A Three-stage Parameter Estimation Algorithm for Tracer Concentration Kinetic Modelling with Positron Emission Tomography

Nonlinear regression is one of the routine tools for parameter estimation in tracer kinetic modelling with Positron Emission Tomography (PET) and in general physiological system modelling. The success of nonlinear regression is largely dependent on the parameter initial value guess, especially when the number of parameters to be simultaneously estimated is large. However, parameter initial value guess is deeply involved with human intelligence and experience, which could be extremely difficult if prior information is not available. To overcome this frustration, a three-stage parameter estimation algorithm is proposed, in this paper, which includes initial value estimation, a relaxation optimization and a global optimization. In the initial value estimation stage, particular emphasis is given to the repeated eigenvalues. Those systematic procedures were shown to be quite helpful in our practical studies. The principle used here can also be generalized into those similar situations easily.