Motion compensation for PET image reconstruction using deformable tetrahedral meshes

Respiratory-induced organ motion is a technical challenge to PET imaging. This motion induces displacements and deformation of the organs tissues, which need to be taken into account when reconstructing the spatial radiation activity. Classical image-based methods that describe motion using deformable image registration (DIR) algorithms cannot fully take into account the non-reproducibility of the respiratory internal organ motion nor the tissue volume variations that occur during breathing. In order to overcome these limitations, various biomechanical models of the respiratory system have been developed in the past decade as an alternative to DIR approaches. In this paper, we describe a new method of correcting motion artefacts in PET image reconstruction adapted to motion estimation models such as those based on the finite element method. In contrast with the DIR-based approaches, the radiation activity was reconstructed on deforming tetrahedral meshes. For this, we have re-formulated the tomographic reconstruction problem by introducing a time-dependent system matrix based calculated using tetrahedral meshes instead of voxelized images. The MLEM algorithm was chosen as the reconstruction method. The simulations performed in this study show that the motion compensated reconstruction based on tetrahedral deformable meshes has the capability to correct motion artefacts. Results demonstrate that, in the case of complex deformations, when large volume variations occur, the developed tetrahedral based method is more appropriate than the classical DIR-based one. This method can be used, together with biomechanical models controlled by external surrogates, to correct motion artefacts in PET images and thus reducing the need for additional internal imaging during the acquisition.