Time-Domain Optimal Experimental Design in Human Seated Postural Control Testing

Inferring Control Intent during Seated Balance using Inverse Model Predictive Control

Patients with Low Back Pain (LBP) are suggested to follow a protective coping strategy. Therefore, rehabilitation of these patients requires estimating their motor control strategies (the control intent). In this letter, we present an approach that infers the control intent by solving an inverse Model Predictive Control (iMPC) problem. The standard Model Predictive Control (MPC) structure includes constraints, therefore, it allows us to model the physiological constraints of motor control. We devised an iMPC algorithm to solve iMPC problems with experimentally collected output trajectories. We used experimental data of one healthy subject during a seated balance test that used a physical Human-Robot Interaction (pHRI). Results show that the estimated MPC weights reflected the task instructions given to the subject and yielded an acceptable goodness of fit. The iMPC solution suggests that the subject's control intent was dominated by minimizing the squared sum of a combination of the upper-body and lower-body angles and velocities.

Feasibility of Incorporating Test-Retest Reliability and Model Diversity in Identification of Key Neuromuscular Pathways During Head Position Tracking

To study the complex neuromuscular control pathways in human movement, biomechanical parametric models and system identification methods are employed. Although test-retest reliability is widely used to validate the outcomes of motor control tasks, it was not incorporated in system identification methods. This study investigates the feasibility of incorporating test-retest reliability in our previously published method of selecting sensitive parameters. We consider the selected parameters via this novel approach to be the key neuromuscular parameters, because they meet three criteria: reduced variability, improved goodness of fit, and excellent reliability. These criteria ensure that the parameter variability is below a user-defined value, the number of these parameters is maximized to enhance goodness of fit, and their test-retest reliability is above a user-defined value. We measured variability, the goodness of fit, and reliability using Fisher information matrix, variance accounted for, and intraclass correlation, respectively. We also incorporated model diversity as a fourth optional criterion to narrow down the solution space of key parameters. We applied this approach to the head position tracking tasks in axial rotation and flexion/extension. A total of forty healthy subjects performed the tasks during two visits. With variability and reliability measures ≤0.35 and ≥0.75, respectively, we selected three key parameters out of twelve with the goodness of fit >69%. The key parameters were associated with at least two neuromuscular pathways out of four modeled pathways (visual, proprioceptive, vestibular, and intrinsic), which is a measure of model diversity. Therefore, it is feasible to incorporate reliability and diversity in system identification of key neuromuscular pathways in our application.

Selecting Sensitive Parameter Subsets in Dynamical Models With Application to Biomechanical System Identification

Estimating many parameters of biomechanical systems with limited data may achieve good fit but may also increase 95% confidence intervals in parameter estimates. This results in poor identifiability in the estimation problem. Therefore, we propose a novel method to select sensitive biomechanical model parameters that should be estimated, while fixing the remaining parameters to values obtained from preliminary estimation. Our method relies on identifying the parameters to which the measurement output is most sensitive. The proposed method is based on the Fisher information matrix (FIM). It was compared against the nonlinear least absolute shrinkage and selection operator (LASSO) method to guide modelers on the pros and cons of our FIM method. We present an application identifying a biomechanical parametric model of a head position-tracking task for ten human subjects. Using measured data, our method (1) reduced model complexity by only requiring five out of twelve parameters to be estimated, (2) significantly reduced parameter 95% confidence intervals by up to 89% of the original confidence interval, (3) maintained goodness of fit measured by variance accounted for (VAF) at 82%, (4) reduced computation time, where our FIM method was 164 times faster than the LASSO method, and (5) selected similar sensitive parameters to the LASSO method, where three out of five selected sensitive parameters were shared by FIM and LASSO methods.

Reliability of assessing postural control during seated balancing using a physical human-robot interaction

This study evaluated the within- and between-visit reliability of a seated balance test for quantifying trunk motor control using input-output data. Thirty healthy subjects performed a seated balance test under three conditions: eyes open (EO), eyes closed (EC), and eyes closed with vibration to the lumbar muscles (VIB). Each subject performed three trials of each condition on three different visits. The seated balance test utilized a torque-controlled robotic seat, which together with a sitting subject resulted in a physical human-robot interaction (pHRI) (two degrees-of-freedom with upper and lower body rotations). Subjects balanced the pHRI by controlling trunk rotation in response to pseudorandom torque perturbations applied to the seat in the coronal plane. Performance error was expressed as the root mean square (RMSE) of deviations from the upright position in the time domain and as the mean bandpass signal energy (E_mb) in the frequency domain. Intra-class correlation coefficients (ICC) quantified the between-visit reliability of both RMSE and E_mb. The empirical transfer function estimates (ETFE) from the perturbation input to each of the two rotational outputs were calculated. Coefficients of multiple correlation (CMC) quantified the within- and between-visit reliability of the averaged ETFE. ICCs of RMSE and E_mb for all conditions were ≥0.84. The mean within- and between-visit CMCs were all ≥0.96 for the lower body rotation and ≥0.89 for the upper body rotation. Therefore, our seated balance test consisting of pHRI to assess coronal plane trunk motor control is reliable.

Time-Domain Optimal Experimental Design in Human Seated Postural Control Testing

We are developing a series of systems science-based clinical tools that will assist in modeling, diagnosing, and quantifying postural control deficits in human subjects. In line with this goal, we have designed and constructed a seated balance device and associated experimental task for identification of the human seated postural control system. In this work, we present a quadratic programming (QP) technique for optimizing a time-domain experimental input signal for this device. The goal of this optimization is to maximize the information present in the experiment, and therefore its ability to produce accurate estimates of several desired seated postural control parameters. To achieve this, we formulate the problem as a nonconvex QP and attempt to locally maximize a measure (T-optimality condition) of the experiment's Fisher information matrix (FIM) under several constraints. These constraints include limits on the input amplitude, physiological output magnitude, subject control amplitude, and input signal autocorrelation. Because the autocorrelation constraint takes the form of a quadratic constraint (QC), we replace it with a conservative linear relaxation about a nominal point, which is iteratively updated during the course of optimization. We show that this iterative descent algorithm generates a convergent suboptimal solution that guarantees monotonic nonincreasing of the cost function value while satisfying all constraints during iterations. Finally, we present successful experimental results using an optimized input sequence.