Topographic factor analysis: a Bayesian model for inferring brain networks from neural data

BrainIAK: The Brain Imaging Analysis Kit

Functional magnetic resonance imaging (fMRI) offers a rich source of data for studying the neural basis of cognition. Here, we describe the Brain Imaging Analysis Kit (BrainIAK), an open-source, free Python package that provides computationally optimized solutions to key problems in advanced fMRI analysis. A variety of techniques are presently included in BrainIAK: intersubject correlation (ISC) and intersubject functional connectivity (ISFC), functional alignment via the shared response model (SRM), full correlation matrix analysis (FCMA), a Bayesian version of representational similarity analysis (BRSA), event segmentation using hidden Markov models, topographic factor analysis (TFA), inverted encoding models (IEMs), an fMRI data simulator that uses noise characteristics from real data (fmrisim), and some emerging methods. These techniques have been optimized to leverage the efficiencies of high-performance compute (HPC) clusters, and the same code can be seamlessly transferred from a laptop to a cluster. For each of the aforementioned techniques, we describe the data analysis problem that the technique is meant to solve and how it solves that problem; we also include an example Jupyter notebook for each technique and an annotated bibliography of papers that have used and/or described that technique. In addition to the sections describing various analysis techniques in BrainIAK, we have included sections describing the future applications of BrainIAK to real-time fMRI, tutorials that we have developed and shared online to facilitate learning the techniques in BrainIAK, computational innovations in BrainIAK, and how to contribute to BrainIAK. We hope that this manuscript helps readers to understand how BrainIAK might be useful in their research.

A Computational Neural Model for Mapping Degenerate Neural Architectures

Degeneracy in biological systems refers to a many-to-one mapping between physical structures and their functional (including psychological) outcomes. Despite the ubiquity of the phenomenon, traditional analytical tools for modeling degeneracy in neuroscience are extremely limited. In this study, we generated synthetic datasets to describe three situations of degeneracy in fMRI data to demonstrate the limitations of the current univariate approach. We describe a novel computational approach for the analysis referred to as neural topographic factor analysis (NTFA). NTFA is designed to capture variations in neural activity across task conditions and participants. The advantage of this discovery-oriented approach is to reveal whether and how experimental trials and participants cluster into task conditions and participant groups. We applied NTFA on simulated data, revealing the appropriate degeneracy assumption in all three situations and demonstrating NTFA's utility in uncovering degeneracy. Lastly, we discussed the importance of testing degeneracy in fMRI data and the implications of applying NTFA to do so.

Brain kernel: A new spatial covariance function for fMRI data

A key problem in functional magnetic resonance imaging (fMRI) is to estimate spatial activity patterns from noisy high-dimensional signals. Spatial smoothing provides one approach to regularizing such estimates. However, standard smoothing methods ignore the fact that correlations in neural activity may fall off at different rates in different brain areas, or exhibit discontinuities across anatomical or functional boundaries. Moreover, such methods do not exploit the fact that widely separated brain regions may exhibit strong correlations due to bilateral symmetry or the network organization of brain regions. To capture this non-stationary spatial correlation structure, we introduce the brain kernel, a continuous covariance function for whole-brain activity patterns. We define the brain kernel in terms of a continuous nonlinear mapping from 3D brain coordinates to a latent embedding space, parametrized with a Gaussian process (GP). The brain kernel specifies the prior covariance between voxels as a function of the distance between their locations in embedding space. The GP mapping warps the brain nonlinearly so that highly correlated voxels are close together in latent space, and uncorrelated voxels are far apart. We estimate the brain kernel using resting-state fMRI data, and we develop an exact, scalable inference method based on block coordinate descent to overcome the challenges of high dimensionality (10-100K voxels). Finally, we illustrate the brain kernel's usefulness with applications to brain decoding and factor analysis with multiple task-based fMRI datasets.

High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns

Our thoughts arise from coordinated patterns of interactions between brain structures that change with our ongoing experiences. High-order dynamic correlations in neural activity patterns reflect different subgraphs of the brain's functional connectome that display homologous lower-level dynamic correlations. Here we test the hypothesis that high-level cognition is reflected in high-order dynamic correlations in brain activity patterns. We develop an approach to estimating high-order dynamic correlations in timeseries data, and we apply the approach to neuroimaging data collected as human participants either listen to a ten-minute story or listen to a temporally scrambled version of the story. We train across-participant pattern classifiers to decode (in held-out data) when in the session each neural activity snapshot was collected. We find that classifiers trained to decode from high-order dynamic correlations yield the best performance on data collected as participants listened to the (unscrambled) story. By contrast, classifiers trained to decode data from scrambled versions of the story yielded the best performance when they were trained using first-order dynamic correlations or non-correlational activity patterns. We suggest that as our thoughts become more complex, they are reflected in higher-order patterns of dynamic network interactions throughout the brain.

Predicting Brain Regions Related to Alzheimer's Disease Based on Global Feature

Alzheimer's disease (AD) is a neurodegenerative disease that commonly affects the elderly; early diagnosis and timely treatment are very important to delay the course of the disease. In the past, most brain regions related to AD were identified based on imaging methods, and only some atrophic brain regions could be identified. In this work, the authors used mathematical models to identify the potential brain regions related to AD. In this study, 20 patients with AD and 13 healthy controls (non-AD) were recruited by the neurology outpatient department or the neurology ward of Peking University First Hospital from September 2017 to March 2019. First, diffusion tensor imaging (DTI) was used to construct the brain structural network. Next, the authors set a new local feature index 2hop-connectivity to measure the correlation between different regions. Compared with the traditional graph theory index, 2hop-connectivity exploits the higher-order information of the graph structure. And for this purpose, the authors proposed a novel algorithm called 2hopRWR to measure 2hop-connectivity. Then, a new index global feature score (GFS) based on a global feature was proposed by combing five local features, namely degree centrality, betweenness centrality, closeness centrality, the number of maximal cliques, and 2hop-connectivity, to judge which brain regions are related to AD. As a result, the top ten brain regions identified using the GFS scoring difference between the AD and the non-AD groups were associated to AD by literature verification. The results of the literature validation comparing GFS with the local features showed that GFS was superior to individual local features. Finally, the results of the canonical correlation analysis showed that the GFS was significantly correlated with the scores of the Mini-Mental State Examination (MMSE) scale and the Montreal Cognitive Assessment (MoCA) scale. Therefore, the authors believe the GFS can also be used as a new biomarker to assist in diagnosis and objective monitoring of disease progression. Besides, the method proposed in this paper can be used as a differential network analysis method for network analysis in other domains.

Finding Distributed Needles in Neural Haystacks

The human cortex encodes information in complex networks that can be anatomically dispersed and variable in their microstructure across individuals. Using simulations with neural network models, we show that contemporary statistical methods for functional brain imaging-including univariate contrast, searchlight multivariate pattern classification, and whole-brain decoding with L1 or L2 regularization-each have critical and complementary blind spots under these conditions. We then introduce the sparse-overlapping-sets (SOS) LASSO-a whole-brain multivariate approach that exploits structured sparsity to find network-distributed information-and show in simulation that it captures the advantages of other approaches while avoiding their limitations. When applied to fMRI data to find neural responses that discriminate visually presented faces from other visual stimuli, each method yields a different result, but existing approaches all support the canonical view that face perception engages localized areas in posterior occipital and temporal regions. In contrast, SOS LASSO uncovers a network spanning all four lobes of the brain. The result cannot reflect spurious selection of out-of-system areas because decoding accuracy remains exceedingly high even when canonical face and place systems are removed from the dataset. When used to discriminate visual scenes from other stimuli, the same approach reveals a localized signal consistent with other methods-illustrating that SOS LASSO can detect both widely distributed and localized representational structure. Thus, structured sparsity can provide an unbiased method for testing claims of functional localization. For faces and possibly other domains, such decoding may reveal representations more widely distributed than previously suspected.SIGNIFICANCE STATEMENT Brain systems represent information as patterns of activation over neural populations connected in networks that can be widely distributed anatomically, variable across individuals, and intermingled with other networks. We show that four widespread statistical approaches to functional brain imaging have critical blind spots in this scenario and use simulations with neural network models to illustrate why. We then introduce a new approach designed specifically to find radically distributed representations in neural networks. In simulation and in fMRI data collected in the well studied domain of face perception, the new approach discovers extensive signal missed by the other methods-suggesting that prior functional imaging work may have significantly underestimated the degree to which neurocognitive representations are distributed and variable across individuals.

Comparing supervised and unsupervised approaches to emotion categorization in the human brain, body, and subjective experience

Machine learning methods provide powerful tools to map physical measurements to scientific categories. But are such methods suitable for discovering the ground truth about psychological categories? We use the science of emotion as a test case to explore this question. In studies of emotion, researchers use supervised classifiers, guided by emotion labels, to attempt to discover biomarkers in the brain or body for the corresponding emotion categories. This practice relies on the assumption that the labels refer to objective categories that can be discovered. Here, we critically examine this approach across three distinct datasets collected during emotional episodes—measuring the human brain, body, and subjective experience—and compare supervised classification solutions with those from unsupervised clustering in which no labels are assigned to the data. We conclude with a set of recommendations to guide researchers towards meaningful, data-driven discoveries in the science of emotion and beyond.

A Gaussian Process Model of Human Electrocorticographic Data

We present a model-based method for inferring full-brain neural activity at millimeter-scale spatial resolutions and millisecond-scale temporal resolutions using standard human intracranial recordings. Our approach makes the simplifying assumptions that different people's brains exhibit similar correlational structure, and that activity and correlation patterns vary smoothly over space. One can then ask, for an arbitrary individual's brain: given recordings from a limited set of locations in that individual's brain, along with the observed spatial correlations learned from other people's recordings, how much can be inferred about ongoing activity at other locations throughout that individual's brain? We show that our approach generalizes across people and tasks, thereby providing a person- and task-general means of inferring high spatiotemporal resolution full-brain neural dynamics from standard low-density intracranial recordings.

Incorporating structured assumptions with probabilistic graphical models in fMRI data analysis

With the wide adoption of functional magnetic resonance imaging (fMRI) by cognitive neuroscience researchers, large volumes of brain imaging data have been accumulated in recent years. Aggregating these data to derive scientific insights often faces the challenge that fMRI data are high-dimensional, heterogeneous across people, and noisy. These challenges demand the development of computational tools that are tailored both for the neuroscience questions and for the properties of the data. We review a few recently developed algorithms in various domains of fMRI research: fMRI in naturalistic tasks, analyzing full-brain functional connectivity, pattern classification, inferring representational similarity and modeling structured residuals. These algorithms all tackle the challenges in fMRI similarly: they start by making clear statements of assumptions about neural data and existing domain knowledge, incorporate those assumptions and domain knowledge into probabilistic graphical models, and use those models to estimate properties of interest or latent structures in the data. Such approaches can avoid erroneous findings, reduce the impact of noise, better utilize known properties of the data, and better aggregate data across groups of subjects. With these successful cases, we advocate wider adoption of explicit model construction in cognitive neuroscience. Although we focus on fMRI, the principle illustrated here is generally applicable to brain data of other modalities.

A probabilistic approach to discovering dynamic full-brain functional connectivity patterns

Recent research shows that the covariance structure of functional magnetic resonance imaging (fMRI) data - commonly described as functional connectivity - can change as a function of the participant's cognitive state (for review see Turk-Browne, 2013). Here we present a Bayesian hierarchical matrix factorization model, termed hierarchical topographic factor analysis (HTFA), for efficiently discovering full-brain networks in large multi-subject neuroimaging datasets. HTFA approximates each subject's network by first re-representing each brain image in terms of the activities of a set of localized nodes, and then computing the covariance of the activity time series of these nodes. The number of nodes, along with their locations, sizes, and activities (over time) are learned from the data. Because the number of nodes is typically substantially smaller than the number of fMRI voxels, HTFA can be orders of magnitude more efficient than traditional voxel-based functional connectivity approaches. In one case study, we show that HTFA recovers the known connectivity patterns underlying a collection of synthetic datasets. In a second case study, we illustrate how HTFA may be used to discover dynamic full-brain activity and connectivity patterns in real fMRI data, collected as participants listened to a story. In a third case study, we carried out a similar series of analyses on fMRI data collected as participants viewed an episode of a television show. In these latter case studies, we found that the HTFA-derived activity and connectivity patterns can be used to reliably decode which moments in the story or show the participants were experiencing. Further, we found that these two classes of patterns contained partially non-overlapping information, such that decoders trained on combinations of activity-based and dynamic connectivity-based features performed better than decoders trained on activity or connectivity patterns alone. We replicated this latter result with two additional (previously developed) methods for efficiently characterizing full-brain activity and connectivity patterns.

Decoding brain activity using a large-scale probabilistic functional-anatomical atlas of human cognition

A central goal of cognitive neuroscience is to decode human brain activity—that is, to infer mental processes from observed patterns of whole-brain activation. Previous decoding efforts have focused on classifying brain activity into a small set of discrete cognitive states. To attain maximal utility, a decoding framework must be open-ended, systematic, and context-sensitive—that is, capable of interpreting numerous brain states, presented in arbitrary combinations, in light of prior information. Here we take steps towards this objective by introducing a probabilistic decoding framework based on a novel topic model—Generalized Correspondence Latent Dirichlet Allocation—that learns latent topics from a database of over 11,000 published fMRI studies. The model produces highly interpretable, spatially-circumscribed topics that enable flexible decoding of whole-brain images. Importantly, the Bayesian nature of the model allows one to “seed” decoder priors with arbitrary images and text—enabling researchers, for the first time, to generate quantitative, context-sensitive interpretations of whole-brain patterns of brain activity.

A central goal of cognitive neuroscience is to decode human brain activity—i.e., to be able to infer mental processes from observed patterns of whole-brain activity. However, existing approaches to brain decoding suffer from a number of important limitations—for example, they often work only in one narrow domain of cognition, and cannot be easily generalized to novel contexts. Here we address such limitations by introducing a simple probabilistic framework based on a novel topic modeling approach. We use our approach to extract a set of highly interpretable latent “topics” from a large meta-analytic database of over 11,000 published fMRI studies. Each topic is associated with a single brain region and a set of semantically coherent cognitive functions. We demonstrate how these topics can be used to automatically “decode” brain activity in an open-ended way, enabling researchers to draw tentative conclusions about mental function on the basis of virtually any pattern of whole-brain activity. We highlight several important features of our framework, notably including the ability to take into account knowledge of the experimental context and/or prior experimenter belief.

Computational approaches to fMRI analysis

Analysis methods in cognitive neuroscience have not always matched the richness of fMRI data. Early methods focused on estimating neural activity within individual voxels or regions, averaged over trials or blocks and modeled separately in each participant. This approach mostly neglected the distributed nature of neural representations over voxels, the continuous dynamics of neural activity during tasks, the statistical benefits of performing joint inference over multiple participants and the value of using predictive models to constrain analysis. Several recent exploratory and theory-driven methods have begun to pursue these opportunities. These methods highlight the importance of computational techniques in fMRI analysis, especially machine learning, algorithmic optimization and parallel computing. Adoption of these techniques is enabling a new generation of experiments and analyses that could transform our understanding of some of the most complex-and distinctly human-signals in the brain: acts of cognition such as thoughts, intentions and memories.

Identification of Functionally Interconnected Neurons Using Factor Analysis

The advances in electrophysiological methods have allowed registering the joint activity of single neurons. Thus, studies on functional dynamics of complex-valued neural networks and its information processing mechanism have been conducted. Particularly, the methods for identifying neuronal interconnections are in increasing demand in the area of neurosciences. Here, we proposed a factor analysis to identify functional interconnections among neurons via spike trains. This method was evaluated using simulations of neural discharges from different interconnections schemes. The results have revealed that the proposed method not only allows detecting neural interconnections but will also allow detecting the presence of presynaptic neurons without the need of the recording of them.

Why more is better: Simultaneous modeling of EEG, fMRI, and behavioral data

The need to test a growing number of theories in cognitive science has led to increased interest in inferential methods that integrate multiple data modalities. In this manuscript, we show how a method for integrating three data modalities within a single framework provides (1) more detailed descriptions of cognitive processes and (2) more accurate predictions of unobserved data than less integrative methods. Specifically, we show how combining either EEG and fMRI with a behavioral model can perform substantially better than a behavioral-data-only model in both generative and predictive modeling analyses. We then show how a trivariate model - a model including EEG, fMRI, and behavioral data - outperforms bivariate models in both generative and predictive modeling analyses. Together, these results suggest that within an appropriate modeling framework, more data can be used to better constrain cognitive theory, and to generate more accurate predictions for behavioral and neural data.

A cascade computer model for mocrobicide diffusivity from mucoadhesive formulations

Background

The cascade computer model (CCM) was designed as a machine-learning feature platform for prediction of drug diffusivity from the mucoadhesive formulations. Three basic models (the statistical regression model, the K nearest neighbor model and the modified version of the back propagation neural network) in CCM operate sequentially in close collaboration with each other, employing the estimated value obtained from the afore-positioned base model as an input value to the next-positioned base model in the cascade.

The effects of various parameters on the pharmacological efficacy of a female controlled drug delivery system (FcDDS) intended for prevention of women from HIV-1 infection were evaluated using an in vitro apparatus “Simulant Vaginal System” (SVS). We used computer simulations to explicitly examine the changes in drug diffusivity from FcDDS and determine the prognostic potency of each variable for in vivo prediction of formulation efficacy. The results obtained using the CCM approach were compared with those from individual multiple regression model.

Results

CCM significantly lowered the percentage mean error (PME) and enhanced r² values as compared with those from the multiple regression models. It was noted that CCM generated the PME value of 21.82 at 48169 epoch iterations, which is significantly improved from the PME value of 29.91 % at 118344 epochs by the back propagation network model. The results of this study indicated that the sequential ensemble of the classifiers allowed for an accurate prediction of the domain with significantly lowered variance and considerably reduces the time required for training phase.

Conclusion

CCM is accurate, easy to operate, time and cost-effective, and thus, can serve as a valuable tool for prediction of drug diffusivity from mucoadhesive formulations. CCM may yield new insights into understanding how drugs are diffused from the carrier systems and exert their efficacies under various clinical conditions.

Decomposing spatiotemporal brain patterns into topographic latent sources

This paper extends earlier work on spatial modeling of fMRI data to the temporal domain, providing a framework for analyzing high temporal resolution brain imaging modalities such as electroencapholography (EEG). The central idea is to decompose brain imaging data into a covariate-dependent superposition of functions defined over continuous time and space (what we refer to as topographic latent sources). The continuous formulation allows us to parametrically model spatiotemporally localized activations. To make group-level inferences, we elaborate the model hierarchically by sharing sources across subjects. We describe a variational algorithm for parameter estimation that scales efficiently to large data sets. Applied to three EEG data sets, we find that the model produces good predictive performance and reproduces a number of classic findings. Our results suggest that topographic latent sources serve as an effective hypothesis space for interpreting spatiotemporal brain imaging data.