Efficient spline regression for neural spiking data

Detecting rhythmic spiking through the power spectra of point process model residuals

Objective

Oscillations figure prominently as neurological disease hallmarks and neuromodulation targets. To detect oscillations in a neuron's spiking, one might attempt to seek peaks in the spike train's power spectral density (PSD) which exceed a flat baseline. Yet for a non-oscillating neuron, the PSD is not flat: The recovery period ("RP", the post-spike drop in spike probability, starting with the refractory period) introduces global spectral distortion. An established "shuffling" procedure corrects for RP distortion by removing the spectral component explained by the inter-spike interval (ISI) distribution. However, this procedure sacrifices oscillation-related information present in the ISIs, and therefore in the PSD. We asked whether point process models (PPMs) might achieve more selective RP distortion removal, thereby enabling improved oscillation detection.

Approach

In a novel "residuals" method, we first estimate the RP duration (nr) from the ISI distribution. We then fit the spike train with a PPM that predicts spike likelihood based on the time elapsed since the most recent of any spikes falling within the preceding nr milliseconds. Finally, we compute the PSD of the model's residuals.

Main results

We compared the residuals and shuffling methods' ability to enable accurate oscillation detection with flat baseline-assuming tests. Over synthetic data, the residuals method generally outperformed the shuffling method in classification of true- versus false-positive oscillatory power, principally due to enhanced sensitivity in sparse spike trains. In single-unit data from the internal globus pallidus (GPi) and ventrolateral anterior thalamus (VLa) of a parkinsonian monkey -- in which alpha-beta oscillations (8-30 Hz) were anticipated -- the residuals method reported the greatest incidence of significant alpha-beta power, with low firing rates predicting residuals-selective oscillation detection.

Significance

These results encourage continued development of the residuals approach, to support more accurate oscillation detection. Improved identification of oscillations could promote improved disease models and therapeutic technologies.

Individualized temporal patterns dominate cortical upstate and sleep depth in driving human sleep spindle timing

Sleep spindles are critical for memory consolidation and strongly linked to neurological disease and aging. Despite their significance, the relative influences of factors like sleep depth, cortical up/down states, and spindle temporal patterns on individual spindle production remain poorly understood. Moreover, spindle temporal patterns are typically ignored in favor of an average spindle rate. Here, we analyze spindle dynamics in 1008 participants from the Multi-Ethnic Study of Atherosclerosis using a point process framework. Results reveal fingerprint-like temporal patterns, characterized by a refractory period followed by a period of increased spindle activity, which are highly individualized yet consistent night-to-night. We observe increased timing variability with age and distinct gender/age differences. Strikingly, and in contrast to the prevailing notion, individualized spindle patterns are the dominant determinant of spindle timing, accounting for over 70% of the statistical deviance explained by all of the factors we assessed, surpassing the contribution of slow oscillation (SO) phase (~14%) and sleep depth (~16%). Furthermore, we show spindle/SO coupling dynamics with sleep depth are preserved across age, with a global negative shift towards the SO rising slope. These findings offer novel mechanistic insights into spindle dynamics with direct experimental implications and applications to individualized electroencephalography biomarker identification.

Integrating Statistical and Machine Learning Approaches for Neural Classification

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.

Dynamic models of obstructive sleep apnea provide robust prediction of respiratory event timing and a statistical framework for phenotype exploration

Obstructive sleep apnea (OSA), in which breathing is reduced or ceased during sleep, affects at least 10% of the population and is associated with numerous comorbidities. Current clinical diagnostic approaches characterize severity and treatment eligibility using the average respiratory event rate over total sleep time (apnea-hypopnea index). This approach, however, does not characterize the time-varying and dynamic properties of respiratory events that can change as a function of body position, sleep stage, and previous respiratory event activity. Here, we develop a statistical model framework based on point process theory that characterizes the relative influences of all these factors on the moment-to-moment rate of event occurrence. Our results provide new insights into the temporal dynamics of respiratory events, suggesting that most adults have a characteristic event pattern that involves a period of normal breathing followed by a period of increased probability of respiratory event occurrence, while significant differences in event patterns are observed among gender, age, and race/ethnicity groups. Statistical goodness-of-fit analysis suggests consistent and substantial improvements in our ability to capture the timing of individual respiratory events using our modeling framework. Overall, we demonstrate a more statistically robust approach to characterizing sleep disordered breathing that can also serve as a basis for identifying future patient-specific respiratory phenotypes, providing an improved pathway towards developing individualized treatments.