Surface geometric analysis of anatomic structures using biquintic finite element interpolation

The surface geometry of anatomic structures can have a-direct impact upon t heir mechanical behavior in health and disease. Thus, mechanical analysis r equires the accurate quantification of three-dimensional in vivo surface ge ometry. We present a fully generalized surface fitting method for surface g eometric analysis that uses finite element based hermite biquintic polynomi al interpolation functions. The method generates a contiguous surface of C- 2 continuity, allowing computation of the finite strain and curvature tenso rs over the entire surface with respect to a single in-surface coordinate s ystem. The Sobolev norm, which restricts element length and curvature, was utilized to stabilize the interpolating polynomial at boundaries and in reg ions of sparse data. A major advantage of the current method is its ability to fully quantify surface deformation from an unstructured grid of data po ints using a single interpolation scheme. The method was validated by compu ting both the principal curvature distributions for phantoms of known curva tures and the principal stretch and principal change of curvature distribut ions for a synthetic spherical patch warping into an ellipsoidal shape. To demonstrate the applicability to biomedical problems, the method was applie d to quantify surface curvatures of an abdominal aortic aneurysm and the pr incipal strains and change of curvatures of a deforming bioprosthetic heart valve leaflet. The method proved accurate for the computation of surface c urvatures, as well as for strains and curvature change for a surface underg oing large deformations. (C) 2000 Biomedical Engineering Society. [sS0090-6 964(00)00806-7].