A latent low-dimensional common input drives a pool of motor neurons: a probabilistic latent state-space model

Abstract

Motor neurons appear to be activated with a common input signal that modulates the discharge activity of all neurons in the motor nucleus. It has proven difficult for neurophysiologists to quantify the variability in a common input signal, but characterization of such a signal may improve our understanding of how the activation signal varies across motor tasks. Contemporary methods of quantifying the common input to motor neurons rely on compiling discrete action potentials into continuous time series, assuming the motor pool acts as a linear filter, and requiring signals to be of sufficient duration for frequency analysis. We introduce a space-state model in which the discharge activity of motor neurons is modeled as inhomogeneous Poisson processes and propose a method to quantify an abstract latent trajectory that represents the common input received by motor neurons. The approach also approximates the variation in synaptic noise in the common input signal. The model is validated with four data sets: a simulation of 120 motor units, a pair of integrate-and-fire neurons with a Renshaw cell providing inhibitory feedback, the discharge activity of 10 integrate-and-fire neurons, and the discharge times of concurrently active motor units during an isometric voluntary contraction. The simulations revealed that a latent state-space model is able to quantify the trajectory and variability of the common input signal across all four conditions. When compared with the cumulative spike train method of characterizing common input, the state-space approach was more sensitive to the details of the common input current and was less influenced by the duration of the signal. The state-space approach appears to be capable of detecting rather modest changes in common input signals across conditions. We propose a state-space model that explicitly delineates a common input signal sent to motor neurons and the physiological noise inherent in synaptic signal transmission. This is the first application of a deterministic state-space model to represent the discharge characteristics of motor units during voluntary contractions.

Variability in common synaptic input to motor neurons modulates both force steadiness and pegboard time in young and older adults

“…Because it is not possible to infer the population dynamics of a motor pool from single motor units, contemporary methods, such as state‐space models (Feeney et al . 2017) and the cumulative spike train approach (Farina et al . 2014), estimate the common synaptic input to all motor neurons from the discharge times of multiple concurrently active units.…”

“…We validated this model in previous work (Feeney et al . 2017) using both computational simulations and experimental data. The present study extends the theoretical framework to examine its utility in quantifying variability in common synaptic input during steadiness tasks.…”

“…2016a) with a robust mathematical model of common synaptic input to the motor pool (Feeney et al . 2017).…”

“…The motor unit discharge times were used to fit the parameters of a state‐space model (Feeney et al . 2017) to estimate the common synaptic input signal to motor neurons during the force steadiness tasks. In this model, discharge rate (γ) of the i th recorded motor unit is parameterized as a Poisson process and is represented by eqs and : …”

“…The EM algorithm was terminated when either a maximum number of iterations (100) was reached or when the relative error in log‐likelihood became less than 10 –3 (Feeney et al . 2017). The model assumes the variance in common synaptic input is constant over the window of interest.…”