Hadron therapy is an advanced radiotherapy technique for cancer treatment. It offers a better irradiation ballistic than conventional techniques and requires an appropriate quality assurance procedures. Tumor motion during irradiation reduces target coverage and increases dose to healthy tissues. Unfortunately, the continuous organ density changes due to respiratory motion and affect the ranges of ions which can lead to unwanted dose distributions in the case of lung tumors. Accurate 4D dosimetry calculations are important for treatment planning verification and evaluation. They require temporal information about the tumor position, size and shape, as well as information regarding the tissue density variation along the beam path during treatment. For more precision, several studies have focused on the biomechanical models of the respiratory system based on finite element method. These approaches are based on continuum mechanics of materials properties, mesh organ geometry, as well as anatomical boundary conditions. However, so far, they do not take completely into account density variations needed for dose calculations. In this context, Velec et al. have developed a model that incorporates rigid body motion and deformation (RBD) in order to study the impact of respiratory-induced organ motion on dose calculation for liver tumors. They use linear interpolation to modulate the dose distribution previously calculated from exhale position to inhale position in each tetrahedral element for these intermediate breathing states.