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A new method deforms a 3D liver mesh in an arbitrary phase of respiration. During preprocessing, the method step defines a patient-specific deformation space using two polar shapes of the liver during respiration. 3D magnetic resonance imaging captures patient livers during exhaling and inhaling. Next, using a fully automated nonrigid mesh registration, this method creates the two phases' corresponding surface meshes. Then, it defines the respiration's deformation space by extracting deformation gradients between the exhalation and inhalation meshes. At runtime, the method uses sparse local features suitably obtained from 2D ultrasound imaging to solve the constraint optimization problem that minimizes dissimilarity of deformation gradients between the target deformation and the patient-specific deformation space. Researchers used real patient data to evaluate this method, which could be applicable to image-guided tumor ablations.