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Surface geometric analysis of anatomic structures using biquintic finite element interpolation
Annals of Biomedical Engineering, 28 (6): 598-611 (2000)
Аннотация
The surface geometry of anatomic structures can have a-direct impact
upon their mechanical behavior in health and disease. Thus, mechanical
analysis requires the accurate quantification of three-dimensional
in vivo surface geometry. We present a fully generalized surface
fitting method for surface geometric analysis that uses finite element
based hermite biquintic polynomial interpolation functions. The method
generates a contiguous surface of C-2 continuity, allowing computation
of the finite strain and curvature tensors over the entire surface
with respect to a single in-surface coordinate system. The Sobolev
norm, which restricts element length and curvature, was utilized
to stabilize the interpolating polynomial at boundaries and in regions
of sparse data. A major advantage of the current method is its ability
to fully quantify surface deformation from an unstructured grid of
data points using a single interpolation scheme. The method was validated
by computing both the principal curvature distributions for phantoms
of known curvatures and the principal stretch and principal change
of curvature distributions for a synthetic spherical patch warping
into an ellipsoidal shape. To demonstrate the applicability to biomedical
problems, the method was applied to quantify surface curvatures of
an abdominal aortic aneurysm and the principal strains and change
of curvatures of a deforming bioprosthetic heart valve leaflet. The
method proved accurate for the computation of surface curvatures,
as well as for strains and curvature change for a surface undergoing
large deformations. (C) 2000 Biomedical Engineering Society. sS0090-6964(00)00806-7
тэги
- abdominal
- aneurysm
- aortic
- bladder
- curvature
- deformation
- dog
- elements
- finite
- fitting
- free
- health
- heart
- length
- model
- shape
- surface
- system
- valves
- ventricular
- wall
