USE OF THE BOUNDARY-ELEMENT METHOD FOR BIOLOGICAL MORPHOMETRICS

Tensorial morphometric assessments of form difference can aid in the understanding of the cause of the form difference by providing reference frame independent, anisotropic, non-homogenous descriptions. The majority of biological and prosthetic structures cannot be adequately analyzed by current methods due to the paucity of anatomical landmarks and methodological requirements of subdivision through the domain. Internal subdivisions can be eliminated with the boundary element method (BEM). A non-landmark (NL) method can be developed by the combination of elliptical Fourier analysis (EFA) and BEM. The appropriateness of NL and BEM was investigated. The growth of the female rat neural skull from 7 to 14 postnatal days was calculated with respect to increase in area. Linear and quadratic BEM landmark analysis were made using 10 and 5 elements, respectively. Five hundred linear BEM elements were constructed from the EFA equations for NL. The form change tensors were obtained by the solution of the Laplace equation using boundary displacements as the essential boundary conditions. For comparison, simplex triangular finite element analysis (FEA), quadrilateral FEA and macroelement analysis were made on the same structure. Results correspond well to the two major growth process in this time period; (1) high cerebellar growth, and (2) relatively higher facial versus neural growth. The results in other regions are dose to the biologically observed 36% increase in area. The average difference between BEM, NL versus FEA is 1.9 and 2.8%. Trends in results with position are almost identical for BEM, NL, MEM and quadrilateral FEA. The morphometric landmark BEM technique requires an additional numerical scheme to eliminate the singularities near the boundary. NL may prove to be a morphometric tool capable of analyzing form change in structures which do not possess anatomical landmarks and had therefore previously eluded tensorial analysis.