Surface geometric analysis of anatomic structures using biquintic finite element interpolation.

Area of Science:

• Biomechanics
• Medical Imaging
• Computational Geometry

Background:

• Surface geometry significantly influences the mechanical behavior of anatomic structures in both healthy and diseased states.
• Accurate quantification of three-dimensional (3D) in vivo surface geometry is crucial for mechanical analysis.
• Existing methods may struggle with unstructured data or quantifying complex deformations.

Purpose of the Study:

• To present a fully generalized surface fitting method for precise surface geometric analysis.
• To enable the computation of finite strain and curvature tensors over the entire surface.
• To demonstrate the method's applicability to biomedical problems involving complex surface deformations.

Main Methods:

• Utilized finite element-based Hermite biquintic polynomial interpolation functions for surface fitting.
• Generated a C2 continuous surface for accurate computation of strain and curvature tensors.
• Employed the Sobolev norm to stabilize interpolating polynomials in regions with sparse data or complex boundaries.

Main Results:

• The method accurately quantifies surface deformation from unstructured data points using a single interpolation scheme.
• Validation included computing principal curvatures for known phantoms and principal stretch/curvature changes for a deforming synthetic shape.
• Demonstrated successful application to an abdominal aortic aneurysm and a deforming bioprosthetic heart valve leaflet.

Conclusions:

• The developed surface fitting method accurately computes surface curvatures, strains, and curvature changes, even for surfaces undergoing large deformations.
• This technique offers a robust tool for quantitative surface geometric analysis in biomechanics and medical applications.
• The method's ability to handle unstructured data and provide C2 continuity enhances its utility for complex biological structures.