Maximum likelihood decoding of neuronal inputs from an interspike interval distribution

An expression for the probability distribution of the interspike interval of a leaky integrate-and-fire (LIF) model neuron is rigorously derived, based on recent theoretical developments in the theory of stochastic processes. This enables us to find for the first time a way of developing maximum likelihood estimates (MLE) of the input information (e.g., afferent rate and variance) for an LIF neuron from a set of recorded spike trains. Dynamic inputs to pools of LIF neurons both with and without interactions are efficiently and reliably decoded by applying the MLE, even within time windows as short as 25 msec

Multiscale relevance and informative encoding in neuronal spike trains

Neuronal responses to complex stimuli and tasks can encompass a wide range of time scales. Understanding these responses requires measures that characterize how the information on these response patterns are represented across multiple temporal resolutions. In this paper we propose a metric -- which we call multiscale relevance (MSR) -- to capture the dynamical variability of the activity of single neurons across different time scales. The MSR is a non-parametric, fully featureless indicator in that it uses only the time stamps of the firing activity without resorting to any a priori covariate or invoking any specific structure in the tuning curve for neural activity. When applied to neural data from the mEC and from the ADn and PoS regions of freely-behaving rodents, we found that neurons having low MSR tend to have low mutual information and low firing sparsity across the correlates that are believed to be encoded by the region of the brain where the recordings were made. In addition, neurons with high MSR contain significant information on spatial navigation and allow to decode spatial position or head direction as efficiently as those neurons whose firing activity has high mutual information with the covariate to be decoded and significantly better than the set of neurons with high local variations in their interspike intervals. Given these results, we propose that the MSR can be used as a measure to rank and select neurons for their information content without the need to appeal to any a priori covariate.Comment: 38 pages, 16 figure

Reconstructing Stimuli from the Spike Times of Leaky Integrate and Fire Neurons

Reconstructing stimuli from the spike trains of neurons is an important approach for understanding the neural code. One of the difficulties associated with this task is that signals which are varying continuously in time are encoded into sequences of discrete events or spikes. An important problem is to determine how much information about the continuously varying stimulus can be extracted from the time-points at which spikes were observed, especially if these time-points are subject to some sort of randomness. For the special case of spike trains generated by leaky integrate and fire neurons, noise can be introduced by allowing variations in the threshold every time a spike is released. A simple decoding algorithm previously derived for the noiseless case can be extended to the stochastic case, but turns out to be biased. Here, we review a solution to this problem, by presenting a simple yet efficient algorithm which greatly reduces the bias, and therefore leads to better decoding performance in the stochastic case

Bayesian decoding of tactile afferents responsible for sensorimotor control

In daily activities, humans manipulate objects and do so with great precision. Empirical studies have demonstrated that signals encoded by mechanoreceptors facilitate the precise object manipulation in humans, however, little is known about the underlying mechanisms. Models used in literature to analyze tactile afferent data range from advanced—for example some models account for skin tissue properties—to simple regression fit. These models, however, do not systematically account for factors that influence tactile afferent activity. For instance, it is not yet clear whether the first derivative of force influences the observed tactile afferent spike train patterns. In this study, I use the technique of microneurography—with the help of Dr. Birznieks—to record tactile afferent data from humans. I then implement spike sorting algorithms to identify spike occurrences that pertain to a single cell. For further analyses of the resulting spike trains, I use a Bayesian decoding framework to investigate tactile afferent mechanisms that are responsible for sensorimotor control in humans. The Bayesian decoding framework I implement is a two stage process where in a first stage (encoding model) the relationships between the administered stimuli and the recorded tactile afferent signals is established, and a second stage uses results based on the first stage to make predictions. The goal of encoding model is to increase our understanding of the mechanisms that underlie dexterous object manipulation and, from an engineering perspective, guide the design of algorithms for inferring stimulus from previously unseen tactile afferent data, a process referred to as decoding. Specifically, the objective of the study was to devise quantitative methods that would provide insight into some mechanisms that underlie touch, as well as provide strategies through which real-time biomedical devices can be realized. Tactile afferent data from eight subjects (18 - 30 years) with no known form of neurological disorders were recorded by inserting a needle electrode in the median nerve at the wrist. I was involved in designing experimental protocols, designing mechanisms that were put in place for safety measures, designing and building electronic components as needed, experimental setup, subject recruitment, and data acquisition. Dr. Ingvars Birznieks (performed the actual microneurography procedure by inserting a needle electrode into the nerve and identifying afferent types) and Dr. Heba Khamis provided assistance with the data acquisition and experimental design. The study took place at Neuroscience Research Australia (NeuRA). Once the data were acquired, I analyzed the data recorded from slowly adapting type I tactile afferents (SA-I). The initial stages of data analysis involved writing software routines to spike sort the data (identify action potential waveforms that pertain to individual cells). I analyzed SA-I tactile afferents because they were more numerous (it was difficult to target other types of afferents during experiments). In addition, SA-I tactile afferents respond during both the dynamic and the static phase of a force stimulus. Since they respond during both the dynamic and static phases of the force stimulus, it seemed reasonable to hypothesize that SA-I’s alone could provide sufficient information for predicting the force profile, given spike data. In the first stage, I used an inhomogeneous Poisson process encoding model through which I assessed the relative importance of aspects of the stimuli to observed spike data. In addition I estimated the likelihood for SA-I data given the inhomogeneous Poisson model, which was used during the second stage. The likelihood is formulated by deriving the joint distribution of the data, as a function of the model parameters with the data fixed. In the second stage, I used a recursive nonlinear Bayesian filter to reconstruct the force profile, given the SA-I spike patterns. Moreover, the decoding method implemented in this thesis is feasible for real-time applications such as interfacing with prostheses because it can be realized with readily available electronic components. I also implemented a renewal point process encoding model—as a generalization of the Poisson process encoding model—which can account for some history dependence properties of neural data. I discovered that under my encoding model, the relative contributions of the force and its derivative are 1.26 and 1.02, respectively. This suggests that the force derivative contributes significantly to the spiking behavior of SA-I tactile afferents. This is a novel contribution because it provides a quantitative result to the long standing question of whether the force derivative contributes towards SA-I tactile afferent spiking behavior. As a result, I incorporated the first derivative of force, along with the force, in the encoding models I implemented in this thesis. The decoding model shows that SA-I fibers provide sufficient information for an approximation of the force profile. Furthermore, including fast adapting tactile afferents would provide better information about the first moment of contact and last moment of contact, and thus improved decoding results. Finally I show that a renewal point process encoding model captures interspike time and stimulus features better than an inhomogeneous Poisson point process encoding model. This is useful because it is now possible to generate synthetic data with statistical structure that is similar to real SA-I data: This would enable further investigations of mechanisms that underlie SA-I tactile afferents

A point process framework for modeling electrical stimulation of the auditory nerve

Model-based studies of auditory nerve responses to electrical stimulation can provide insight into the functioning of cochlear implants. Ideally, these studies can identify limitations in sound processing strategies and lead to improved methods for providing sound information to cochlear implant users. To accomplish this, models must accurately describe auditory nerve spiking while avoiding excessive complexity that would preclude large-scale simulations of populations of auditory nerve fibers and obscure insight into the mechanisms that influence neural encoding of sound information. In this spirit, we develop a point process model of the auditory nerve that provides a compact and accurate description of neural responses to electric stimulation. Inspired by the framework of generalized linear models, the proposed model consists of a cascade of linear and nonlinear stages. We show how each of these stages can be associated with biophysical mechanisms and related to models of neuronal dynamics. Moreover, we derive a semi-analytical procedure that uniquely determines each parameter in the model on the basis of fundamental statistics from recordings of single fiber responses to electric stimulation, including threshold, relative spread, jitter, and chronaxie. The model also accounts for refractory and summation effects that influence the responses of auditory nerve fibers to high pulse rate stimulation. Throughout, we compare model predictions to published physiological data and explain differences in auditory nerve responses to high and low pulse rate stimulation. We close by performing an ideal observer analysis of simulated spike trains in response to sinusoidally amplitude modulated stimuli and find that carrier pulse rate does not affect modulation detection thresholds.Comment: 1 title page, 27 manuscript pages, 14 figures, 1 table, 1 appendi

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