A computer graphics program for measuring two- and three-dimensional form change in developing craniofacial cartilages using finite element methods.

Allometric analysis of chondrocranial growth seeks to provide objective measures of morphogenetic form change during ontogeny of the primordial skull. Linear measures, typically employed to study differential growth, become problematic at the histological level since an external referencing system is impossible to achieve for microscopic anatomies in embryos. The purpose of this paper is to describe a computer graphics program which generates spatially invariant measures of two- and three-dimensional form change using finite element methods. Anatomical form change is viewed as a continuous deformation of an initial finite element representing an anatomical unit into a second configuration. The algorithm consists of isoparametric scaling of finite elements, strain matrix formulation, and size/shape variable derivation. The routine includes four segments serving to extract nodal data, generate the strain matrix relating the two morphologies as well as deriving corresponding size/shape variables, reference the major and minor axes of form change, and provide graphic display of the anatomical geometries. Applications are provided measuring two- and three-dimensional form change in the developing craniofacial cartilages of rats subjected to treatment with the known teratogen diazo-oxo-norleucine (DON). The finite element routine provides craniofacial form change variables which are expected in light of cellular alterations induced by DON administration. Finally, computational differences between this routine and similar approaches using finite element methods for analyzing biological form change are examined.