Dynamic brain synergy uncovers functional neural coordination in Parkinson’s disease under dopaminergic modulation

Abstract

Background

Brain synergy and redundancy are emerging as pivotal aspects to understand neural functions, providing insights into high-order information that traditional functional connectivity (FC) methods cannot access. Despite their significance, these aspects have not been investigated in Parkinson’s disease (PD). This paper advances the understanding of synergy and redundancy by integrating them with dynamic analysis, which is essential in the investigation of PD.

Methods

Dynamic brain synergy and redundancy were developed and quantified by the constructed dynamic information decomposition framework, and was applied to walking-state functional near-infrared spectroscopy (fNIRS) signals of 63 PD patients undergoing dopaminergic treatment and 36 healthy controls.

Results

Dynamic brain synergy was restored to normal levels following dopaminergic treatment. Dynamic FC could not access high-order neural information and had insignificant variations in dopaminergic modulation among PD patients, and dynamic brain redundancy also exhibited insignificant treatment-induced variations.

Conclusion

Dynamic brain synergy offers an advancing perspective on neural dynamics and promises to uncover high-order functional biomarkers for PD early diagnosis and individualized treatment.

Trial registration

This study has been registered in Chinese Clinical Trial Registry (ChiCTR1900022655).

Introduction

Parkinson’s disease (PD) is a common brain disorder associated with degenerative brain functions with remarkable complexity of neural networks, particularly in motor control [1]. This complexity arises not only from the independent roles of specific brain regions but also from the coordination between different regions [2, 3]. The brain coordination process of PD is increasingly approached by functional near-infrared spectroscopy (fNIRS) [4–7]. Compared with positron emission tomography (PET), functional magnetic resonance imaging (fMRI), and electroencephalogram (EEG), fNIRS is robust to movement artifacts, portable for task-related measurement, convenient to transfer and use, etc [8, 9]. With fNIRS, an increasingly number of studies tried to use functional connectivity (FC) to investigate brain information processing of PD patients following different treatments [10], such as dopaminergic medication [11]. FC quantifies the similarity between regional activity to characterize brain-wide information interactions [12]. However, the human brain operates as a complex distributed information-processing system, of which the crucial synergistic and redundant information cannot be characterized by FC [13, 14]. Furthermore, it is challenging for FC to capture the high-order abnormalities within the complex brain networks of PD [15, 16].

Brain synergy and redundancy are emerging as crucial concepts to understand brain coordination mechanisms with synergistic and redundant information [13, 14]. Taking “bilateral brain hemispheres” as an example, each hemisphere processes unique information that the other does not access, referred to as “unique information”. Information that can be independently processed by the left or right hemisphere is referred to as “redundant information”. Information that arises from the integration of both hemispheres is referred to as “synergistic information”. Redundant information enhances system robustness, while synergistic information facilitates functional integration of the brain [17–19]. Brain synergy and redundancy can facilitate the characterization of sophisticated information transmission in complex brain networks and hold significant promise for elucidating the functional mechanisms of PD.

In addition to brain synergy and redundancy, dynamic analysis should also be explored to enhance the functional investigation of PD. Dynamic analysis offers critical insights into the brain’s temporal responses to varying task demands, which static analyses cannot capture. Previous studies have collected resting-state brain signals and constructed dynamic FC and microstates to analyze temporal pattern variations of brain activity [20–24]. In addition to the resting-state analyses, Lu et al. developed a dynamic walking-state FC framework to signify functional neurodegeneration of PD [25]. They found that compared with healthy controls, PD patients had a higher probability of transiting to brain states associated with high-strength interactions during walking. The above studies demonstrated that dynamic analysis was essential for the exploration of PD.

In this study, we conceptualized and developed the methodology for dynamic brain synergy and redundancy based on previous foundational analyses, and for the first time to analyze dopaminergic modulation in PD. Dynamic brain synergy and redundancy were quantified through the proposed dynamic information decomposition method. We examined the dynamic variations of synergistic and redundant information during dopaminergic modulation of PD. Specifically, we seek to assess whether analyzing brain functions in terms of synergistic and redundant information offers an advancing perspective on neural information transmission. By incorporating walking-state neuroimaging data, we revealed the critical role of dynamic brain synergy and redundancy in dopaminergic modulation of PD. We hypothesized that dynamic brain synergy was significantly decreased in PD patients under dopaminergic treatment while dynamic brain redundancy and functional connectivity (FC) exhibited insignificant variations based on the compensation mechanism of PD and functional analysis of redundancy and FC [26–28].

Methods

Participants

Sixty-three PD patients (age (years): M = 63.87, s.d. = 8.48; 35 males, 28 females) participated in the study. The inclusion criteria were: (1) aged between 45 and 85 years old, (2) clinically diagnosed as PD based on the 2015 MDS clinical diagnostic criteria [29], (3) walking independently without any assistive devices. The exclusion criteria were: (1) having a history of brain trauma, severe blood pressure fluctuations during dopaminergic treatment, (2) failing to stand or walk for 75 s at a time, (3) any factors affecting the gait performance, such as scoliosis, arthritis, and cardiovascular instability, (4) inability to follow instructions, (5) having psychiatric comorbidity. Thirty-six healthy controls (age(years): M = 61.56, s.d. = 6.12; 13 males, 23 females) were recruited. The inclusion criteria for healthy controls were: (1) aged 45–85 years old, (2) willing to participate in the study and cooperate with the testing. The exclusion criteria were: (1) having a history of neurological diseases or psychiatric conditions, (2) any factor impacting gait performances.

The levodopa equivalent daily dose (LEDD) for patients was: M = 575.82 (mg/d), s.d. = 298.65, and the motor examination scores of movement disorder society unified Parkinson’s disease rating scale (MDS-UPDRS-III) decreased significantly (, from the paired-sample non-parametric Wilcoxon signed rank test) between the OFF state (without dopaminergic treatment, M = 38.25, s.d. = 13.72) and ON state (with dopaminergic treatment, M = 23.50, s.d. = 10.59). The OFF state occurs after patients withdrawn from dopaminergic medications for at least 12 h. The ON state is defined as the period of optimal symptom control, typically occurring 1–2 h after the administration of dopaminergic medication. PD patients under the ON state had significantly larger speed and stride length than patients under the OFF state (speed: ON: 1.01 ± 0.19, OFF: 0.90 ± 0.24, ; stride length: ON: 1.06 ± 0.17, OFF: 0.95 ± 0.23, ; P values calculated from the paired-sample non-parametric Wilcoxon signed rank test). Table 1 presented the clinical characteristics of PD patients and healthy controls. This study was approved by the Ethics Committee of Tianjin Huanhu Hospital, Tianjin, China (No. 2019-31) and registered in Chinese Clinical Trial Registry (ChiCTR1900022655). All participants provided their written consent to take part in the experiment.

Table 1.

Clinical characteristics of PD patients and healthy controls

Clinical characteristics	PD patients	Healthy controls
Number	63	36
Age (years)	63.87 ± 8.48	61.56 ± 6.12
Sex (male/female)	35/28	13/23
LEDDa (mg/d)	575.82 ± 298.65	–
Disease durations (years)	5.40 ± 3.15	–
Hoehn and Yahr Scale	2.89 ± 0.60	–
MMSEb	25.83 ± 3.33	-
MDS-UPDRS-IIIc	OFF: 38.25 ± 13.72	–
	ON: 23.50 ± 10.59	–
Speed (m/s)	OFF: 0.90 ± 0.24	0.14 ± 0.13
	ON: 1.01 ± 0.19
Stride length (m)	OFF: 0.95 ± 0.23	1.19 ± 0.11
	ON: 1.06 ± 0.17

^aLEDD Levodopa equivalent daily dose

^bMMSE Mini-mental state examination

^cMDS-UPDRS-III Part III (motor examination) of movement disorder society unified Parkinson’s disease rating scale

Experimental setup and recording of fNIRS brain signals

Each participant underwent functional near-infrared spectroscopy (fNIRS) recording of walking-state brain signals by a portable and wireless Nirsmart equipment (Danyang Huichuang Medical Equipment Co., Ltd China). Compared with the resting-state experiments, walking-state assessment could provide more valuable signals of PD analysis, given that gait disturbance is common among PD patients and is one of the major disabling symptoms [30, 31]. With walking-state measures, functional near-infrared spectroscopy (fNIRS) was employed in this study since it was portable, flexible for experiment, and had good tolerance to movement artifacts [32, 33].

The protocol in this study contained three 75 s walking tests for healthy controls and totally six 75 s walking tests under the OFF and ON states (a 1–2 h interval between two states) for PD patients. Each walking test included 30 s standing, 35 s walking, and 10 s standing, as depicted in Fig. 1. The walking was constrained to a set 10 meters distance with 180-degree turns around the standing poles (1.8 meters) placed at the starting and end points. No episode of freezing observed during turning or gait initiation. Twenty-six optodes (14 sources and 12 detectors) were used to collect brain signals at a sampling rate of 11 Hz from the prefrontal cortex (PFC), premotor cortex (PMC), and primary somatosensory cortex (S1), which were of great importance in motor planning and controlling during walking [34–36] and were investigated in this study. The source-detector distance was 3 cm, which was commonly used in fNIRS studies [37, 38]. The utilized wavelengths were 730 and 850 nm. The arrangement of fNIRS optodes was consistent with the previous studies [4, 38] and determined based on the analyzed brain regions and Nirspace equipment (Danyang Huichuang Medical Equipment Co., Ltd China). Figure 2 showed the detailed channel distribution for brain signal collection.

Fig. 1.

Experimental protocol. The protocol contained three 75 s walking tests for healthy controls and six 75 s walking tests under the OFF and ON states (a 1–2 h interval between the OFF and ON states) for PD patients. Each walking test included 30 s standing, 35 s walking and 10 s standing

Fig. 2.

Channel distribution. Twenty-six optodes (14 sources and 12 detectors) were placed at the left and right prefrontal cortex (L-PFC and R-PFC), premotor cortex (L-PMC and R-PMC), and primary somatosensory cortex (L-S1 and R-S1), generating 30 fNIRS channels. Ci indicates the i-th channel

Preprocessing of fNIRS brain signals

The collected brain signals were preprocessed with the following steps: (1) Motion artifacts were detected and eliminated by combing sliding window analysis and cubic spline interpolation [39, 40]; (2) Physiological noises were removed by a 0.010.2 Hz bandpass filter [41, 42]; (3) Signals were transformed into the relative concentration change of oxyhemoglobin () by the modified Beer-Lambert law [43]; (4) The scalp blood flow interference was filtered out by principal component analysis [44, 45]. The processed signals during the walking period were corrected with the 5 s pre-walking baseline and extracted for the following analysis. The data preprocessing and the following methods were achieved in MATLAB 2022a.

Dynamic information decomposition

To investigate the role of dynamic brain synergy and redundancy in dopaminergic modulation among PD patients, we constructed a dynamic information decomposition method to dissect walking-state functional near-infrared spectroscopy (fNIRS) data collected from the PFC, PMC, and S1 regions. Through the decomposition method, fNIRS data were deconstructed to quantify dynamic brain synergy and redundancy, uncovering dynamic synergistic and redundant information transmission between different brain regions, as depicted in Fig. 3.

Fig. 3.

The constructed dynamic information decomposition framework. The collected signals were divided into multiple segments. Each segment was processed by Integrated Information Decomposition and used for the construction of brain synergy and redundancy matrices. The constructed matrices were normalized and applied for the extraction of dynamic features, which were utilized for the analysis of dynamic brain synergy and redundancy in dopaminergic modulation of PD

Dynamic brain synergy and redundancy were quantified with the constructed dynamic information decomposition framework. Firstly, the preprocessed brain signals were segmented into multiple overlapping windows by a 20 s sliding window with a 1 s step. For each window, the brain synergy and redundancy matrices were constructed with the Integrated Information Decomposition (IID) method [46]. IID extends the concept of Partial Information Decomposition (PID) [47] to dynamic systems, allowing for the calculation of synergistic and redundant interactions between different brain regions. Specifically, PID extends Shannon’s mutual information theory and divides the mutual information I(X, Y; Z) from two sources X and Y to a target Z into four components: unique information from X about Z, unique information from Y about Z, redundant information shared by both X and Y, synergistic information that is only accessible when X and Y are combined. This decomposition is formulated as:

1

IID extends the PID framework to dynamic systems for time-series analysis. For a time-series system X composed of two variables and , IID analyzes how information from (past state) influences (future state) and captures temporal information of stable redundancy (redred) and synergy (synsyn). In dynamic systems, IID introduces a set of interrelated equations to account for redundant, unique, and synergistic information across time. In practice, this involves a linear system of 15 equations with 16 unknowns, representing the relationships among redundancy, synergy, and unique components. The system can be solved by specifying the redundancy component with minimum mutual information [47]:

2

This enables us to solve the linear system of equations and retrieve all components of IID for X. IID was applied to calculate synergy and redundancy components from different brain channels, which were further used for the construction of brain synergy and redundancy matrices. Brain synergy (or redundancy) matrix M was defined as:

3

where indicated brain synergy (or redundancy) strength between the channel data and from the i-th and j-th channels. N represented channel number and was set as 30 in this study.

The synergy and redundancy matrices of PD patients were standardized by aligning with the corresponding distribution in the group of healthy controls through z-score transformation [14, 48, 49], which obtained the z-score by standardizing the original value with the population average and standard deviation of the healthy control group. Then the positive z-scores of matrices were reset as zero while the negative z-scores were reset as their absolute values, because we focused on the dynamic properties of the highly variable components (negative z-scores) in this study [50, 51]. The normalized matrices were quantified by the global efficiency (GE), clustering coefficient (CC), and local efficiency (LE) using the Brain Connectivity Toolbox [52]. GE (or CC) and LE measures the global and local parallel information processing within the network. GE was calculated as:

4

where indicated the shortest path length between channels i and j, C represented the set of all channels, was the channel number. quantified the most information route across channels i and j under the synergy representation. GE was calculated for the matrix in each window, resulting in a dynamic GE vector , where T indicated the window number. CC was computed as:

5

where was the number of triangles around the i-th channel, and was the degree of the i-th channel. CC was computed for the matrix in each window, generating a dynamic CC vector . LE was calculated as:

6

where Re indicated the prefrontal cortex (PFC), premotor cortex (PMC), or primary somatosensory cortex (S1). denoted the channel number in Re. represented the shortest path length between channels j and h, that contains only neighbors of channel i in . LE was also evaluated for the matrix in each window, generating a dynamic LE vector . The dynamic features were constructed as:

7

8

where V represented , or , E denoted GE, CC or LE, indicated the mean of E. Large range and variance indicated that the brain had high fluctuation and variability in task execution.

Dynamic functional connectivity

Dynamic functional connectivity was constructed to demonstrate the effectiveness of the proposed method. Specifically, the same sliding window (a 20 s sliding window with a 1 s step) was used to divide the preprocessed brain signals into overlapping windows. For each window, functional connectivity matrix was formulated. Concretely, the Pearson’s correlation coefficient between the i-th and j-th fNIRS channels and was calculated as:

9

where m was the length of and . and was the mean of and . Ci and Cj represented the i-th and j-th channels. The Pearson’s correlation coefficient of each channel pair was computed and applied to construct the functional connectivity matrix :

10

where N was the channel number. After formulating dynamic functional connectivity, the process (same as the previous analysis) was performed, including normalization, calculation of dynamic global efficiency and local efficiency, and computation of the range and variance features.

Statistical analysis

Given that the data did not conform to the assumption of normality with the Kolmogorov-Smirnov test, the paired-sample non-parametric Wilcoxon signed rank test was used to determine whether the dynamic features had significant variations after dopaminergic treatment. The non-parametric Wilcoxon rank sum test was applied to analyze the statistical difference of dynamic features and clinical characteristics between healthy controls and PD patients. The false discovery rate (FDR) correction was adopted for multiple comparisons according to the Benjamini-Hochberg procedure. Statistical results were reported with the FDR-adjusted alpha level P, z-value Z, and effect size r. All corrections were assessed by Spearman’s rank-based non-parametric correlation analysis. The correction results were reported with the alpha level P and the coefficient rho. All tests were two-sided and with an alpha level of 0.05. The effect size r is conventionally considered low at around 0.1, medium at around 0.3, and large at around 0.5 or greater [53].

Results

Analysis of dynamic brain synergy and redundancy in dopaminergic modulation of PD

Dynamic brain synergy had substantial variations after dopaminergic treatment, whereas dynamic brain redundancy exhibited minor treatment-induced changes, as depicted in Fig. 4.

Fig. 4.

Dynamic variations of brain synergy and redundancy features under the OFF (without dopaminergic treatment) and ON states (with dopaminergic treatment)

With global and local efficiency calculation, the features of dynamic brain synergy among PD patients had significant reductions after dopaminergic treatment (synergy range between OFF and ON: FDR, Z = 3.48, r = 0.44; synergy variance between OFF and ON: FDR, Z = 2.42, r = 0.31) while the features of dynamic brain redundancy had no substantial treatment-induced variations (redundancy range between OFF and ON: FDR, Z = 0.11, r = 0.01; redundancy variance between OFF and ON: FDR, Z = 0.10, r = 0.01) (Fig. 5A). The features of both dynamic brain synergy and redundancy showed significant differences between healthy controls (HC) and PD patients under the OFF state. After administering dopaminergic treatment, dynamic brain synergy returned to the normal level (no significant difference between ON and HC, synergy range: FDR, Z = 0.59, r = 0.06; synergy variance: FDR, Z = 0.60, r = 0.06) while dynamic brain redundancy continued to exhibit significant deviations from the normal level (significant difference between ON and HC, redundancy range: FDR, Z = 3.68, r = 0.37; redundancy variance: FDR, Z = 3.50, r = 0.35). Regional analyses of dynamic brain synergy between one region and other regions were also performed (Fig. 5B). The features of dynamic brain synergy also showed significant treatment-induced variations among different regions (synergy range in PFC, PMC, S1: FDR, Z = 2.07, r = 0.26; FDR, Z = 3.44, r = 0.43; FDR, Z = 2.07, r = 0.26; synergy variance in PFC, PMC, S1: FDR, Z = 2.76, r = 0.35; FDR, Z = 2.88, r = 0.36; FDR, Z = 2.09, r = 0.26) (Synergy features in one brain region Re are based on the analysis between Re and other regions).

Fig. 5.

Analysis of dynamic brain synergy and redundancy in dopaminergic modulation of PD. The features were calculated with global and local efficiency. A Statistical analysis for features of dynamic brain synergy and redundancy (calculated with global efficiency GE) between PD patients (n = 63) under the OFF and ON states and healthy controls (HC) (n = 36). The features of dynamic brain synergy had significant treatment-induced variations, as denoted by red (range OFF: M = 0.550, s.d. = 0.109, range ON: M = 0.483, s.d. = 0.085, variance OFF: M = 0.027, s.d. = 0.012, variance ON: M = 0.022, s.d. = 0.008; * FDR, ** FDR, from two-sided non-parametric paired-sample Wilcoxon signed rank test and Wilcoxon rank sum test with FDR correction). B Statistical analysis for features of dynamic brain synergy (calculated with local efficiency LE) in the prefrontal cortex (PFC), premotor cortex (PMC), and primary somatosensory cortex (S1). The features of dynamic brain synergy showed significant treatment-induced variations among different regions (range PFC OFF: M = 0.376, s.d. = 0.096, range PFC ON: M = 0.333, s.d. = 0.065; range PMC OFF: M = 0.393, s.d. = 0.104, range PMC ON: M = 0.344, s.d. = 0.059; range S1 OFF: M = 0.387, s.d. = 0.117, range S1 ON: M = 0.346, s.d. = 0.059; variance PFC OFF: M = 0.014, s.d. = 0.009, variance PFC ON: M = 0.010, s.d. = 0.004; variance PMC OFF: M = 0.015, s.d. = 0.010, variance PMC ON: M = 0.010, s.d. = 0.004; variance S1 OFF: M = 0.015, s.d. = 0.011, variance S1 ON: M = 0.011, s.d. = 0.004; * FDR, ** FDR, from two-sided non-parametric paired-sample Wilcoxon signed rank test with FDR correction) (Synergy features in one brain region Re are calculated based on the analysis between Re and other regions). For the violin plots, each colored circle indicates one participant, white circles indicate median values, central lines indicate the mean values, box limits indicate upper and lower quartiles and whiskers represent 1.5 the interquartile range

The results by clustering coefficient calculation were consistent with those by global efficiency, as shown in Fig. 6. For PD patients, the features of dynamic brain synergy had significant treatment-induced reductions (synergy range between OFF and ON: FDR, Z = 2.87, r = 0.36; synergy variance between OFF and ON: FDR, Z = 2.38, r = 0.30) while the features of dynamic brain redundancy did not show significant variations after dopaminergic treatment (redundancy range between OFF and ON: FDR, Z = 0.43, r = 0.05; redundancy variance between OFF and ON: FDR, Z = 0.62, r = 0.08). For both dynamic brain synergy and redundancy, the features showed significant differences between HC and PD patients under the OFF state. After dopaminergic treatment, dynamic brain synergy reverted to its normal state (no significant difference between ON and HC, synergy range: FDR, Z = 1.04, r = 0.10; synergy variance: FDR, Z = 0.85, r = 0.09), whereas dynamic brain redundancy still showed a significant deviation from the normal state (significant difference between ON and HC, redundancy range: FDR, Z = 3.09, r = 0.31; redundancy variance: FDR, Z = 3.03, r = 0.30).

Fig. 6.

Statistical analysis for features of dynamic brain synergy and redundancy (calculated with clustering coefficient) between PD patients (n = 63) under the OFF and ON states and healthy controls (HC) (n = 36). The features of dynamic brain synergy had significant treatment-induced variations, as denoted by red (range OFF: M = 0.346, s.d. = 0.110, range ON: M = 0.300, s.d. = 0.057, variance OFF: M = 0.012, s.d. = 0.010, variance ON: M = 0.008, s.d. = 0.003; * FDR, ** FDR, from two-sided non-parametric paired-sample Wilcoxon signed rank test and Wilcoxon rank sum test with FDR correction). For the violin plots, each colored circle indicates one participant, white circles indicate median values, central lines indicate the mean values, box limits indicate upper and lower quartiles and whiskers represent 1.5 the interquartile range

The above results exhibited that dynamic brain synergy showed significant treatment-induced variations and was crucial to reveal dopaminergic modulation in PD patients while dynamic brain redundancy exhibited insignificant treatment-induced changes in this study.

Analysis of dynamic functional connectivity, static brain features, and correlations between dynamic brain synergy and clinical characteristics

To further demonstrate the importance of dynamic brain synergy, dynamic functional connectivity (dynamic FC) was constructed for dopaminergic treatment analysis, as depicted in the previous subsection “2.5 Dynamic functional connectivity”. Dynamic FC exhibited insignificant variations in PD patients following dopaminergic treatment (GE range: FDR, Z = 1.42, r = 0.18; GE variance: FDR, Z = 1.23, r = 0.16; CC range: FDR, Z = 1.41, r = 0.17; CC variance: FDR, Z = 1.23, r = 0.16), as depicted in Fig. 7.

Fig. 7.

Statistical analysis of dynamic FC features. Dynamic FC had no significant changes after dopaminergic treatment (GE range OFF: M = 0.459, s.d. = 0.199, GE range ON: M = 0.444, s.d. = 0.184; GE variance OFF: M = 0.032, s.d. = 0.026, GE variance ON: M = 0.031, s.d. = 0.024; CC range OFF: M = 0.202, s.d. = 0.082, CC range ON: M = 0.221, s.d. = 0.070; CC variance OFF: M = 0.006, s.d. = 0.005, CC variance ON: M = 0.007, s.d. = 0.004; n.s. not significant, FDR, from two-sided non-parametric paired-sample Wilcoxon signed rank test with FDR correction)

Static brain synergy, redundancy, and FC were quantified in PD. No significant differences were observed in static brain synergy, redundancy, or FC between the OFF and ON states ( static brain synergy (GE): FDR, Z = 1.27, r = 0.16; static brain redundancy (GE): FDR, Z = 0.23, r = 0.03; static FC (GE): FDR, Z = 2.08, r = 0.26; static brain synergy (CC): FDR, Z = 1.69, r = 0.21; static brain redundancy (CC): FDR, Z = 0.69, r = 0.09; static FC (CC): FDR, Z = 2.20, r = 0.28 ), as depicted in Fig. 8.

Fig. 8.

Statistical analysis of features in static brain synergy, redundancy, and FC. Static brain synergy, redundancy, and FC exhibited no significant treatment-induced variations ( GE synergy OFF: M = 0.807, s.d. = 0.221, GE synergy ON: M = 0.744, s.d. = 0.186, FDR, Z = 1.27, r = 0.16; GE redundancy OFF: M = 0.450, s.d. = 0.138, GE redundancy ON: M = 0.457, s.d. = 0.116, FDR, Z = 0.23, r = 0.03; GE FC OFF: M = 0.605, s.d. = 0.353, GE FC ON: M = 0.672, s.d. = 0.335, FDR, Z = 2.08, r = 0.26; CC synergy OFF: M = 0.582, s.d. = 0.193, CC synergy ON: M = 0.523, s.d. = 0.124, FDR, Z = 1.69, r = 0.21; CC redundancy OFF: M = 0.256, s.d. = 0.109, CC redundancy ON: M = 0.264, s.d. = 0.096, FDR, Z = 0.69, r = 0.09; CC FC OFF: M = 0.185, s.d. = 0.140, CC FC ON: M = 0.220, s.d. = 0.136, FDR, Z = 2.20, R=0.28 ). For the violin plots, each colored circle indicates one participant, white circles indicate median values, central lines indicate the mean values, box limits indicate upper and lower quartiles and whiskers represent 1.5 the interquartile range

The correlations between features of dynamic brain synergy and clinical characteristics were calculated, as depicted in Tables 2 and 3. Dynamic brain synergy calculated from CC and was significantly correlated with the age of PD patients (synergy range PFC: rho=0.35, FDR; synergy variance PFC: rho=0.36, FDR; synergy variance CC: rho=0.3433, FDR), as depicted in Fig. 9.

Table 2.

The correlations between features of dynamic brain synergy and clinical characteristics including age, LEDD, motor improvement, and MMSE

Dynamic brain synergy featuresa		Age	LEDD	Motor improvementb	MMSE
GE	Range	0.0067 (0.9587)	0.0792 (0.6711)	0.1416 (0.9957)	0.0923 (0.9941)
	Variance	0.1942 (0.1631)	0.0926 (0.6711)	0.0724 (0.9957)	0.0165 (0.9941)
CC	Range	0.2918 (0.0508)	0.0998 (0.6711)	0.0007 (0.9957)	0.0453 (0.9941)
	Variance	–0.3433 (0.0197)	0.0550 (0.6711)	0.0109 (0.9957)	0.1195 (0.9941)
	Range	–0.3544 (0.0197)	0.0586 (0.6711)	0.1031 (0.9957)	0.1935 (0.6435)
	Variance	–0.3643 (0.0197)	0.0580 (0.6711)	0.0978 (0.9957)	0.2371 (0.6130)
	Range	0.1387 (0.3092)	0.1114 (0.6711)	0.0535 (0.9957)	0.0229 (0.9941)
	Variance	0.1981 (0.1631)	0.1733 (0.6711)	0.0183 (0.9957)	0.0009 (0.9941)
	Range	0.1926 (0.1631)	0.1128 (0.6711)	0.0166 (0.9957)	0.0082 (0.9941)
	Variance	0.2102 (0.1631)	0.0570 (0.6711)	0.0985 (0.9957)	0.0071 (0.9941)

The number indicates the Spearman correlation coefficient and the corresponding P-value with FDR correction. Bold denotes significant correlation ( FDR)

^aDifference between ON state and OFF state

^bCalculated as (-)/, and indicate the MDS-UPDRS III scores under the OFF and ON states

Table 3.

The correlations between features of dynamic brain synergy and clinical characteristics including disease duration, Hoehn and Yahr scale, speed, and stride length

Dynamic brain synergy featuresa		Disease duration	Hoehn and Yahr scale	Speed improvementb	Stride length Improvementb
GE	Range	0.0466 (0.8986)	0.0833 (0.9923)	0.0808 (0.9246)	0.1561 (0.9069)
	Variance	0.0697 (0.8431)	0.0289 (0.9923)	0.0745 (0.9246)	0.0919 (0.9069)
CC	Range	0.1719 (0.4932)	0.0013 (0.9923)	0.0516 (0.9246)	0.0888 (0.9069)
	Variance	0.1349 (0.4932)	0.0265 (0.9923)	0.0123 (0.9246)	0.0151 (0.9069)
	Range	0.2291 (0.4932)	0.0737 (0.9923)	0.0306 (0.9246)	0.0590 (0.9069)
	Variance	0.2003 (0.4932)	0.0042 (0.9923)	0.0282 (0.9246)	0.0294 (0.9069)
	Range	0.1561 (0.4932)	0.0158 (0.9923)	0.0207 (0.9246)	0.0311 (0.9069)
	Variance	0.1401 (0.4932)	0.0459 (0.9923)	0.0528 (0.9246)	0.0302 (0.9069)
	Range	0.0314 (0.8986)	0.0589 (0.9923)	0.1467 (0.9246)	0.1285 (0.9069)
	Variance	0.0017 (0.9897)	0.0127 (0.9923)	0.1143 (0.9246)	0.0880 (0.9069)

The number indicates the Spearman correlation coefficient and the corresponding P-value with FDR correction

^a Difference between ON state and OFF state. ^b Calculated as (ON-OFF)/OFF, ON and OFF indicate speed or stride length under the OFF and ON states

Fig. 9.

Correlation analysis between dynamic features of brain synergy and clinical characteristics. Dynamic brain synergy calculated from CC and was significantly correlated with age of PD patients (synergy range PFC: rho=0.35, FDR; synergy variance PFC: rho=0.36, FDR; synergy variance CC: rho=0.34, FDR, from Spearman’s rank-based non-parametric correlation analysis with FDR correction)

The above results showed that: (1) Dynamic FC could not access high-order neural information and exhibited insignificant variations in PD patients under dopaminergic treatment. (2) Dynamic brain redundancy did not exhibit treatment-induced variations and need to be further explored; (3) Dynamic analysis was essential for dopaminergic treatment analysis of PD; (4) Dynamic brain synergy in PFC was of great significance for the exploration of brain functional mechanisms among PD patients.

Randomization-based Validations

Three randomization-based validation analyses: time-shuffled surrogates, phase-randomized surrogates, and null-network controls were performed, as detailed as follows: (1) Time-shuffled surrogate analysis: For each fNIRS channel’s time series, the temporal order of data points was permuted independently across channels, destroying any time-locked relationships between channels while preserving the univariate amplitude distribution. One thousand surrogate datasets were generated, and our entire pipeline was rerun. The significant difference () of dynamic synergy GE between the OFF and ON states in the original data became entirely non-significant in all surrogates (Range: all , median surrogate ; Variance: all , median surrogate ). (2) Phase-randomized surrogates: For each fNIRS channel, a Fourier transform was performed, followed by randomization of the phase spectrum while preserving the amplitude spectrum. Then the inverse Fourier transform was applied to generate a new time series, preserving linear properties but destroying nonlinear phase couplings between channels. One thousand surrogate datasets were generated, and our entire pipeline was rerun. Similar to the time-shuffling results, no significant difference was observed between the OFF and ON states in the phase randomized surrogate data (Range: all , median surrogate ; Variance: all , median surrogate ). (3) Null-network control: For each synergy matrix in the time window, a null network was created with the edge weight shuffling null model that randomly permuted the connection weights while preserving the exact topology of the original network. One thousand null-networks were generated, and the entire pipeline was rerun. For all null-networks, dynamic brain synergy GE did not show significant differences between the OFF and ON states (Range: all , median surrogate ; Variance: all , median surrogate ). The original dynamic brain synergy had significant variations after dopaminergic treatment while dynamic brain synergy with time-shuffled surrogates, phase-randomized surrogates, or null-network controls did not have significant treatment-induced variations, which demonstrated that the dynamic brain synergy arose from genuine neural information dynamics rather than from statistical or methodological artifacts.

Comparison with Other Connectivity Measures

The effectiveness of dynamic brain synergy was compared with dynamic multivariate mutual information [54], partial correlations [55], and Granger causality [56], as shown in Fig. 10. Dynamic brain synergy exhibited significant treatment-induced variations after dopaminergic treatment while dynamic multivariate mutual information, partial correlations, and Granger causality exhibited no significant difference between the OFF and ON states, which demonstrated the crucial role of dynamic brain synergy for dopaminergic modulation analysis of PD.

Fig. 10.

Statistical analysis of dynamic multivariate mutual information (MMI), partial correlations (PC), and Granger causality (GC). Dynamic MMI, PC, and GC had no significant variations after dopaminergic treatment (MMI GE range OFF: M = 0.3819, s.d. = 0.0488, MMI GE range ON: M = 0.3885, s.d. = 0.0601; MMI GE variance OFF: M = 0.0133, s.d. = 0.0040, MMI GE variance ON: M = 0.0130, s.d. = 0.0040; PC GE range OFF: M = 0.1014, s.d. = 0.0156, PC GE range ON: M = 0.1006, s.d. = 0.0147; PC GE variance OFF: M = 0.0008, s.d. = 0.0003, PC GE variance ON: M = 0.0009, s.d. = 0.0002; GC GE range OFF: M = 0.0810, s.d. = 0.0122, GC GE range ON: M = 0.0768, s.d. = 0.0127; GC GE variance OFF: M = 0.0006, s.d. = 0.0002, GC GE variance ON: M = 0.0005, s.d. = 0.0002; n.s.: not significant, FDR, from two-sided non-parametric paired-sample Wilcoxon signed rank test with FDR correction

Discussion

Analysis of dynamic brain synergy, redundancy, and functional connectivity in dopaminergic modulation

In this study, dynamic brain synergy had significant treatment-induced variations while dynamic brain redundancy and functional connectivity (FC) exhibited insignificant variations following dopaminergic treatment. In PD patients, dopaminergic modulation appears to selectively affect dynamic brain synergy, thereby facilitating a partial restoration of information dynamics toward a healthier state, while redundancy remains relatively stable. This selective modulation suggests that dopaminergic treatments may preferentially enhance integrative processing abilities within the brain, which are essential for complex behaviors such as movement, whereas the robustness provided by redundancy [18, 19] is barely impacted by such treatments. The dynamic FC analysis had insignificant treatment-induced changes, indicating that traditional FC failed to capture treatment-responsive high-order information that are essential for brain functions. Moreover, the insignificant variations of dynamic redundancy and FC suggested a similarity in brain organization between redundancy and FC [28].

Our core finding is that dopaminergic medication normalizes pathologically elevated dynamic brain synergy in PD patients during a walking task, bringing it closer to levels in healthy controls, and this normalization is concomitant with clinical improvement. Specifically, the reduction in dynamic brain synergy reflects a decrease in the compensatory effort and restoration of automated processing. In the OFF state of PD, due to dysfunction of the cortico-basal ganglia circuits that normally dominate motor execution, the brain needs to recruit additional neural resources through an effortful and conscious compensatory mechanism to maintain motor outputs [26, 57]. This compensatory effort may manifest as over-engagement of higher-order association cortices (such as the prefrontal cortex [58, 59]) and an abnormal elevation of network synergy. Sorrentino et al. [60] found that PD patients exhibited a reduced functional repertoire (the ability to access different activity patterns) and decreased flexibility, which is associated with beta-band hyper-synchronization. This suggests that brain dynamics in the OFF state are more stereotyped and restricted. Agouram et al. [61] showed that levodopa selectively modulated the occurrence rate of specific beta burst waveform motifs in the sensorimotor cortex and enhanced the STN-cortical connectivity corresponding to these motifs. This indicates that treatment promotes a more specific and efficient mode of neural communication. The high dynamic brain synergy in the OFF state signifies the effortful and high-cost compensatory process. Dopaminergic therapy restores the function of the primary motor circuits, making motor control more efficient and automated, thereby reducing the demand for additional compensatory mechanisms. Consequently, the reduction in synergy signifies the brain’s return from a high-energy-consumption and low-efficiency compensatory state to a low-energy-consumption and high-efficiency automated processing state. This is also consistent with the behavioral improvements.

This study highlights the importance of dynamic brain analysis over traditional static measures, which are limited in capturing the brain’s moment-to-moment responses [62–64]. Through the proposed dynamic information decomposition method, this study reveals the temporal complexities of synergy and redundancy in PD. Dopaminergic treatment induced significant changes in the dynamics of brain synergy, reflected by significant changes of range and variance in dynamic synergy within the prefrontal, premotor, and primary somatosensory regions. The finding reinforces the concept that PD primarily disrupts dynamic information-processing capabilities rather than merely altering stable, baseline connectivity patterns. Furthermore, the significant changes in dynamic synergy following dopaminergic treatment underscore the potential of dynamic synergy as a biomarker to monitor treatment efficacy, particularly given the minimal concurrent changes observed in dynamic redundancy.

The specificity of dynamic brain synergy in response to dopaminergic modulation provides valuable insights into the functional mechanisms underlying PD. Although both dynamic synergy and redundancy distinguish PD patients from healthy controls, only dynamic brain synergy exhibits near-normal restoration following dopaminergic treatment. This distinction suggests that dopaminergic intervention primarily enhances integrative processing capabilities crucial for motor control and cognitive function, aligning with the clinical improvements typically observed in PD patients after treatment. In contrast, the minimal changes observed in dynamic redundancy indicate a potential resilience in redundant processing pathways, which may support brain stability in PD, even as synergistic processes decline, and suggest a similarity in brain organization between redundancy and FC [28].

The observed synergy effects reflected the physiological specificity. First, synergy mathematically analyzed synergistic information, and there was no particular sensitivity difference between synergy and redundancy within their mathematical formulation [46]. Moreover, previous studies demonstrated that brain synergy was more crucial to capture essential physilogical information than redundancy and FC [14, 28].

The estimation of redundancy by minimum mutual information, while a practical solution to an underdetermined system [47], is potentially bias results toward conservative values. Future work could explore alternative estimators, such as those based on the pointwise common change in surprisal [65] or machine learning-based approaches [66], to validate and extend our findings. While the redundancy is associated with stability, its failure to be normalized with treatment warrants a more critical examination. Elevated redundancy may represent a compensatory mechanism, where the brain relies on duplicated information processing to maintain functions in the face of neurodegeneration [59, 67]. Alternatively, it could signify pathological rigidity and a loss of network adaptability [68]. This stability parallels that of functional connectivity, suggesting redundancy may share similar properties with conventional FC measures [13]. The functional implications of redundancy are thus complex and may range from protective to maladaptive, meriting further investigation in longitudinal studies.

The used experimental setup

Walking was a primary concern for PD patients and notably challenging due to gait disturbance [30]. Thus, the walking task provided a clinically relevant context to detect PD-related impairments and treatment-induced changes and was used in this study. The complex treatment-induced brain patterns during walking could be challenging to be captured by the FC methods, such as correlation-based and dynamic multifractal analysis approaches [69–71], and had been proven to be characterized by the developed dynamic brain synergy.

The proposed method could capture significant treatment-induced changes in dynamic brain synergy during walking, suggesting that it was promising to analyze neural mechanisms underlying PD. Applying the proposed method to more complex tasks would yield even more pronounced effects, as such tasks involve a heavier reliance on integrative brain processes and are known to be impaired in PD. Specifically, the same framework could capture PD-related impairments in executive-motor dual-tasks, which could promote more valuable signals of PD patients [72, 73]. In the future, we are set to employ and validate the proposed method in more complex tasks.

During the walking test, fNIRS was utilized for our dynamic brain synergy and redundancy analysis since we want to collect walking-state brain signals and fNIRS is robust to motion artifacts, portable for task-related measurement, flexible for experiments, etc [4, 9]. Gait is a primary concern for PD patients and doctors [30] and the clinical walking test was used as the motor tasks to analyze the efficacy of dopaminergic treatment in this study. EEG has advantages in detecting brain signals , but it s still prone to motion artifacts, necessitating the further development of advanced techniques to ensure signal quality and measurement reliability [74]. Currently, EEG primarily focuses on non-motor tasks [75] and has been used for the analysis of PD resting-state functional brain networks following dopaminergic treatment [76–78]. Thus, we employed fNIRS in this study. In the future, we are set to investigate the application of EEG and integrate EEG and fNIRS through the development of multi-modal algorithms that combine their respective advantages.

Oxyhemoglobin change for brain synergy and redundancy

The perspective for brain synergy and redundancy calculated from was multi-faceted, focusing on the physiological validity of the signal, the nature of our information-theoretic approach, and the internal validation provided by our own results. (1) as a valid proxy for functional brain activity: Although is a hemodynamic signal and not a direct measure of neuronal firing, an extensive body of studies showed that it was a robust and reliable proxy for task-evoked functional brain activity [8, 79]. The neurovascular coupling mechanism ensures that increases in local neuronal activity are followed by a regional hemodynamic response, which is captured by fNIRS. (2) The information-theoretic framework applies regardless of different types of the input signals: Our method was based on dynamic information decomposition, an information-theoretic framework. The key strength of this approach was that it quantified the statistical dependencies and information sharing structure between multiple time series, irrespective of their specific physiological origin. Even if the signal was a surrogate measure, the relative patterns of information sharing could be preserved and evaluated by our information-theoretic framework. (3) Internal validation from our results: Dynamic brain synergy had significant treatment-induced variations while dynamic redundancy and FC had insignificant changes after dopaminergic treatment. These variations aligned with the established compensation theory of PD [59, 80], where synergistic information was critical for complex, integrated motor tasks (such as walking). If the HbO signal was merely a noisy or non-neural correlate, it was highly unlikely that such a clear, specific, and theoretically grounded result was observed. The specificity of the effects suggested that our method successfully elucidated a high-order functional property of the brain dynamics for dopaminergic treatment analysis.

The distinction between optimization and dampening for the reduction of dynamic brain synergy

In isolation, a reduction in a neural metric like dynamic synergy could be ambiguous. However, we posit that the convergence of multiple lines of evidence from our study favors the optimization interpretation rather than a sedative effect. (1) The direction of behavioral change: A sedative effect would predict a deterioration or no change in behavioral performance [81, 82]. In stark contrast, we observed a significant improvement in motor function following dopaminergic treatment: a significant decrease in the MDS-UPDRS-III motor score and a significant increase in both walking speed and stride length. It is physiologically inconsistent to attribute these clear motor improvements to a neural process characterized as a sedation-like dampening. The neural change (reduced dynamic synergy) is therefore most interpreted as part of the mechanism enabling functional improvement, not impairment. (2) The specificity of neural effect: As generalized, sedative dampening of cortical engagement would be expected to cause a widespread reduction in most measures of brain activity and functional interaction [83, 84]. Our data showed the opposite—a highly specific neural effect: Dynamic synergy was significantly decreased with dopaminergic treatment while dynamic redundancy and FC exhibited insignificant variations after dopaminergic treatment. A sedative effect would likely suppress all forms of neural communication, blurring the distinction between synergistic and redundant information sharing. The fact that the reduction was isolated to synergy alone indicates a targeted reconfiguration of information processing, not a global dampening. (3) The normalization towards the healthy baseline: A sedative effect would push the brain’s functional state away from its healthy and optimal configuration. Our interpretation of optimization is strengthened by the fact that the change in PD patients moved their neural dynamics closer to those observed in the healthy control (HC) group. After treatment, the level of dynamic synergy in PD patients was statistically indistinguishable from that of HC, whereas it was significantly elevated in the OFF state. This normalization towards the healthy benchmark is a strong argument for the change being beneficial.

The role of dopamine on the statistical properties of Dopamine on the large-scale alterations

Angiolelli et al. provided a compelling computational framework [85], the virtual Parkinsonian patient, which used a whole-brain model to infer the dopaminergic tone from EEG and deep brain recordings. Their work successfully demonstrated that model inversion could distinguish between the OFF and ON dopaminergic states by inferring a higher dopaminergic tone in the ON state, linking this parameter to changes in large-scale brain dynamics, particularly through the analysis of aperiodic bursts and Avalanche Transition Matrices (ATMs). Our study offers a complementary yet distinct perspective by focusing on high-order information dynamics—specifically, dynamic brain synergy and redundancy—during a walking task in PD patients, assessed via fNIRS. While Angiolelli et al. model the effect of dopamine on large-scale electrophysiological dynamics and infer a latent dopaminergic parameter, we directly quantify how dopaminergic modulation alters the information-sharing architecture of the brain in a behaviorally relevant context. The findings align with and extend the insights from Angiolelli et al. are presented as follows: (1) Dopamine modulates high-order information processing: Angiolelli et al. show that dopamine alters the spatiotemporal spreading of aperiodic bursts (captured by ATMs), which are indicative of large-scale network communication. Similarly, we found that dynamic brain synergy—a measure of complex, integrative information processing—is significantly restored following dopaminergic treatment. This suggests that dopamine not only modulates rhythmic or aperiodic electrophysiological activities but also improves the brain’s capacity for synergistic information processing, which is critical for coordinated motor behavior. (2) Specificity of dopaminergic effects: Both studies highlight the specificity of dopamine’s action. Angiolelli et al. show that inferred clearly separates ON and OFF states. We similarly found that only dynamic synergy (not dynamic redundancy or functional connectivity) showed significant normalization with treatment. This aligns with the idea that dopamine preferentially restores integrative and adaptive neural processes—those captured by both ATMs and synergy—rather than broadly amplifying all forms of neural communication. (3) Dynamic analysis reveals treatment-sensitive mechanisms: Angiolelli et al. use dynamic features (ATMs) for model inversion and state discrimination. We also emphasize dynamics—temporal fluctuations in synergy—which proved essential for detecting treatment effects. Static measures (including static FC and static synergy/redundancy) failed to show significant changes, underscoring the importance of time-resolved analysis to capture dopamine’s impact on neural flexibility and integration. (4) Complementary methodologies and biomarkers: While Angiolelli et al. use a model-based approach to infer dopamine tone from EEG/LFP, we use an information-theoretic approach to directly quantify how dopamine alters information sharing patterns during walking. Both approaches converge on the conclusion that dopamine facilitates efficient and adaptive large-scale brain dynamics, and both propose novel biomarkers (inferred vs. dynamic synergy) for monitoring PD treatment.

Conclusion

This paper constructed a dynamic information decomposition framework to evaluate dynamic brain synergy and employed it for the first time to uncover functional neural coordination in PD patients under dopaminergic treatment. Clinical experiments demonstrated that dynamic brain synergy was restored to the normal level following dopaminergic treatment and could uncover high-order information that traditional FC could not access. Dynamic brain synergy was promising to uncover high-order biomarkers for early PD diagnosis and personalized treatment.

Abbreviations

FC

Functional connectivity

PD

Parkinson’s disease

HC

Healthy control

IID

Integrated information decomposition

PID

Partial information decomposition

GE

Global efficiency

LE

Local efficiency

Red

Redundancy

Syn

Synergy

PFC

Prefrontal cortex

PMC

Premotor cortex

S1

Primary somatosensory cortex

FDR

False discovery rate

ΔHbo

Relative concentration change of oxyhemoglobin

Author contributions

J.L. and Y.C. conceived the idea, designed the experiments, and analyzed the data. X.Z., Z.Z., Y.Y., and Y.W. performed the experiments with the input from J.W., J.H., and N.Y.. J.L and N.Y. wrote the manuscript. All authors have seen the paper, agree to its content, and approve the submission.

Funding

The experimental design and data collection of this study were supported by National Key R&D Program of China (2024YFB4709900), National Natural Science Foundation of China (U24A20284, 62473214), and Tianjin Health Research Project (TJWJ2022MS033).

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

This study was approved by the Ethics Committee of Tianjin Huanhu Hospital, Tianjin, China (No. 2019-31) and registered in Chinese Clinical Trial Registry (ChiCTR1900022655). All participants provided their written consent to take part in the experiment.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.