In the context of thoracic CT-PET volume registration, we present a novel method to incorporate a breathing model in a non-linear registration procedure, guaranteeing physiologically plausible deformations. The approach also accounts for the rigid motions of lung tumors during breathing. We performed a set of registration experiments on one healthy and four pathological data sets. Initial results demonstrate the interest of this method to significantly improve the accuracy of multimodal volume registration for diagnosis and radiotherapy applications.