||The advancement of Positron Emission Tomography led the biomedical imaging into the time of functional images at molecular level. This powerful technology has provided in vivo information for physiological process which has significant research and clinical values in oncology, neurology and other disciplines. Combined with compartmental modeling techniques, time-resolved dynamic PET imaging has the capability of quantifying tracer kinetics which is important in describing drug-tissue interactions. Based on this technology, in vivo activities of small molecules could be understood and drug development could be greatly facilitated. The use of compartmental modeling in dynamic PET data has been studied for a long time, yet is still a challenging problem. The major target is to identify the parameters of physiological models based on the input and output PET data. In this process the identifiability problem arises. The model has to have a unique solution corresponding to the data set. Otherwise, it is not physiologically plausible. We propose a unified system identification approach to tackle this problem and the identifiability test. By establishing the equivalence of differential equation and statistical model, we can perform parameter estimations of the compartmental models and identifiability test simultaneously. PET also plays a unique role in brain neurotransmitter imaging. Compared to the time-invariant compartments in most tracer kinetic modeling, the neurotransmitter model is often described as time-varying compartmental model. The time-varying nature of this model makes it difficult to identify compared to linear compartmental models. We propose a nonlinear system identification approach to partly quantify this model and one of the most important parameters could be identified using our method. In this approach, nonlinear kernel of input-output data is extracted to label the physiological meaningful parameters, which is essential in identifying chemicals associated with diseases.