Examination of Inertial Sensor-Based Estimation Methods of Lower Limb Joint Moments and Ground Reaction Force: Results for Squat and Sit-to-Stand Movements in the Sagittal Plane

Abstract

Joint moment estimation by a camera-based motion measurement system and a force plate has a limitation of measurement environment and is costly. The purpose of this paper is to evaluate quantitatively inertial sensor-based joint moment estimation methods with five-link, four-link and three-link rigid body models using different trunk segmented models. Joint moments, ground reaction forces (GRF) and center of pressure (CoP) were estimated for squat and sit-to-stand movements in the sagittal plane measured with six healthy subjects. The five-link model and the four-link model that the trunk was divided at the highest point of the iliac crest (four-link-IC model) were appropriate for joint moment estimation with inertial sensors, which showed average RMS values of about 0.1 Nm/kg for all lower limb joints and average correlation coefficients of about 0.98 for hip and knee joints and about 0.80 for ankle joint. Average root mean square (RMS) errors of horizontal and vertical GRFs and CoP were about 10 N, 15 N and 2 cm, respectively. Inertial sensor-based method was suggested to be an option for estimating joint moments of the trunk segments. Inertial sensors were also shown to be useful for the bottom-up estimation method using measured GRFs, in which average RMS values and average correlation coefficients were about 0.06 Nm/kg and larger than about 0.98 for all joints.

Possible predictive formulas for quantitative and time-based estimation of muscle strength during motion

“…However, pursuing the accuracy makes it difficult to use in the clinics as more factors should be considered or more sensors are required 23,24) . Kodama et al 10) required at least total 32 parameters in both horizontal and vertical for estimation of joint moments. However, the prediction formulas in this study created from maximum 9 parameters using only three sensors and can obtain good to excellent correlations between actual joint moments for most of the motions.…”

“…Three Wearable inertial motion sensors (LP-WSD1101-OA Ver.1.0.0, 1,000 Hz, LOGICAL PRODUCT, Fukuoka, Japan) were attached to the outside of right limbs by using double-sided adhesive tape 10) (Fig. 1).…”

“…1). Wearable inertial motion sensors, often consist of tri-axial accelerometer, gyroscopes and magnetic sensors 16) can measure angular velocity and have a high accuracy in calculating lower limb segmental angles during motions 10,17) . The sensors were oriented to have its sensitive axis of rotation perpendicular to the sagittal plane of motion 18) in order to obtain the angular information in the segment CoM position.…”

“…Currently, the most common methods to measure of joint moments are combining three dimensional motion analysis system with force plate analyses 9) . However, this apparatus is too expensive, requires considerable space and thus is limited to use in clinics 10) .…”

“…Kodama et al 10) have been suggested the way to estimate joint moments of squat and sit-to-stand by using the wearable inertial motion sensors. Their estimation applied the segment parameters calculated based on inertial properties of body segments 11) and the segment inclination angles calculated from the motion sensors to Newton's equation of motion.…”