Comparison of three methods to estimate the center of mass during balance assessment

Abstract

Evaluation of postural control is generally based on the interpretation of the center of pressure (COP) and the center of mass (COM) time series. The purpose of this study is to compare three methods to estimate the COM which are based on different biomechanical considerations. These methods are: (1) the kinematic method; (2) the zero-point-to-zero-point double integration technique (GLP) and (3) the COP low-pass filter method (LPF). The COP and COM time series have been determined using an experimental setup with a force plate and a 3D kinematic system on six healthy young adult subjects during four different 30 s standing tasks: (a) quiet standing; (b) one leg standing; (c) voluntary oscillation about the ankles and (d) voluntary oscillation about the ankles and hips. To test the difference between the COM trajectories, the root mean square (RMS) differences between each method (three comparisons) were calculated. The RMS differences between kinematic–LPF and GLP–LPF are significantly larger than kinematic–GLP. Our results show that the GLP method is comparable to the kinematic method. Both agree with the unified theory of balance during upright stance. The GLP method is attractive in the clinical perspective because it requires only a force plate to determine the COP–COM variable, which has been demonstrated to have a high reliability.

Introduction

The most common model used to characterise the postural control during quiet standing is the inverted pendulum. In this model, the postural control is defined by the relation between the center of pressure (COP) and the center of mass (COM). The COP oscillates on either side of the COM where the COP displacement always exceeds the COM. The COP is the integrated control variable whereas the COM is the controlled variable (Winter, 1995). The variable COP–COM, which is defined as the time course arithmetic difference of the COP and COM position, is highly correlated to the horizontal acceleration of the COM (Winter et al., 1996). The variable COP–COM is reported as the ‘error’ of the postural control system and provides important insight into the postural control mechanism. It was recently shown that the root mean square (RMS) error of the COP–COM is greater in elderly with neurological impairments compared with healthy elderly (Corriveau et al., 2000a). Metrological studies also demonstrated that the COP–COM variable has a high reliability in elderly subjects (Corriveau et al (2000b), Corriveau et al (2001); 2001).

The COP is defined as the point of application of the ground reaction forces under the feet measured by one or two force platforms. It is the outcome of the inertial forces of the body and the restoring equilibrium forces of the postural control system. The COM is an imaginary point at which the total body mass can be assumed to be concentrated. The position of the COM is hypothesised to be subject to body postural control. For convenience of certain calculations, it can be computed as the weighted average position of the segments. Several methods have been suggested to estimate the COM. The kinematic method (also known as ‘segmental method’) is based on the definition of the COM and has been frequently used in quiet standing (Hasan et al (1996a), Hasan et al (1996b); Winter et al., 1998; Corriveau et al (2000a), Corriveau et al (2000b), Corriveau et al (2001)). Recently, the mechanical relationships between COM and COP during quiet standing allowed researchers to define the COM based on Newtonian mechanics (King and Zatsiorsky, 1997; Levin and Mizrahi, 1996; Morasso et al., 1999; Shimba, 1984; Zatsiorky and King, 1998). Since the frequency content of the COP is higher than the COM, other estimation methods have been proposed using a low-pass filter (LPF) on the COP time series (Benda et al., 1994; Caron et al., 1997).

The COM estimation methods based on Newtonian mechanics are attractive in the clinical perspective because they require only a force platform to calculate the COP–COM. The purpose of this study is to compare three different methods to estimate the COM displacement during different standing tasks. Although earlier comparisons have been reported (Eng and Winter, 1993), to our knowledge this is the first time that techniques from three different methods to estimate the COM location are directly compared under different standing conditions. This comparison may help potential users to choose a method for estimating the COM location.