Classification and Clustering Applications - An Invariant Approach to Statistical Analysis of Shapes - page 255

STEP 3: Apply the Hierarchical clustering method to draw
dendograms showing the affinities of various individuals. We
used the Splus 2000 (MathSoft, Inc., 2000) program to con-
duct this analysis. The Splus function used to draw these
dendograms is entitled 'hclust' and is described in Venables
and Ripley (1997, 390-391). We also applied the Principal
Coordinates Analysis described in Venables and Ripley (1997,
392) to study the clusters. The results are shown in Figures
6.1 and 6.2.
All methods used to form the dendograms identify the unicoronal
group as distinctly separate from the other four groups. All methods
also show large portions of the sagittal synostosis sample grouped
together, though not all members. All four dendrograms show two
rather large mixed groups made up of sagittal synosotosis, metopic
synostosis, and posterior plagiocephaly cases. The original diagnosis
for these disorders is made on the basis of calvarial shape (followed by
computed tomography scanning), but the data used for this cluster
analysis came from landmarks located on the cranial base; that part of
the skull that underlies the brain (see Figure 1.5a ). The reason that
the cranial base landmarks were able to successfully differentiate the
unicoronal cases is that it represents an asymmetric craniosynostosis;
i.e., only one side of the coronal suture is closed prematurely. The pre-
mature closure of one half of the coronal suture redirects vectors of
growth throughout the skull resulting in asymmetry of the cranial
base (DeLeon et al., 2000). Posterior plagiocephaly, on the other hand,
is a deformation that does not involve craniosynostosis and does not
result in growth patterns that affect the symmetry of the cranial base.
The other two categories, sagittal and metopic synostosis, involve cran-
iosynostosis but do not produce asymmetry of the cranial base.
Although each type of craniosynostosis results in a predictable cal-
varial shape (Richtsmeier et al., 1999; Zumpano et al., 1999; DeLeon et
al., 2001), in a previous study, we found that traditional landmarks
taken on the surface of the calvarium (the intersection of suture lines)
were not sufficient to differentiate sagittal synostosis patients from
unaffected individuals (Richtsmeier et al., 1998) nor to completely dif-
ferentiate the various types of symmetric craniosynostosis (Richtsmeier
et al., 1999). What was needed for discrimination were fuzzy land-
marks (see Chapter 2 ) that mark the location of bosses (bulges) on the
surface of various bones of the calvarium. These fuzzy landmarks,