Bayesian inference of physiologically meaningful parameters from body sway measurements

Abstract

The control of the human body sway by the central nervous system, muscles, and conscious brain is of interest since body sway carries information about the physiological status of a person. Several models have been proposed to describe body sway in an upright standing position, however, due to the statistical intractability of the more realistic models, no formal parameter inference has previously been conducted and the expressive power of such models for real human subjects remains unknown. Using the latest advances in Bayesian statistical inference for intractable models, we fitted a nonlinear control model to posturographic measurements, and we showed that it can accurately predict the sway characteristics of both simulated and real subjects. Our method provides a full statistical characterization of the uncertainty related to all model parameters as quantified by posterior probability density functions, which is useful for comparisons across subjects and test settings. The ability to infer intractable control models from sensor data opens new possibilities for monitoring and predicting body status in health applications.Upright stance is inherently unstable due to the physics of an inverted pendulum-like body and due to the internal perturbations of an individual, such as noise in afferent (sensory) and efferent (motor) nerve pathways, respiration, and hemodynamics [1][2][3][4] . Balance is controlled by co-operating visual, vestibular, and somatosensory systems. The sensory information is integrated in the central nervous system (CNS), which determines the actions needed to maintain balance and which commands the musculoskeletal system to execute corrective actions to maintain an upright stance.Factors that affect the CNS and skeletal muscles also influence postural steadiness. Therefore, quantifying postural steadiness during upright stance may provide insight into the physiological state of a person. In one kind of posturographic measurement a person stands erect on a force plate while the plate measures the net center-of-pressure (COP) along the mediolateral (ML) and anteriorposterior (AP) directions. The COP signal is closely related to the 2D center-of-mass (COM) signal 5,6 , the time-varying vertical projection of the 3D body's center-of-mass. Traditionally COP signals are quantified by statistical sway measures extracted from raw data. These measures typically describe mean sway amplitude, velocity, and frequency 7 . Previously posturographic measurements have been used to quantify effects of aging 7-9 , state of alertness 10-12 , use of anesthetic drugs [13][14][15] , and conditions, such as multiple sclerosis 16,17 , and Parkinson's disease 18,19 . Upright stance can be modeled using an inverted pendulum model that depicts the human body as a rigid rod pivoting around its floor-anchored end. The pendulum may have either one or more links that depict human joints, such as ankles, hips, and knees. A single-link (ankle) model is simple and common, and it can be used to describe quiet, upright stance 9...

Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions

“…Finally, we apply the proposed method to a human body sway problem. This problem has received considerable attention as the body sway may provide information about the physiological status of a person [34]. Several mathematical models have been proposed to describe the sway motion, and here we consider the single-link inverted pendulum (SLIP) model proposed in [2], which assumes that the body is maintained in an upright position by an active and a passive proportional-derivative controller.…”

“…The slope a s depends on the level of control, C ON , as a s = − tan(π(C ON − 0.5)). In this model, five key parameters (P , D, ∆, σ, and C ON ) can not be measured directly and need to be inferred from the body sway measurements, while the other parameters can either be measured or specified in advance [34]. The COM signal,…”

“…Computing the posterior in this problem is rather challenging as the likelihood function p(y|x) is not available, which make the standard Bayesian inference computation methods such as the MCMC algorithms infeasible. In [34], the parameters were inferred with the approximate Bayesian computation (ABC) method which does not use the likelihood function. Here we compute the posterior with the proposed method.…”

Direct estimation of the parameters of a delayed, intermittent activation feedback model of postural sway during quiet standing

“…To obtain statistical information about estimated parameters, summary statistic methods have been combined with approximate Bayesian inference [17]. This method was used to acquire empirical posterior distributions of five out of the eight parameters of interest [18].…”

“…Many of the parameters have previously been estimated in a variety of ways, sometimes with highly varied results. Tietäväinen et al [18] used the approximate Bayesian inference [17] with data simulation to estimate P , D , a , τ , and σ . Among these, the method failed to obtain precise distributions for D in both simulations and empirical application.…”