Models for temporal-spatial parameters in walking with cadence ratio as the independent variable

Accurate models that describe temporal-spatial parameters are desirable in gait estimation and rehabilitation. This study aimed to explore simple but relatively accurate models to describe stride length (SL), speed (SP) and walk ratio (WR) at various cadences. Twenty-four able-bodied participants (16 in a test group and 8 in a validation group) walked at seven cadence ratios (CRs). The individual and group mean SL, SP and WR were studied. Suitable temporal-spatial model structures were proposed and used to approximate the individual SL, SP and WR at various CRs. After the temporal-spatial model structures were found to be feasible, the general temporal-spatial models were analysed using the test group mean SL, SP and WR. Accuracy was assessed using the validation group mean values. Individual approximation accuracies showed that the proposed model structure deduced from the linear SL model was suitable for WR approximation. The linear, deduced quadratic and power functions approximated the individual SL, SP and WR, respectively, with high accuracy. Based on the test group mean SL, SP and WR, the general temporal-spatial models were obtained and produced comparable approximation accuracies in the validation group. The general temporal-spatial models predicted well the individual gait parameters with similar individual errors for both groups. These temporal-spatial models clearly describe SL, SP and especially WR at various cadences. They provide accurate reference data for gait estimation and have potential to guide speed modulation in robot-assisted gait rehabilitation. Graphical abstract Twenty-four able-bodied participants (16 in test group and 8 in validation group) walked at seven cadence ratios (CRs), with the individual and group mean stride length (SL), speed (SP) and walk ratio (WR) studied. This work selected the cadence ratio as the independent variable and yielded general temporal-spatial models based on the test group data, which were a linear model for SL, a quadratic function for SP and a power function for WR. The general temporal-spatial model produced comparable approximation accuracies in the validation group. Clearly describing SL, SP and especially WR at various cadences, these temporal-spatial models provide accurate references for gait estimation and have the potential to guide speed modulation in robot-assisted gait rehabilitation. Approximation of the group mean temporal-spatial parameters at seven cadences. Solid lines in parts (a, b): the general linear SL model. Solid lines in (c, d): the general quadratic SP model. Solid lines in (e, f): the general WR model. Dots and stars in (a, c, e): the individual and group mean values for the test group. Dots and stars in (b, d, f): the individual and group mean values for the validation group.