MODELING METHODOLOGY FOR NONLINEAR PHYSIOLOGICAL SYSTEMS

A general modeling approach for a broad class of nonlinear systems is presented that uses the concept of principal dynamic modes (PDMs). The se PDMs constitute a filter bank whose outputs feed into a multi-input static nonlinearity of multinomial (polynomial) form to yield a gener al model for the broad class of Volterra systems. Because the practica lly obtainable models (from stimulus-response data) are of arbitrary o rder of nonlinearity, this approach is applicable to many nonlinear ph ysiological systems heretofore beyond our methodological means. Two sp ecific methods are proposed for the estimation of these PDMs and the a ssociated nonlinearities from stimulus-response data. Method I uses ei gendecomposition of a properly constructed matrix using the first two kernel estimates (obtained by existing methods). Method II uses a part icular class of feedforward artificial neural networks with polynomial activation functions. The efficacy of these two methods is demonstrat ed with computer-simulated examples, and their relative performance is discussed. The advent of this approach promises a practicable solutio n to the vexing problem of modeling highly nonlinear physiological sys tems, provided that experimental data be available for reliable estima tion of the requisite PDMs.