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 multi-modal volume registration for diagnosis and radiotherapy applications.