Differential method of characterizing gait strategies from step lengths and frequencies: strategy of velocity modulation

The differential method consists of the analysis of the variation of gait parameters length, frequency, and velocity with respect to their mean values, respectively, Delta L = L - L(m), Delta f = f - f(m), and Delta v = v - vm, where L(m), f(m), and v(m) represent the mean values of those parameters. Assuming that the strategy of modulation of velocity implies that L and f are functions of v and that statistical analyses of ratios Delta L/Delta v and Delta f/Delta v have established that there is a very significant linear correlation, close to 1, between those ratios, the mathematical procedure allows one to determine the equation of step length, L = a x f + b x v + K, where a and b are the slope and the intercept of the linear regression and K is close to L(m). The equation was experimentally tested on 140 gait sequences performed by 6 participants and for gait velocities ranging from 0.6 to 2.2 m/s and was found to be very representative of all individual values. The differential method provides another way of using the derivative of velocity, v = L x f, to characterize the strategy of velocity modulation, which then permits one to determine the linear equation of velocity, v = f x L + L x f(m) - L(m) x f(m), and to show that the respective parts played by each parameter in the progression velocity are approximately equal. The author establishes the uniqueness of the different linear adjustments and discusses the differential method's own modes of use, that is, interindividually or globally.