Brain Temporal-Spectral Functional Variability Reveals Neural Improvements of DBS Treatment for Disorders of Consciousness

Deep brain stimulation (DBS) is establishing itself as a promising treatment for disorders of consciousness (DOC). Measuring consciousness changes is crucial in the optimization of DBS therapy for DOC patients. However, conventional measures use subjective metrics that limit the investigations of treatment-induced neural improvements. The focus of this study is to analyze the regulatory effects of DBS and explain the regulatory mechanism at the brain functional level for DOC patients. Specifically, this paper proposed a dynamic brain temporal-spectral analysis method to quantify DBS-induced brain functional variations in DOC patients. Functional near-infrared spectroscopy (fNIRS) that promised to evaluate consciousness levels was used to monitor brain variations of DOC patients. Specifically, a fNIRS-based experimental procedure with auditory stimuli was developed, and the brain activities during the procedure from thirteen DOC patients before and after the DBS treatment were recorded. Then, dynamic brain functional networks were formulated with a sliding-window correlation analysis of phase lag index. Afterwards, with respect to the temporal variations of global and regional networks, the variability of global efficiency, local efficiency, and clustering coefficient were extracted. Further, dynamic networks were converted into spectral representations by graph Fourier transform, and graph energy and diversity were formulated to assess the spectral global and regional variability. The results showed that DOC patients under DBS treatment exhibited increased global and regional functional variability that was significantly associated with consciousness improvements. Moreover, the functional variability in the right brain regions had a stronger correlation with consciousness enhancements than that in the left brain regions. Therefore, the proposed method well signifies DBS-induced brain functional variations in DOC patients, and the functional variability may serve as promising biomarkers for consciousness evaluations in DOC patients.


I. INTRODUCTION
D ISORDERS of consciousness (DOC) refer to a broad spectrum of neurologic conditions mainly characterized by impaired awareness and arousal [1].These disorders encompass various clinical entities, including vegetative state and minimally conscious state [2], [3].A comprehensive understanding of these conditions is essential for accurate clinical diagnosis, prognosis assessment, and treatment planning [4], [5].
Deep brain stimulation (DBS) is a promising therapeutic approach for DOC [6], involving the implantation of stimulating electrodes in the brain to modulate neural activity [7].In [8], Schiff showed that DBS modulates behavioral responsiveness in a patient with minimally conscious state.In [9], Magrassi et al. found that DBS could improve the clinical status of patients in the vegetative state and minimally Fig. 1.The framework of the proposed method, including (1) fNIRS recording of DOC patients, (2) dynamic brain functional network construction with a sliding-window correlation analysis of phase lag index, (3) extraction of dynamic brain temporal-spectral features, and (4) global and regional variability assessment.conscious state.In [10], Yang et al. demonstrated that DBS led to significant functional improvements of DOC patients and had better effects in patients with minimally conscious state than patients with vegetative state.Besides DBS, other treatment methods for DOC include rehabilitative therapies, sensory stimulation, pharmacological interventions, etc [11], [12], [13].Compared with these treatments, DBS allows for precise and localized stimulation of specific brain regions implicated in consciousness and has the potential to induce long-term changes in neural circuitry involved in DOC [14].
DBS has been used for the treatment of DOC.However, the specific effects of DBS for DOC patients and the underlying neural mechanism have not been well explored.Assessing DBS effects in DOC is essential in the optimization of DBS therapy for DOC patients.A number of studies tried to evaluate the performance of DBS in DOC patients with Coma Recovery Scale-Revised (CRS-R), which was powerful in the assessment and monitoring of patients with DOC [15], [16].In addition, an effective modified CRS-R (named CRS-R index) was proposed for the diagnosis of DOC patients [17].Compared with conventional CRS-R, CRS-R index accounted for the hierarchical structure of the individual items (auditory, visual, motor, oromotor, communication, and arousal) in the CRS-R assessment and had better diagnostic precision to distinguish between patients with vegetative state and minimally conscious state.However, CRS-R relies on the expertise and judgment of doctors and is prone to intra-rater and inter-rater variability.Moreover, CRS-R is incapable of detecting brain variations and thus has inherent limitations in assessing the state of consciousness.
A growing number of studies approached the evaluation of DBS effects for DOC patients at the brain functional level with functional magnetic resonance imaging (fMRI), electroencephalography (EEG), positron emission tomography (PET), etc [18], [19], [20], [21].In addition, functional near-infrared spectroscopy (fNIRS), an emerging neuroimaging technique, is increasingly utilized to analyze brain functional variations of neurological disorders for its adaptability for diverse experimental setups, portability for task-related measurement, robustness to motion-related interference, etc [22], [23].fNIRS monitored the cortical hemodynamic changes which occur in response to neural activity.With fNIRS, it can be observed how DBS affects the neural activity in specific brain regions implicated in regulatory mechanisms.Previous studies found that fNIRS could effectively detect DBS-induced brain functional variations in patients with Parkinson's disease [24], [25].Moreover, fNIRS showed promise in evaluating the levels of consciousness in DOC patients [26], [27], [28].Thus, fNIRS could be applied to analyze the regulatory mechanisms of DBS in DOC patients.
In our previous work, we assessed the DBS-induced brain functional variations in DOC patients with fNIRS-based functional connectivity analysis [29].However, the investigations of network dynamics remained limited.Networks dynamics characterized the temporal expression of brain functional networks and was associated with a variety of neurological disorders [30], [31].Specifically, network dynamics was related to the levels of consciousness and contributed to investigating the underlying neural mechanism of DOC [32], [33].In [34], Cai et al. found that the loss of consciousness was associated with the declined spatial and temporal variability of dynamic functional networks.In [35], López-González showed that the loss of consciousness reduced network interactions and heterogeneity of brain dynamics.Thus, the enhanced network dynamics was related to the improvements of consciousness levels and promising in characterizing DBS-induced improvements at the brain functional level among DOC patients.
This paper proposed an analysis method to clarify the DBS-induced improvements at the brain functional level for DOC patients with respect to brain network dynamics.Specifically, dynamic brain features were extracted to quantify the functional variability in the temporal and spectral representations of brain functional networks.The results showed that brain temporal-spectral functional variability well signified brain functional variations of DBS treatment for DOC patients and could be applied to evaluate consciousness in DOC patients.

II. METHODS
The proposed dynamic brain temporal-spectral analysis method was presented in Figure 1.fNIRS recording of DOC patients during auditory stimuli was introduced first.Then, the construction of dynamic brain functional networks was detailed.Afterwards, the extraction of dynamic brain temporal-spectral features for the assessment of global and regional functional variability was presented.

A. Participants
This study obtained ethical approval from the Ethics Committee of Tianjin Huanhu Hospital, Tianjin, China (No. 2020-105).Before the experiment, written informed consents were provided by caregivers of the patients.Thirteen DOC patients with DBS surgery were included in the experiment, as depicted in Table I.The inclusion criteria of DOC patients were: (1) age between 18 and 75 years; (2) a minimum duration of 6 months of stable DOC for patients with traumatic injuries and 3 months for those with non-traumatic injuries; (3) intact thalamus in the surgical side.The exclusion criteria were: (1) deafness; (2) psychiatric or neurological Patients with cranial defects on the left side of the nucleus were subjected to treatment targeting the right centromedianparafascicular (CM-PF) nuclei while patients without cranial defects underwent treatment targeting the bilateral CM-PF nuclei.The implantation procedure of the Permanent Electrode leads (PINS L301 model, PINS Inc., Beijing, China) was carried out under the guidance of the Leksell frame.With the utilization of targeting software (Framelink 5.1, Medtronic, Minneapolis, MN, USA), the surgical team planned the anatomical target and identified the optimal trajectory by magnetic resonance imaging (MRI) and computed tomography (CT) scans.Lead DBS software was applied to reconstruct the relationship between the electrode and the nucleus, ensuring that the electrode contacts were within the nucleus of CM-PF [36].From the third day after the DBS surgery, monopolar stimulation was administered continuously with a frequency of 100 Hz and a pulse width of 210 ms.Doctors gradually increased the voltage without producing any side effects, such as facial tension, limb hypertonia, and spasms [9].The voltage ranged from 2.5 V to 3.5 V, depending on the patient's condition.Stimulation was applied for 15 minutes every 30 minutes throughout the daytime.

B. Recording of fNIRS Brain Signals During the Experimental Procedures
fNIRS brain signals were captured by a portable Nirsmart system (Danyang Huichuang Medical Equipment Co., Ltd China) at a sampling rate of 11 Hz.The wavelengths of the Nirsmart system were 730 nm and 850 nm.Eighteen sources and fourteen detectors were symmetrically placed at bilateral Optode distribution.Thirty-two optodes including eighteen sources and fourteen detectors were symmetrically distributed in frontal cortex (FL), parietal lobe (PL), and occipital lobe (OL).Each pair of source and detector produces an fNIRS channel, and a total of 34 channels are generated in this study.Ci indicates the i-th fNIRS channel.
hemispheres, covering frontal lobe, parietal lobe, and occipital lobe.Each pair of source and detector produced an fNIRS channel, and a total of 34 channels were generated in this study, as illustrated in Figure 2.
With the portable fNIRS system, an experimental procedure was developed according to the CRS-R auditory subscore, involving the utilization of auditory stimuli.Previous studies found that auditory stimuli could effectively stimulate the brain of DOC patients [37], [38], [39].The experimental procedure consisted of: (1) an auditory stimuli trial under the Pre stage (two days before the DBS surgery), and (2) an auditory stimuli trial under the Post stage (one month after the surgery).The auditory stimuli trial included a rest of 30 s and an auditory stimuli of 30 s and was performed in a quiet ward.The auditory stimuli consisted of recursive sequential instructions from one specialist to look left, right, up, and down.The instructions were administered at a standard speaking rate, devoid of any interposed pauses.Another specialist evaluated the response of patients to the auditory stimuli to examine whether the instructions elicited corresponding ocular movements.The experimental procedure was illustrated in Figure 3.
The recorded fNIRS signals during the experimental procedure were preprocessed with the following steps: (1) Motion artifacts were detected by combining a time window of 0.5 s and two thresholds.The first threshold was the standard deviation and set as 6.The second threshold was amplitude and set as 0.5.Motion artifacts were defined as the data within specific time windows, of which the standard deviation exceeds the first threshold or the peak amplitude exceeds the second threshold.The detected artifacts were corrected by cubic spline interpolation [40], [41].(2) Physiological noises (such as cardiac and respiration) were filtered by a 0.01-0.2Hz bandpass filter [30], [42], [43].(3) The modified Beer-Lambert law was applied to transform the filtered signals into the concentration changes of oxyhemoglobin [44].(4) Visual inspection was performed for the examination of signal quality.The channels located in the occipital lobe for P4 and P10, as well as channel 14 for P10 in the Pre stage, were excluded due to their poor signal quality.

C. Dynamic Brain Functional Networks
Dynamic brain functional networks were constructed for the analysis of time-varying coupling between different brain regions.Specially, the preprocessed signals were separated into multiple pieces using a sliding window with a size of 20 s and a step of 1 s.For each piece, the Hilbert transformation c hi of each separated channel signal c i at time t was computed as: where C pr was the Cauchy principle value.The phase difference △φ at time t between c i and c j was calculated as: Then the phase lag index P c i ,c j was calculated as: where T denoted the length of separated channel signals.sign(•) indicated the signum function.P c i ,c j ranged from 0 (the weakest correlation) to 1 (the strongest correlation).The brain functional network B f n of each piece was construct with P c i ,c j from all pairs of separated channel signals: where N c indicated the channel number.B f n was undirected, i.e. ∀i, j, P c i ,c j = P c j ,c i .

D. Dynamic Brain Temporal-Spectral Features
Dynamic brain temporal-spectral features were extracted to quantify the global and local functional variability and utilized to analyze DBS-induced brain functional variations in DOC patients.
1) Brain Temporal Features: Three brain graph features including global efficiency, local efficiency, and clustering coefficient were applied for the characterization of brain functional networks.Specifically, global efficiency measured the integration of brain networks and was calculated as: where N c denoted the channel number, C was the channel set.d i j was the shortest path length between the i-th and Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
j-th channels.Local efficiency and clustering coefficient assessed the segregation of the networks and were computed as: where Re denoted the brain region and set as whole (all brain regions), L-FL (the left frontal cortex), R-FL (the right frontal cortex), L-PL (the left parietal lobe), R-PL (the right parietal lobe), L-OL (the left occipital lobe), or R-OL (the right occipital lobe).N Re was the channel number in Re.C Re indicated the channel set of Re. d i h (C Re (i)) represented the shortest path length between channels j and h, that contains only neighbors of channel i in C Re .a i j was the connection status between channels i and j in C Re .k i was the degree of channel i. t i denoted the triangle number around channel i.
The variability of global efficiency, local efficiency, and clustering coefficient were defined as: where N pi the number of separated pieces.G E(B f n ), L E Re (B f n ), and CC Re (B f n ) were the mean of G E(B f n ), L E Re (B f n ), and CC Re (B f n ) in all pieces, respectively.
2) Brain Spectral Features: Graph spectral analysis permits the transformation of graph signals into a spectral representation (graph Fourier transform) and extraction of graph pieces associated with different modes of variations, which were of great significance in the analysis of neurological diseases [45], [46].Moreover, it facilitates a spatial variability analysis with respect to brain connectivity patterns [47].In this study, a brain graph was defined as G = (V, B f n ), where V = {v 1 , v 2 , . . ., v n c } was the vertice set.The degree matrix M D ∈ R N c ×N c of G was constructed as a diagonal matrix with the i-th diagonal element M ii D = N c j=1 P ci,cj .The Laplacian matrix M L was defined as M D − B f n and decomposed as: whereE = [e 1 , e 2 , . . ., e n c ] is the eigenvector matrix, e i denoted the i-th eigenvector.E H was the Hermitian of E. was the diagonal eigenvalue matrix = diag(λ 1 , λ 2 , . . ., λ N c ) ∈ R N c ×N c , λ i is the i-th eigenvalue for e i .The graph energy was defined as: The graph diversity (GD) was defined to quantify the changes in each brain region: where Re indicated the brain region and set as L-FL (the left frontal cortex), R-FL (the right frontal cortex), L-PL (the left parietal lobe), R-PL (the right parietal lobe), L-OL (the left occipital lobe), or R-OL (the right occipital lobe).K was the number of eigenvectors.P c i ,c j denoted the phase lag index between the i-th and j-th channels (as defined in Equ.( 3)).v i k represented the i-th element in the k-th eigenvector.S high was set as K − r ound(K /3) + 1 and indicated the start point for the eigenvectors with high graph frequencies that were potentially associated with the high frequency DBS treatment for DOC patients in this study.
Then the graph energy variability and graph diversity variability were defined as: where N pi the number of separated pieces.energy(B f n ) and G D Re (B f n ) were the mean of energy(B f n ) and G D Re (B f n ) in all pieces.Distance correlation analysis was conducted to investigate the correlation between the treatment-induced changes of dynamic brain temporal-spectral features and changes of CRS-R index, an effective modified version of CRS-R scores with a linear relationship to consciousness [17].The changes of dynamic features and CRS-R index were calculated by subtracting the values in the Post stage from the values in the Pre stage.

A. Clinical Analysis
The CRS-R evaluations of patients were conducted three times in the Pre and Post stages.The evaluations were carried out before and after surgery by the same specialist who was blinded to the experimental results.The CRS-R scores exhibited consistency across all three assessments in all patients.
The clinical results of thirteen DOC patients were presented in Table II.After DBS treatment, four patients (P1, P2, P3, P4, P13) with trauma exhibited an increase in CRS-R scores and CRS-R index, with the increment ranging from 2 to 3 and from 2.080 to 17.720.P5 patient with hypothalamus hemorrhage had a one-point increase of CRS-R score and 1.04 increase of CRS-R index.The CRS-R score and CRS-R index of P6 patient with basal ganglia hemorrhage showed an increase of 1 and 8.340.P7 patient with cerebellar hemorrhage had a 1 and 1.04 decrease of CRS-R scores and CRS-R index.The CRS-R scores and CRS-R indexes of patients

B. Analysis of Dynamic Brain Temporal-Spectral Features
The global efficiency variability, local efficiency variability (in the whole brain regions), clustering coefficient variability (in the whole brain regions), and graph energy variability in the Pre and Post stages were shown in Table III.The global efficiency variability of ten patients (P1, P3, P4, P5, P6, P7, P9, P10, P12, P13) in the Post stage was consistently higher than that in the Pre stage while three patients (P2, P8, P11) under the Post stage exhibited decrease variations compared with those under the Pre stage.Eight patients (P1, P4, P5, P6, P7, P9, P10, P13) showed consistent treatment-induced increases of local efficiency variability, clustering variability, and graph energy variability while five patients (P2, P3, P8, P11, P12) had opposite variations.The results showed that DOC patients exhibited increased functional variability after DBS treatment.
The local efficiency variability, clustering coefficient variability, and graph diversity variability of different brain regions under the Pre and Post stages were presented in Table IV, V, and VI.The local efficiency variability and clustering Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

C. Correlation Analysis of Dynamic Brain Temporal-Spectral Features and CRS-R Index
The correlations between changes of CRS-R index and changes of global efficiency variability, local efficiency variability (in the whole brain regions), clustering coefficient variability (in the whole brain regions), and graph energy variability were presented in Figure 4.The changes of local efficiency variability and clustering coefficient were significantly correlated with the changes of CRS-R index.The results showed that the consciousness improvements of DOC patients were significantly associated with functional variability.
The correlations between changes of CRS-R index and changes of local efficiency variability, clustering efficiency variability, graph diversity variability in different brain regions were shown in Figure 5 and Table VII.The changes of local efficiency variability and clustering coefficient variability in the right frontal lobe and parietal lobe as well as graph diversity variability in the right occipital lobe were significantly  correlated with the changes of CRS-R index, indicating that consciousness improvements of DOC patients were significantly associated with the variability in the right hemisphere.
The above results found that: (1) The increases of functional variability were significantly correlated with the improvements of consciousness.(2) The functional variability in the right brain regions had stronger correlations with consciousness enhancements than that in the left brain regions.

IV. DISCUSSION
Dynamic brain networks characterized the temporal variations of brain networks and were critical for the exploration of cognitive, behavioral, and physiological processes [48], [49], [50].Network variability was a crucial property of dynamic brain networks and associated with cognitive task performance [45], [51], [52].In this study, an analysis method was proposed to discover dynamic brain temporal-spectral  features, which quantified the variability in the temporal and spectral representations of brain functional networks.
Our study showed that DOC patients exhibited an increase of network variability and consciousness improvements after DBS treatment.Previous studies found that patients with Parkinson's disease had a decrease of network variability compared with healthy controls [53], suggesting that decreased network variability was correlated with the impairment of motor and cognitive functions.In [54], patients with schizophrenia had decreased variance in the dynamic graph metrics in comparison to healthy controls, showing that the impairment of mental functions could be reflected by the decrease of network variability.In [34], Cai et al. found decreased temporal fluctuations of global metrics in DOC patients compared to the healthy controls.In [55], Lee et al. demonstrated that the reduced diversity of functional connectivity patterns was associated with the loss of consciousness.In line with these studies, Lee et al. explored the relationships between the temporal diversity of phase synchronization and critical dynamics [56].They reported that the brain networks with low diversity were away from the normal critical point.Our study was consistent with the results, demonstrating the significant correlation between enhanced network variability and improved consciousness.
Our study showed that the right brain regions of DOC patients were better improved by DBS compared with the left brain regions.In [57], Arnts et al. found that DBS was associated with the increase of functional connectivity among DOC patients in frontoparietal and occipital areas, especially within the right brain regions.This finding suggested that increased connectivity in the right brain regions was more correlated with the consciousness improvements of DOC patients than that in the left brain regions.In [58], the complexity of neural activities between regions in the right hemisphere exhibited a significantly stronger correlation with CRS-R compared with that between regions in the left hemisphere, which was in line with our results.One potential explanation for our finding is that the brain regions in the right hemisphere primarily engage in interactions with components of the ascending arousal system.These interactions are responsible for regulating behavioral arousal, consciousness, and motivation, as they receive and process information from this system [59].Therefore, the variability features in the right brain regions may achieve better reflections of the consciousness-related brain functional variations than those in the left brain regions.Another possible explanation is that the right hemisphere may have the potential to promote communication [60], [61], and the extensive preservation of functionality in the right cerebral hemisphere among DOC patients could indicate a motivation for communication [62].The maintained functionality in the right hemisphere, as opposed to the left hemisphere, may be crucial in initiating attention to verbal stimulation and facilitating communication.In DOC patients, motivation to engage in communication related to the right hemisphere is paramount and may precede the execution of verbal and motor functions during communication involving the left hemisphere.Our study was consistent with the above results, demonstrating that the right brain regions had a stronger correlation with consciousness improvements of DOC patients than the left brain regions.
We hope this work can encourage more study, and more clinical evidence will promisingly enable quantified and individualized optimization of DBS therapy for each DOC patient.This work also had the potential to enable objective analysis of rehabilitation, medication, and surgical treatment of other brain disorders, such as stroke and Parkinson's disease, by providing definitive evidence in the neural functional levels.The sham stimuli will be explored in the future.Moreover, in the future, we will consider trying to record multiple trials.

V. CONCLUSION
The evaluation of consciousness variations plays a critical role in the treatment optimization of DBS therapy for DOC patients.This paper proposed an analysis method for the effectiveness evaluation and mechanism exploration of DBS and discovered that dynamic brain temporal-spectral features well signified DBS-induced brain functional variations and could be applied to evaluate consciousness in DOC patients.Dynamic brain temporal-spectral features were extracted for the assessment of global and local functional variability before and after DBS treatment.The results showed that the brain temporal-spectral functional variability was promising for consciousness assessment in DOC patients.

Fig. 2 .
Fig. 2.Optode distribution.Thirty-two optodes including eighteen sources and fourteen detectors were symmetrically distributed in frontal cortex (FL), parietal lobe (PL), and occipital lobe (OL).Each pair of source and detector produces an fNIRS channel, and a total of 34 channels are generated in this study.Ci indicates the i-th fNIRS channel.

Fig. 3 .
Fig. 3.The experimental procedures.fNIRS brain signals were recorded under the Pre (two days before the DBS surgery) and Post (one month after the DBS surgery) stages.The auditory stimuli trial included a rest of 30 s and an auditory stimuli of 30 s that consisted of recursive sequential instructions from one specialist to look left, right, up, and down.The instructions were delivered at a standard speaking rate, without any intervening pauses.

Fig. 4 .
Fig. 4. Correlation between changes of CRS-R index and changes of global efficiency variability (a), local efficiency variability in the whole brain regions (b), clustering coefficient variability in the whole brain regions and graph energy variability (d).Red denotes significant correlation.p and r indicate the p-value and correlation strength.

Fig. 5 .
Fig. 5. Significant correlation between changes of CRS-R index and (a) changes of the local efficiency variability in the right frontal lobe V LE R-FL and parietal lobe V LE R-PL , (b) clustering coefficient variability in the right frontal lobe V CC R-FL and parietal lobe V CC R-PL , (c) and graph diversity variability in the right occipital lobe V GD R-OL .Red denotes significant correlation.p and r indicate the p-value and correlation strength.

TABLE II CLINICAL
RESULTS OF DBS TREATMENT FOR DOC PATIENTSTABLE III THE GLOBAL EFFICIENCY VARIABILITY, LOCAL EFFICIENCY VARIABILITY, CLUSTERING COEFFICIENT VARIABILITY, AND GRAPH ENERGY VARIABILITY IN THE PRE AND POST STAGES

TABLE VI THE
GRAPH DIVERSITY VARIABILITY IN DIFFERENT BRAIN REGIONS UNDER THE PRE AND POST STAGES

TABLE VII CORRELATION
ANALYSIS BETWEEN THE CHANGES OF CRS-R INDEX AND CHANGES OF LOCAL EFFICIENCY VARIABILITY, CLUSTERING COEFFICIENT VARIABILITY, AND GRAPH DIVERSITY VARIABILITY IN DIFFERENT BRAIN REGIONS.THE NUMBER REPRESENTS P-VALUE.RED DENOTES SIGNIFICANT CORRELATION (p < 0.05)