Discrete modeling of patellar-tendon-reflexes as logistic phenomena

The present paper proposes a logistic model to represent patellar-tendon-reflexes (PTR) from the release-angle of the tapping-hammer to the peak angular-speed of the knee joint. The experimental data obtained are discrete in nature and, thus, they are modeled as a discrete system. However, the model is formulated such that parameters of the underlying continuous model are directly obtained so that the discrete results can be related to continuous counterpart with ease. From the observation of PTR data, it was noticed that they resemble well some of the features exhibited by a system whose characteristics are governed by a logistic equation. For these reasons, a technique developed recently for exact time-discretization of nonlinear systems was applied to this non-temporal discrete system. A discrete logistic model was identified from the experimental data obtained from human reflexes. Furthermore, a method is presented to determine an appropriate initial condition to reproduce the data curve using the identified model. The overall scheme was found to give results that were closer to actual data than the popular forward difference method, even with a very large discrete interval. This is important since the modeling can be achieved using a small number of tapping on the patients.