Individual Resting-State Brain Networks Enabled by Massive Multivariate Conditional Mutual Information.

Individual-level resting-state networks (RSNs) based on resting-state fMRI (rs-fMRI) are of great interest due to evidence that network dysfunction may underlie some diseases. Most current rs-fMRI analyses use linear correlation. Since correlation is a bivariate measure of association, it discards most of the information contained in the spatial variation of the thousands of hemodynamic signals within the voxels in a given brain region. Subject-specific functional RSNs using typical rs-fMRI data, are therefore dominated by indirect connections and loss of spatial information and can only deliver reliable connectivity after group averaging. While bivariate partial correlation can rule out indirect connections, it results in connectivity that is too sparse due to lack of sensitivity. We have developed a method that uses all the spatial variation information in a given parcel by employing a multivariate information-theoretic association measure based on canonical correlations. Our method, multivariate conditional mutual information (mvCMI) reliably constructs single-subject connectivity estimates showing mostly direct connections. Averaging across subjects is not needed. The method is applied to Human Connectome Project data and compared to diffusion MRI. The results are far superior to those obtained by correlation and partial correlation.

Exact topological inference of the resting-state brain networks in twins.

A cycle in a brain network is a subset of a connected component with redundant additional connections. If there are many cycles in a connected component, the connected component is more densely connected. Whereas the number of connected components represents the integration of the brain network, the number of cycles represents how strong the integration is. However, it is unclear how to perform statistical inference on the number of cycles in the brain network. In this study, we present a new statistical inference framework for determining the significance of the number of cycles through the Kolmogorov-Smirnov (KS) distance, which was recently introduced to measure the similarity between networks across different filtration values by using the zeroth Betti number. In this paper, we show how to extend the method to the first Betti number, which measures the number of cycles. The performance analysis was conducted using the random network simulations with ground truths. By using a twin imaging study, which provides biological ground truth, the methods are applied in determining if the number of cycles is a statistically significant heritable network feature in the resting-state functional connectivity in 217 twins obtained from the Human Connectome Project. The MATLAB codes as well as the connectivity matrices used in generating results are provided at http://www.stat.wisc.edu/∼mchung/TDA.

Connectivity in fMRI: Blind Spots and Breakthroughs.

In recent years, driven by scientific and clinical concerns, there has been an increased interest in the analysis of functional brain networks. The goal of these analyses is to better understand how brain regions interact, how this depends upon experimental conditions and behavioral measures and how anomalies (disease) can be recognized. In this paper, we provide, first, a brief review of some of the main existing methods of functional brain network analysis. But rather than compare them, as a traditional review would do, instead, we draw attention to their significant limitations and blind spots. Then, second, relevant experts, sketch a number of emerging methods, which can break through these limitations. In particular we discuss five such methods. The first two, stochastic block models and exponential random graph models, provide an inferential basis for network analysis lacking in the exploratory graph analysis methods. The other three addresses: network comparison via persistent homology, time-varying connectivity that distinguishes sample fluctuations from neural fluctuations, and network system identification that draws inferential strength from temporal autocorrelation.

On the Reliability of Individual Brain Activity Networks.

There is intense interest in fMRI research on whole-brain functional connectivity, and however, two fundamental issues are still unresolved: the impact of spatiotemporal data resolution (spatial parcellation and temporal sampling) and the impact of the network construction method on the reliability of functional brain networks. In particular, the impact of spatiotemporal data resolution on the resulting connectivity findings has not been sufficiently investigated. In fact, a number of studies have already observed that functional networks often give different conclusions across different parcellation scales. If the interpretations from functional networks are inconsistent across spatiotemporal scales, then the whole validity of the functional network paradigm is called into question. This paper investigates the consistency of resting state network structure when using different temporal sampling or spatial parcellation, or different methods for constructing the networks. To pursue this, we develop a novel network comparison framework based on persistent homology from a topological data analysis. We use the new network comparison tools to characterize the spatial and temporal scales under which consistent functional networks can be constructed. The methods are illustrated on Human Connectome Project data, showing that the DISCOH2 network construction method outperforms other approaches at most data spatiotemporal resolutions.

Topological Distances Between Brain Networks.

Many existing brain network distances are based on matrix norms. The element-wise differences may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A few extreme edge weights may severely affect the distance. Thus it is necessary to develop network distances that recognize topology. In this paper, we introduce Gromov-Hausdorff (GH) and Kolmogorov-Smirnov (KS) distances. GH-distance is often used in persistent homology based brain network models. The superior performance of KS-distance is contrasted against matrix norms and GH-distance in random network simulations with the ground truths. The KS-distance is then applied in characterizing the multimodal MRI and DTI study of maltreated children.

State-Space Analysis of Granger-Geweke Causality Measures with Application to fMRI.

The recent interest in the dynamics of networks and the advent, across a range of applications, of measuring modalities that operate on different temporal scales have put the spotlight on some significant gaps in the theory of multivariate time series. Fundamental to the description of network dynamics is the direction of interaction between nodes, accompanied by a measure of the strength of such interactions. Granger causality and its associated frequency domain strength measures (GEMs) (due to Geweke) provide a framework for the formulation and analysis of these issues. In pursuing this setup, three significant unresolved issues emerge. First, computing GEMs involves computing submodels of vector time series models, for which reliable methods do not exist. Second, the impact of filtering on GEMs has never been definitively established. Third, the impact of downsampling on GEMs has never been established. In this work, using state-space methods, we resolve all these issues and illustrate the results with some simulations. Our analysis is motivated by some problems in (fMRI) brain imaging, to which we apply it, but it is of general applicability.

Spatially Sparse, Temporally Smooth MEG Via Vector ℓ0 .

In this paper, we describe a new method for solving the magnetoencephalography inverse problem: temporal vector ℓ0-penalized least squares (TV-L0LS). The method calculates maximally sparse current dipole magnitudes and directions via spatial ℓ0 regularization on a cortically-distributed source grid, while constraining the solution to be smooth with respect to time. We demonstrate the utility of this method on real and simulated data by comparison to existing methods.

Brain activity: connectivity, sparsity, and mutual information.

We develop a new approach to functional brain connectivity analysis, which deals with four fundamental aspects of connectivity not previously jointly treated. These are: temporal correlation, spurious spatial correlation, sparsity, and network construction using trajectory (as opposed to marginal) Mutual Information. We call the new method Sparse Conditional Trajectory Mutual Information (SCoTMI). We demonstrate SCoTMI on simulated and real fMRI data, showing that SCoTMI gives more accurate and more repeatable detection of network links than competing network estimation methods.

Point-process principal components analysis via geometric optimization.

There has been a fast-growing demand for analysis tools for multivariate point-process data driven by work in neural coding and, more recently, high-frequency finance. Here we develop a true or exact (as opposed to one based on time binning) principal components analysis for preliminary processing of multivariate point processes. We provide a maximum likelihood estimator, an algorithm for maximization involving steepest ascent on two Stiefel manifolds, and novel constrained asymptotic analysis. The method is illustrated with a simulation and compared with a binning approach.

Identifying FMRI model violations with Lagrange multiplier tests.

The standard modeling framework in functional magnetic resonance imaging (fMRI) is predicated on assumptions of linearity, time invariance and stationarity. These assumptions are rarely checked because doing so requires specialized software, although failure to do so can lead to bias and mistaken inference. Identifying model violations is an essential but largely neglected step in standard fMRI data analysis. Using Lagrange multiplier testing methods we have developed simple and efficient procedures for detecting model violations such as nonlinearity, nonstationarity and validity of the common double gamma specification for hemodynamic response. These procedures are computationally cheap and can easily be added to a conventional analysis. The test statistic is calculated at each voxel and displayed as a spatial anomaly map which shows regions where a model is violated. The methodology is illustrated with a large number of real data examples.

Computing the trajectory mutual information between a point process and an analog stochastic process.

In a number of application areas such as neural coding there is interest in computing, from real data, the information flows between stochastic processes one of which is a point process. Of particular interest is the calculation of the trajectory (as opposed to marginal) mutual information between an observed point process which is influenced by an underlying but unobserved analog stochastic process i.e. a state. Using particle filtering we develop a model based trajectory mutual information calculation for apparently the first time.

Dynamic Granger-Geweke causality modeling with application to interictal spike propagation.

A persistent problem in developing plausible neurophysiological models of perception, cognition, and action is the difficulty of characterizing the interactions between different neural systems. Previous studies have approached this problem by estimating causal influences across brain areas activated during cognitive processing using structural equation modeling (SEM) and, more recently, with Granger-Geweke causality. While SEM is complicated by the need for a priori directional connectivity information, the temporal resolution of dynamic Granger-Geweke estimates is limited because the underlying autoregressive (AR) models assume stationarity over the period of analysis. We have developed a novel optimal method for obtaining data-driven directional causality estimates with high temporal resolution in both time and frequency domains. This is achieved by simultaneously optimizing the length of the analysis window and the chosen AR model order using the SURE criterion. Dynamic Granger-Geweke causality in time and frequency domains is subsequently calculated within a moving analysis window. We tested our algorithm by calculating the Granger-Geweke causality of epileptic spike propagation from the right frontal lobe to the left frontal lobe. The results quantitatively suggested that the epileptic activity at the left frontal lobe was propagated from the right frontal lobe, in agreement with the clinical diagnosis. Our novel computational tool can be used to help elucidate complex directional interactions in the human brain.

Spatiotemporal wavelet analysis for functional MRI.

Characterizing the spatiotemporal behavior of the BOLD signal in functional Magnetic Resonance Imaging (fMRI) is a central issue in understanding brain function. While the nature of functional activation clusters is fundamentally heterogeneous, many current analysis approaches use spatially invariant models that can degrade anatomic boundaries and distort the underlying spatiotemporal signal. Furthermore, few analysis approaches use true spatiotemporal continuity in their statistical formulations. To address these issues, we present a novel spatiotemporal wavelet procedure that uses a stimulus-convolved hemodynamic signal plus correlated noise model. The wavelet fits, computed by spatially constrained maximum-likelihood estimation, provide efficient multiscale representations of heterogeneous brain structures and give well-identified, parsimonious spatial activation estimates that are modulated by the temporal fMRI dynamics. In a study of both simulated data and actual fMRI memory task experiments, our new method gave lower mean-squared error and seemed to result in more localized fMRI activation maps compared to models using standard wavelet or smoothing techniques. Our spatiotemporal wavelet framework suggests a useful tool for the analysis of fMRI studies.

Dynamic analysis of neural encoding by point process adaptive filtering.

Neural receptive fields are dynamic in that with experience, neurons change their spiking responses to relevant stimuli. To understand how neural systems adapt their representations of biological information, analyses of receptive field plasticity from experimental measurements are crucial. Adaptive signal processing, the well-established engineering discipline for characterizing the temporal evolution of system parameters, suggests a framework for studying the plasticity of receptive fields. We use the Bayes' rule Chapman-Kolmogorov paradigm with a linear state equation and point process observation models to derive adaptive filters appropriate for estimation from neural spike trains. We derive point process filter analogues of the Kalman filter, recursive least squares, and steepest-descent algorithms and describe the properties of these new filters. We illustrate our algorithms in two simulated data examples. The first is a study of slow and rapid evolution of spatial receptive fields in hippocampal neurons. The second is an adaptive decoding study in which a signal is decoded from ensemble neural spiking activity as the receptive fields of the neurons in the ensemble evolve. Our results provide a paradigm for adaptive estimation for point process observations and suggest a practical approach for constructing filtering algorithms to track neural receptive field dynamics on a millisecond timescale.

Dynamic analyses of information encoding in neural ensembles.

Neural spike train decoding algorithms and techniques to compute Shannon mutual information are important methods for analyzing how neural systems represent biological signals. Decoding algorithms are also one of several strategies being used to design controls for brain-machine interfaces. Developing optimal strategies to design decoding algorithms and compute mutual information are therefore important problems in computational neuroscience. We present a general recursive filter decoding algorithm based on a point process model of individual neuron spiking activity and a linear stochastic state-space model of the biological signal. We derive from the algorithm new instantaneous estimates of the entropy, entropy rate, and the mutual information between the signal and the ensemble spiking activity. We assess the accuracy of the algorithm by computing, along with the decoding error, the true coverage probability of the approximate 0.95 confidence regions for the individual signal estimates. We illustrate the new algorithm by reanalyzing the position and ensemble neural spiking activity of CA1 hippocampal neurons from two rats foraging in an open circular environment. We compare the performance of this algorithm with a linear filter constructed by the widely used reverse correlation method. The median decoding error for Animal 1 (2) during 10 minutes of open foraging was 5.9 (5.5) cm, the median entropy was 6.9 (7.0) bits, the median information was 9.4 (9.4) bits, and the true coverage probability for 0.95 confidence regions was 0.67 (0.75) using 34 (32) neurons. These findings improve significantly on our previous results and suggest an integrated approach to dynamically reading neural codes, measuring their properties, and quantifying the accuracy with which encoded information is extracted.

Motion and ballistocardiogram artifact removal for interleaved recording of EEG and EPs during MRI.

Artifacts generated by motion (e.g., ballistocardiac) of the head inside a high magnetic field corrupt recordings of EEG and EPs. This paper introduces a method for motion artifact cancellation. This method is based on adaptive filtering and takes advantage of piezoelectric motion sensor information to estimate the motion artifact noise. This filter estimates the mapping between motion sensor and EEG space, subtracting the motion-related noise from the raw EEG signal. Due to possible subject motion and changes in electrode impedance, a time-varying mapping of the motion versus EEG is required. We show that this filter is capable of removing both ballistocardiogram and gross motion artifacts, restoring EEG alpha waves (8-13 Hz), and visual evoked potentials (VEPs). This adaptive filter outperforms the simple band-pass filter for alpha detection because it is also capable of reducing noise within the frequency band of interest. In addition, this filter also removes the transient responses normally visible in the EEG window after echo planar image acquisition, observed during interleaved EEG/fMRI recordings. Our adaptive filter approach can be implemented in real-time to allow for continuous monitoring of EEG and fMRI during clinical and cognitive studies.

Contrasting patterns of receptive field plasticity in the hippocampus and the entorhinal cortex: an adaptive filtering approach.

Neural receptive fields are frequently plastic: a neural response to a stimulus can change over time as a result of experience. We developed an adaptive point process filtering algorithm that allowed us to estimate the dynamics of both the spatial receptive field (spatial intensity function) and the interspike interval structure (temporal intensity function) of neural spike trains on a millisecond time scale without binning over time or space. We applied this algorithm to both simulated data and recordings of putative excitatory neurons from the CA1 region of the hippocampus and the deep layers of the entorhinal cortex (EC) of awake, behaving rats. Our simulation results demonstrate that the algorithm accurately tracks simultaneous changes in the spatial and temporal structure of the spike train. When we applied the algorithm to experimental data, we found consistent patterns of plasticity in the spatial and temporal intensity functions of both CA1 and deep EC neurons. These patterns tended to be opposite in sign, in that the spatial intensity functions of CA1 neurons showed a consistent increase over time, whereas those of deep EC neurons tended to decrease, and the temporal intensity functions of CA1 neurons showed a consistent increase only in the "theta" (75-150 msec) region, whereas those of deep EC neurons decreased in the region between 20 and 75 msec. In addition, the minority of deep EC neurons whose spatial intensity functions increased in area over time fired in a significantly more spatially specific manner than non-increasing deep EC neurons. We hypothesize that this subset of deep EC neurons may receive more direct input from CA1 and may be part of a neural circuit that transmits information about the animal's location to the neocortex.