ORBITAL STABILITY ANALYSIS OF HUMAN MOVEMENT: IN-SILICO PRELIMINARY EVALUATION FOR THE DEFINITION OF EXPERIMENTAL TRIALS

INTRODUCTION Falls in the elderly represent a well-known problem, having large clinical and economic consequences [1]. Locomotion on stairs is among the most challenging and hazardous activities of daily living for older individuals [2]. Many human tasks, like stairs climbing, are structurally cyclic, and result in several biomechanical time-varying variables (i.e. kinematic) that are all manifestation of the same motion pattern. Hence, kinematic data should not be analyzed independently when studying the kinematic stability during the temporal evolution of the task. Orbital stability analysis of time series allows studying the stability of cyclic motor tasks [3] considering all these variables together, but the number of task cycles to be included in the analysis for obtaining reliable results is still unclear. CLINICAL SIGNIFICANCE A better comprehension of the stability of kinematic patterns during motor tasks could give a significant contribution in assessing the risk of fall. The aim of the present study is to identify the minimum number of cycles required making the results of orbital stability analysis significant for motion evaluation, then to evaluate the results obtained on a sample of subjects during step climbing. METHODS In-silico: orbital stability analysis was performed on a 3-dimensional limit cycle system (Hastings & Powell [4]) for which the theoretical value of the maximum Floquet multiplier is known (maxFM = 0.9). The equations of the model were integrated in Matlab (Mathworks, Natick, NA). The state space included the time series coming from the three integrated variables of the model. Maximum Floquet multipliers were calculated numerically using an established technique [5], on increasing number of cycles (Fig. 1a). Experimental: three healthy participants [25±0y, 1.74±0.02m, 70±4kg], with normal BMI and no prior history of falling, performed a step-climbing test. During the tests force plate (FP4060-07-1000, Bertec, USA) and kinematic (SmartE, BTS, Milan, Italy) data were acquired. An 8-segment model of the subject was obtained from kinematic data using CAST [6]. Data quantifying joint angles of lower limbs and trunk defined a 21-dimensional state space. Maximum Floquet multipliers were calculated numerically [5] to quantify the sensitivity of kinematic patterns to small perturbations that naturally occur during step climbing. The magnitudes of maxFM were computed at the most significant time events of the task (leading heel off, leading toe off, leading heel strike, trailing toe off, trailing heel strike), identified from force plate data. 278 RESULTS Values of maximum Floquet multiplier of the Hastings & Powell model close to the "true" value of 0.9 were obtained from approximately 10 cycles on (Fig. 1a). Experimental analysis showed values < 1 for all the maximum Floquet multipliers (Fig. 1b). The values of maximum Floquet multipliers in proximity of the trailing toe off phase were slightly higher than in the other phases. Fig 1a Maximum Floquet multipliers obtained from the limit cycle model depending on the number of cycles analysed. DISCUSSION In-silico preliminary results showed that at least 10 cycles must be analysed to obtain reliable values for the maximum Floquet multipliers. Experimental preliminary results seemed to confirm that the technique is adequate for studying human motor tasks. Maximum Floquet multipliers showed values < 1 in all the task phases; hence, orbital stability is maintained. The slightly higher value of mean max FM in proximity of the trailing toe off phase may entail a physiological loss of stability in correspondence of that phase, probably due to the lower confidence of the subject in performing a phase of the task that actively involves the trailing limb. Orbital stability analysis of step climbing in the elderly will be the object of further studies.