amplitude thresholds was used to identify the motion artifacts of filtered signals, which were further removed by cubic spline interpolation [40], [41]. (4) principal component analysis was utilized to eliminate physiological interference [42], [43]. The processed fNIRS signals during the walking period were extracted for the following analysis.
2) Dynamic Functional Connectivity: The dynamics of brain functional networks were explored with the sliding-window correlation analysis method. Specifically, a 20 s sliding window with a 1 s step was selected and used to divide the preprocessed △H bO signals into multiple overlapped temporal windows. The functional connectivity matrix was calculated for each temporal window. Concretely, given the i-th and j-th fNIRS channels x Ci and x C j , the Pearson's correlation coefficient P x Ci x C j between x Ci and x C j was defined as follows: where m is the length of x Ci and x C j .
x Ci andx C j is the mean of x Ci and x C j . Ci and C j indicate the i-th and j-th channels. The Pearson's correlation coefficient of each channel pair was computed and used to construct the functional connectivity matrix M FC : where N is the channel number. M FC is undirected and symmetric, i.e. ∀i, j, P x C i x C j = P x C j x C i .
3) Clustering: The constructed dynamic functional connectivity matrices represent different network patterns and are suitable to be classified by an unsupervised learning method for the lack of prior knowledge about the categorization of brain network patterns. Thus, k-means clustering, an effective heuristic method with low computation complexity, was conducted to classify the functional connectivity matrices into k brain connectivity states. Concretely, the upper triangular elements of the functional connectivity matrices were extracted as (x 1 , x 2 , . . . , x M ), where x i indicates the upper triangular elements of the i-th functional connectivity matrix, M is the number of matrices. K-means clustering aims to classify M functional connectivity matrices into k sets S = {S 1 , S 2 , . . . , S k } by optimizing the loss function: where µ i is the mean of matrices in S i . The state number needs to be carefully selected to avoid mismatch or overfitting in clustering. To identify the optimal state number, functional connectivity matrices were analyzed by k-means clustering analysis, with the state number k ranging from 1 to 10. Then the optimal state number was determined by the elbow method with the minimum within-cluster sum of distance [44]. K-means clustering was repeated 500 times with random initialization of cluster centers, and the resulting cluster medians were used for the analysis of brain connectivity states. In this study, three key brain connectivity states, named low-strength, medium-strength, and high-strength brain connectivity states, were derived to characterize the dynamic network patterns. The details of the derived brain connectivity states were shown in the subsection "B. Brain Connectivity States" of Section III. RESULTS. 4) Properties of Brain Connectivity States: Two properties: global efficiency E and clustering coefficient C were computed and used to quantify the derived brain connectivity states. Global efficiency E measures the integration of brain connectivity states and is with the following definition: where Z is the set of all channels, and z is the channel number. d i j is the shortest path length between channels i and j. Clustering coefficient C is the measure of segregation of brain connectivity states, which is defined as: where t i is the number of triangles around the i-th channel, and k i is the degree of the i-th channel.

5) Dynamic State Features:
Three kinds of features: state occurrence probability, state transition percentage, and state statistical features were extracted to assess the variations of brain functional networks.
State occurrence probability (SOP): indicates the likelihood that a specific brain connectivity state will occur during the course of the sliding time. S O P is defined as follows: where s i is the i-th brain connectivity state, S(t) represents the brain connectivity state at time t, and T is the entire sliding period. In this study, s 1 , s 2 , and s 3 represent the low-strength, medium-strength, and high-strength brain connectivity states and are set as 1, 2, and 3, respectively. c f (·) is the condition function. c f (·) is set as 1 (condition is met) or 0 (condition is not met). State transition percentage (ST P): describes the transition likelihood from one state to another: where s i and s j indicates the i-th and j-th brain connectivity state. ST P i j (i = j) represents the inner-state transition percentage while ST P i j (i ̸ = j) indicates the inter-state transition percentage. State statistical features: includes the mean, maximum and minimum states, which were defined as the mean, maximum and minimum values of set [s(1), s(2), . . . , s(T )]. s(t) = i indicates that the brain connectivity state at t is s i . 6) Classifier: The extracted dynamic state features were normalized by the min-max scaler and applied for the training of support vector machine (SVM). SVM is a commonly used classifier to categorize data and has demonstrated its effectiveness in brain signal processing [45]. In this study, SVM projects the data with dynamic state features into a new space with a maximum margin to the two classes (0: healthy controls, 1: PD patients). SVM is with RBF kernel.
C. Performance Evaluation 1) Evaluation Process: K-fold cross validation, a widely utilized evaluation technique, was applied to assess the classification performance. k was set as 5 in this study. During each round of cross validation, brain connectivity states were derived with k-means clustering from the training set and used for the analysis of dynamic networks of the test subjects. Two evaluation metrics: accuracy and F1 score were applied for the measurement of classification performance.
2) Statistical Analysis: Wilcoxon rank sum test and chi-squared test were utilized to investigate the difference of dynamic state features, network properties, age, weight, height, and gender between PD patients and healthy controls. The correlation between the MDS-UPDRS sub-score of gait and dynamic state features was calculated by Pearson correlations. In this study, p < 0.05 represents significant difference.

A. Identification of Optimal State Number
The optimal state number was learned by the elbow method with the greatest perpendicular distance to the oblique line in   [46]. In this study, the optimal state number was 3 during each round of cross validation. Figure 4 shows an example of the curve of within-cluster sum of distance against state number.

B. Brain Connectivity States
With k-means clustering, three key brain connectivity states, named low-strength, medium-strength, and high-strength brain connectivity states, were generated to represent different brain network patterns, as shown in Figure 5. It seems that the high-strength brain connectivity state has the largest connectivity strength (the brightest color) while the low-strength brain connectivity state has the smallest connectivity strength (the lightest color).
Global efficiency and clustering coefficient were calculated to characterize brain connectivity states, as shown in Figure 6. The high-strength brain connectivity state had significantly higher global efficiency and cluster coefficient than the low-strength and medium-strength brain connectivity states, indicating that the high-strength brain connectivity state had hyper-parallel information transmission in brain functional networks. Moreover, the low-strength brain connectivity state had the lowest global efficiency and clustering coefficient among all brain connectivity states, indicating that the low-strength brain connectivity state had less information exchange across brain functional networks. Figure 7 presents the state transition percentage. PD patients had significantly higher inner-state transition percentages in the medium-strength and high-strength brain connectivity states than healthy controls while healthy controls had significantly higher inner-state transition percentage in the low-strength brain connectivity state than PD patients. Moreover, PD patients had higher transition percentage from high-strength brain connectivity state to medium-strength brain connectivity state than healthy controls. Figure 8 shows the state occurrence probability and mean, minimum and maximum state of brain connectivity states. PD patients had Three key brain connectivity states, named low-strength, medium-strength, and high-strength brain connectivity states. Ci indicates the i-th channel. L-PFC, R-PFC, L-PMC, R-PMC, L-S1, and R-S1 represent the left prefrontal cortex, right prefrontal cortex, left premotor cortex, right premotor cortex, left primary somatosensory cortex, and right primary somatosensory cortex, respectively. significantly higher probabilities with the medium-strength and high-strength brain connectivity states during walking than healthy controls while healthy controls had a significantly higher probability with the low-strength brain connectivity state during walking than PD patients. Moreover, PD patients had significantly higher mean, minimum and maximum states than healthy controls. The above results showed that PD patients were with a higher probability of transiting to brain connectivity states with high levels of information transmission compared with healthy controls.

D. Correlation Between MDS-UPDRS Sub-Score of Gait and Dynamic State Features
The mean and maximum states as well as the state occurrence probability of low-strength and high-strength brain connectivity states and the MDS-UPDRS sub-score of gait were strongly associated, as depicted in Figure 9. Moreover, the inner-state transition percentages in the low-strength and highstrength brain connectivity states were significantly correlated with the MDS-UPDRS sub-score of gait. The above results showed that the gait performance was substantially associated with dynamic state features. Figure 10 presents the correlation between functional strength and MDS-UPDRS Sub-score of Gait. Functional strength of L-S1 was significantly correlated with MDS-UPDRS sub-score of gait. Figure 11 shows the performance of the proposed method compared with three available methods using fNIRS [25], [26], [27]. The proposed method outperformed method 1, 2, and 3 with Accuracy = 0.7708 ± 0.1134 and F1 = 0.8152 ± 0.0959.

IV. DISCUSSION
Dynamic functional connectivity could provide promising fundamental properties of brain functional networks and has been commonly used to analyze the dynamical behavior of brain functional networks. In [47], Allen et al. investigated resting-state functional magnetic resonance imaging (fMRI) of young adults with whole-brain dynamic functional connectivity. In [48], Dimitriadis et al. analyzed the resting-state electroencephalogram (EEG) brain signals of students with dynamic functional connectivity. In [49], Qi et al. analyzed the effects of rest-break on mental recovery using dynamic functional connectivity. In [50], Guan et al. explored the mental workloads of operators based on EEG-based dynamic functional connectivity.
Dynamic functional connectivity describes the temporal variations of brain functional networks over a short time and is related to different neurological disorders [51], [52]. PD affects the dynamics of brain functional networks and may deteriorate the brain information transmission [34], [35], [36]. Our study explored the dynamic functional connectivity of PD patients in clinical walking tests and extracted dynamic state features to quantify the time-varying properties of brain networks. Experimental results demonstrated the capability of our method to signify functional neurodegeneration of PD.
Our study showed that three brain connectivity states occurred among PD patients and healthy controls. The brain connectivity states represented different levels of information transmission within brain functional networks. PD patients had a higher probability of transiting to brain connectivity states with high levels of information transmission compared with healthy controls. PD affects motor function and deteriorates information transmission across brain functional networks [53], [54]. Thus, PD patients need to enlarge the  . State occurrence probability (left) and mean, minimum and maximum states (right) of brain connectivity states. * indicates significant difference. Fig. 9. Correlation between dynamic state features (state occurrence probability(a), state transition percentage(b), the mean, maximum and minimum states(c)) and the MDS-UPDRS sub-score of gait. p and r are the p-value and correlation. Red denotes a significant correlation. Fig. 10. Functional Strength of left and right premotor cortex (L-PMC and R-PMC) and primary somatosensory cortex (L-S1 and R-S1).p and r are the p-value and correlation. Red denotes a significant correlation. Performance comparison between our method and method 1 [25], method 2 [26], method 3 [27].
information transmission to compensate for the functional impairment caused by PD [55], [56].
The proposed method had better performances than the available fNIRS-based methods. The better performances may be attributed to the fact that the variations of brain functional networks are crucial to the analysis of PD [15], [57], [58]. Dynamic functional connectivity could track temporal fluctuations and may effectively capture the full extent of brain activity for PD diagnosis. Thus, it is of vital importance to explore the variations of brain functional networks for PD.

V. CONCLUSION
This paper presents a method to signify functional neurodegeneration of PD with dynamic functional connectivity analysis. Three key brain connectivity states were derived with dynamic functional connectivity and k-means clustering. The variations of brain functional networks were quantified by the proposed dynamic state features, including state occurrence probability, state transition percentage and state statistical features. The results showed that the proposed method well signified functional neurodegeneration of PD.