A unified system identification approach to dynamic PET parametric imaging

Dynamic PET is becoming more popular and preferable in bioimaging community nowadays. It owns powerful capability of estimating physiological parameters with tracer kinetics modeling in a non-invasive manner. There are three main parts of this task: design of a priori identifiable tracer kinetic model, parameter estimation methods and parameter sensitivity analysis. In this paper, we proposed a unified approach to dynamic PET parametric imaging based on system identification theory to address the tasks mentioned above. The continuous compartmental physiological model is transformed into a discrete state-space model which can be converted into an autoregressive moving average model (ARMAX) by similarity transformation. Then the parameters of this ARMAX model can be estimated from the input-output dynamic PET data using prediction error method (PEM) with robust and computational efficient gradient based algorithm. The prior information of physiological system is then combined with parameters of ARMAX model to come up with a compact representation of polynomial equations whose solutions are the physiological parameters and the a priori identiflability of physiological system is identical to the uniqueness of the solutions. We use a 2-tissue compartmental model to demonstrate our method and test the parameter sensitivity using computer simulations. Our preliminary results show the effectiveness and validity of proposed framework for parameter estimation task. With the sensitivity analysis the critical parameters can also be discriminated.