Kernel bandwidth optimization in spike rate estimation

Kernel smoother and a time-histogram are classical tools for estimating an instantaneous rate of spike occurrences. We recently established a method for selecting the bin width of the time-histogram, based on the principle of minimizing the mean integrated square error (MISE) between the estimated rate and unknown underlying rate. Here we apply the same optimization principle to the kernel density estimation in selecting the width or “bandwidth” of the kernel, and further extend the algorithm to allow a variable bandwidth, in conformity with data. The variable kernel has the potential to accurately grasp non-stationary phenomena, such as abrupt changes in the firing rate, which we often encounter in neuroscience. In order to avoid possible overfitting that may take place due to excessive freedom, we introduced a stiffness constant for bandwidth variability. Our method automatically adjusts the stiffness constant, thereby adapting to the entire set of spike data. It is revealed that the classical kernel smoother may exhibit goodness-of-fit comparable to, or even better than, that of modern sophisticated rate estimation methods, provided that the bandwidth is selected properly for a given set of spike data, according to the optimization methods presented here

ELECTROPHYSIOLOGY OF BASAL GANGLIA (BG) CIRCUITRY AND DYSTONIA AS A MODEL OF MOTOR CONTROL DYSFUNCTION

The basal ganglia (BG) is a complex set of heavily interconnected nuclei located in the central part of the brain that receives inputs from the several areas of the cortex and projects via the thalamus back to the prefrontal and motor cortical areas. Despite playing a significant part in multiple brain functions, the physiology of the BG and associated disorders like dystonia remain poorly understood. Dystonia is a devastating condition characterized by ineffective, twisting movements, prolonged co-contractions and contorted postures. Evidences suggest that it occurs due to abnormal discharge patterning in BG-thalamocortocal (BGTC) circuitry. The central purpose of this study was to understand the electrophysiology of BGTC circuitry and its role in motor control and dystonia. Toward this goal, an advanced multi-target multi-unit recording and analysis system was utilized, which allows simultaneous collection and analysis of multiple neuronal units from multiple brain nuclei. Over the cause of this work, neuronal data from the globus pallidus (GP), subthalamic nucleus (STN), entopenduncular nucleus (EP), pallidal receiving thalamus (VL) and motor cortex (MC) was collected from normal, lesioned and dystonic rats under awake, head restrained conditions. The results have shown that the neuronal population in BG nuclei (GP, STN and EP) were characterized by a dichotomy of firing patterns in normal rats which remains preserved in dystonic rats. Unlike normals, neurons in dystonic rat exhibit reduced mean firing rate, increased irregularity and burstiness at resting state. The chaotic changes that occurs in BG leads to inadequate hyperpolarization levels within the VL thalamic neurons resulting in a shift from the normal bursting mode to an abnormal tonic firing pattern. During movement, the dystonic EP generates abnormally synchronized and elongated burst duration which further corrupts the VL motor signals. It was finally concluded that the loss of specificity and temporal misalignment between motor neurons leads to corrupted signaling to the muscles resulting in dystonic behavior. Furthermore, this study reveals the importance of EP output in controlling firing modes occurring in the VL thalamus

Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings

状態空間法による神経スパイク発火率の推定

要旨あり原著論