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Medial techniques for automating finite element analysis

Finite element analysis provides a principled method for modeling physical deformation and is an ideal tool to apply when a medical imaging problem requires the simulation of tissue deformation. The drawback to using finite element analysis for imaging problems is the significant amount of labor and computational time that is often required to construct a finite element model and solve the resulting large system of equations. In particular, challenging questions include (1) how to generate a mesh from an image, (2) how to derive boundary conditions from images of deformed objects, and (3) how to solve the system of finite element equations as efficiently as possible. These problems make the finite element method prohibitively expensive for some applications and thus make it unlikely to be used in a clinical setting. 
The use of medial models called m-reps opens the door to techniques that provide solutions for these challenges. (1) A new meshing algorithm is presented that automatically generates a hexahedral mesh from an m-rep segmentation of an image. (2) M-rep segmentations of an object in different stages of deformation can be used to establish an approximate correspondence between points on the surfaces of the different object configurations. This is sufficient to initialize finite element displacement boundary conditions that enable the computation of a mapping between two shape configurations. (3) An m-rep based mesh subdivision algorithm is presented which together with a multi-grid solution algorithm to improves solution speed for the finite element system of equations. 
Taken together, these m-rep based algorithms allow the finite element method to be applied to non-rigid registration problems in an automatic and efficient way. 
The methods have been tested using CT images of a phantom pelvis. Deformation accuracy estimates were obtained by calculating the difference between (a) the observed locations of a constellation of brachytherapy seeds in an image of a deformed prostate and (b) the predicted seed locations that result from applying the finite element deformation to an image of the undeformed prostate. The average error was of the same order as the seed segmentation error that was due to image resolution.