Effects of pre-weaning undernutrition on 21 day-old male rat skull form as described by the finite element method

Conventional Roentgenographic Cephalometric Methods (RCM) have certain conceptual and geometric constraints that ensure that their descriptions of cephalic growth and comparisons of cephalic form are reference-frame-dependent; and it is impossible to determine which, if any, RCM reference frame provides a biologically more correct description or comparison. The use of the concepts of continuum mechanics and of the numerical techniques of the Finite Element Method (FEM) overcomes these constraints and provides reference-frame-independent (invariant) growth descriptions and form comparisons. In the FEM, the structure of the head is subdivided (discretized) into a number of smaller, finite, elements. The FEM then describes the growth behavior, or compares the form, of the entire continuum of points enclosed with each element independently; in RCM only the behaviors, or comparisons, of the landmark points are described. The FEM is described and its use illustrated by a comparison of the cephalic forms of 4 groups of weanling (21 d old) rats. The 1st (control) group is derived from normally nourished dams, while the other 3 groups are derived from dams who were malnourished throughout the weaning period in 3 group specific manners. The FEM permitted reference-frame-independent comparisons of the 4 different, and group specific, head forms. These differences were reflected in the forms of each of the finite elements. The differences in element forms between the 4 groups were shown to be related primarily to nutritionally produced alterations of either neurocranial or splanchocranial viscera. These differences were expressed in the alterations of the forms of the continua enclosed within the boundaries of the several finite elements, and secondarily in the form of the cranial skeleton.