Temporally Segmented Directionality in the Motor Cortex

Developing models of the dynamic and complex patterns of information processing that take place during behavior is a major thrust of systems neuroscience. An underlying assumption of many models is that the same set of rules applies across different conditions. This has been the case for directional tuning during volitional movement; a single cosine function has been remarkably robust for describing the encoding of movement direction in different types of neurons, in many locations of the nervous system, and even across species. However, detailed examination of the tuning time course in motor cortex suggests that direction coding may be labile. Here, we show that there are discrete time epochs within single reaches, between which individual neurons change their tuning. Our findings suggest that motor cortical activity patterns may reflect consistent changes in the state of the control system during center-out reaching. These transitions are likely linked to different behavioral components, suggesting that the task defines changes in the operational structure of the control system.

Statistical Signal Processing and the Motor Cortex

Over the past few decades, developments in technology have significantly improved the ability to measure activity in the brain. This has spurred a great deal of research into brain function and its relation to external stimuli, and has important implications in medicine and other fields. As a result of improved understanding of brain function, it is now possible to build devices that provide direct interfaces between the brain and the external world. We describe some of the current understanding of function of the motor cortex region. We then discuss a typical likelihood-based state-space model and filtering based approach to address the problems associated with building a motor cortical-controlled cursor or robotic prosthetic device. As a variation on previous work using this approach, we introduce the idea of using Markov chain Monte Carlo methods for parameter estimation in this context. By doing this instead of performing maximum likelihood estimation, it is possible to expand the range of possible models that can be explored, at a cost in terms of computational load. We demonstrate results obtained applying this methodology to experimental data gathered from a monkey.

Recursive Bayesian Decoding of Motor Cortical Signals by Particle Filtering

The population vector (PV) algorithm and optimal linear estimation (OLE) have been used to reconstruct movement by combining signals from multiple neurons in the motor cortex. While these linear methods are effective, recursive Bayesian decoding schemes, which are nonlinear, can be more powerful when probability model assumptions are satisfied. We have implemented a recursive Bayesian algorithm for reconstructing hand movement from neurons in the motor cortex. The algorithm uses a recently developed numerical method known as “particle filtering” and follows the same general strategy as that used by Brown et al. to reconstruct the path of a foraging rat from hippocampal place cells. We investigated the method in a numerical simulation study in which neural firing rate was assumed to be positive, but otherwise a linear function of movement velocity, and preferred directions were not uniformly distributed. In terms of mean-squared error, the approach was ∼10 times more efficient than the PV algorithm and 5 times more efficient than OLE. Thus use of recursive Bayesian decoding can achieve the accuracy of the PV algorithm (or OLE) with ∼10 times (or 5 times) fewer neurons. The method was also used to reconstruct hand movement in an ellipse-drawing task from 258 cells in the ventral premotor cortex. Recursive Bayesian decoding was again more efficient than the PV and OLE methods, by factors of roughly seven and three, respectively.

Shrinkage estimators for covariance matrices

Estimation of covariance matrices in small samples has been studied by many authors. Standard estimators, like the unstructured maximum likelihood estimator (ML) or restricted maximum likelihood (REML) estimator, can be very unstable with the smallest estimated eigenvalues being too small and the largest too big. A standard approach to more stably estimating the matrix in small samples is to compute the ML or REML estimator under some simple structure that involves estimation of fewer parameters, such as compound symmetry or independence. However, these estimators will not be consistent unless the hypothesized structure is correct. If interest focuses on estimation of regression coefficients with correlated (or longitudinal) data, a sandwich estimator of the covariance matrix may be used to provide standard errors for the estimated coefficients that are robust in the sense that they remain consistent under misspecification of the covariance structure. With large matrices, however, the inefficiency of the sandwich estimator becomes worrisome. We consider here two general shrinkage approaches to estimating the covariance matrix and regression coefficients. The first involves shrinking the eigenvalues of the unstructured ML or REML estimator. The second involves shrinking an unstructured estimator toward a structured estimator. For both cases, the data determine the amount of shrinkage. These estimators are consistent and give consistent and asymptotically efficient estimates for regression coefficients. Simulations show the improved operating characteristics of the shrinkage estimators of the covariance matrix and the regression coefficients in finite samples. The final estimator chosen includes a combination of both shrinkage approaches, i.e., shrinking the eigenvalues and then shrinking toward structure. We illustrate our approach on a sleep EEG study that requires estimation of a 24 x 24 covariance matrix and for which inferences on mean parameters critically depend on the covariance estimator chosen. We recommend making inference using a particular shrinkage estimator that provides a reasonable compromise between structured and unstructured estimators.

A spike-train probability model

Poisson processes usually provide adequate descriptions of the irregularity in neuron spike times after pooling the data across large numbers of trials, as is done in constructing the peristimulus time histogram. When probabilities are needed to describe the behavior of neurons within individual trials, however, Poisson process models are often inadequate. In principle, an explicit formula gives the probability density of a single spike train in great generality, but without additional assumptions, the firing-rate intensity function appearing in that formula cannot be estimated. We propose a simple solution to this problem, which is to assume that the time at which a neuron fires is determined probabilistically by, and only by, two quantities: the experimental clock time and the elapsed time since the previous spike. We show that this model can be fitted with standard methods and software and that it may used successfully to fit neuronal data.

Neuronal activity in macaque supplementary eye field during planning of saccades in response to pattern and spatial cues

The aim of this study was to determine whether neuronal activity in the macaque supplementary eye field (SEF) is influenced by the rule used for saccadic target selection. Two monkeys were trained to perform a variant of the memory-guided saccade task in which any of four visible dots (rightward, upward, leftward, and downward) could be the target. On each trial, the cue identifying the target was either a spot flashed in superimposition on the target (spatial condition) or a foveally presented digitized image associated with the target (pattern condition). Trials conforming to the two conditions were interleaved randomly. On recording from 439 SEF neurons, we found that two aspects of neuronal activity were influenced by the nature of the cue. 1) Activity reflecting the direction of the impending response developed more rapidly following spatial than following pattern cues. 2) Activity throughout the delay period tended to be higher following pattern than following spatial cues. We consider these findings in relation to the possible involvement of the SEF in processes underlying attention, arousal, response-selection, and motor preparation.

Nonconjugate Bayesian analysis of variance component models

We consider the usual normal linear mixed model for variance components from a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs sampling is easy to implement; however, simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors, thus leading one to consider alternative Markov chain Monte Carlo schemes. We propose and investigate a method for posterior simulation based on an independence chain. The method is customized to exploit the structure of the variance component model, and it works with arbitrary prior distributions. As a default reference prior, we use a version of Jeffreys' prior based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data.

Response latency and verbal complexity: stochastic models of individual differences in children with specific language impairments

Within-subject statistical modeling techniques were employed to investigate individual differences in the extent to which two possible indicators of processing time predicted changes in utterance complexity during spontaneous discourse for 10 children ages 7;1 to 10;1 with specific language impairments (SLI) who differed in receptive language abilities. The two indicators of processing time that were modeled were response latency and the use of a specific discourse marker (Verbal Pause) that provided children with additional time to respond. Longer response latencies were not a strong predictor of increased utterance length for any of the children. However, results indicated that children with better receptive skills used substantially more verbal pauses than children with both expressive and receptive deficits and that the use of these pauses was a strong predictor of increased utterance length for children with better comprehension skills.

Differential age-related loss of pigmented locus coeruleus neurons in suicides, alcoholics, and alcoholic suicides

We previously reported fewer locus coeruleus (LC) neurons in both suicide victims and alcoholics than among a group of nonpsychiatric controls. In the present paper we examine the rate of decline in the number of LC neurons with age, looking for possible differential rates among suicide victims, alcoholics, and controls. We also compare these groups with a group of alcoholics who died by suicide, and consider the effects of sex, race, and postmortem interval. LC neuron counts were obtained from a total of 32 subjects. In all groups, the number of neurons decreased with age, but by roughly age 40 the average LC count among the three suicide and/or alcoholic groups was lower than among controls. The rate of LC neuron loss was greater among suicides than among controls, but the rate of loss among alcoholics who were at least 30 years old was the same as that among the controls. Our group of alcoholic suicides had counts that were statistically indistinguishable from those of suicides. Differences among groups appear to be most pronounced in the middle third of the LC. Further studies are needed to determine the mechanisms of noradrenergic neuron loss and whether it is associated with an underlying major depression in suicide victims, or acquired after a period of excessive alcohol consumption.

Family functioning and metabolic control of school-aged children with IDDM

The relationship of two aspects of family life to metabolic control were examined as part of a longitudinal study of school-aged children with newly diagnosed insulin-dependent diabetes mellitus (IDDM). Glycosylated hemoglobin level was the primary index of metabolic control; weight-adjusted insulin dosage served as an indirect index. Neither the quality of family life nor aspects of the parents' marriage predicted the child's metabolic control over the next 3-4 mo, and they were also unrelated to concurrent weight-adjusted insulin dosage. Longitudinal data spanning a 6-yr period of the child's diabetes also failed to reveal an association between aspects of family life and metabolic control. The significance of the findings are discussed in light of the sample's characteristics and possible methodological constraints.

Fitting nonlinear models with ARMA errors to biological rhythm data

Many behavioural and physiological processes are periodic with a period of approximately 24 hours. For descriptive purposes, linear regression using a simple sinusoid with a fixed 24 hour period is sometimes an adequate tool for analysing data from such processes. Inference based on regression models under the assumption of independent and identically distributed errors, however, can often mislead seriously. In this paper we present a general class of models for fitting biological rhythms, with use of higher-order harmonic terms of one or more unknown fundamentals and ARMA processes for the errors. We describe the procedures for model specification and estimation and give the theoretical justification for these procedures. Analysis of a series of human core body temperature illustrates the methodology.