Nonrigid registration for tracking incompressible soft tissues with sliding motion

Purpose: Respiration causes the deformation and sliding motion of the soft tissues, and affects the accuracy of the assessment of minimally invasive abdominal surgery. Nonrigid registration is used to eliminate the effects of respiration for the assessment. Because the soft tissues with high water content are volume preserving during deformation, incompressibility has to be considered when tracking soft tissues for nonrigid registration. The purpose of the study was to develop an incompressible nonrigid registration for tracking deformable soft tissues with sliding motion. Methods: The nonrigid registration framework proposed in the present study includes two main steps: (a) The solution in the subspace of diffeomorphisms is searched and encoded to stationary velocity field in the log domain. (b) The divergence-free component and harmonic remainder are extracted by Fourier-based Helmholtz-Hodge decomposition (FHHD) and further integrated by an adaptive weight to simultaneously retain the incompressibility of deformation and compensate the sliding motion. The method was evaluated on 11 groups of synthetic datasets and five groups of clinical images. Registration accuracy is evaluated by using four quantitative measures, including mean surface distance (MSD), Hausdorff distance (HD), mean corresponding distance (MCD), and Dice similarity coefficient (DSC). Incompressibility is evaluated by using two quantitative measures, including relative volume change (RVC) and Jacobian determinant (J). Results: Compared with three state-of-the-art nonrigid registration methods, the proposed method shows an advantage in handling the incompressible deformation of images with large sliding motion. The lowest (MSD, 0.631 mm), (HD, 6.000 mm), and (MCD, 3.555 mm) and the highest (DSC, 0.970) are obtained proving the high registration accuracy with sliding motion compensation of the proposed method. The (RVC, 0.006) and Jacobian determinant (J, 1.008 ± 0.070) are nearly close to 0 and 1, respectively, showing the strong incompressibility of the proposed method. The proposed method improves registration accuracy in nearly all cases, which maintains the incompressibility of tissue transformation while simultaneously compensating the sliding motion on clinical datasets. Conclusions: The proposed method improves the registration accuracy of incompressible tissues when dealing with large sliding motion, and thus has the potential to improve current minimally invasive abdominal surgery.