The Study of Growth - An Invariant Approach to Statistical Analysis of Shapes - page 214

disease process and can be used in the planning of surgical or non-sur-
gical interventions in the case of human malformations (Dufresne and
Richtsmeier, 1995).
Studies of growth patterns can provide information about the
attainment of features in varying species. Increase in snout length in
mammalian species might be attained by growth changes local to the
maxillae and premaxillae or by changes in the relative positions and
sizes of the pterygoid plates, sphenoidal body or the vomer, as these
osseous components determine in part how the face is hafted onto the
cranial base. Careful growth analyses can provide information about
the timing of developmental events, or changes in magnitudes and
rates of growth. This can, in turn, be used to determine the ways in
which differences in local growth patterns contribute to difference in
morphological traits among species (Richtsmeier, Corner, et al., 1993).
The challenge in any analysis of growth is to go beyond quantitative
description; it is to use the study of growth to explore aspects of the
biology of the organism such as the genetic basis of morphogenesis,
phylogenetic underpinnings of developmental patterns, or the role of
hormones, teratogens, dietary elements, and other environmental vari-
ables on the growth process.
In previous chapters, we discussed in detail the problems relating
to registration and lack of a common coordinate system. These prob-
lems are equally important when the study concerns growth and the
comparison of growth patterns. To give an example, the field of
Roentgencephalometry (Broadbent, 1975) was developed to enable
quantitative comparison of x-rays. The method was developed to study
craniofacial form and growth. It became the method of choice for clini-
cal studies in the 1950s and 1960s and is still commonly used today
e.g., (Kreiborg and Pruzansky, 1981; Kreiborg, Aduss, et al., 1999).
Figure 5.1 contains a growth series of immature human skulls and
shows a fairly standard description of cranial growth based on data
from lateral x-rays. According to the method of roentgencephalometry,
the center of the pituitary fossa (the landmark sella) is the registration
point onto which all cases are superimposed. A line that stretches from
sella to the landmark nasion (the intersection of the frontal and nasal
bones) is used to define the line of orientation of all x-rays being com-
pared. Following this registration method, all cases are first matched
at sella and then rotated such that the orientation of the sella-nasion
lines match. This system of registration results in the description and
quantification of growth shown in Figure 5.1 . This system doesn't
allow for growth at sella and doesn't allow for non-linear growth