Error analysis in parameter estimation of physiological systems with uncertain model inputs and assigned model constants

Mathematical models of physiological systems often include model parameters and inputs that are considered as known, e.g. from measurements, and that are assigned as constants in the identification/parameter estimation process. Usually, assigned variables are considered error-free but uncertainty in their value affects estimation precision of the remaining parameters. This problem is addressed in this paper for dynamic models described by non-linear ordinary differential equations and for non-linear weighted least squares parameter estimation. The theory is applied to a model of glucose disappearance for quantifying the individual contribution of various error sources.