Structural correlation method for model reduction and practical estimation of patient specific parameters illustrated on heart rate regulation

We consider the inverse and patient specific problem of short term (seconds to minutes) heart rate regulation specified by a system of nonlinear ODEs and corresponding data. We show how a recent method termed the structural correlation method (SCM) can be used for model reduction and for obtaining a set of practically identifiable parameters. The structural correlation method includes two steps: sensitivity and correlation analysis. When combined with an optimization step, it is possible to estimate model parameters, enabling the model to fit dynamics observed in data. This method is illustrated in detail on a model predicting baroreflex regulation of heart rate and applied to analysis of data from a rat and healthy humans. Numerous mathematical models have been proposed for prediction of baroreflex regulation of heart rate, yet most of these have been designed to provide qualitative predictions of the phenomena though some recent models have been developed to fit observed data. In this study we show that the model put forward by Bugenhagen et al. (2010) can be simplified without loss of its ability to predict measured data and to be interpreted physiologically. Moreover, we show that with minimal changes in nominal parameter values the simplified model can be adapted to predict observations from both rats and humans. The use of these methods make the model suitable for estimation of parameters from individuals, allowing it to be adopted for diagnostic procedures.