We propose a patient-specific model based on partial differential equation to predict the evolution of lung tumors during radiotherapy. The evolution of tumor cell density is formulated by three terms: 1) advection describing the advective flux transport of tumor cells, 2) proliferation representing the tumor cell proliferation modeled as Gompertz differential equation, and 3) treatment quantifying the radiotherapeutic efficacy from linear quadratic formulation. We consider that tumor cell density variation can be derived from positron emission tomography images, the novel idea is to model the advection term by calculating 3D optical flow field from sequential images. To estimate patient-specific parameters, we propose an optimization between the predicted and observed images, under a global constraint that the tumor volume decreases exponentially as radiation dose increases. A thresholding on the predicted tumor cell densities is then used to define tumor contours, tumor volumes and maximum standardized uptake values (SUVmax). Results obtained on seven patients show a satisfying agreement between the predicted tumor contours and those drawn by an expert.