The estimation of energy and dose distribution patterns in respiratory-induced organ motion constitutes a significant challenge in hadron therapy treatment planning and dosimetry. Notably for lung cancer in which many difficulties arise, like tissue densities variation and the tumor position shifting during respiration. All these parameters affect the ranges of protons or ions used in treatment when passing through different tissues and can easily result in unexpected dose distribution. The present work consists of calculating the dose distributions of moving organs by means of Monte Carlo simulations and patient-specific modeling tools. The dose distributions are calculated using a time-dependent tetrahedral density map, describing the internal anatomy of the human body. Additionally, the internal motion can be described using either a biomechanical modeling based on Finite Element Analysis (FEA) or deformable image registration displacement map. Unlike methods based on the conventional voxel-based structures, the deposited energy is accumulated inside each tetrahedron during deformation, thus overcoming the problem of tissue tracking since that the tetrahedron is defined as a part of a tissue whose chemical composition and topology do not change. The first part of the Ph.D. project proposes a dose calculation method that generates a 4D dose map using a patient-specific tetrahedral model. Besides, we study the effect of the level of detail of tetrahedral meshes on the accuracy of the resulted dose distribution. In the second part, we focus on the optimization of the tetrahedral geometry to address the problem of time simulation, since obtaining a precise dose distribution can be very time-consuming. To overcome this issue, we've defined a new approach that takes into account the direction of the beam to minimize the error of the water equivalent thickness of the tetrahedrons before the tumor volume. This method allows for a coarsened tetrahedral mesh and as a result, improved computational performance in Monte Carlo simulations while guaranteeing a precise dose distribution in the target volume.