Point process modeling and estimation: advances in the analysis of dynamic neural spiking data

A common interest of scientists in many fields is to understand the relationship between the dynamics of a physical system and the occurrences of discrete events within such physical system. Seismologists study the connection between mechanical vibrations of the Earth and the occurrences of earthquakes so that future earthquakes can be better predicted. Astrophysicists study the association between the oscillating energy of celestial regions and the emission of photons to learn the Universe's various objects and their interactions. Neuroscientists study the link between behavior and the millisecond-timescale spike patterns of neurons to understand higher brain functions. Such relationships can often be formulated within the framework of state-space models with point process observations. The basic idea is that the dynamics of the physical systems are driven by the dynamics of some stochastic state variables and the discrete events we observe in an interval are noisy observations with distributions determined by the state variables. This thesis proposes several new methodological developments that advance the framework of state-space models with point process observations at the intersection of statistics and neuroscience. In particular, we develop new methods 1) to characterize the rhythmic spiking activity using history-dependent structure, 2) to model population spike activity using marked point process models, 3) to allow for real-time decision making, and 4) to take into account the need for dimensionality reduction for high-dimensional state and observation processes. We applied these methods to a novel problem of tracking rhythmic dynamics in the spiking of neurons in the subthalamic nucleus of Parkinson's patients with the goal of optimizing placement of deep brain stimulation electrodes. We developed a decoding algorithm that can make decision in real-time (for example, to stimulate the neurons or not) based on various sources of information present in population spiking data. Lastly, we proposed a general three-step paradigm that allows us to relate behavioral outcomes of various tasks to simultaneously recorded neural activity across multiple brain areas, which is a step towards closed-loop therapies for psychological diseases using real-time neural stimulation. These methods are suitable for real-time implementation for content-based feedback experiments

Evolution and Analysis of Embodied Spiking Neural Networks Reveals Task-Specific Clusters of Effective Networks

Elucidating principles that underlie computation in neural networks is currently a major research topic of interest in neuroscience. Transfer Entropy (TE) is increasingly used as a tool to bridge the gap between network structure, function, and behavior in fMRI studies. Computational models allow us to bridge the gap even further by directly associating individual neuron activity with behavior. However, most computational models that have analyzed embodied behaviors have employed non-spiking neurons. On the other hand, computational models that employ spiking neural networks tend to be restricted to disembodied tasks. We show for the first time the artificial evolution and TE-analysis of embodied spiking neural networks to perform a cognitively-interesting behavior. Specifically, we evolved an agent controlled by an Izhikevich neural network to perform a visual categorization task. The smallest networks capable of performing the task were found by repeating evolutionary runs with different network sizes. Informational analysis of the best solution revealed task-specific TE-network clusters, suggesting that within-task homogeneity and across-task heterogeneity were key to behavioral success. Moreover, analysis of the ensemble of solutions revealed that task-specificity of TE-network clusters correlated with fitness. This provides an empirically testable hypothesis that links network structure to behavior.Comment: Camera ready version of accepted for GECCO'1

A hybrid systems model for supervisory cognitive state identification and estimation in neural prosthetics

This paper presents a method to identify a class of hybrid system models that arise in cognitive neural prosthetic medical devices that aim to help the severely handicapped. In such systems a “supervisory decoder” is required to classify the activity of multi-unit extracellular neural recordings into a discrete set of modes that model the evolution of the brain’s planning process. We introduce a Gibbs sampling method to identify the key parameters of a GLHMM, a hybrid dynamical system that combines a set of generalized linear models (GLM) for dynamics of neuronal signals with a hidden Markov model (HMM) that describes the discrete transitions between the brain’s cognitive or planning states. Multiple neural signals of mixed type, including local field potentials and spike arrival times, are integrated into the model using the GLM framework. The identified model can then be used as the basis for the supervisory decoding (or estimation) of the current cognitive or planning state. The identification algorithm is applied to extracellular neural recordings obtained from set of electrodes acutely implanted in the posterior parietal cortex of a rhesus monkey. The results demonstrate the ability to accurately decode changes in behavioral or cognitive state during reaching tasks, even when the model parameters are identified from small data sets. The GLHMM models and the associated identification methods are generally applicable beyond the neural application domain

Neural Mechanisms of Sensory Integration: Frequency Domain Analysis of Spike and Field Potential Activity During Arm Position Maintenance with and Without Visual Feedback

abstract: Understanding where our bodies are in space is imperative for motor control, particularly for actions such as goal-directed reaching. Multisensory integration is crucial for reducing uncertainty in arm position estimates. This dissertation examines time and frequency-domain correlates of visual-proprioceptive integration during an arm-position maintenance task. Neural recordings were obtained from two different cortical areas as non-human primates performed a center-out reaching task in a virtual reality environment. Following a reach, animals maintained the end-point position of their arm under unimodal (proprioception only) and bimodal (proprioception and vision) conditions. In both areas, time domain and multi-taper spectral analysis methods were used to quantify changes in the spiking, local field potential (LFP), and spike-field coherence during arm-position maintenance. In both areas, individual neurons were classified based on the spectrum of their spiking patterns. A large proportion of cells in the SPL that exhibited sensory condition-specific oscillatory spiking in the beta (13-30Hz) frequency band. Cells in the IPL typically had a more diverse mix of oscillatory and refractory spiking patterns during the task in response to changing sensory condition. Contrary to the assumptions made in many modelling studies, none of the cells exhibited Poisson-spiking statistics in SPL or IPL. Evoked LFPs in both areas exhibited greater effects of target location than visual condition, though the evoked responses in the preferred reach direction were generally suppressed in the bimodal condition relative to the unimodal condition. Significant effects of target location on evoked responses were observed during the movement period of the task well. In the frequency domain, LFP power in both cortical areas was enhanced in the beta band during the position estimation epoch of the task, indicating that LFP beta oscillations may be important for maintaining the ongoing state. This was particularly evident at the population level, with clear increase in alpha and beta power. Differences in spectral power between conditions also became apparent at the population level, with power during bimodal trials being suppressed relative to unimodal. The spike-field coherence showed confounding results in both the SPL and IPL, with no clear correlation between incidence of beta oscillations and significant beta coherence.Dissertation/ThesisDoctoral Dissertation Biomedical Engineering 201

Functional magnetic resonance imaging : an intermediary between behavior and neural activity

Blood oxygen level dependent (BOLD) functional magnetic resonance imaging is a non-invasive technique used to trace changes in neural dynamics in reaction to mental activity caused by perceptual, motor or cognitive tasks. The BOLD response is a complex signal, a consequence of a series of physiological events regulated by increased neural activity. A method to infer from the BOLD signal onto underlying neuronal activity (hemodynamic inverse problem) is proposed in Chapter 2 under the assumption of a previously proposed mathematical model on the transduction of neural activity to the BOLD signal. Also, in this chapter we clarify the meaning of the neural activity function used as the input for an intrinsic dynamic system which can be viewed as an advanced substitute for the impulse response function. Chapter 3 describes an approach for recovering neural timing information (mental chronometry) in an object interaction decision task via solving the hemodynamic inverse problem. In contrast to the hemodynamic level, at the neural level, we were able to determine statistically significant latencies in activation between functional units in the model used. In Chapter 4, two approaches for regularization parameter tuning in a regularized-regression analysis are compared in an attempt to find the optimal amount of smoothing to be imposed on fMRI data in determining an empirical hemodynamic response function. We found that the noise autocorrelation structure can be improved by tuning the regularization parameter but the whitening-based criterion provides too much smoothing when compared to cross-validation. Chapter~5 illustrates that the smoothing techniques proposed in Chapter 4 can be useful in the issue of correlating behavioral and hemodynamic characteristics. Specifically, Chapter 5, based on the smoothing techniques from Chapter 4, seeks to correlate several parameters characterizing the hemodynamic response in Broca's area to behavioral measures in a naming task. In particular, a condition for independence between two routes of converting print to speech in a dual route cognitive model was verified in terms of hemodynamic parameters

Spiking neural models & machine learning for systems neuroscience: Learning, Cognition and Behavior.

Learning, cognition and the ability to navigate, interact and manipulate the world around us by performing appropriate behavior are hallmarks of artificial as well as biological intelligence. In order to understand how intelligent behavior can emerge from computations of neural systems, this thesis suggests to consider and study learning, cognition and behavior simultaneously to obtain an integrative understanding. This involves building detailed functional computational models of nervous systems that can cope with sensory processing, learning, memory and motor control to drive appropriate behavior. The work further considers how the biological computational substrate of neurons, dendrites and action potentials can be successfully used as an alternative to current artificial systems to solve machine learning problems. It challenges the simplification of currently used rate-based artificial neurons, where computational power is sacrificed by mathematical convenience and statistical learning. To this end, the thesis explores single spiking neuron computations for cognition and machine learning problems as well as detailed functional networks thereof that can solve the biologically relevant foraging behavior in flying insects. The obtained results and insights are new and relevant for machine learning, neuroscience and computational systems neuroscience. The thesis concludes by providing an outlook how application of current machine learning methods can be used to obtain a statistical understanding of larger scale brain systems. In particular, by investigating the functional role of the cerebellar-thalamo-cortical system for motor control in primates

Contributions to statistical analysis methods for neural spiking activity

With the technical advances in neuroscience experiments in the past few decades, we have seen a massive expansion in our ability to record neural activity. These advances enable neuroscientists to analyze more complex neural coding and communication properties, and at the same time, raise new challenges for analyzing neural spiking data, which keeps growing in scale, dimension, and complexity. This thesis proposes several new statistical methods that advance statistical analysis approaches for neural spiking data, including sequential Monte Carlo (SMC) methods for efficient estimation of neural dynamics from membrane potential threshold crossings, state-space models using multimodal observation processes, and goodness-of-fit analysis methods for neural marked point process models. In a first project, we derive a set of iterative formulas that enable us to simulate trajectories from stochastic, dynamic neural spiking models that are consistent with a set of spike time observations. We develop a SMC method to simultaneously estimate the parameters of the model and the unobserved dynamic variables from spike train data. We investigate the performance of this approach on a leaky integrate-and-fire model. In another project, we define a semi-latent state-space model to estimate information related to the phenomenon of hippocampal replay. Replay is a recently discovered phenomenon where patterns of hippocampal spiking activity that typically occur during exploration of an environment are reactivated when an animal is at rest. This reactivation is accompanied by high frequency oscillations in hippocampal local field potentials. However, methods to define replay mathematically remain undeveloped. In this project, we construct a novel state-space model that enables us to identify whether replay is occurring, and if so to estimate the movement trajectories consistent with the observed neural activity, and to categorize the content of each event. The state-space model integrates information from the spiking activity from the hippocampal population, the rhythms in the local field potential, and the rat's movement behavior. Finally, we develop a new, general time-rescaling theorem for marked point processes, and use this to develop a general goodness-of-fit framework for neural population spiking models. We investigate this approach through simulation and a real data application

Endogenous and exogenous hemodynamic signals in primary visual cortex of alert non-human primates

The advent of neuroimaging techniques in particular the ones suitable for studies in alert humans has disseminated fast. Research in fields involving neuro-correlates of cognitive processes has flourished. Still the neural underpinnings of the neuroimaging signals remain to be fully characterized; this field is an active topic of research. In the context of behavior/cognition, the interpretation of neuroimaging signals is even more intricate