This work is devoted to modeling gastrointestinal stromal tumor (GIST) metastases to the liver, their growth and resistance to therapies. More precisely, resistance to two standard treatments based ontyrosine kinase inhibitors (imatinib and sunitinib) is observed clinically. Using observations from medical images, we build a spatial model consisting in a set of nonlinear partial differential equations. After calibration of its parameters with clinical data, this model reproduces qualitatively and quantitatively the spatial tumor evolution of one specific patient. Important features of the growth such as the appearance of spatial heterogeneities and the therapeutical failures may be explained by our model. We then investigate numerically the possibility of optimizing the treatment in order to increase the progression free survival time and the minimum tumor size reachable by varying the dose of the first treatment. We find that according to our model, the progression free survival timereaches a plateau with respect to this dose. We also demonstrate numerically that the spatial structure of thetumor may provide much more insights on the cancer cell activities thanthe standard RECIST criteria, which only consists in the measurementof the tumor diameter.Read less <