Seminar in applied mathematics and statistics

SPEAKER: Luis Salasar

TITLE: A Hierarchical Bayesian Approach to Human Gait Analysis

ABSTRACT:
The analysis of human motion plays a key role in understanding the typical and altered movement patterns, and to propose and evaluate the effects of preventive or rehabilitation programs. Knee injuries are very common in athletes and population in general, and these disorders may often influence gait features. During gait, knee movements occur in sagittal, frontal and transverse plans. The knee flexion-extension, which is the movement that occurs in the sagittal plan, is the most prominent and studied movement. Usually, gait motion is divided in cycles (the period between two consecutive heel strikes on the ground) which are described by the curves of angular rotation versus the percentage of the total cycle duration. Each cycle can be divided in two phases: stance phase (when the limb is supported on the ground), and balance phase (when the limb is swinging).

In the present study, 16 healthy male subjects were investigated. The subjects walked in a treadmill in a fixed speed of 5 km/h during 90 seconds. Using a flexible goniometer, the knee flexion-extension angles were obtained as a function of time for both dominant and non-dominant legs. The main goals of this study were to construct credibility bands for the mean curve of the population, and to construct prediction bands for future observations as a first step towards detecting possible dysfunctions. To achieve these, we modelled the gait cycle as a finite Fourier sum and adopted a hierarchical prior distribution for the model parameters. In order to make inferences, we applied a MCMC procedure to draw from the posterior distribution of the parameters.

Tea and chocolate will be served in room 04.3.15 after the seminar.