G. Ferrari-Trecate and D. Liberati. Representing logic and dynamics: the role of piecewise affine models in the biomedical field. 5th European Conference of the European Society of Mathematical and Theoretical Biology , 2002. Milan, Italy, 2-6 July.
Linear time-invariant (LTI) modeling is a powerful and simple tool to describe biomedical systems dynamics around given working points for a limited time horizon. However, when a larger range of behaviors is considered, and/or the time horizon becomes wider, nonlinear and time-varying effects often can not be neglected in order to obtain realistic models. A classical way to resort to LTI systems also in such a more general context is to piecewise approximate the model to a linear one in subsequent time windows, each of which is ruled by an almost linear behavior. In such a case, besides identifying every single LTI model, it is also needed to capture the switching times between different submodels. For instance, when analyzing EEG data, whose stationary behavior can hardly be guaranteed over few seconds even in absence of specific stimulation, linear autoregressive models need to be retuned when the prediction error increases. Recently, an algorithm which is able to cope with both linear dynamics identification and logical switching at a time has been proposed within the framework of piecewise affine models by Ferrari-Trecate et al. This also allows modeling output jumps when switching between submodels occurs. Such method can offer a powerful tool for preprocessing brain waves in attempting brain-computer interfacing, while having a wider applicability. Among others fields of application, one may cite: otolaryngology, for identifying saccades from nystagmus in vestibulo-ocular reflex analysis; dialysis, for identifying the switching from the fast clearance induced by the dialyzer and the slowest one imposed by physiology; endocrinology, for detecting significant pulses in hormone concentration.