Direct calculation of mid sensitivity functions

Mathematical analysis of chemical kinetic studies, e.g., multiple indicator dilution (MID) data, often involves the use of nonlinear least squares fitting to estimate model parameters. The fitting procedures usually employ derivatives with respect to the parameters under study (the model sensitivity functions). When the mathematical model is a system of partial differential equations (PDE), the sensitivity functions are often obtained by finite differences of the numerically computed model function which results in numerous time consuming calls to the PDE solver. We present an alternative method of simultaneously calculating both solutions and sensitivity functions by solving a class PDE's involving reactions and convection for MID studies of endothelial surface reactions: ∂c/∂t + w/1 + a ∂c/∂x = -bc, ∂/∂t ∂c/∂b + w/1 + a ∂/∂x ∂c/∂b = -c - b∂c/∂b, ∂/∂t ∂c/∂a + w/1 + a ∂/∂x ∂c/∂a = -b∂c/∂a + w/(1+a)² ∂c/∂x.