Search

The utilization of Artificial Intelligence (AI) for assessing motor performance in Parkinson's Disease (PD) offers substantial potential, particularly if the results can be integrated into clinical decision-making processes. However, the precise quantification of PD symptoms remains a persistent challenge. The current standard Unified Parkinson's Disease Rating Scale (UPDRS) and its variations serve as the primary clinical tools for evaluating motor symptoms in PD, but are time-intensive and prone to inter-rater variability. Recent work has applied data-driven machine learning techniques to analyze videos of PD patients performing motor tasks, such as finger tapping, a UPDRS task to assess bradykinesia. However, these methods often use abstract features that are not closely related to clinical experience. In this paper, we introduce a customized machine learning approach for the automated scoring of UPDRS bradykinesia using single-view RGB videos of finger tapping, based on the extraction of detailed features that rigorously conform to the established UPDRS guidelines. We applied the method to 75 videos from 50 PD patients collected in both a laboratory and a realistic clinic environment. The classification performance agreed well with expert assessors, and the features selected by the Decision Tree aligned with clinical knowledge. Our proposed framework was designed to remain relevant amid ongoing patient recruitment and technological progress. The proposed approach incorporates features that closely resonate with clinical reasoning and shows promise for clinical implementation in the foreseeable future. [ABSTRACT FROM AUTHOR]

This paper tackles a novel and challenging problem—3D hand pose estimation (HPE) from a single RGB image using partial annotation. Most HPE methods ignore the fact that the keypoints could be partially visible (e.g., under occlusions). In contrast, we propose a deep-learning framework, PA-Tran, that jointly estimates the keypoints status and 3D hand pose from a single RGB image with two dependent branches. The regression branch consists of a Transformer encoder which is trained to predict a set of target keypoints, given an input set of status, position, and visual features embedding from a convolutional neural network (CNN); the classification branch adopts a CNN for estimating the keypoints status. One key idea of PA-Tran is a selective mask training (SMT) objective that uses a binary encoding scheme to represent the status of the keypoints as observed or unobserved during training. In addition, by explicitly encoding the label status (observed/unobserved), the proposed PA-Tran can efficiently handle the condition when only partial annotation is available. Investigating the annotation percentage ranging from 50–100%, we show that training with partial annotation is more efficient (e.g., achieving the best 6.0 PA-MPJPE when using about 85% annotations). Moreover, we provide two new datasets. APDM-Hand, is for synthetic hands with APDM sensor accessories, which is designed for a specific hand task. PD-APDM-Hand, is a real hand dataset collected from Parkinson's Disease (PD) patients with partial annotation. The proposed PA-Tran can achieve higher estimation accuracy when evaluated on both proposed datasets and a more general hand dataset. [ABSTRACT FROM AUTHOR]

Background. Activating vestibular afferents via galvanic vestibular stimulation (GVS) has been recently shown to have a number of complex motor effects in Parkinson's disease (PD), but the basis of these improvements is unclear. The evaluation of network-level connectivity changes may provide us with greater insights into the mechanisms of GVS efficacy. Objective. To test the effects of different GVS stimuli on brain subnetwork interactions in both health control (HC) and PD groups using fMRI. Methods. FMRI data were collected for all participants at baseline (resting state) and under noisy, 1 Hz sinusoidal, and 70-200 Hz multisine GVS. All stimuli were given below sensory threshold, blinding subjects to stimulation. The subnetworks of 15 healthy controls and 27 PD subjects (on medication) were identified in their native space, and their subnetwork interactions were estimated by nonnegative canonical correlation analysis. We then determined if the inferred subnetwork interaction changes were affected by disease and stimulus type and if the stimulus-dependent GVS effects were influenced by demographic features. Results. At baseline, interactions with the visual-cerebellar network were significantly decreased in the PD group. Sinusoidal and multisine GVS improved (i.e., made values approaching those seen in HC) subnetwork interactions more effectively than noisy GVS stimuli overall. Worsening disease severity, apathy, depression, impaired cognitive function, and increasing age all limited the beneficial effects of GVS. Conclusions. Vestibular stimulation has widespread system-level brain influences and can improve subnetwork interactions in PD in a stimulus-dependent manner, with the magnitude of such effects associating with demographics and disease status. [ABSTRACT FROM AUTHOR]

Graph theoretical analysis is a powerful tool for quantitatively evaluating brain connectivity networks. Conventionally, brain connectivity is assumed to be temporally stationary, whereas increasing evidence suggests that functional connectivity exhibits temporal variations during dynamic brain activity. Although a number of methods have been developed to estimate time-dependent brain connectivity, there is a paucity of studies examining the utility of brain dynamics for assessing brain disease states. Therefore, this paper aims to assess brain connectivity dynamics in Parkinson's disease (PD) and determine the utility of such dynamic graph measures as potential components to an imaging biomarker. Resting-state functional magnetic resonance imaging data were collected from 29 healthy controls and 69 PD subjects. Time-varying functional connectivity was first estimated using a sliding windowed sparse inverse covariance matrix. Then, a collection of graph measures, including the Fiedler value, were computed and the dynamics of the graph measures were investigated. The results demonstrated that PD subjects had a lower variability in the Fiedler value, modularity, and global efficiency, indicating both abnormal dynamic global integration and local segregation of brain networks in PD. Autoregressive models fitted to the dynamic graph measures suggested that Fiedler value, characteristic path length, global efficiency, and modularity were all less deterministic in PD. With canonical correlation analysis, the altered dynamics of functional connectivity networks, and particularly dynamic Fiedler value, were shown to be related with disease severity and other clinical variables including age. Similarly, Fiedler value was the most important feature for classification. Collectively, our findings demonstrate altered dynamic graph properties, and in particular the Fiedler value, provide an additional dimension upon which to non-invasively and quantitatively assess PD. [ABSTRACT FROM AUTHOR]

The human brain is a highly dynamic structure requiring dynamic coordination between different neural systems to perform numerous cognitive and behavioral tasks. Emerging perspectives on basal ganglia (BG) and thalamic functions have highlighted their role in facilitating and mediating information transmission among cortical regions. Thus, changes in BG and thalamic structures can induce aberrant modulation of cortico-cortical interactions. Recent work in deep brain stimulation (DBS) has demonstrated that externally applied electrical current to BG structures can have multiple downstream effects in large-scale brain networks. In this work, we identified EEG-based altered resting-state cortical functional connectivity in Parkinson's disease (PD) and examined effects of dopaminergic medication and electrical vestibular stimulation (EVS), a non-invasive brain stimulation (NIBS) technique capable of stimulating the BG and thalamus through vestibular pathways. Resting EEG was collected from 16 PD subjects and 18 age-matched, healthy controls (HC) in four conditions: sham (no stimulation), EVS1 (4–8 Hz multisine), EVS2 (50–100 Hz multisine) and EVS3 (100–150 Hz multisine). The mean, variability, and entropy were extracted from time-varying phase locking value (PLV), a non-linear measure of pairwise functional connectivity, to probe abnormal cortical couplings in the PD subjects. We found the mean PLV of Cz and C3 electrodes were important for discrimination between PD and HC subjects. In addition, the PD subjects exhibited lower variability and entropy of PLV (mostly in theta and alpha bands) compared to the controls, which were correlated with their clinical characteristics. While levodopa medication was effective in normalizing the mean PLV only, all EVS stimuli normalized the mean, variability and entropy of PLV in the PD subject, with the exact extent and duration of improvement a function of stimulus type. These findings provide evidence demonstrating both low- and high-frequency EVS exert widespread influences on cortico-cortical connectivity, likely via subcortical activation. The improvement observed in PD in a stimulus-dependent manner suggests that EVS with optimized parameters may provide a new non-invasive means for neuromodulation of functional brain networks. [ABSTRACT FROM AUTHOR]

Falls and balance difficulties remain a major source of morbidity in Parkinson's Disease (PD) and are stubbornly resistant to therapeutic interventions. The mechanisms of gait impairment in PD are incompletely understood but may involve changes in the Pedunculopontine Nucleus (PPN) and its associated connections. We utilized fMRI to explore the modulation of PPN connectivity by Galvanic Vestibular Stimulation (GVS) in healthy controls (n = 12) and PD subjects even without overt evidence of Freezing of Gait (FOG) while on medication (n = 23). We also investigated if the type of GVS stimuli (i.e., sinusoidal or stochastic) differentially affected connectivity. Approximate PPN regions were manually drawn on T1 weighted images and 58 other cortical and subcortical Regions of Interest (ROI) were obtained by automatic segmentation. All analyses were done in the native subject's space without spatial transformation to a common template. We first used Partial Least Squares (PLS) on a subject-by-subject basis to determine ROIs across subjects that covaried significantly with the voxels within the PPN ROI. We then performed functional connectivity analysis on the PPN-ROI connections. In control subjects, GVS did not have a significant effect on PPN connectivity. In PD subjects, baseline overall magnitude of PPN connectivity was negatively correlated with UPDRS scores (p < 0.05). Both noisy and sinusoidal GVS increased the overall magnitude of PPN connectivity (p = 6 × 10−5, 3 × 10−4, respectively) in PD, and increased connectivity with the left inferior parietal region, but had opposite effects on amygdala connectivity. Noisy stimuli selectively decreased connectivity with basal ganglia and cerebellar regions. Our results suggest that GVS can enhance deficient PPN connectivity seen in PD in a stimulus-dependent manner. This may provide a mechanism through which GVS assists balance in PD, and may provide a biomarker to develop individualized stimulus parameters. [ABSTRACT FROM AUTHOR]

Studying interactions using resting-state functional magnetic resonance imaging (fMRI) signals between discrete brain loci is increasingly recognized as important for understanding normal brain function and may provide insights into many neurodegenerative disorders such as Parkinson's disease (PD). Though much work has been done investigating ways to infer brain connectivity networks, the temporal dynamics of brain coupling has been less well studied. Assuming that brain connections are purely static or purely dynamic is assuredly unrealistic, as the brain must strike a balance between stability and flexibility. In this paper, we propose making joint inference of time-invariant connections as well as time-varying coupling patterns by employing a multitask learning model followed by a least-squares approach to accurately estimate the connectivity coefficients. We applied this method to resting state fMRI data from PD and control subjects and estimated the eigenconnectivity networks to obtain the representative patterns of both static and dynamic brain connectivity features. We found lower network variations in the PD group, which were partially normalized with L-dopa medication, consistent with previous studies suggesting that cognitive inflexibility is characteristic of PD. [ABSTRACT FROM PUBLISHER]

Despite recent progress on brain connectivity modeling using neuroimaging data such as fMRI, most current approaches assume that brain connectivity networks have time-invariant topology/coefficients. This is clearly problematic as the brain is inherently nonstationary. Here, we present a time-varying model to investigate the temporal dynamics of brain connectivity networks. The proposed method allows for abrupt changes in network structure via a fused least absolute shrinkage and selection operator (LASSO) scheme, as well as recovery of time-varying networks with smoothly changing coefficients via a weighted regression technique. Simulations demonstrate that the proposed method yields improved accuracy on estimating time-dependent connectivity patterns when compared to a static sparse regression model or a weighted time-varying regression model. When applied to real resting-state fMRI datasets from Parkinson's disease (PD) and control subjects, significantly different temporal and spatial patterns were found to be associated with PD. Specifically, PD subjects demonstrated reduced network variability over time, which may be related to impaired cognitive flexibility previously reported in PD. The temporal dynamic properties of brain connectivity in PD subjects may provide insights into brain dynamics associated with PD and may serve as a potential biomarker in future studies. [ABSTRACT FROM PUBLISHER]

Corticomuscular coupling analysis based on multiple datasets such as electroencephalography (EEG) and electromyography (EMG) signals provides a useful tool for understanding human motor control systems. A popular conventional method to assess corticomuscular coupling has been the pair-wise magnitude-squared coherence (MSC) between EEG and concomitant EMG recordings. However, there are certain limitations associated with the MSC, including the difficulty in robustly assessing group inference, only dealing with two types of datasets simultaneously and the biologically implausible assumption of pair-wise interactions. To overcome such limitations, in this paper, we propose assessing corticomuscular coupling by combining multiset canonical correlation analysis (M-CCA) and joint independent component analysis (jICA). The proposed method takes advantage of the M-CCA and jICA to ensure that the extracted components are maximally correlated across multiple datasets and meanwhile statistically independent within each dataset. Simulations were performed to illustrate the performance of the proposed method. We also applied the proposed method to concurrent EEG, EMG, and behavior data collected in a Parkinson’s disease (PD) study. The results reveal highly correlated temporal patterns among the three types of signals and corresponding spatial activation patterns. In addition to the expected motor areas, the corresponding spatial activation patterns demonstrate enhanced occipital connectivity in the PD subjects, consistent with previous medical findings. [ABSTRACT FROM PUBLISHER]

Corticomuscular coupling analysis based on multiple data sets such as electroencephalography (EEG) and electromyography (EMG) signals provides a useful tool for understanding human motor control systems. Two probably most popular methods are the pair-wise magnitude-squared coherence (MSC) between EEG and simultaneously-recorded EMG signals, and partial least square (PLS). Unfortunately, MSC and PLS generally deal with only two types of data sets at the same time, while we may need to analyze more than two types of data sets. Moreover, it is not straightforward to extend MSC to the group level for combining results across subjects. Also, PLS can have the information mixing problem since only the variations in one data set are used to predict the other data set. To address these concerns, we propose a joint multimodal analysis framework for corticomuscular coupling analysis. The proposed framework models multiple data spaces simultaneously in a multidirectional fashion. Furthermore, to address the inter-subject variability concern in real-world medical applications, we extend the proposed framework from the individual subject level to the group level to obtain common corticomuscular coupling patterns across subjects. We apply the proposed framework to concurrent EEG, EMG and behavior data collected in a Parkinson's disease (PD) study. The results reveal several highly correlated temporal patterns among the three types of signals and their corresponding spatial activation patterns. In PD subjects, there are enhanced connections between occipital region and other regions, which is consistent with the previous medical finding. The proposed framework is a promising technique for performing multi-subject and multi-modal data analysis. [ABSTRACT FROM PUBLISHER]

Corticomuscular activity modeling based on multiple data sets such as electroencephalography (EEG) and electromyography (EMG) signals provides a useful tool for understanding human motor control systems. In this paper, we propose modeling corticomuscular activity by combining partial least squares (PLS) and canonical correlation analysis (CCA). The proposedmethod takes advantage of both PLS and CCA to ensure that the extracted components are maximally correlated across two data sets and meanwhile can well explain the information within each data set. This complementary combination generalizes the statistical assumptions beyond both PLS and CCA methods. Simulations were performed to illustrate the performance of the proposed method. We also applied the proposedmethod to concurrent EEG and EMG data collected in a Parkinson's disease (PD) study. The results reveal several highly correlated temporal patterns between EEG and EMG signals and indicate meaningful corresponding spatial activation patterns. In PD subjects, enhanced connections between occipital region and other regions are noted, which is consistent with previous medical knowledge. The proposed framework is a promising technique for performing multisubject and bimodal data analysis. [ABSTRACT FROM AUTHOR]

Abstract: Electroencephalography (EEG) and simultaneously-recorded electromyography (EMG) data are a means to assess integrity of the functional connection between the cortex and the muscle during movement. EEG-EMG coupling is typically assessed with pair-wise squared coherence, resulting in a small, but statistically-significant coherence between a single EEG and a single EMG channel. However, a means to combine results across subjects is not straightforward with this approach because the exact frequency of maximal EEG–EMG coupling may vary between individuals, and it emphasizes the role of an individual locus in the brain in driving the muscle activity, when interactions between head regions may in fact be more influential on ongoing EMG activity. To deal with these issues, we implemented a multiblock Partial Least Squares (mbPLS) procedure, previously proposed in chemical applications, which incorporates a hierarchical structure into the ordinary two-block PLS often used in neuroimaging studies. In the current implementation, each subject''s data features are collected in individual data blocks on a sub-level, while simultaneously aggregating the sub-level information to obtain a super-level group “consensus”. We further extended the mbPLS model to include 3-dimensional matrices: time–frequency–EEG channel and a time–frequency–connection utilizing Partial Directed Coherence (PDC). We applied the proposed method to concurrent EEG and EMG data collected from ten normal subjects and nine patients with mild–moderate Parkinson''s disease (PD) performing a dynamic motor task—that of sinusoidal squeezing. The results demonstrate that connections between EEG electrodes, rather than activity at individual electrodes, correspond more closely to ongoing EMG activity. In PD subjects, there was enhanced connectivity to and from occipital regions, likely related to the previously-described enhanced use of visual information during motor performance in this group. The proposed mbPLS framework is a promising technique for performing multi-subject, multi-modal data analysis and it allows for robust group inferences even in the face of large inter-subject variability. [Copyright &y& Elsevier]

Studying brain connectivity has provided new insights to the understanding of brain function. While connectivity measures are conventionally computed from electroencephalogram (EEG) signals directly, the presence of volume conduction represents a serious confound affecting interpretation of results. A common solution is to use a two-stage approach which involves estimating underlying brain sources from scalp EEG recordings and subsequently estimating the connectivity between the inferred sources. Recently, a state-space framework which jointly models the instantaneous mixing effects of volume conduction and the causal relationships between underlying brain sources is proposed. In this paper, we extend the state-space framework and model the source activity by a generalized multivariate autoregressive (mAR) process with possibly non-Gaussian noise. A maximum likelihood estimation approach is developed which allows simultaneous estimation of both the mixing matrix and AR model parameters directly from scalp EEG. The proposed technique was verified with simulated EEG data generated using the single-shell spherical head model and demonstrated improved estimation accuracies compared to conventional two-stage connectivity estimation approaches. Furthermore, the proposed technique was applied to EEG data collected from normal and Parkinson's subjects performing a right-handed force-tracking task with differing amounts of visual feedback. The partial directed coherence (PDC) between sources showed significant differences between groups and conditions. These results suggest that the proposed technique is a powerful method to extract connectivity information from EEG recordings. [ABSTRACT FROM PUBLISHER]

Background: Monitoring the functional connectivity between brain regions is becoming increasingly important in elucidating brain functionality in normal and disease states. Current methods of detecting networks in the recorded electroencephalogram (EEG) such as correlation and coherence are limited by the fact that they assume stationarity of the relationship between channels, and rely on linear dependencies. In contrast to diseases of the brain cortex (e.g. Alzheimer's disease), with motor disorders such as Parkinson's disease (PD) the EEG abnormalities are most apparent during performance of dynamic motor tasks, but this makes the stationarity assumption untenable. Methods: We therefore propose a novel EEG segmentation method based on the temporal dynamics of the cross-spectrogram of the computed Independent Components (ICs). We then utilize mutual information (MI) as the metric for determining also nonlinear statistical dependencies between EEG channels. Graphical theoretical analysis is then applied to the derived MI networks. The method was applied to EEG data recorded from six normal subjects and seven PD subjects off medication. One-way analysis of variance (ANOVA) tests demonstrated statistically significant difference in the connectivity patterns between groups. Results: The results suggested that PD subjects are unable to independently recruit different areas of the brain while performing simultaneous tasks compared to individual tasks, but instead they attempt to recruit disparate clusters of synchronous activity to maintain behavioral performance. Conclusion: The proposed segmentation/MI network method appears to be a promising approach for analyzing the EEG recorded during dynamic behaviors. [ABSTRACT FROM AUTHOR]

Abstract : Bayesian network (BN) modeling has recently been introduced as a tool for determining the dependencies between brain regions from functional-magnetic-resonance-imaging (fMRI) data. However, studies to date have yet to explore the optimum way for meaningfully combining individually determined BN models to make group inferences. We contrasted the results from three broad approaches: the “virtual-typical- subject” (VTS) approach which pools or averages group data as if they are sampled from a single, hypothetical virtual typical subject; the “individual-structure” (IS) approach that learns a separate BN for each subject, and then finds commonality across the individual structures, and the “common-structure” (CS) approach that imposes the same network structure on the BN of every subject, but allows the parameters to differ across subjects. To explore the effects of these three approaches, we applied them to an fMRI study exploring the motor effect of L-dopa medication on ten subjects with Parkinson''s disease (PD), as the profound clinical effects of this medication suggest that fMRI activation in PD subjects after medication should start approaching that of age-matched controls. We found that none of these approaches is generally superior over the others, according to Bayesian-information-criterion (BIC) scores, and that they led to considerably different group-level results. The IS approach was more sensitive to the normalization effect of the L-dopa medication on brain connectivity. However, for the more homogeneous control population, the VTS approach was superior. Group-analysis approaches should be selected carefully with consideration of both statistical and biomedical evidence. [Copyright &y& Elsevier]

Graphical models appear well suited for inferring brain connectivity from fMRI data, as they can distinguish between direct and indirect brain connectivity. Nevertheless, biological interpretation requires not only that the multivariate time series are adequately modeled, but also that there is accurate error-control of the inferred edges. The PCfdr algorithm, which was developed by Li and Wang, was to provide a computationally efficient means to control the false discovery rate (FDR) of computed edges asymptotically. The original PCfdr algorithm was unable to accommodate a priori information about connectivity and was designed to infer connectivity from a single subject rather than a group of subjects. Here we extend the original PCfdr algorithm and propose a multisubject, error-rate-controlled brain connectivity modeling approach that allows incorporation of prior knowledge of connectivity. In simulations, we show that the two proposed extensions can still control the FDR around or below a specified threshold. When the proposed approach is applied to fMRI data in a Parkinson's disease study, we find robust group evidence of the disease-related changes, the compensatory changes, and the normalizing effect of L-dopa medication. The proposed method provides a robust, accurate, and practical method for the assessment of brain connectivity patterns from functional neuroimaging data. [ABSTRACT FROM AUTHOR]

Abstract: Recent animal studies have suggested that cortical areas may play a greater role in the modulation of abnormal oscillatory activity in Parkinson''s disease (PD) than previously recognized. We investigated task and medication-dependent, EEG-based directional cortical connectivity in the θ (4–7Hz), α (8–12Hz), β (13–30Hz) and low γ (31–50Hz) frequency bands in 10 PD subjects and 10 age-matched controls. All subjects performed a visually guided task previously shown to modulate abnormal oscillatory activity in PD subjects. We examined the connectivity in the simultaneously-recorded EEG between 5 electrode regions of interest (fronto-central, left and right sensorimotor, central and occipital) using a sparse, multivariate, autoregressive-based partial directed coherence method. For comparison, we utilized traditional Fourier analysis to evaluate task-dependent frequency spectra modulation in these same regions. While the spectral analysis revealed some overall differences between PD and control subjects, it demonstrated relatively modest changes between regions. In contrast, the partial directed coherence-based analysis revealed multifaceted, regionally and directionally-dependent alterations of connectivity in PD subjects during both movement preparation and execution. Connectivity was particularly altered posteriorly, suggesting abnormalities in visual and visuo-motor processing in PD. Moreover, connectivity measures in the α, β and low γ frequency ranges correlated with motor Unified Parkinson''s Disease Rating Scores in PD subjects withdrawn from medication. Levodopa administration only partially restored connectivity, and in some cases resulted in further exacerbation of abnormalities. Our results support the notion that PD is associated with significant alterations in connectivity between brain regions, and that these changes can be non-invasively detected in the EEG using partial directed coherence methods. Thus, the role of EEG to monitor PD may need to be further expanded. [Copyright &y& Elsevier]

Motor dysfunction in Parkinson's Disease (PD) patients is typically assessed by clinicians employing the Movement Disorder Society's Unified Parkinson's Disease Rating Scale (MDS-UPDRS). Such comprehensive clinical assessments are time-consuming, expensive, semi-subjective, and may potentially result in conflicting labels across different raters. To address this problem, we propose an automatic, objective, and weakly-supervised method for labeling PD patients' gait videos. The proposed method accepts videos of patients and classifies their gait scores as normal (Gait score in MDS-UPDRS = 0) or PD (MDS-UPDRS ≥ 1). Unlike previous work, the proposed method does not require a priori MDS-UPDRS ratings for training, utilizing only domain-specific knowledge obtained from neurologists. We propose several labeling functions that classify patients' gait and use a generative model to learn the accuracy of each labeling function in a self-supervised manner. Since results depended upon the estimated values of the patients' 3D poses, and existing pre-trained 3D pose estimators did not yield accurate results, we propose a weakly-supervised 3D human pose estimation method for fine-tuning pre-trained models in a clinical setting. Using leave-one-out evaluations, the proposed method obtains an accuracy of 89% on a dataset of 29 PD subjects – a significant improvement compared to previous work by 7%–10% depending upon the dataset. The method obtained state-of-the-art results on the Human3.6M dataset. Our results suggest that the use of labeling functions may provide a robust means to interpret and classify patient-oriented videos involving motor tasks. • A weakly-supervised learning method for labeling Parkinson's Disease. • A weakly-supervised learning 3D pose estimation for medical use. • Using a leave-one-out evaluation, our method obtains an accuracy of 89%. [ABSTRACT FROM AUTHOR]