Anatomical macroelements in the study of craniofacial rat growth

In order to avoid the arbitrary division of biological structures, rational polynomial interpolants are utilized to study growth. The major advantage of this method is the elimination of artificial internal element boundaries through anatomical structures. Since the boundary element methodology is employed in the finite element setting, other benefits, without additional computer coding, include the ability to use elements with any number of sides and reference frame invariance. Longitudinal landmark coordinates from midsagittal X-ray tracings of 22 albino female rat skulls of various ages were averaged. The skull was partitioned into three macroelements: a neural skull and two functionally distinct portions of the facial skull--olfactory and respiratory. The digital computer programming was carried out in the computer mathematics environment of Mathematica. Maximum elongation ratios were calculated for approximately 400 interior points. The elongation ratios in the neural skull compared well with previously documented growth behavior of internal brain structures. The calculated ratios from the facial skull were used to analyze the behavior of macroelement interpolation close to common anatomical boundaries.