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Analyzing the functional connectivity of the brain is an enormous challenge, as deciphering functional connectivity requires knowledge of functional responses and connections. One promising strategy is analyzing the spatial pattern of activity correlations across cell populations. In the primary auditory cortex (A1), cells respond to different sound features. On the large scale, there exists a tonotopic map, which is fractured at the small scale, raising the question of whether functional connections are spatially ordered or disordered. To test whether functional connectivity on a local and a global scale is also disordered, we first designed a robust statistical model to estimate parameters and test for the significance of the estimated correlation maps. We developed an inference method that allows efficient model fitting and statistical testing to project the correlation maps to 2D space. We then performed in vivo two-photon calcium imaging in layer 2/3 of A1 with pure tones (PT) or a combination of two tones (TT; harmonically related or not). We found that the spatial patterns of signal correlations (SCs) depend on the type of sound stimuli that were presented. The functional 2D maps of PT-driven SCs are more restricted to local neurons than TT signal correlations which showed more global textures. 2D SC patterns for harmonic stimuli showed spatially distinct relationships. TT SCs revealed spatially precise functional connectivity between harmonically related neurons. Thus, even though the frequency preference of neighboring neurons in A1 is functionally diverse, the functional connection pattern of these neurons is functionally precise and harmonically related. 

Characterizing neuronal responses to natural stimuli remains a central goal in sensory neuroscience. In auditory cortical neurons, the stimulus selectivity of elicited spiking activity is summarized by a spectrotemporal receptive field (STRF) that relates neuronal responses to the stimulus spectrogram. Though effective in characterizing primary auditory cortical responses, STRFs of non-primary auditory neurons can be quite intricate, reflecting their mixed selectivity. The complexity of non-primary STRFs hence impedes understanding how acoustic stimulus representations are transformed along the auditory pathway. Here, we focus on the relationship between ferret primary auditory cortex (A1) and a secondary region, dorsal posterior ectosylvian gyrus (PEG). We propose estimating receptive fields in PEG with respect to a well-established high-dimensional computational model of primary-cortical stimulus representations. These “cortical receptive fields” (CortRF) are estimated greedily to identify the salient primary-cortical features modulating spiking responses and in turn related to corresponding spectrotemporal features. Hence, they provide biologically plausible hierarchical decompositions of STRFs in PEG. Such CortRF analysis was applied to PEG neuronal responses to speech and temporally orthogonal ripple combination (TORC) stimuli and, for comparison, to A1 neuronal responses. CortRFs of PEG neurons captured their selectivity to more complex spectrotemporal features than A1 neurons; moreover, CortRF models were more predictive of PEG (but not A1) responses to speech. Our results thus suggest that secondary-cortical stimulus representations can be computed as sparse combinations of primary-cortical features that facilitate encoding natural stimuli. Thus, by adding the primary-cortical representation, we can account for PEG single-unit responses to natural sounds better than bypassing it and considering as input the auditory spectrogram. These results confirm with explicit details the presumed hierarchical organization of the auditory cortex. 

Complex systems, such as in brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often difficult. We propose using a Vector Autoregressive model with eXogenous input (VARX) to capture delayed interactions between internal and external variables. Whereas this model aligns with Granger’s statistical formalism for testing “causal relations”, the connection between the two is not widely understood. Here, we bridge this gap by providing fundamental equations, user-friendly code, and demonstrations using simulated and real-world data from neuroscience, physiology, sociology, and economics. Our examples illustrate how the model avoids spurious correlation by factoring out external influences from internal dynamics, leading to more parsimonious explanations of these systems. For instance, in neural recordings we find that prolonged response of the brain can be explained as a short exogenous effect, followed by prolonged internal recurrent activity. In recordings of human physiology, we find that the model recovers established effects such as eye movements affecting pupil size and a bidirectional interaction of respiration and heart rate. We also provide methods for enhancing model efficiency, such as L2 regularization for limited data and basis functions to cope with extended delays. Additionally, we analyze model performance under various scenarios where model assumptions are violated. MATLAB, Python, and R code are provided for easy adoption:https://github.com/lcparra/varx. 

Central in the study of population codes, coordinated ensemble spiking activity is widely observable in neural recordings with hypothesized roles in robust stimulus representation, interareal communication, and learning and memory formation. Model-free measures of synchrony characterize coherent pairwise activity but not higher-order interactions, a limitation transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require repeated trials to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding statistical inference framework to identify significant higher-order coordination. In the course of developing a precise statistical test, we show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings from human and rat cortical assemblies, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states. 

Mass spectrometry imaging (MSI) is a powerful scientific tool for understanding the spatial distribution of biochemical compounds in tissue structures. In this paper, we introduce three novel approaches in MSI data processing to perform the tasks of data augmentation, feature ranking, and image registration. We use these approaches in conjunction with non-negative matrix factorization (NMF) to resolve two of the biggest challenges in MSI data analysis, namely: 1) the large file sizes and associated computational resource requirements and 2) the complexity of interpreting the very high dimensional raw spectral data. There are many dimensionality reduction techniques that address the first challenge but do not necessarily result in readily interpretable features, leaving the second challenge unaddressed. We demonstrate that NMF is an effective dimensionality reduction algorithm that reduces the size of MSI datasets by three orders of magnitude with limited loss of information, yielding spatial and spectral components with meaningful correlation to tissue structure that may be used directly for subsequent data analysis without the need for additional clustering steps. This analysis is demonstrated on an MSI dataset from female Sprague-Dawley rats for an animal model of comorbid visceral pain hypersensitivity (CPH). We find that high-dimensional MSI data (∼ 100,000 ions per pixel) can be reduced to 20 spectral NMF components with < 20% loss in reconstruction accuracy. The resulting spatial NMF components are reproducible and correlate well with H&E-stained tissue images. These components may also be used to generate images with enhanced specificity for different tissue types. Small patches of NMF data (i.e., 20 spatial NMF components over 20 × 20 pixels) provide an accuracy of ∼ 87% in classifying CPH vs naïve control subjects. This paper presents the novel data processing methodologies that were used to produce these results, encompassing novel data processing pipelines for data augmentation to support training for classification, ranking of features according to their contribution to classification, and image registration to enhance tissue-specific imaging. 

Optogenetic stimulation has opened up a new avenue to probe neuronal circuitry at high spatiotemporal resolutions. A key challenge in optogenetic stimulation is deciding which subset out of thousands of neurons should be stimulated to elicit a desired network activation or affect behavior. In this work, we introduce a reinforcement learning approach to adaptively narrow down the multitude of stimulation possibilities and robustly identify Granger causal networks that underlie neuronal activity. We use realistic simulations with different underlying circuitry to show the effectiveness of reinforcement learning in identifying an optimal policy for selecting stimulation targets. 

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results. 

Understanding how networks of neurons transmit information is crucial to uncovering the underlying mechanisms of brain function. A common measure of communication in neuronal networks is functional connectivity. But, due to the presence of many latent confounding factors in existing experimental paradigms, functional connectivity estimates do not allow a direct interpretation of causal interactions in a network. Here, we aim at addressing this challenge using a quasi-experimental approach, namely Instrumental Variables, in a concurrent optogenetic stimulation of two-photon calcium imaging paradigm. We propose a methodology based on variational inference that allows estimating the spiking activity from blurred and noisy two-photon observations. We then use maximum likelihood estimation to construct a statistical testing framework that allows to distinguish between direct and confounding pairwise effects, by taking a set of random stimulation patterns as the instrumental variables. We demonstrate the utility of our approach using simulated data and compare its performance with existing work. Our results show that the proposed method can achieve high sensitivity and specificity in functional network discovery in presence of confounding effects and using a limited number of stimulation patterns and trials. 

Functional connectivity is among the widely used metrics to assess the network-level attributes of brain function. While most existing analysis frameworks assume static functional connectivity during the course of an experiment, to capture neural dynamics over short time scales, a time-varying notion of functional connectivity is required. By revealing how neural networks reconfigure in response to changing external stimuli, internal states, and task demands, time-varying functional connectivity can be leveraged to study flexible cognition, such as working memory, attention, and decision-making. A major challenge in estimating time-varying functional connectivity from high-dimensional neural is the associated computational complexity. Existing methods trade off accuracy for computational efficiency, especially in applications that require real-time or near real-time processing. Here, we build on existing work using covariance-domain state-space models and introduce a framework based on variational inference that allows low-complexity estimation of time-varying functional connectivity and construction of confidence intervals. We validate the performance of the proposed method using simulation studies. Our results reveal significant gains in computational complexity compared to existing methods, while maintaining high accuracy. 

Extracting directional connectivity in a neuronal ensemble from spiking observations is a key challenge in understanding the circuit mechanisms of brain function. Existing methods proceed in two stages, by first estimating the latent processes that govern spiking, followed by characterizing connectivity using said estimates. As such, the extracted networks in the second stage are highly sensitive to the accuracy of the estimates in the first stage. In this work, we introduce a framework to directly extract Granger causal links from spiking observations, without requiring intermediate time-domain estimation, by explicitly modeling the endogenous and exogenous latent processes that underlie spiking activity. Our proposed method integrates several techniques such as point processes, state-space modeling and Pólya-Gamma augmentation. We demonstrate the utility of our proposed approach using simulated data and application to real data from the rat brain during sleep.