Modeling of Personalized Anatomy using Plastic Strains

We give a method for modeling solid objects undergoing large spatially varying and/or anisotropic strains, and use it to reconstruct human anatomy from medical images. Our novel shape deformation method uses plastic strains and the Finite Element Method to successfully model shapes undergoing large and/or anisotropic strains, specified by sparse point constraints on the boundary of the object. We extensively compare our method to standard second-order shape deformation methods, variational methods and surface-based methods and demonstrate that our method avoids the spikiness, wiggliness and other artefacts of previous methods. We demonstrate how to perform such shape deformation both for attached and un-attached ("free flying") objects, using a novel method to solve linear systems with singular matrices with a known nullspace. While our method is applicable to general large-strain shape deformation modeling, we use it to create personalized 3D triangle and volumetric meshes of human organs, based on MRI or CT scans. Given a medically accurate anatomy template of a generic individual, we optimize the geometry of the organ to match the MRI or CT scan of a specific individual. Our examples include human hand muscles, a liver, a hip bone, and a gluteus medius muscle ("hip abductor").