A method for biomedical system modelling and physiological parameter estimation using indirectly measured input functions

Abstract

Tracer kinetic modelling with positron emission tomography (PET) requires measurements of the time-activity curves in both plasma (PTAC) and tissue (TTAC) to estimate physiological parameters, i.e. to fit the parameters of certain compartmental models using PTAC and TTAC as local tissue model input and output functions respectively. Ideally, this PTAC should be the local tracer capillary plasma time-activity curve (CPTAC). However, due to the inaccessibility of direct measurement of CPTAC from the capillary blood vessel, the tracer arterial plasma time-activity curve (APTAC) is normally used to replace CPTAC as PTAC. The physiological parameter estimation error caused by this replacement is not yet clear. In this paper, a PTAC model based on [18F] 2-fluoro-2-deoxy-D-glucose (FDG) experimental data is employed, in which CPTAC is the observable state variable. Therefore, the CPTAC time function can be constructed from the measured APTAC. This CPTAC is then used as the local input of a five-parameter FDG model, to study the effects of the replacement and APTAC measurement errors on the estimation of the FDG model's impulse response function parameters (macro-parameters), the rate constants (microparameters) and the physiological parameter-local cerebral metabolic rate of glucose (LCMRGlc). The results show that using APTAC directly in parameter estimation can cause considerable biases and increase the uncertainty of parameter estimation. The technique used in this paper to construct a tracer capillary plasma time-activity curve from the measured noisy arterial time-activity curve provides a general approach to measure the inaccessible true input function indirectly in biomedical systems and, therefore, to improve the physiological parameter estimation reliability