Predicting lung tumor evolution during radiotherapy from PET images using a patient specific model

We propose a patient-specific model based on PDE to predict the evolution of lung tumors during radiotherapy. The evolution of tumor cell densities is formulated by three terms: 1) advection describing the mobility, 2) reaction representing the proliferation modeled as Gompertz differential equation, and 3) treatment quanti tying the radiotherapeutic efficacy modeled as exponential function. As tumor cell density variation can be derived from PET 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 carry out an optimization between the predicted and observed images, under a volume-dose model constraint. Threshold method is then used to define tumor contours and maximum standardized uptake values, based on the predicted tumor cell densities. We present the results obtained in 8 patients, where the predicted tumor contours are compared to those drawn by an expert.