Identifying brain network topology changes in task processes and psychiatric disorders

A central goal in neuroscience is to understand how dynamic networks of neural activity produce effective representations of the world. Advances in the theory of graph measures raise the possibility of elucidating network topologies central to the construction of these representations. We leverage a result from the description of lollipop graphs to identify an iconic network topology in functional magnetic resonance imaging data and characterize changes to those networks during task performance and in populations diagnosed with psychiatric disorders. During task performance, we find that task-relevant subnetworks change topology, becoming more integrated by increasing connectivity throughout cortex. Analysis of resting state connectivity in clinical populations shows a similar pattern of subnetwork topology changes; resting scans becoming less default-like with more integrated sensory paths. The study of brain network topologies and their relationship to cognitive models of information processing raises new opportunities for understanding brain function and its disorders.

Metrics for graph comparison: A practitioner's guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees yield insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies at different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and real world networks. We put forward a multi-scale picture of graph structure wherein we study the effect of global and local structures on changes in distance measures. We make recommendations on the applicability of different distance measures to the analysis of empirical graph data based on this multi-scale view. Finally, we introduce the Python library NetComp that implements the graph distances used in this work.

A latent low-dimensional common input drives a pool of motor neurons: a probabilistic latent state-space model

Motor neurons appear to be activated with a common input signal that modulates the discharge activity of all neurons in the motor nucleus. It has proven difficult for neurophysiologists to quantify the variability in a common input signal, but characterization of such a signal may improve our understanding of how the activation signal varies across motor tasks. Contemporary methods of quantifying the common input to motor neurons rely on compiling discrete action potentials into continuous time series, assuming the motor pool acts as a linear filter, and requiring signals to be of sufficient duration for frequency analysis. We introduce a space-state model in which the discharge activity of motor neurons is modeled as inhomogeneous Poisson processes and propose a method to quantify an abstract latent trajectory that represents the common input received by motor neurons. The approach also approximates the variation in synaptic noise in the common input signal. The model is validated with four data sets: a simulation of 120 motor units, a pair of integrate-and-fire neurons with a Renshaw cell providing inhibitory feedback, the discharge activity of 10 integrate-and-fire neurons, and the discharge times of concurrently active motor units during an isometric voluntary contraction. The simulations revealed that a latent state-space model is able to quantify the trajectory and variability of the common input signal across all four conditions. When compared with the cumulative spike train method of characterizing common input, the state-space approach was more sensitive to the details of the common input current and was less influenced by the duration of the signal. The state-space approach appears to be capable of detecting rather modest changes in common input signals across conditions.NEW & NOTEWORTHY We propose a state-space model that explicitly delineates a common input signal sent to motor neurons and the physiological noise inherent in synaptic signal transmission. This is the first application of a deterministic state-space model to represent the discharge characteristics of motor units during voluntary contractions.

A joint acquisition-reconstruction paradigm for correcting inhomogeneity artifacts in MR echo planar imaging

One of the main sources of signal degradation in rapid MR acquisitions, such as Echo Planar Imaging (EPI), is magnetic field variations caused by field inhomogeneities and susceptibility gradients. If unaccounted for during the reconstruction process, this spatially-varying field can cause severe image artifacts. In this paper, we show that correcting for the resulting degradations can be formulated as a blind image deconvolution problem. We propose a novel joint acquisition-processing paradigm to solve this problem. We describe a practical implementation of this paradigm using a multi-image acquisition strategy and a corresponding joint estimation-reconstruction algorithm. The estimation step computes the spatial distribution of the field maps, while the reconstruction step yields a Minimum Mean Squared Error (MMSE) estimate of the imaged slice. Our simulations show that this proposed joint acquisition-reconstruction method is robust and efficient, offering factors of improvement in the quality of the reconstructed image as compared to other traditional methods.

Detection and segmentation of concealed objects in terahertz images

Terahertz imaging makes it possible to acquire images of objects concealed underneath clothing by measuring the radiometric temperatures of different objects on a human subject. The goal of this work is to automatically detect and segment concealed objects in broadband 0.1-1 THz images. Due to the inherent physical properties of passive terahertz imaging and associated hardware, images have poor contrast and low signal to noise ratio. Standard segmentation algorithms are unable to segment or detect concealed objects. Our approach relies on two stages. First, we remove the noise from the image using the anisotropic diffusion algorithm. We then detect the boundaries of the concealed objects. We use a mixture of Gaussian densities to model the distribution of the temperature inside the image. We then evolve curves along the isocontours of the image to identify the concealed objects. We have compared our approach with two state-of-the-art segmentation methods. Both methods fail to identify the concealed objects, while our method accurately detected the objects. In addition, our approach was more accurate than a state-of-the-art supervised image segmentation algorithm that required that the concealed objects be already identified. Our approach is completely unsupervised and could work in real-time on dedicated hardware.

Low-dimensional embedding of fMRI datasets

We propose a novel method to embed a functional magnetic resonance imaging (fMRI) dataset in a low-dimensional space. The embedding optimally preserves the local functional coupling between fMRI time series and provides a low-dimensional coordinate system for detecting activated voxels. To compute the embedding, we build a graph of functionally connected voxels. We use the commute time, instead of the geodesic distance, to measure functional distances on the graph. Because the commute time can be computed directly from the eigenvectors of (a symmetric version) the graph probability transition matrix, we use these eigenvectors to embed the dataset in low dimensions. After clustering the datasets in low dimensions, coherent structures emerge that can be easily interpreted. We performed an extensive evaluation of our method comparing it to linear and nonlinear techniques using synthetic datasets and in vivo datasets. We analyzed datasets from the EBC competition obtained with subjects interacting in an urban virtual reality environment. Our exploratory approach is able to detect independently visual areas (V1/V2, V5/MT), auditory areas, and language areas. Our method can be used to analyze fMRI collected during "natural stimuli".

Classification of fMRI time series in a low-dimensional subspace with a spatial prior

We propose a new method for detecting activation in functional magnetic resonance imaging (fMRI) data. We project the fMRI time series on a low-dimensional subspace spanned by wavelet packets in order to create projections that are as non-Gaussian as possible. Our approach achieves two goals: it reduces the dimensionality of the problem by explicitly constructing a sparse approximation to the dataset and it also creates meaningful clusters allowing the separation of the activated regions from the clutter formed by the background time series. We use a mixture of Gaussian densities to model the distribution of the wavelet packet coefficients. We expect activated areas that are connected, and impose a spatial prior in the form of a Markov random field. Our approach was validated with in vivo data and realistic synthetic data, where it outperformed a linear model equipped with the knowledge of the true hemodynamic response.

Analysis of event-related fMRI data using diffusion maps

The blood oxygen level-dependent (BOLD) signal in response to brief periods of stimulus can be detected using event-related functional magnetic resonance imaging (ER-fMRI). In this paper, we propose a new approach for the analysis of ER-fMRI data. We regard the time series as vectors in a high dimensional space (the dimension is the number of time samples). We believe that all activated times series share a common structure and all belong to a low dimensional manifold. On the other hand, we expect the background time series (after detrending) to form a cloud around the origin. We construct an embedding that reveals the organization of the data into an activated manifold and a cluster of non-activated time series. We use a graph partitioning technique-the normalized cut to find the separation between the activated manifold and the background time series. We have conducted several experiments with synthetic and in-vivo data that demonstrate the performance of our approach.

Sensitivity of the cross-correlation between simulated surface EMGs for two muscles to detect motor unit synchronization

The purpose of the study was to evaluate the use of cross-correlation analysis between simulated surface electromyograms (EMGs) of two muscles to quantify motor unit synchronization. The volume conductor simulated a cylindrical limb with two muscles and bone, fat, and skin tissues. Models of two motor neuron pools were used to simulate 120 s of surface EMG that were detected over both muscles. Short-term synchrony was established using a phenomenological model that aligned the discharge times of selected motor units within and across muscles to simulate physiological levels of motor unit synchrony. The correlation between pairs of surface EMGs was estimated as the maximum of the normalized cross-correlation function. After imposing four levels of motor unit synchrony across muscles, five parameters were varied concurrently in the two muscles to examine their influence on the correlation between the surface EMGs: 1) excitation level (5, 10, 15, and 50% of maximum); 2) muscle size (350 and 500 motor units); 3) fat thickness (1 and 4 mm); 4) skin conductivity (0.1 and 1 S/m); and 5) mean motor unit conduction velocity (2.5 and 4 m/s). Despite a constant and high level of motor unit synchronization among pairs of motor units across the two muscles, the cross-correlation index ranged from 0.08 to 0.56, with variation in the five parameters. For example, cross-correlation of EMGs from pairs of hand muscles, each having thin layers of subcutaneous fat and mean motor unit conduction velocities of 4 m/s, may be relatively insensitive to the level of synchronization across muscles. In contrast, cross-correlation of EMGs from pairs of leg muscles, with larger fat thickness, may exhibit a different sensitivity. These results indicate that cross correlation of the surface EMGs from two muscles provides a limited measure of the level of synchronization between motor units in the two muscles.

Diminished task-related adjustments of common inputs to hand muscle motor neurons in older adults

The purpose of this study was to quantify correlated motor unit activity during isometric, shortening and lengthening contractions of a hand muscle in older adults. Thirteen old subjects (69.6+/-5.9 years, six women) lifted and lowered a light load with abduction-adduction movements of the index finger over 10 degrees using 6-s shortening and lengthening contractions of the first dorsal interosseus muscle. The task was repeated 10-20 times while activity in 23 pairs of motor units was recorded with intramuscular electrodes. The data were compared with 23 motor-unit pairs in 15 young (25.9+/-4.6 years, five women) subjects obtained using a similar protocol in a previous study. Correlated motor unit activity was quantified using time-domain (synchronization index; Common Input Strength) and frequency-domain (coherence) analyses for the same motor-unit pairs. For all contractions, there was no difference with age for the strength of motor-unit synchronization, although age-related differences were observed for synchronous peak widths (young, 17.6+/-7.4 ms; old, 13.7+/-4.9 ms) and motor-unit coherence at 6-9 Hz (z score for young, 3.0+/-1.8; old, 2.2+/-1.5). Despite increased synchrony during lengthening contractions and narrower peak widths for shortening contractions in young subjects, there was no difference in the strength of motor unit synchronization (CIS approximately 0.8 imp/s), or the width of the synchronous peak (approximately 14 ms) during the three tasks in old subjects. Furthermore, no significant differences in motor-unit coherence were observed between tasks at any frequency for old adults. These data suggest that the strategy used by the central nervous system to control isometric, shortening, and lengthening contractions varies in young adults, but not old adults. The diminished task-related adjustments of common inputs to motor neurons are a likely consequence of the neural adaptations that occur with advancing age.

Frequency Modulation of Motor Unit Discharge Has Task-Dependent Effects on Fluctuations in Motor Output

The rate of change in the fluctuations in motor output differs during the performance of fatiguing contractions that involve different types of loads. The purpose of this study was to examine the contribution of frequency modulation of motor unit discharge to the fluctuations in the motor output during sustained contractions with the force and position tasks. In separate tests with the upper arm vertical and the elbow flexed to 1.57 rad, the seated subjects maintained either a constant upward force at the wrist (force task) or a constant elbow angle (position task). The force and position tasks were performed in random order at a target force equal to 3.6 ± 2.1% (mean ± SD) of the maximal voluntary contraction (MVC) force above the recruitment threshold of an isolated motor unit from the biceps brachii. Each subject maintained the two tasks for an identical duration (161 ± 93 s) at a mean target force of 22.4 ± 13.6% MVC. As expected, the rate of increase in the fluctuations in motor output (force task: SD for detrended force; position task: SD for vertical acceleration) was greater for the position task than the force task ( P < 0.001). The amplitude of the coefficient of variation (CV) and the power spectra for motor unit discharge were similar between tasks ( P > 0.1) and did not change with time ( P > 0.1), and could not explain the different rates of increase in motor output fluctuations for the two tasks. Nonetheless, frequency modulation of motor unit discharge differed during the two tasks and predicted ( P < 0.001) both the CV for discharge rate (force task: 1–3, 12–13, and 14–15 Hz; position task: 0–1, and 1–2 Hz) and the fluctuations in motor output (force task: 5–6, 9–10, 12–13, and 14–15 Hz; position task: 6–7, 14–15, 17–19, 20–21, and 23–24 Hz). Frequency modulation of motor unit discharge rate differed for the force and position tasks and influenced the ability to sustain steady contractions.

Coherence at 16-32 Hz Can Be Caused by Short-Term Synchrony of Motor Units

Time- and frequency-domain measures of discharge times for pairs of motor units are used to infer the proportion of common synaptic input received by motor neurons. The physiological mechanisms that can produce the experimentally observed peaks in the cross-correlation histogram and the coherence spectrum are uncertain. The present study used a computational model to impose synchronization on the discharge times of motor units. Randomly selected discharge times of a unit that was being synchronized to a reference unit were aligned with some of the discharge times of the reference unit, provided the original discharge time was within 30 ms of the discharge by the reference unit. All time-domain measures (indexes CIS, E, and k′) were sensitive to changes in the level of imposed motor-unit synchronization ( P < 0.01). In addition, synchronization caused a peak between 16 and 32 Hz in the coherence spectrum. The shape of the cross-correlogram determined the frequency at which the peak occurred in the coherence spectrum. Further, the magnitude of the coherence peak was highly correlated with the time-domain measures of motor-unit synchronization ( r2 > 0.80), with the highest correlation occurring for index E ( r2 = 0.98). Thus the peak in the 16- to 32-Hz band of the coherence spectrum can be caused by the time that individual discharges are advanced or delayed to produce synchrony. Although the in vivo processes that adjust the timing of motor-unit discharges are not fully understood, these results suggest that they may not depend entirely on an oscillatory drive by the CNS.

Motor-unit coherence and its relation with synchrony are influenced by training

The purpose of the study was to quantify the strength of motor-unit coherence from the left and right first dorsal interosseous muscles in untrained, skill-trained (musicians), and strength-trained (weightlifters) individuals who had long-term specialized use of their hand muscles. The strength of motor-unit coherence was quantified from a total of 394 motor-unit pairs in 13 subjects using data from a previous study in which differences were found in the strength of motor-unit synchronization depending on training status. In the present study, we found that the strength of motor-unit coherence was significantly greater in the left compared with the right hand of untrained right-handed subjects with the largest differences observed between 21 and 24 Hz. The strength of motor-unit coherence was lower in both hands of skill-trained subjects (21-27 Hz) and the right (skilled) hand of untrained subjects (21-24 Hz), whereas the largest motor-unit coherence was observed in both hands of strength-trained subjects (3-9 and 21-27 Hz). A strong curvilinear association was observed between motor-unit synchronization and the integral of coherence at 10-30 Hz in all motor-unit pairs (r2 = 0.77), and was most pronounced in strength-trained subjects (r2 = 0.90). Furthermore, this association was accentuated when using synchronization data with broad peaks (>11 ms), suggesting that the 10- to 30-Hz coherence is due to oscillatory activity in indirect branched common inputs. The altered coherence with training may be due to an interaction between cortical inhibition and the number of direct common inputs to motor neurons in skill- or strength-trained hands.

Analysis of event-related fMRI data using best clustering bases

We explore a new paradigm for the analysis of event-related functional magnetic resonance images (fMRI) of brain activity. We regard the fMRI data as a very large set of time series x(i) (t), indexed by the position i of a voxel inside the brain. The decision that a voxel i(o) is activated is based not solely on the value of the fMRI signal at i(o), but rather on the comparison of all time series x(i) (t) in a small neighborhood Wi(o) around i(o). We construct basis functions on which the projection of the fMRI data reveals the organization of the time series x(i) (t) into activated and nonactivated clusters. These clustering basis functions are selected from large libraries of wavelet packets according to their ability to separate the fMRI time series into the activated cluster and a nonactivated cluster. This principle exploits the intrinsic spatial correlation that is present in the data. The construction of the clustering basis functions described in this paper is applicable to a large category of problems where time series are indexed by a spatial variable.

Analysis of event-related fMRI data using best clustering bases

We explore a new paradigm for the analysis of event-related functional magnetic resonance images (fMRI) of brain activity. We regard the fMRI data as a very large set of time series x(i)(t), indexed by the position i of a voxel inside the brain. The decision that a voxel i0 is activated is based not solely on the value of the fMRI signal at i0, but rather on the comparison of all time series x(i)(t) in a small neighborhood Wi0 around i0. We construct basis functions on which the projection of the fMRI data reveals the organization of the time-series x(i)(t) into "activated", and "non-activated" clusters. These "clustering basis functions" are selected from large libraries of wavelet packets according to their ability to separate the fMRI time-series into the activated cluster and a non activated cluster. This principle exploits the intrinsic spatial correlation that is present in the data.

Wavelet-based estimation of a semiparametric generalized linear model of fMRI time-series

This paper addresses the problem of detecting significant changes in fMRI time series that are correlated to a stimulus time course. This paper provides a new approach to estimate the parameters of a semiparametric generalized linear model of fMRI time series. The fMRI signal is described as the sum of two effects: a smooth trend and the response to the stimulus. The trend belongs to a subspace spanned by large scale wavelets. The wavelet transform provides an approximation to the Karhunen-Loève transform for the long memory noise and we have developed a scale space regression that permits to carry out the regression in the wavelet domain while omitting the scales that are contaminated by the trend. In order to demonstrate that our approach outperforms the state-of-the art detrending technique, we evaluated our method against a smoothing spline approach. Experiments with simulated data and experimental fMRI data, demonstrate that our approach can infer and remove drifts that cannot be adequately represented with splines.

Adaptive wavelet packet basis selection for zerotree image coding

Image coding methods based on adaptive wavelet transforms and those employing zerotree quantization have been shown to be successful. We present a general zerotree structure for an arbitrary wavelet packet geometry in an image coding framework. A fast basis selection algorithm is developed; it uses a Markov chain based cost estimate of encoding the image using this structure. As a result, our adaptive wavelet zerotree image coder has a relatively low computational complexity, performs comparably to state-of-the-art image coders, and is capable of progressively encoding images.

Image compression with adaptive local cosines: a comparative study

The goal of this work is twofold. First, we demonstrate that an advantage can be gained by using local cosine bases over wavelets to encode images that contain periodic textures. We designed a coder that outperforms one of the best wavelet coders on a large number of images. The coder finds the optimal segmentation of the image in terms of local cosine bases. The coefficients are encoded using a scalar quantizer optimized for Laplacian distributions. This new coder constitutes the first concrete contribution of the paper. Second, we used our coder to perform an extensive comparison of several optimized bells in terms of rate-distortion and visual quality for a large collection of images. This study provides for the first time a rigorous evaluation in realistic conditions of these bells. Our experiments show that bells that are designed to reproduce exactly polynomials of degree 1 resulted in the worst performance in terms of the PSNR. However, a visual inspection of the compressed images indicates that these bells often provide reconstructed images with very few visual artifacts, even at low bit rates. The bell with the most narrow Fourier transform gave the best results in terms of the PSNR on most images. This bell tends however to create annoying visual artifacts in very smooth regions at low bit rate.

Multilayered image representation: application to image compression

The main contribution of this work is a new paradigm for image representation and image compression. We describe a new multilayered representation technique for images. An image is parsed into a superposition of coherent layers: piecewise smooth regions layer, textures layer, etc. The multilayered decomposition algorithm consists in a cascade of compressions applied successively to the image itself and to the residuals that resulted from the previous compressions. During each iteration of the algorithm, we code the residual part in a lossy way: we only retain the most significant structures of the residual part, which results in a sparse representation. Each layer is encoded independently with a different transform, or basis, at a different bitrate, and the combination of the compressed layers can always be reconstructed in a meaningful way. The strength of the multilayer approach comes from the fact that different sets of basis functions complement each others: some of the basis functions will give reasonable account of the large trend of the data, while others will catch the local transients, or the oscillatory patterns. This multilayered representation has a lot of beautiful applications in image understanding, and image and video coding. We have implemented the algorithm and we have studied its capabilities.

Fast adaptive wavelet packet image compression

Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients, which are often quantized to zero, even at high bit rates. Our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis is placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four times faster than a standard convolution-decimation. An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly out performs one of the best wavelet coder on images such as Barbara and fingerprints, both visually and in term of PSNR.

Tracking myocardial deformation using phase contrast MR velocity fields: a stochastic approach

The authors propose a new approach for tracking the deformation of the left-ventricular (LV) myocardium from two-dimensional (2-D) magnetic resonance (MR) phase contrast velocity fields. The use of phase contrast MR velocity data in cardiac motion problems has been introduced by others (N.J. Pelc et al., 1991) and shown to be potentially useful for tracking discrete tissue elements, and therefore, characterizing LV motion. However, the authors show here that these velocity data: 1) are extremely noisy near the LV borders; and 2) cannot alone be used to estimate the motion and the deformation of the entire myocardium due to noise in the velocity fields. In this new approach, the authors use the natural spatial constraints of the endocardial and epicardial contours, detected semiautomatically in each image frame, to help remove noisy velocity vectors at the LV contours. The information from both the boundaries and the phase contrast velocity data is then integrated into a deforming mesh that is placed over the myocardium at one time frame and then tracked over the entire cardiac cycle. The deformation is guided by a Kalman filter that provides a compromise between 1) believing the dense field velocity and the contour data when it is crisp and coherent in a local spatial and temporal sense and 2) employing a temporally smooth cyclic model of cardiac motion when contour and velocity data are not trustworthy. The Kalman filter is particularly well suited to this task as it produces an optimal estimate of the left ventricle's kinematics (in the sense that the error is statistically minimized) given incomplete and noise corrupted data, and given a basic dynamical model of the left ventricle. The method has been evaluated with simulated data; the average error between tracked nodes and theoretical position was 1.8% of the total path length. The algorithm has also been evaluated with phantom data; the average error was 4.4% of the total path length. The authors show that in their initial tests with phantoms that the new approach shows small, but concrete improvements over previous techniques that used primarily phase contrast velocity data alone. They feel that these improvements will be amplified greatly as they move to direct comparisons in in vivo and three-dimensional (3-D) datasets.