As a consequence of the random nature of photon emissions and detections, the data collected by a positron emission tomography (PET) imaging system can be shown to be Poisson distributed. Meanwhile, there have been considerable efforts within the tracer kinetic modeling communities aimed at establishing the relationship between the PET data and physiological parameters that affect the uptake and metabolism of the tracer. Both statistical and physiological models are important to PET reconstruction. The majority of previous efforts are based on simplified, nonphysical mathematical expression, such as Poisson modeling of the measured data, which is, on the whole, completed without consideration of the underlying physiology. In this paper, we proposed a graphics processing unit (GPU)-accelerated reconstruction strategy that can take both statistical model and physiological model into consideration with the aid of state-space evolution equations. The proposed strategy formulates the organ activity distribution through tracer kinetics models and the photon-counting measurements through observation equations, thus making it possible to unify these two constraints into a general framework. In order to accelerate reconstruction, GPU-based parallel computing is introduced. Experiments of Zubal-thorax-phantom data, Monte Carlo simulated phantom data, and real phantom data show the power of the method. Furthermore, thanks to the computing power of the GPU, the reconstruction time is practical for clinical application.