Comparative nonlinear modeling of renal autoregulation in rats: Volterra approach versus artificial neural networks

Volterra models have been increasingly popular in modeling studies of nonlinear physiological systems. In this paper, feedforward artificial neural networks with two types of activation functions (sigmoidal and polynomial) are utilized for modeling the nonlinear dynamic relation between renal blood pressure and flow data, and their performance is compared to Volterra models obtained by use of the leading kernel estimation method based on Laguerre expansions. The results for the two types of artificial neural networks (sigmoidal and polynomial) and the Volterra models are comparable in terms of normalized mean-square error (NMSE) of the respective output prediction for independent testing data. However, the Volterra models obtained via the Laguerre expansion technique achieve this prediction NMSE with approximately half the number of free parameters relative to either neural-network model. Nonetheless, both approaches are deemed effective in modeling nonlinear dynamic systems and their cooperative use is recommended in general, since they may exhibit different strengths and weaknesses depending on the specific characteristics of each application.