Volume of Convex Hull: A Technique for Quantifying Human Postural Stability

Abstract

Many disorders, such as nervous system disorders, can affect orientation of the body segments in 3D space negatively. Patients with these disorders often show body segments instability during stance tasks. Nowadays, 3-axis gyroscopes are about to be used to measure postural stability. The main objective of the paper is to describe a method which would be suitable for quantifying postural stability and 3D movement as a whole using a cheap 3-axis gyroscope. New method based on the volume of a 3D convex hull (CH) obtained by plotting pitch, roll and yaw angles versus each other was proposed for quantitative evaluation of 3D trunk sway. The sway was measured while patients with degenerative cerebellar disorder (Pts) and eleven healthy subjects (HSs) performed quiet stance on a firm surface (FiS) and foam surface (FoS) with open eyes (OE) and closed eyes (CE). The CH was used to identify differences in balance control, and there were significant differences found between the two groups. The median (Mdn) of the volume of Pts with OE on FiS is four times larger than the Mdn of the volume of HS with OE on FiS. The Mdn of the volume of Pts with CE on FoS is 80 times larger than the Mdn of the volume of HS with CE on FoS. It was therefore found that the volume of CH is suitable for quantifying postural sway and identifying differences in balance control.

Postural Stability Evaluation of Patients Undergoing Vestibular Schwannoma Microsurgery Employing the Inertial Measurement Unit

“…The novel method for identification of pathologies affecting balance control is based on the mathematical tools for static posturography [ 8 , 23 ]. The distribution of the measured data can be modelled by a method which refers to the sector formula of Leibniz [ 8 ].…”

“…The method used to calculate the volume of each elemental pyramid is based on a calculation of the convex polyhedron volume [ 23 ]. In mathematics, the convex hull of a set of points (SP) in the Euclidean space is the smallest convex set that contains SP [ 24 , 25 ].…”