A Kalman Filter Approach for Estimating Tendon Wave Speed from Skin-Mounted Accelerometers

Abstract

Shear wave tensiometry is a noninvasive approach for assessing in vivo tendon forces based on the speed of a propagating shear wave. Wave speed is measured by impulsively exciting a shear wave in a tendon and then assessing the wave travel time between skin-mounted accelerometers. Signal distortion with wave travel can cause errors in the estimated wave travel time. In this study, we investigated the use of a Kalman filter to fuse spatial and temporal accelerometer measurements of wave propagation. Spatial measurements consist of estimated wave travel times between accelerometers. Temporal measurements are the change in wave arrival at a fixed accelerometer between successive impulsive taps. The Kalman filter substantially improved the accuracy of estimated wave speeds when applied to simulated tensiometer data. The variability of estimated wave speed was reduced by ~55% in the presence of random sensor noise. It was found that increasing the number of accelerometers from two to three further reduced wave speed errors by 45%. The use of redundant accelerometers (>2) also improved the robustness of wave speed measures in the presence of uncertainty in accelerometer location. We conclude that the use of a Kalman filter and redundant accelerometers can enhance the fidelity of using shear wave tensiometers to track tendon wave speed and loading during movement.

Achilles Tendon Loading during Running Estimated Via Shear Wave Tensiometry: A Step Toward Wearable Kinetic Analysis

“…Improvements to tensiometer sensor design and wave speed interpretation are ongoing to address potential sensor noise. For example, we have shown that the use of additional accelerometers and a Kalman filter (36) can enhance the accuracy of wave speed measurements in the presence of noise.…”

A Single-Sensor Approach for Noninvasively Tracking Phase Velocity in Tendons during Dynamic Movement

“…Third, the single-sensor technique is particularly sensitive to positional accuracy, with only a single dimension used to determine the wave propagation speed. In [ 20 ], computation of wave speed using more than two measurement points showed potential improvements in accuracy when compared to the standard dual-sensor technique. While there are advantages to the single-sensor method, the increased importance of accurately constraining spacing is acknowledged.…”

“…Independent Kalman filters were implemented for both the group and phase delay computations. The a priori estimates of the system states were computed from the change in group and phase delay of consecutive events [ 20 ]. Phase velocity for the shear wave was computed from the known distance from the transducer to the accelerometer ( D = 20 mm) and the arrival times (Equation (4)).…”

“…Dual-sensor wave speeds were computed as described previously [ 20 ]. Cross-correlations determined the between-sensor time delay and the between-event changes in time delay using signals captured by both accelerometers.…”