A common goodness-of-fit framework for neural population models using marked point process time-rescaling

A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem and assess model quality using rescaled spike times. Recently, there has been increasing interest in statistical models that describe the simultaneous spiking activity of neuron populations, either in a single brain region or across brain regions. Classically, such models have used spike sorted data to describe relationships between the identified neurons, but more recently clusterless modeling methods have been used to describe population activity using a single model. Here we develop a generalization of the time-rescaling theorem that enables comprehensive goodness-of-fit analysis for either of these classes of population models. We use the theory of marked point processes to model population spiking activity, and show that under the correct model, each spike can be rescaled individually to generate a uniformly distributed set of events in time and the space of spike marks. After rescaling, multiple well-established goodness-of-fit procedures and statistical tests are available. We demonstrate the application of these methods both to simulated data and real population spiking in rat hippocampus. We have made the MATLAB and Python code used for the analyses in this paper publicly available through our Github repository at https://github.com/Eden-Kramer-Lab/popTRT.This work was supported by grants from the NIH (MH105174, NS094288) and the Simons Foundation (542971). (MH105174 - NIH; NS094288 - NIH; 542971 - Simons Foundation)Published versio

Timing matters: impact of anticonvulsant drug treatment and spikes on seizure risk in benign epilepsy with centrotemporal spikes

OBJECTIVE: Benign epilepsy with centrotemporal spikes (BECTS) is a common, self-limited epilepsy syndrome affecting school-age children. Classic interictal epileptiform discharges (IEDs) confirm diagnosis, and BECTS is presumed to be pharmacoresponsive. As seizure risk decreases in time with this disease, we hypothesize that the impact of IEDs and anticonvulsive drug (ACD) treatment on the risk of subsequent seizure will differ based on disease duration. METHODS: We calculate subsequent seizure risk following diagnosis in a large retrospective cohort of children with BECTS (n = 130), evaluating the impact of IEDs and ACD treatment in the first, second, third, and fourth years of disease. We use a Kaplan-Meier survival analysis and logistic regression models. Patients were censored if they were lost to follow-up or if they changed group status. RESULTS: Two-thirds of children had a subsequent seizure within 2 years of diagnosis. The majority of children had a subsequent seizure within 3 years despite treatment. The presence of IEDs on electroencephalography (EEG) did not impact subsequent seizure risk early in the disease. By the fourth year of disease, all children without IEDs remained seizure free, whereas one-third of children with IEDs at this stage had a subsequent seizure. Conversely, ACD treatment corresponded with lower risk of seizure early in the disease but did not impact seizure risk in later years. SIGNIFICANCE: In this cohort, the majority of children with BECTS had a subsequent seizure despite treatment. In addition, ACD treatment and IEDs predicted seizure risk at specific points of disease duration. Future prospective studies are needed to validate these exploratory findings.Published versio

Integrating Statistical and Machine Learning Approaches to Identify Receptive Field Structure in Neural Populations

Neurons can code for multiple variables simultaneously and neuroscientists are often interested in classifying neurons based on their receptive field properties. Statistical models provide powerful tools for determining the factors influencing neural spiking activity and classifying individual neurons. However, as neural recording technologies have advanced to produce simultaneous spiking data from massive populations, classical statistical methods often lack the computational efficiency required to handle such data. Machine learning (ML) approaches are known for enabling efficient large scale data analyses; however, they typically require massive training sets with balanced data, along with accurate labels to fit well. Additionally, model assessment and interpretation are often more challenging for ML than for classical statistical methods. To address these challenges, we develop an integrated framework, combining statistical modeling and machine learning approaches to identify the coding properties of neurons from large populations. In order to demonstrate this framework, we apply these methods to data from a population of neurons recorded from rat hippocampus to characterize the distribution of spatial receptive fields in this region

The problem of perfect predictors in statistical spike train models

https://doi.org/10.51628/001c.27667Published versio

Characterizing the spiking dynamics of subthalamic nucleus neurons in Parkinson's disease using generalized linear models

Accurately describing the spiking patterns of neurons in the subthalamic nucleus (STN) of patients suffering from Parkinson's disease (PD) is important for understanding the pathogenesis of the disease and for achieving the maximum therapeutic benefit from deep brain stimulation (DBS). We analyze the spiking activity of 24 subthalamic neurons recorded in Parkinson's patients during a directed hand movement task by using a point process generalized linear model (GLM). The model relates each neuron's spiking probability simultaneously to factors associated with movement planning and execution, directional selectivity, refractoriness, bursting, and oscillatory dynamics. The model indicated that while short-term history dependence related to refractoriness and bursting are most informative in predicting spiking activity, nearly all of the neurons analyzed have a structured pattern of long-term history dependence such that the spiking probability was reduced 20–30 ms and then increased 30–60 ms after a previous spike. This suggests that the previously described oscillatory firing of neurons in the STN of Parkinson's patients during volitional movements is composed of a structured pattern of inhibition and excitation. This point process model provides a systematic framework for characterizing the dynamics of neuronal activity in STN

Estimating fluctuations in neural representations of uncertain environments

Neural Coding analyses often reflect an assumption that neural populations respond uniquely and consistently to particular stimuli. For example, analyses of spatial remapping in hippocampal populations often assume that each environment has one unique representation and that remapping occurs over long time scales as an animal traverses between distinct environments. However, as neuroscience experiments begin to explore more naturalistic tasks and stimuli, and reflect more ambiguity in neural representations, methods for analyzing population neural codes must adapt to reflect these features. In this paper, we develop a new state-space modeling framework to address two important issues related to remapping. First, neurons may exhibit significant trial-to-trial or moment-to-moment variability in the firing patterns used to represent a particular environment or stimulus. Second, in ambiguous environments and tasks that involve cognitive uncertainty, neural populations may rapidly fluctuate between multiple representations. The statespace model addresses these two issues by integrating an observation model, which allows for multiple representations of the same stimulus or environment, with a state model, which characterizes the moment-by-moment probability of a shift in the neural representation. These models allow us to compute instantaneous estimates of the stimulus or environment currently represented by the population. We demonstrate the application of this approach to the analysis of population activity in the CA1 region of hippocampus of a mouse moving through ambiguous virtual environments. Our analyses demonstrate that many hippocampal cells express significant trial-to-trial variability in their representations and that the population representation can fluctuate rapidly between environments within a single trial when spatial cues are most ambiguous.Accepted manuscrip

Assessing dynamics, spatial scale, and uncertainty in task-related brain network analyses

This is the publisher's version, also available electronically from http://journal.frontiersin.org/Journal/10.3389/fncom.2014.00031/abstractThe brain is a complex network of interconnected elements, whose interactions evolve dynamically in time to cooperatively perform specific functions. A common technique to probe these interactions involves multi-sensor recordings of brain activity during a repeated task. Many techniques exist to characterize the resulting task-related activity, including establishing functional networks, which represent the statistical associations between brain areas. Although functional network inference is commonly employed to analyze neural time series data, techniques to assess the uncertainty—both in the functional network edges and the corresponding aggregate measures of network topology—are lacking. To address this, we describe a statistically principled approach for computing uncertainty in functional networks and aggregate network measures in task-related data. The approach is based on a resampling procedure that utilizes the trial structure common in experimental recordings. We show in simulations that this approach successfully identifies functional networks and associated measures of confidence emergent during a task in a variety of scenarios, including dynamically evolving networks. In addition, we describe a principled technique for establishing functional networks based on predetermined regions of interest using canonical correlation. Doing so provides additional robustness to the functional network inference. Finally, we illustrate the use of these methods on example invasive brain voltage recordings collected during an overt speech task. The general strategy described here—appropriate for static and dynamic network inference and different statistical measures of coupling—permits the evaluation of confidence in network measures in a variety of settings common to neuroscience

Impact of brain tissue filtering on neurostimulation fields: A modeling study

Electrical neurostimulation techniques, such as deep brain stimulation (DBS) and transcranial magnetic stimulation (TMS), are increasingly used in the neurosciences, e.g., for studying brain function, and for neurotherapeutics, e.g., for treating depression, epilepsy, and Parkinson's disease. The characterization of electrical properties of brain tissue has guided our fundamental understanding and application of these methods, from electrophysiologic theory to clinical dosing-metrics. Nonetheless, prior computational models have primarily relied on ex-vivo impedance measurements. We recorded the in-vivo impedances of brain tissues during neurosurgical procedures and used these results to construct MRI guided computational models of TMS and DBS neurostimulatory fields and conductance-based models of neurons exposed to stimulation. We demonstrated that tissues carry neurostimulation currents through frequency dependent resistive and capacitive properties not typically accounted for by past neurostimulation modeling work. We show that these fundamental brain tissue properties can have significant effects on the neurostimulatory-fields (capacitive and resistive current composition and spatial/temporal dynamics) and neural responses (stimulation threshold, ionic currents, and membrane dynamics). These findings highlight the importance of tissue impedance properties on neurostimulation and impact our understanding of the biological mechanisms and technological potential of neurostimulatory methods.United States. Defense Advanced Research Projects Agency (Contract W31P4Q-09-C-0117)National Institute of Neurological Disorders and Stroke (U.S.) (Award R43NS062530)National Institute of Neurological Disorders and Stroke (U.S.) (Award 1R44NS080632