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Comparative study of normal Crouzon and Apert craniofacial morphology using finite element scaling analysis.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 74~473-493(1987)
Comparative Study of Normal, Crouzon, and Apert Craniofacial
Morphology Using Finite Element Scaling Analysis
JOAN T.RICHTSMEIER
Department of Cell Biology and Anatomy, The Johns Hopkins University
School of Medicine, Baltimore, Maryland 21205
KEY WORDS
Apert syndrome, Crouzon syndrome, Shape, Size
ABSTRACT
Finite element scaling analysis is used to study differences in
morphology between the craniofacial complex of normal individuals and those
affected with the syndromes of Apert and Crouzon. Finite element scaling
quantifies the differences in shape and size between forms without reference
to any fixed, arbitrary registration point or orientation line and measures the
amount of form change required to deform one object into another. Twodimensional coordinates of landmarks digitized from annual sets of cephalometric radiographs were used in the analysis. A simple tabulation shows no
difference in variances between the normal and pathological samples. A test
of mean differences depicts the Apert and Crouzon morphologies as significantly different from normal. The Apert palate differs from normal in shape in
the older age groups analyzed, and palatal size differences are most common
at the posterior nasal spine. The Apert pituitary fossa and basi-occiput are
significantly larger than normal. The Crouzon pituitary fossa is also larger
than normal, but the difference is not always significant. The typical morphology of the Crouzon nose is due more to differences in shape than size. The
Crouzon basi-occiput is significantly smaller than normal. An age association
of the differences between the normal and pathological craniofacies was found
in Apert syndrome but not in Crouzon syndrome. Apert syndrome is characterized by a more homogeneous pattern of craniofacial dysmorphology from 6
months to 18 years of age than Crouzon syndrome.
There are 64 genetic syndromes involving
craniosynostosis (Cohen, 1986).Of these, nine
are reasonably common (David et al., 1982).
This study is concerned with the craniofacial
form of two of the more common of theseApert and Crouzon syndromes,
Premature craniosynostosis (see Cohen,
1986) is a component of both syndromes. In
Apert syndrome the coronal suture is most
commonly involved. In Crouzon disease, the
coronal, lambdoid, and/or sagittal sutures
may fuse prematurely. Irregularity of the
patterns of craniosynostosis is common in
both syndromes. In addition, the craniofacies
of Crouzon and Apert individuals are marked
by shallow orbits, hypertelorism, and maxillary hypoplasia. Other facial abnormalities
also occur in both syndromes, and variability
in expression of the facial phenotype is common. Patients with Apert syndrome resem-
0 1987 ALAN R.LISS, INC
ble those with Crouzon syndrome in facial
appearance, but Apert syndrome also involves osseous or cutaneous syndactyly of the
hands and feet. A complete description of
Crouzon and Apert craniofacial and bony
morphology, with a comprehensive bibliography, is presented by Kreiborg (1981, 1986).
Morphometric studies of these syndromes
routinely use cephalometric radiographs. A
cephalometric radiograph (roentgenogram) is
a n X-ray produced under controlled conditions which allow for correction of distortion
and enlargement which occur during exposure of the film by a n X-ray beam (see Thurow, 1951; Broadbent et al., 1975; Firmin et
al., 1974;Nanda, 1956;Pruzansky, 1976).The
use of roentgenographic cephalometry (RCM)
Received April 25, 1986; accepted December 22,1986.
474
J.T. RICHTSMEIER
\
b
~ _ _ A_p e r t
~ M o r r n a l
Fig. 1. Superimposition of a radiographic tracing of
a n Apert individual on that of a normal individual using
differing lines of orientation. Comparison A is registered
on sella and oriented on the sella-nasion line. All points
on the Apert palate appear superiorly and posteriorly
placed in relation to the normal palate. Basion is rotated
superiorly and posteriorly in the Apert case, while the
entire Apert occiput appears somewhat smaller and superiorly displaced. Comparison B is registered on sella
but oriented on the sella-basion line. Here, the entire
Apert face is rotated superiorly, but the Apert palate is
not as posteriorly placed as in comparison A. The dissimilarity between the normal and Apert posterior cranial
base appears as a size difference. The occipital region of
the normal and Apert cases are similar in shape in
comparison B, the Apert case appearing slightly smaller
than normal (Richtsmeier and Cheverud, 1986).
is widespread in the evaluation and management of patients for orthodontics, as well as
craniofacial and orthognathic surgery. RCM
is routinely used to quantitatively document
the growth of an individual, assess morphological differences in relation to a chosen
norm, and to evaluate postoperative change.
The greatest advantage of RCM is the ease
in which it can be performed.
The goal of any RCM study is to summarize the differences between two radiographic films, or groups of films, in terms of
the direction and degree of differences at specific loci. Morphological comparisons are
made by matching films according to a single
landmark (registration point) and overlying
them on a line (orientation) which stretches
between the registration point and another
landmark. Sella, the midpoint of the pituitary fossa determined by inspection, is most
often used as the registration point, and films
are commonly oriented on the sella-nasion
line. This convention was adopted in the
1950s on the assumption that growth in the
registration-orientation region is functionally unrelated to changes in the orthodontically relevant maxillary and mandibular
regions (the RCM method does not allow for
change local to the registration point) and on
the assumption that the relationship between sella and nasion during growth can be
accurately depicted by a straight line which
changes only in length (does not bend)
throughout ontogeny (Bjork, 1955; Moyers
and Bookstein, 1979). These assumptions
have been critiqued (Moyers and Bookstein,
1979; Bookstein, 1983; Moss, 1982, 1984;
Richtsmeier and Cheverud, 1986). The most
obvious problem with RCM is that the results of comparison of films is totally dependent upon the registration system used.
It is critical to understand that this problem is not one concerning sella-nasion registration specifically, or the choice of landmarks on which to register. It is a problem
intrinsic to any registration system, RCM
being a specialized case of linear measurement (see Cheverud and Richtsmeier, 1986).
Consider, for example, the comparison of two
crania diagrammed in Figure 1. The same
crania are used in the comparisons, but relative movement of structure changes according to the line of orientation used, and no
differences are recorded local to the registration point (sella). If instead of manipulating
the line of orientation, another point was
selected for registration, variation would occur at sella, and yet another trajectory for
each point would be produced. Since the two
registration systems illustrated yield varying observations of morphological differences
(see caption, Fig. l), any measurements taken
47 5
CROUZON AND APERT CRANIOFACIAL MORPHOLOGY
are observer inherent (Cheverud et al., 1983),
meaning that they are dependent upon the
form of registration and not necessarily on
the biological forms being analyzed (Bookstein, 1978; Moyers and Bookstein, 1979; see
also Krogman and Sassouni, 1957).This simple example demonstrates a need for the application of registration-free methods to
problems in craniofacial morphology.
The finite element scaling (FES) method,
based on a composite of principles developed
in finite element analysis and continuum
mechanics, has recently been applied to the
study of variation in biological forms (Niklas,
1977;Lew and Lewis, 1977;Lewis et al., 1980;
Cheverud et al., 1983; Patel, 1983; Moss et
al., 1985, 1987; Richtsmeier, 1985, 1987;
Cheverud and Richtsmeier, 1986; Richtsmeier and Cheverud, 1986;Lozanoff and Diewart, 1986). By using this registration-free
method, observer invariant quantities are
obtained which measure localized morphological change without reference to any fixed,
arbitrary center.
Application of FES to biologic phenomena
requires some modification from the original
design and purpose of the method. In the
engineering environment, specifically quantified forces are applied to a form composed
of known material properties. The purpose is
to predict the deformation of an initial form
after the application of force. In this application, the morphologies of the initial and target forms are known. Measurement of the
form change required to transform one form
into the other is the goal. No force is applied
and the various material properties of the
elements which combine to form a biological
entity are not considered. Further, the
method assumes a constancy of the material
of which a form is composed.
The purpose of this study is to evaluate the
differences in craniofacial morphology between three samples of cephalometric roentgenograms by using FES methods. Morphological comparisons will be made between
normal individuals and those affected with
two craniofacial syndromes: Apert and Crouzon syndromes. Results are presented in
terms of age-specific localized differences in
form.
THE FES METHOD
Theoretical and mathematically sophisticated explanations of the foundations of the
FES method can be found in Malvern (1969),
Bathe and Wilson (1976), and Mase (1970).
Explanation of the method and its application to the study of biologic form are presented by Lew and Lewis (1977),Lewis et al.
(1980), Cheverud et al. (1983), Patel (1983),
Skalak et al. (19821, Moss et al. (1985, 19871,
Richtsmeier (1985), Cheverud and Richtsmeier (1986), and Richtsmeier and Cheverud
(1986). Bookstein’s method of biorthogonal
grids (1983, 1984a,b; Lavelle, 1985; Grayson
et al., 1985) is a depiction of landmark
changes by way of a single, global finite element. The methods used in this study (Bachrach, 1981; Bachrach and Hanmer, 1984)
were introduced by Lew and Lewis (1977)
and Lewis et al. (1980). The methods were
developed to analyze form change in three
dimensions but can be adapted to two-dimensional space (see Richtsmeier, 1985).
The FES method is registration-free. This
means that the difference between forms is
measured independent of any specific coordinate system and is not expressed as the
movement of landmarks from or toward a
chosen center. Instead, morphological differences are measured local to each landmark
in terms of the direction and degree of form
change of material surrounding that landmark. The morphological differences between forms are calculated such that no
correction is required to compare morphological differences at various landmarks, or differences between varying sets of comparisons
(Lewis et al., 1980).
In FES analysis, an initial or reference
form is compared to a second, target, form.
What is measured is the difference between
the two forms, or the morphological change
required to deform the reference into the target form. The deformation is calculated eleAForm
=
ASize
t
AShape
Fig. 2. Geometric representation of change in form
and its components change in size and change in shape
as calculated by finite element scaling analysis. Circle
to left of arrow represents reference form before deformation into target form and sphere to the right of arrow
is the deformed area. PI and P2 are the principal axes
of strain of the deformation. Lines are dashed for size
tensor because strain is equal in all directions (redrawn
from Richtsmeier and Cheverud, 1986).
476
J.T. RICHTSMEIER
TABLE 1. Abbreviation and description of landmarks used
as nodal points in analysis.
Nodal
point
number
Landmark
abbreviation
NAS
NSL
ANS
IDS
IGW
6
7
PNS
CP1
8
9
TBS
SEF
10
CP2
11
12
13
14
15
PSL
CP3
BAS
CRU
CP4
Landmark location and description
nasion
nasale
anterior nasal spine
intradentale superior
intersection of the greater wings of the
sphenoid with planum sphenoidale and/or the
cribriform plate.
posterior nasal spine
constructed point 1. CP1 is constructed by
drawing a line in a n inferior direction from
PNS forming a 90 degree angle with the
ANS-PNS line, and a line in a posterior
direction from IDS parallel to the line
stretching from ANS to PNS. The lines meet
at CP1.
tuberculum sella
sella floor. Most inflexive point of sella turcica.
Sella turcica is defined as that area along the
pituitary fossa bounded by TBS and PSL.
Constructed point 2. CP2 and CP3 are
constructed by drawing a line to connect SEL
and BAS. At the midpoint of this line, a
perpendicular is drawn. This constructed line
approximates the spheno-occipital
synchondrosis. The point at which this line
intersects with the external surface of the
body of the sphenoid and/or the external
surface of the basal portion of the occipital
bone is defined as CP2. The point at which
this line intersects the intra-cranial surface
of the basal portion of the occipital bone is
defined as CP3.
posterior sella
constructed point 3. See description of CP2.
basion
cruciate eminence
constructed ooint 4. CP4 is constructed bv
drawing a i i n e which connects BAS and CRU.
This line is then bisected by a perpendicular.
The point at which this perpendicular meets
with the exterior surface of the squamous
portion of the occipital bone is CP4.
ment by element. Form change occurring
local to each landmark is expressed as a form
tensor (known as the Lagrangian strain tensor in continuum mechanics). The form tensor is a symmetric matrix, the number of
rows (columns) being equal to the number of
dimensions analyzed.
The form tensor contains all information
about morphological change occurring local
to each landmark considered. It can be split
into two component tensors-the size tensor
and the shape tensor (Fig. 2). These measures of size and shape change are mutually
independent. In geometric terms, the size
tensor measures size change as the relative
change of the radius of an infinitely small
circle centered on the landmark of interest.
The circle represents the material occupying
the space surrounding the landmark and the
size tensor measures radia change required
to deform the initial into the target form. The
shape tensor measures shape change as the
degree to which the circle described in the
reference object is deformed into an ellipse
due to change in angle between any two line
segments through the landmark of interest
(Cheverud et al., 1983).
The form tensor can be subjected to a spectral decomposition in order to derive the
principle values (eigenvalues) and directions
(eigenvectors) of strain local to each landmark point. The principal directions are mutually orthogonal vectors containing the
directional cosines relating the principal directions to the coordinate system of the reference form. A principal value is associated
477
CROUZON AND APERT CRANIOFACIAL MORPHOLOGY
15
Fig. 3. Human craniofacial complex divided into elements used in two-dimensional finite element analysis.
Definition and boundary trace of each element follow:
element 1-upper face: nodes, 1, 5, 10, 2; element 2nasomaxillary area: nodes 2, 10,6,3; element 3-palate:
nodes, 3, 6, 7, 4; element 4-anterior portion of anterior
cranial base: nodes 5, 8, 9, 10; element 5-posterior portion of anterior cranial base; element 6-basal and squamous portion of occiput: nodes 10,14, 15, 13.
with each direction-one representing the direction of maximal strain, the other the direction of minimal strain of the deformation.
For our purposes, strain simply measures the
difference in form between two objects and is
not considered as a condition which results
from the application of an external force, as
it is normally defined. When depicted graphically, the principal directions and values
provide a visual representation of the form
change required to deform the initial into the
target form (see Figs. 4, 5). This representation of form change as orthogonal tensors
with associated values is central to Bookstein’s method of biorthogonal grids (Bookstein, 1978, 1984a,b). The similarity allows
application of statistical methods for the
analysis of tensors developed by Bookstein
(1984a,b) to be directly applied to those produced by two-dimensional FES analysis.
TABLE 2. Number of individuals in each of the three
samples used in analysis organized by age group
Age in
years
f .5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Totals
Normal
12
14
16
19
20
20
19
20
20
20
20
17
20
19
18
20
15
17
13
339
ADert
Crouzon
5
2
3
4
3
5
5
3
3
2
4
4
4
3
2
5
6
3
4
5
1
71
4
3
4
4
3
4
4
3
5
3
4
5
2
3
1
1
2
60
DATA
The data analyzed consist of two-dimensional coordinates of landmarks from cephalometric radiographs. The landmarks used in
analysis are defined in Table 1. The number
of landmarks which can be accurately located on a lateral radiograph is limited. In
order to increase the number, points were
constructed by using the available biological
landmarks. Although these constructed
points are not as meaningful as true biological loci, they were included to increase the
number of finite elements. Finer resolution
available from CT scans and magnetic resonance imaging will increase the number of
usable landmarks for future studies.
Each cephalomatic radiograph of the pathological individuals was traced a minimum
of two times and compared. Cases were excluded from analysis when the independent
tracings did not agree, or when the film quality was poor. The author’s tracings were also
compared to those done previously by Center
for Craniofacial Anomalies, U. IL,Chicago
478
J.T. RICHTSMEIER
(CCFA), personnel. Details of tracing and cepted as representative of the two
digitization procedures can be found in syndromes.
Richtsmeier (1985).
METHODS OF ANALYSIS
The finite element scaling method analyzes form change according to elements
To quantify morphological differences bedesigned to approximate biologically mean- tween two forms by using the FES method, a
ingful regions of the total form under study. reference object is deformed into a target
The six quadralateral finite elements used in form. Bookstein's (1984a,b)development of a
this two-dimensional analysis of craniofacial mean tensor algorithm suggested the orgamorphology are presented in Figure 3.
nization of the deformations and allowed staHomologous landmarks digitized from tistical analysis of the tensors produced.
three samples of serial cephalometric radio- Identical analyses are performed to compare
graphs are used in analysis (Table 2). All normal with Crouzon and normal with Apert
individuals analyzed are male. Although the craniofacies.
data are longitudinal, they are grouped ac- Initially a mean form is calculated from
cording to age and examined using a cross- landmark coordinate data for each age group
sectional design. The data are examined lon- within each sample: normal, Crouzon, and
gitudinally in alternate studies (Richtsmeier, Apert. One by one, within each age class, the
1985,1987;Richtsmeier and Cheverud, 1986). age-specific standard (normal mean) is deReaders interested in the composition of the formed into each of the normal individuals
three samples by individual and age group which combine to make the mean. The result
are referred to Richtsmeier (1985).
is a sample of normal deformations for each
The normal sample consists of lateral ra- age group. Next, the normal mean is dediographs of 20 individuals from the records formed into each available pathological case.
of the Bolton-Brush Growth Study Center, Three samples of deformations for each age
Case Western Reserve University (Broad- class are ultimately produced: normal, Apert,
bent et al., 1975) (Table 2). Age classes are and Crouzon.
organized in yearly intervals ranging from To evaluate the morphological difference
less than 6 months to 18 years of age. Each between the normal and pathological forms,
age class spans a 12-month period from 6 the age-specific samples of form strain tenmonths before to 6 months after the birth- sors produced by individual deformations are
date. Since the aim of the Bolton study was statistically analyzed. Sample size is equal
to collect age-specific growth data, the date to the number of cases available for that
of the annual radiographs closely approxi- particular age class (see Table 2). The author
mates the individual's actual birthdate.
regrets the small size of the pathological
The samples representing the syndromes samples; however, size reflects the rarity of
of Aped (N = 14 individuals) and Crouzon unoperated cases of Crouzon and Apert syn(N=23 individuals) come from the data bank drome. Samples of this size are not foreign to
of the CCFA. Some of the patients underwent physical anthropology, but should be noted
early suture release, but none experienced when evaluating the results of this study.
any sort of facial repair. Because CCFA is a
Normal strain (increase or decrease in a
clinic, and patients are recalled on the basis line segment) is expressed by the diagonal
of medical need, the serial records of the elements of the form strain tensor. Shear
Apert and Crouzon cases (Table 2) are not as strain describes the change in angle of any
complete or chronologically regular as their two line segments originally at 90" to one
normal counterpart.
another and is expressed in the off-diagonal
Since the pathological samples are patient elements of the form strain tensor. In this
populations and both syndromes encompass study, the magnitudes of sue and shape difa spectrum of phenotypic severity, it is rea- ferences are defined by using the normal
sonable to assume that the patients analyzed strain values of the form strain tensor:
represent the more severe end of the spectrum, i.e., those whose deformity was severe
size = del + dea
(1)
enough to warrant a clinic visit. In addition,
individuals included in the earliest age
size = del - dea
(2)
groups and those seen repeatedly are probably more severely affected than those seen
late in life or infrequently. No attempt was where del and dea are the first and second
made to control for these possible ascertain- diagonal elements of the form strain tensor,
ment biases. The patient samples are ac- respectively. The statistical analysis of these
479
CROUZON AND APERT CRANIOFACIAL MORPHOLOGY
tensors was designed to legitimize the use of transformed form strain tensors el and e2,
normal strain exclusive of shear strain.
respectively. To test for significance, the .05
Before statistical tests for significant dif- probability level is read from any standard
ferences between tensors can be performed, table of t-values and multiplied by a scaling
tensor components of individual systems factor, a 1 2 = -71, used as the rough convermust be expressed in the same coordinate sion from the sum of the standard errors of
space (Bookstein, 1984a,b).This requires the the two variables presumed independent to
choice of a single deformation to be used as the standard error of their sum (Bookstein,
the standard coordinate system. Given the 1984a:500). The newly computed probability
definition of change in shape and change in value is compared to tsize to determine
size (equations 1 and 2), the goal is to choose whether or not the samples are significantly
a coordinate system which eliminates as different in size local to the landmark in
much shear strain as possible in each indi- question.
vidual deformation given the constraint of
The test for significant differences in mean
shape between the samples takes the form
comparability.
For each age-specific set of deformations,
the individual form strain tensors were rotated to a coordinate system describing the
tshape = (el - e2)lsedl + sedd
(4)
urinciual directions of the deformation from
ihe ndrmal mean into the age-matched pathological mean. (See Richtsmeier, 1985,for details of the tensor transformation.)There is The ratio, tshape,is evaluated in a manner
no shear strain in the coordinate system de- similar to that outlined for tsize;however the
fined by the Principal directions. When rough conversion factor is e ual to the square
transformed, all form strain tensors t o be root of pi divided by two ( ~ / =
2 .go) (Bookcompared are expressed in the same coordi- stein,1 9 ~ 4 ~ ) .
Beyond the tests for differences in means,
nate system, shear strain is eliminated to the
best Of my
given the constraint Of the numerator of tsizeand tshaper representcomparability, and measures of size and ing the transformed magnitudes of intersamshape differences (equations 1 and 2) can be ple differences in size and shape, are used to
manipulated by using standard statistical study form difference patterns. For any set of
procedures.
deformations, the magnitudes of intersample
To test for differences in means of two-di- differences in shape and
can be comemensional tensors, the procedures outlined lated with age. This
measures the
by Bookstein (1984a)were followed. Readers age association of intersample shape and size
interested in the explanation and verifica- differences local to each landmark. m i l e the
tion of a statistical methodologywhich avoids sign of the size difference magnitude signipotential biases introduced in the selection fies whether the target form is bigger or
of axes of Principal strain based on magni- smaller than the reference form, shape
tude are referred directly to Bookstein change magnitudes are expressed as abso(1984a,b).
lute values. The correlation analyses of ageFor each age-specific comparison, a mean related changes are limited to the study of
is computed for each of the diagonal terms of the magnitude of shape and
change, igthe rotated form strain tensors. The values noringthe geometricdirection of the change.
were tested for significant differencesin Sam- ~ ~ ~ patterns
- ~ of~ size
~ and~shape
i diff i
Ple variances and means by using standard ferences between the normal and patholog$F- and t-test procedures. Since these tests are cal samples are
by using
biased, (see Bookstein, 1984a), the results of correlations of localized shape and size differthese analyses are merely summarized here. ence magnitudes between the age groups.
(See aPPendicesA,B,E, and F in Richtsmeier, Within each sample form difference magni1985,for details.)
tudes for all landmarks of a certain age group
The unbiased test for differencesin mean are correlated with those calculated for every
size between the normal and Pathological other age group. A significant positive corresamples is
lation indicates that the overall pattern of
(3) intersample differences are similar for the
tsize= (el + e2)/sedl + sed2)
age groups considered, while a negative corwhere sedl and sed2 are the standard errors relation indicates that the pathology takes
of the mean of the diagonal elements of the on contrasting patterns at varying ages.
?-
~
-.lo2
-.040
-.128*
-.057
-.237*
- .293*
-.354*
-.294*
-.316*
-.331*
-.296*
- ,310
-.219*
- ,095
-.461*
-.090
-.413*
-.348*
-.371*
-.255*
-.297*
-.357*
-.499
.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18 +++
IDS
-.217*
-.036
-.223*
-.211*
-.171*
-.077
-.189*
-.271*
-.196*
-.070
-.038
,128
-.016
.044
-.055
-.008
,081
-.077
,137
ANS
-.181
,029
-.116
-.123*
- .092
.006
-.089*
-.235*
-.162*
- ,093
-.063
.029
m.080
-.042
-.096*
-.179*
-.091
-.166*
-.001
,027
,096
-.016
.269
,060
,118
.289
.555*
.042
,117
.361*
,099
,210
,264
.192
,040
,077
,094
524
IGW
,077
-.020
.014
-.081
-.048
,032
-.116
.091
-.050
-.211*
-.080
-.217*
-.216*
-.174*
- .087
- .204*
-.278*
-.203*
-.113
- .263*
-.035
- .239*
- .243*
-.238*
-.155*
-.244*
-.366*
-.284*
-.216*
-.169*
-.074
-.152*
-.158*
-.216*
-.223*
-.I13
-.248*
-.079
CP1
PNS
I*’
SEF
,546
,350
,337
,387
,087
.051
,238
.499*
.487*
.513*
.298*
.510*
,713
1.010*
1.520* 1.603
.627* 1.140*
.969* 2.143*
1.749* 4.761*
1.223* 3.406*
2.713
1.355
1.664* 3.291*
1.194* 2.091*
2.555*
,737
1.286* 4.695*
1.208* 3.213*
2.200
7.109
TBS
are marked with an
-.094
-.078
-.053
.039
-.022
-.001
,035
,011
-.052
-.133*
-.063
-.lo6
-.127*
-.098
-.096
-.145*
-.141*
-.128*
-.009
CP2
-.114
,160
.233
.123
.181
,074
.599*
.529*
,146
,189
,524
.545*
.084
,557
,356
,127
,245
,238
1.393
PSL
-.288*
-.034
-.157
-.079
-.160*
-.063
-.148
-.172*
-.195*
-.353*
-.366*
-.319*
-.338*
-.319*
-.295*
-.392*
-.361*
-.354*
-.218
CP3
.593*
.658*
.363*
.541*
.779*
,524
.739*
,315
.439*
206
,258
.284*
-.006
,221
.228
-.012
,485
.242
.068
BAS
CP4
,042
,108
.338* .431*
.141* .188*
.216* .336*
.146* .213*
,126
.181*
.193* .289*
.165* .279*
.153* ,254
.114*
_ ~.270
- ..
.327* .614*
,119
,249
.287* .605*
.168* .358*
.202* .400*
.092
,249
.167
.365*
.328* .618*
.204
.376
CRU
+ e d between the normal and Apert samples. Magnitudes with corresponding significant tSizevalues (p=.05)
+ t +Apert sample size for age 18 is equal to 1 precluding a test for significant differences in sample means
-.234
-.223*
-.232*
-.187*
-.274*
-.273*
-.292
-.085
- ,048
-.066
-.158*
- .098*
-.073
-.210*
-.080
NSL
NAS
Age in
years
TABLE 3. Magnitude of the size differences (el
,072
.122*
,012
,066
,076
,126
.110*
.107*
,071
,156
.189*
,174"
.224*
.192*
,173"
.192*
.217*
.191*
,183
ANS
,191
,164
,225
,129
,294
,041
,007
,040
,138
,109
,057
,266
,050
,135
,149
.168
,244
,232
.225*
~~
-043
.163*
.077*
,061
,079
,148"
,131
,072
,051
.327*
,302"
.427*
.383*
.408*
.303*
.395*
.485*
.344*
,449
..
IGW
IDS
,108
.076*
,038
,129
,076
,084
.135*
,148
,059
,151
,088"
,227"
,010
.119*
.105*
,099
,048
.135*
.139*
PNS
,021
,037
.216*
.230*
.276*
,343"
.317*
.226*
.347*
.401*
,275"
,321
,016
.049
,032
.067
,028
,023
,089
CP1
~~
304
,191
,293
.323
,024
,218
.503
,557
,068
,122
,768
,781"
,481
,812
,418
,168
,606
,553
1.342
TBS
,608
,395
,105
.429*
.815*
.758*
1.018
1.990
1.424*
2.680*
5.409*
3.954*
3.419
3.795"
2.568*
2.992"
5.261*
3.702*
7.711
SEF
(p=.05) are marked with an '*'
,030
,022
,062
,077
,055
,053
,077
,112
,075
,178"
.130*
.148*
.213*
.126*
,110
.173*
,093
.148*
,233
CP2
.789*
,339
.568*
.972*
.845*
,621
975"
.~
.710*
,553
,667'
,648"
1.865
.858
,163
,253
,291
,219
,293
.184
PSL
,288
.166*
,092
,063
.218*
.207*
,181"
,221"
,168"
,095
,087
,126
,390
,058
.073
.lo4
,114
,029
,098
CP3
.833*
.803*
,515"
.795"
1.063"
,668
1.095"
,642"
.631*
.630*
,781"
,587"
.819*
639"
.628*
.526*
,768"
.743*
,622
BAS
,186
,138
,133"
,132"
.092*
,132
.154*
.178*
,132"
,149"
.310*
,229
,210
.158*
,159
,137
,262
,262
,178
CRU
,287
,354
.038
,085
,134
,042
,073
,021
,128
,107
,172
,407
,215
,397
.207
,218
,085
,110
,098
CP4
+ ed between the normal and Apert samples. Magnitudes with corresponding significant t s h a p e values
+ + +Apert sample size for age 18 is equal to 1 precluding a test for significant differences in sample means.
~~
,022
,054
,060
.020
.026
,033
.040
,077
,056
,051
,135
.137*
,071
.146*
.153*
.114*
.155*
.119*
.172
.147
,055
,027
,203
,128
.198*
,204
,308
.213*
,417"
,095
,329"
256"
,208
,153
,225
,255"
,146
.025
.5
1
2
3
4
5
9
10
11
12
13
14
15
16
17
18 + + +
NSL
NAS
Years
Age in
TABLE 4. Magnitude of the shape differences (el
482
J.T. RICHTSMEIER
ANALYSIS OF APERT SYNDROME
For every age class, two samples of deformations are used to study the morphological
differences between normal and Apert individuals. A simple (but biased, see preceding
section) t-test of intersample differences in
mean values of principal strain (el, ez) resulted in 326 (57%)significant 0, = .lo) differences in means out of a total of 570 tests
(Richtsmeier, 1985). The F-test of differences
in sample variances is also biased, but it
shows the Apert sample to have significantly
larger variances 0, = .05) in only 102 (19%)
of the 540 separate tests (for age 17 years,
N = 1, precluding tests for variance differences) (Richtsmeier, 1985). A simple tally of
variance difference shows the Apert sample
variance to be greater than the normal sample variance by 0.005 or more only 54% of
the time. These findings do not demonstrate
that either sample is significantly more variable than the other. The Apert variances are,
however, most frequently greater than normal for landmarks located on the cranium
and basi-occiput.
Intersample differences in shape and size
The magnitude of intersample differences
in size and shape (equations 1 and 2) are
presented in Tables 3 and 4. Those which
proved significant Cp = .05) (equations 4 and
5) are marked with an asterisk. (A listing of
the tsi, and tshape values of the test for significant intersample differences is found in
Richtsmeier, 1985.) The reader is reminded
that the exact value representing the .05
probability level varies with age according to
sample size.
In reviewing Tables 3 and 4, it is evident
that not all significant magnitudes are maximal. Alternatively, extreme magnitudes are
not necessarily significant. This is because
the sample variances of the values of the
principal strain are included in the calculation of tsizeand tshape (equations 4 and 5).
Larger variances minimize, and smaller
variances inflate, the calculated t-value.
The information presented in Tables 3 and
4 is summarized below according to craniofacial regions.
Upper and midface: Excepting the size
changes local to the intersection of the
greater wings of the sphenoid with planum
sphenoidale, Table 3 shows the Apert face t o
be generally smaller than normal. Significant shape and size differences between normal and Apert morphology local to the
intersection of the greater wings of the
sphenoid with planum sphenoidale are infrequent. The Apert upper face differs from normal sue at nasion and nasale throughout
ontogeny. Shape differences are also apparent at these landmarks but are confined to
the older age groups. Significant shape and
size differences local to constructed point 2
occur after age 9.
Palate: Table 3 shows that significant size
differences in palatal morphology result in a
smaller Apert palate. Significant differences
in palatal size prevail in the earlier age
groups, and size difference local to the posterior nasal spine is significantly negative in
Apert individuals throughout the older age
classes studied. Since localized size change
refers to the material surrounding the landmark, a decrease results in a smaller palatal
length as measured from the anterior to the
posterior nasal spine. Significant shape differences occur more frequently after age 9 at
anterior nasal spine, intra dentale superior,
and constructed point 1, but are more common before age 10 local to posterior nasal
spine.
Cranial base: Significant intersample differences in size local to these landmarks
which border sella turcica are uniformly positive, indicating enlargement of the pituitary
fossa in Apert syndrome. Of these landmarks
sella floor and posterior sella show frequent
significant differences in shape while tuberculum sella varies significantly from the normal shape during only one of the age
intervals studied (11 years). Significant differences in shape local to constructed point 3
occur exclusively from age 7 to 14 years. Significant shape differences local to constructed point 2 occur from age 9 to age 17.
Significant differences in size local to constructed points 2 and 3 are consistently negative. The direction of the differences
suggests a thinning of the sphenoid and occipital bones a t the level of the spheno-occipital synchondrosis (Richtsmeier, 1985).
Basi-occiput: The area surrounding basion
is significantly greater than normal up to
age 11 years and is significantly different
from normal shape in nearly all age groups
analyzed. Size differences local to the cruciate eminence and constructed point 4 are
greater than normal in 72% and 84% of the
age classes, respectively. This indicates that
the squamous portion of the Apert occiput is
generally larger than normal. Intersample
differences in shape are absent at constructed point 4 but occur local to constructed
483
CROUZON AND APERT CRANIOFACIAL MORPHOLOGY
TABLE 5. Spearman rank correlation of inter-sample differences in shape and size with
age, Apert sample
Landmark
NAS
NSL
ANS
IDS
IGW
PNS
CP1
TBS
SEF
CP2
PSL
CP3
BAS
CRU
CP4
Difference
in shape
.180
.837**
.816**
.819**
- ,282
.080
.786**
.525**
.875**
.784**
.684**
.423*
- .407*
.549**
.404*
Difference
in size
-.374
- .796**
,107
.692**
.228
.298
.682**
.737**
.856**
-.623**
.463**
-.719**
-.740**
.218
.519**
**p=.05
*p=.10.
point 2 from ages 9 to 17 and at the cruciate sale, tuberculum sella, sella floor, constructed point 2, posterior sella, constructed
eminence from age 2 to 13 years.
point 3, constructed point 4) indicate ageAgeassociated patterns of differences in
progressive size difference between the
shape and size
samples.
Spearman rank correlations of age with
Landmarks which show opposite signs in
the magnitudes of intersample size and shape the correlation of shape and size with age
differences are presented in Table 5. Noting (e.g., intra dentale superior, constructed point
that the research is cross-sectional, the cor- 1) indicate that while size differences diminrelation coefficients suggest that Apert syn- ish with age, shape differences increase. This
drome is an age-progressive disease. This is suggests the occurrence of shape differences
in agreement with conclusions of Pruzansky between the two samples at a morphological
(1977) and Kreiborg and F’ruzansky (1981), level other than that being directly analyzed
who state that the conditions associated with here.
Apert syndrome worsen with advancing age.
To evaluate age association of intersample
It is noted that previous conclusions were differences in overall cranial shape and size,
based on analyses which include mandibular the absolute value of the difference magniand orbital morphology.
tudes for all landmarks in each age group
Sixty percent of the landmarks show a sig- were correlated with those for all landmarks
nificant positive correlation of the absolute in every other age group. The Spearman rank
values of shape differences with age (p = .05). correlation of shape magnitudes is presented
The number of significant correlations in- in the upper half of the matrix in Table 6,
crease to 80%when .10 is used as the level of while correlation coefficients of size differsignificance. The negative association of ence magnitudes are presented in the lower
shape difference at basion with age is unique. half of the same matrix.
All interage correlations of size difference
Although significant shape differences local
to basion occur consistently, the area is less magnitudes are significant (p = .lo) and 78%
of the interage correlations of shape differdysmorphic in the older age groups.
Sixty-seven percent of the landmarks stud- ences are significant (p = .lo). This indicates
ied showed a significant 0, = .05)age-related a homogeneous pattern of dysmorphology aspattern of intersample size differences. A re- sociated with Apert syndrome throughout the
view of the size difference magnitudes used age groups studied. OveralI shape differences
to calculate the correlations (Table 3) indi- recorded for ages 12,13,14,15,16,17,and 18
cate that the area surrounding intra dentale years stand out from the younger ages. Shape
superior, constructed point 1, and basion be- differences for these older age classes are,
came more normal in size at later ages. The however, strongly correlated- with one anremainder of the significant correlatrons (na- other. I propose that shape change specific to
484
J.T. RICHTSMEIER
the maturation of the normal and Apert faces dentale superior (29%).The majority of the
during adolescence are responsible for the significant differences in size local to landage-graded pattern of the correlations.
marks on the anterior border of the palate
(intra dentale superior, anterior nasale spine)
occur before age 8 while significant differANALYSIS OF CROUZON SYNDROME
ences in shape local to these same landmarks
o u t Of 570 tests for intersample differences are more common after age 9. At age 18, the
in mean Values Of Principal strain, 50% oldest age class for which I have data, all
(N=344) showed significant (P = .lo) mean landmarks on the Crouzon palate are signifdifferences. Fourteen percent Of 510 tests in- icantly different from normal in size, but not
dicated a significant difference (p = .05) in so in shape.
sample variances (for ages 15 and 16 Years,
Cranial base: Significant differences in size
N = l ) michtsmeier, 1985). A simple tally Of local to sella turcica (tuberculum sella, sella
differences in sample variance shows the floor, posterior sells) are not as frequent as
Crouzon sample variance to be greater than found with Apert syndrome, but the majority
the normal sample variance by at least .005 of these values are positive, indicating a
in 54% of the cases analyzed. In general, larger pituitary fossa in Crowon syndrome.
sample vm%nces do not appear to be differ- This is consistent with previous studies (e.g.,
~
commonly Kreiborg, 1981). Significant differences in
ent, but when present, O C C most
on the Palate, Pituitary fossa, and basi-occi- shape are common local to sella floor (59%)
put (Richtsmeier, 1985). As discussed previ- and posterior sella (71%)but infrequent at
ously, the values considered in these simple tuberculum sella (18%).Constructed point 2
tests were chosen for their magnitude, Pro- and constructed point 3 on the Crouzon craducing biased results. we turn now to a dis- nial base are generally significantly smaller
cussion of the unbiased tests for mar- than normal. This represents a thinning of
PhohiWal differences between the ~ r o u ~ othe
n basi-sphenoid in a posterior-superior to
and normal samples.
anterior-inferior direction (Richtsmeier, 1985.
Significant differences in shape local to conIntersample diferencein shapeand size
structed points 2 and 3 are less frequent (29%
Tests for significant differences in localized and 1g%,respectively).
shape and size between the normal and CrouBasi-occiput: The crowon
basi-occiput is
zon samples are Presented in
and '. smaller than normal, though size difference
They are summarized according to
is never significant local to constructed point
cia1 regions.
4. Significant differences in shape between
Upper and midface: Significant
the normal and Crowon basi-occiput occur
ple differences in shape local to nasion and local to constructed point 3 and basion, but
than
nasale are more
not at the cruciate eminence or constructed
differences in size at these same landmarks. point 4. This indicates that the squamous
Nasion differs from normal in size during portion ofthe occiputis less severely affected
only one age €YOUP (8 Years). This
that than the basal portion in Crowon syndrome.
the nose typically associated with Crouzon
syndrome is due more t o shape differences at
Ageassociated patterns of differences in
nasion than size differences. Both shape and
shape and size
size differences are involved in nasale. The
majority of significant differences in size and
The correlation of differences in shape and
shape local to the intersection of the greater size with age are presented in Table 9. The
wings of the sphenoid with planum sphenoi- majority of the correlation coefficients are
dal occur prior to age 6. Shape differences low and insignificant, indicating that differlocal to this landmark terminate by age 11 ences in shape and size between the normal
and Crouzon samples are not strongly assoyears.
Palate.: Localized size differences show the ciated with age. With the following excepCrouzon palate to be generally smaller than tions, this cross-sectional analysis does not
normal but not significantly smaller in more support the premise that Crouzon syndrome
than 50% of the age classes studied. Signifi- is an age-progressivedisease.
cant size differences occur most frequently
Differences in shape between the normal
local to posterior nasal spine (47%of the age Crouzon samples increase in magnitude with
groups), followed by anterior nasale spine age a t nasion, nasale, sella floor (p = .05) and
(35%),constructed point 1 (35%),and intra posterior sella (p = .lo) (27% of the land-
”
p=.lO.
’ p=.05.
.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
6%
in
years
.5
1
1.00
.57‘
.83‘ 1.00
.83‘
.92’
.90’
.90‘
.92’
.92’
.93‘
.94’
39’ .87‘
20‘
33‘
.93’
.90’
34‘
.74’
.77’
.76‘
.70’
58’
.79’
.78’
.75‘
.76’
.80’
.81’
.75‘
.71’
.79‘
.79‘
.83‘
.83‘
.66’
63’
2
.72‘
.60’
1.00
29‘
.94‘
.91’
.90’
.83‘
39’
.74’
.74’
.67’
.72‘
.75‘
.79’
.71’
.74‘
.77‘
.64’
3
.85’
.68‘
.64’
1.00
.95’
.95‘
.95’
.90’
.94’
.79‘
.75’
.65’
.76’
.75’
.78’
.70’
.73’
.79’
.65’
4
5
.61’
.65‘
53’
.84‘
.42
.47”
.62‘
22’
1.00
.57’
.98‘ 1.00
.98‘
.95’
.90‘
.92’
.98’
.97’
.84’
34’
30’
30‘
.74’
.73’
.79’
.81’
.81’ .80’
.85’
33‘
.76’
.76’
31‘
.81‘
34‘
.85‘
.70’
.70’
6
7
.76’
.84‘
.69‘
.66‘
.55’
.64’
.88’
.64’
.68’
.73’
.60‘
.71’
1.00
.82’
.96’ 1.00
.96’
.94‘
.84‘
22‘
31
.82’
.75‘
.70‘
.79’
20’
33‘
33‘
.84’
.81
.77’
.79’
.79‘
.73’
.82’
.79‘
.73’
.78‘
8
.81’
26‘
.72’
.85’
.80‘
.69‘
51’
.43
.77‘
.87’
.59’
.63’
26’
1.00
.86
32’
.74‘
.82’
32’
31’
.88’
.35
.56’
.15
.60’
.61’
.75’
.38’
.46”
.58’
1.00
29’
.91’
237’
39’
.89’
.90‘
.91‘
9
11
55’
.45”
.77‘
34’
.49”
.48”
.46”
39‘
,17
.43“
.52’
39’
.51’
.61’
66‘
.46”
.32
.47”
.75’
.42
1.00
.72’
.92
1.00
.99’
39’
.94‘
.99’
.98’
.94
.99’
.92‘
.94‘
.98‘
.97’
.91’
.97’
.88‘
10
Age in years
.94’
.98’
.95‘
.98’
.47“
53’
.27
.55‘
.21
59’
.53’
.46”
.33
.66’
.83’
.77‘
1.00
.96‘
.97
12
30’
.90’
1.00
.98‘
.97’
.95’
.95’
.97’
.86’
34’
.60’
.44”
22
.50“
.18
.40
.68’
.31
37
13
.37
.72‘
.31
.35
.14
.51’
.52‘
.36
.19
.49”
.92’
.74‘
.90‘
.96‘
1.00
.97’
.97’
.99‘
.94‘
14
16
17
.54‘
.46”
.27
69’
.71’
.56’
.34
.08
.36
.54’
.51‘
.38
.22
.16
.42
.66’
56’
.64’
50”
.46” .48”
.42
.33
.44”
.30
27
.29
.58‘
32‘
.63’
93‘
.47” 34’
.81’ .74’
.70’
.96’
.68‘
.90’
38’
.62’
34’
39’
.94‘
.64’
.70’
.63‘
1.00
.91’
.93’ 1.00
.96‘
.96’ 1.00
.88’
.91’
.96‘
15
.34
.75‘
.52’
.38
.30
57‘
.58’
.44”
.18
.44”
.7 1’
.72‘
.59‘
.75’
.75’
.65‘
.58’
.64’
1.00
18
TABLE 6. Inter-age Spearman rank correlation of overall differences in shape and size between the normal and Apert samples. The upper half‘of the matrix
represents change in shape, the lower half of the matrix represents change in size
-.291*
-.159*
-.118
-.137
-.266*
-.252*
- ,199
-.071
-.167
- ,103
-.164
-.165
-.118
- ,188
-.184*
- .099
- ,419
-.272*
- .225*
IGW
-.284*
,018
,010
.342*
,126
,113
.139
,365
,333
,046
,470
.221
,409
.369
- .052
-.011
.278
-.242*
- .194
-.263*
-.181
-.137
- .080
-.139
- .249*
-.169*
,184
- .034
-.126
- .244*
- ,060
.098
,051
- .435
- .355
-.287*
-.335*
- .237*
-.319*
- .269
- ,140
--.171-
-.221*
- .288*
-.184*
-.014
- ,154
-.198
-.222*
- ,074
,035
-.015
- .326
- .093
-.268*
.091
-.188
TBS
CP1
PNS
CP2
-.246*
-.319*
-.055 -.234*
,130 -.213
,017 -.169*
,575 -.285*
,343 -.197*
1.382 -.204*
.911* -.134*
1.158 -.161*
1.337* -.220*
,877 -.248*
1.200 -.262*
,786 -.204*
.639 -.187*
.173 -.213*
,259 -.188
.442 -.336
.629* -.268*
.080
-.008
SEF
+ + +Crowon sample size for ages 16 and 17 are equal to 1,precluding a test for significant differences in sample means.
-.250*
-.170
-.lo9
-.079
-.133
-.220*
-.lo9
,263
,010
-.061
-.224*
-.031
.120
.094
-.440
- .332
-.273*
- ,160
- .180*
-.092*
-.129
-.168*
- ,122
-.048
-.122
-.127*
-.179*
- .057
,072
-.081
-.120
-.172*
-.110
- .044
- ,085
- .366
- .392
- .269*
- ,048
.014
- ,132
- .075
-.221
.018
,051
- ,027
-.040
- .202*
.121
- .007
-.158
-.181
- .070
.020
,076
-.121
,039
.lo2
.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 +++
17 +++
18
-.150*
-.102*
-.lo9
,020
-.115
- .075
-.081*
-.129*
-.028
-.113*
-.136
-.152*
-.167*
-.168*
-.167*
-.213
- ,289
-.124
IDS
ANS
NSL
NAS
Age in
years
-.194
-.277
,091
.152
,181
.215
,158
.217
.408*
.300*
-.568*
.lo3
,158
.201
,268
.013
-.065
,032
-.223*
PSL
-.083
-.339*
-.224*
-.312*
-.236
-.372*
-.238
-.313
-.223*
-.227
-.304*
-,442*
-.442*
-.294*
-.204
-.324*
-.255
-.355
-.370*
CP3
CRU
-.406*
-.310*
-.331
.218*
-.329* -.184
- .227* -.153
- .075
-.246
-.151
-.195
.247
-.168*
-.017
-.173*
,140
.082
-.252* -.173
-.171
-.110*
-.347* -.283*
- .397*
-.197
-.199* -.216*
-.178
-.114
- .205
-.lo4
-.421
-.336
-.199
-.459
-.437* -.283*
BAS
-.266
-.146
-.145
-.120
-.239
-.163
-.148
-.160
,166
-.164
-.026
-.252
-.lo6
-.198
-.077
-.065
-.311
-.439
-.244
CP4
TABLE 7. Magnitude of the size differences (el +ed between the normal and Crouzon samples. Magnitudes with corresponding tsizeualues which were
are marked with an '*'
sienificant 1~=.05)
~
,155
ANS
.112*
,154
,108
.093* .119*
,028
,048
.142*
,140
.126* .lo9
,055
.077
.077* ,074
.118* .159*
,223'
.253*
.152*
~.~.217*
,062
,108
.123* ,136
.138* .196*
.231* ,248
.151* .215
.068
,209
,209
,168
.NO* ,075
NSL
__
NAS
,026
,216
,087
.022
.193
.215*
,115
.074
.219*
.420*
.369*
~.
,148
,185
.338*
.422
.463*
,086
,228
,037
IDS
PNS
.173* .141*
.139* .lo9
.132* ,185*
,112
,149
.256* ,068
.135* ,074
,126
,068
.192
.127*
,055
.179*
.195* .198*
,102
.117
.242* ,080
,155
,075
,059
,204
.364*
.018
,261
.089
,178
,203
.033
,393
,157
,104
IGW
TBS
.053
.118*
.127
,260
.054
.343
.035
.341*
.091
. . ~ ,126
,252
.181
.229
.074
,408
.036
,208
.054
.337* .228
.289*
~.~ ,330
.214
.026
,034
.087
,228
,267
.395* ,107*
.387* .077
,774
.075
I47
,078
.017
,223
CP1
.547*
.709
1.002
1.077*
.459*
,085
,228
.274
,329
.907*
.679*
1.758*
1.022*
1.472
1.798*
1.286
1.696*
1.213*
SEF
,095
.129*
.087
,052
.093
.060*
,102
.087*
.133*
,098
.056
.023
,033
,096
,070
,078
.088
,579
.378*
,387
,546
.259*
.588*
.167*
.124
,116
.113*
,124
,114
,140
.lo7
.207
.159
,114
,088
,040
,071
,081
,015
,061
,031
,034
.125
,210
,070
,066
,086
,130
,223
,112
,010
,179
,043
.007
,033
,074
.032
,141
,187
.021
,033
,168
,121
,196
,069
,039
,237
,010
,088
CP4
.006
-098
.
..~
,140
CRU
.080
BAS
,162
,193
,114
.133*
,191
.241
.525*
,224
,334
.242*
.318*
,166
.211*
.204*
.352*
,219
,107
,363
.189*
CP3
,133
,079
.163*
,173
,048
,120
.034
PSL
,063
,143
.338*
,376"
,390
.509*
.364
.495*
.603*
.629*
1.769*
.498*
.613*
CP2
,064
.076*
the shape differences (el -ed between the normal and Crouzon samples. Magnitudes with corresponding significant t,hapevalues
which were significant (p=.05) are marked with an '*'
.227
.187
.077
.205
.325*
,354
.223*
.263*
.090
.456*
.295*
_.
.288*
.272*
.287*
.369*
.392*
.479
.547
.539*
of
+ + +Crouzon sample size for ages 16 and 17 are equal to 1, precluding a test for significant differences in sample means.
11
12
13
14
15
16 +++
17 +++
18
io
7
8
9
1
2
3
.5
Age in
.5
TABLE 8. Magnitude
488
J.T. RICHTSMEIER
TABLE 9. Spearman rank correlation of inter-sample differences in shape and
size with age, Crouzon sample
Landmark
NAS
NSL
ANS
IDS
IGW
PNS
CP1
TBS
SEF
CP2
PSL
CP3
BAS
CRU
CP4
Difference
in shaDe
Difference
in size
.758**
.577**
,200
,349
- .232
,372
.242
- ,332
.514**
- ,147
.382*
.119
.230
.268
.244
.305
-.688**
- .209
- .023
- .056
.396*
-.028
,063
.428*
,011
- ,014
- .436*
-.181
-.119
-.154
**p = .05.
*p = .lo.
marks studied). The differences in size between the two samples show a significant
relationship with age at posterior nasal spine
and sella floor, but a negative age association
at nasale and constructed point 3. Size differences at sella floor increase with age. At posterior nasal spine, however, the significant
positive correlation indicates that as age increases, the intersample size differences
(negative magnitudes) approach zero, and
posterior nasal spine becomes more normal
with age. Since Crouzon nasale and constructed point 3 are typically smaller than
normal, the significant negative correlations
local to these landmarks indicate age-progressive size differences.
To evaluate the generalized pattern of
Crouzon craniofacial shape and size, intersample differences recorded for all landmarks in each group were correlated with
those recorded for every other age group. Table 10 indicates a generalized but weak association of shape and size of the Crouzon
craniofacial complex across all age goups.
With the .05 level of statistical significance,
47% of the shape correlations (upper half of
the matrix) and 54% of the size correlations
(lower half of the matrix) are significant.
When the significance level is increased to
.lo, 59%of the shape correlations and 67%of
the size correlations are significant. The
ubiquity of low but significant positive correlation coefficients suggests that a general
Crouzon craniofacial pattern exists, but individuals andlor age groups vary from this
pattern. When compared to the normal form
in the age groups considered, the Crouzon
pattern appears to be more variable from age
to age than the Apert form.
Intersample differences in craniofacial
shape for ages 1 and 2 years are generally
unlike the differences between normal and
Crouzon at other ages. It appears that by age
3, and certainly by 4 years, a specific and
consistent Crouzon shape is recognizable.
Sue differences between normal and Crouzon samples (lower half of the matrix) are
generally similar across all age categories
excepting age 6 months and 2 years. Since
the individuals included in the earliest age
groups are probably extremely dysmorphic,
ascertainment bias should be considered in
the evaluation of this pattern.
DISCUSSION
It is commonly noted that there is a large
amount of morphological variation within the
syndromes of Apert and Crouzon. I have
found the frequency of significant variation
in the Crouzon and Apert samples to be small
(11% and 19%, respectively) CRichtsmeier,
1985) and regionalized. Significantly increased variation in the Crouzon sample occurs local to the palate, pituitary fossa, and
basi-occiput. Variance differences are greatest in the Apert sample for landmarks located on the cranial base. Ignoring statistical
significance, a simple tally of variance does
not show the syndromes to be more variable
than the normal group.
The use of a n orientation system suited
primarily to the regularities seen in normal
individuals (sella-nasion line) may be partly
responsible for prior findings of increased
variability within Crouzon and Apert syndromes. Local inconsistencies of increased
morphological variation coupled with the im-
11
12
13
14
15
16
17
18
io
9
.5
1
2
3
4
5
6
7
8
years
Age
in
1
1.00 -.07
.35 1.00
.34
.70
.33
.65'
.54'
.51'
.64'
.54'
.31
.57'
.23
59'
.01
.45"
.59'
~. .64'
~.40
.sir
.50" .75"
.43" .81'
.31
.62'
.35
.58'
.35
.69'
.41
.32
.37
.31
.45" .75'
.5
.35
-.01
1.00
54'
.34
.30
.20
.48"
.22
.15
.46"
.35
.69'
.I6
- .03
.21
.60'
.06
.67'
2
4
.65'
.71'
-.13
.22
.65'
.05
1.00
.31
.60' 1.00
.34
.60'
.43" .66'
.66'
.65'
.76'
.33
.41
.53'
.69'
.55'
.70'
.72'
.80'
.65'
.60'
.64'
.30
.35
.34
.38
.56'
57'
.09
.66'
58'
.60'
3
.62'
.34
.17
.52'
.80'
1.00
.68'
.48"
.25
.65'
.67'
.64'
.50"
.59'
259'
.62'
.36
.65'
.44"
5
7
8
9
10
.46"
55'
.81'
.43
.32
.40
.48" .13
.28
.06
.33
.54'
.60' - .08
.22
.44"
.47" .84'
.16
.36
.72'
.31
.76'
.69'
.70'
.84'
.76'
.90'
.44"
.79'
1.00
.72'
.80'
53'
.72'
.47 "
.84' 1.00
.63'
.41
5~.
9'
.76' 1.00
.44" .65'
37'
1.00
.2 1
.50" .27
.78' 1.00
59'
.60'
.59'
,571
.45" ,441'
.89'
.83
,541 .80'
.59'
51'
.75'
.45"
.50" .37
.83'
.80'
53'
.28
.91'
.31
.76'
.88'
.26
.86'
50" .32
.19
.33
.36
.22
.57'
.66'
.49" .ll
.56'
.39
.56'
.61'
.45" .61'
.31
6
Age in years
.74'
.11
.36
.71'
.80'
.80'
.70'
.89'
.45"
.44"
.61'
1.00
.67'
.93'
,751
.75'
.36
.50"
.60'
11
.01
.04
.23
.73'
56'
.63'
.38
.41
.56'
.48"
58'
1.00
.60'
.48"
.58'
.70'
.41
.88'
62'
12
.93'
39'
.42
.42
1.00
.80'
.78'
.28
54'
.50"
-56'
.~
.34
.28
.09
.29
.55'
.75'
.67'
.44"
13
~~
15
16
.31
.39
.71'
.04
.20
.17
-.16
54'
-.09
.78'
.03
.07"
.54'
.49"
.56'
.74'
.55'
.61'
.48"
.49" 5 3 '
.87'
.26
.22
-49"
.34
.38
.
.34
.86'
.86'
.73'
.73'
58'
.79'
.30
.22
.52'
.50"
.24
.41
.89'
36'
,941 .14
1.00
.93' 1.00
.21
.08 1.00
-.01
.45"
.54'
51'
.73'
.44"
51'
14
18
.89'
,463''
.08
-.07
.44"
.15
,791
.34
.67'
.38
.75'
.34
.43" .63'
.93'
.34'
.41
.59'
.44"
.60'
,471' .58'
.86'
.34
.42
.62'
.41
.66'
.22
.77'
.28
.68'
.go'
.25
.41
1.00
1.00
.60' -
17
TABLE 10. Inter-age Spearman rank correlation of overall differences in shape and size between the normal and Crouzon samples. The upper half of the
matrix represents change in shape, the lower halfof the matrix represents change in size
490
J.T.RICHTSMEIER
plicit assumption of a nonvarying cranial
base could produce an impression of extreme
variability within each of the syndromes
when analyzed in selected registration systems. Alternatively, this study focuses on a
very small number of landmarks and completely ignores several craniofacial regions
(i.e., mandible; orbits, neurocranium). The
variance recognized by other studies may reflect variations in morphology of regions not
considered here.
This analysis has found the Apert and
Crouzon craniofacial complex to be morphologically distinct from normal in most of the
age groups studied. Kreiborg and Pruzansky
(1981) found the morphology of Apert and
Crouzon to be indistinguishable from one another on the basis of cephalometric data. Although Apert and Crouzon morphologies
were not directly compared in this analysis,
the pathologies were compared to the same
normal sample. Certain morphological distinctions between the syndromes are apparent from the results.
First, the cranial base is significantly different from normal in both syndromes, but it
appears t o be primarily involved in the dysmorphology associated with Crouzon syndrome. Significant differences between normal and Crouzon are found at 6 months of
age local to five landmarks of the cranial
base: tuberculum sella, sella floor, constructed point 2, basion, and the cruciate eminence. At the same age, morphological
differences between the Apert and normal
cranial base are significant at constructed
point 3 and basion. This may indicate basic
differences in the etiology and ontogeny of
the two diseases.
In both syndromes, the pituitary fossa is
larger than normal, although this size difference is more commonly significant in Apert
syndrome. Enlargement of the pituitary fossa
and the orientation of the principal directions of the morphological differences at basion pigs. 4, 5; Richstmeier, 1985) may
account for the reduced linear distance from
sella floor to basion (posterior cranial base)
found in Apert (Kreiborg, 1986;Kreiborg and
Pruzansky, 1981; Peterson-Falzone et al.,
1981) and Crouzon (Kreiborg, 1981) syndromes.
The intersection of the greater wings of the
sphenoid with planum sphenoidale is not a
true biological loci because it represents the
intersection of radiographic shadows which
actually coexist on separate planes. Notwith-
standing, the principal directions of the difference in form local to this landmark
(Richtsmeier, 1985) suggest that local differences may be caused by the same process;
i.e., anterior advancement of the greater
wings of the sphenoid and depression of the
cribiform plate. My analysis has indicated,
however, that these differences are greater
and more commonly significant in Crouzon
syndrome.
Significant size differences local to the basiocciput (basion, the cruciate eminence, constructed point 4) are positive in the comparison of normal with Apert syndrome and
negative in the comparison of the Crouzon
syndrome with normal. The Apert basi-occiput is larger than normal while the Crouzon
is smaller. This may result from differential
patterns of early suture closure.
My results demonstrate that Crouzon and
Apert noses are not only dysmorphic in relation to a hypoplastic maxilla, but that the
nose is morphologically distinct independent
of the surrounding face. Apert and Crouzon
noses are generally smaller than normal. The
distinct morphology of the Apert nose appears to be due to significant differences in
size, while shape differences more frequently
distinguish the Crouzon nose. Soft tissue
should be considered in further evaluation of
nasal morphology.
My data support previous findings of a
small palate in Crouzon and Apert syndromes (Bertelsen, 1958; Kreiborg, 1981;
Buckley and Yakolev, 1948; Blank, 1960; Solomon et al., 1981).Morphological differences
between normal and pathological palates
measured at anterior nasal spine, intra dentale superior, posterior nasal spine, and
constructed point 1 are more commonly significant in the Apert sample (Apert
~ = 7 7Crouzon
:
N=48). Additionally, within
the Apert sample, palatal size differences are
more frequently significant at posterior nasal spine, marking the posterior border of the
palate as the site of greatest reduction in
palatal size.
My results agree with those of Pruzansky
(1977) and Kreiborg and Pruzansky (1981),
who characterize Apert syndrome as an ageprogressive disease. However, areas of the
Apert craniofacial complex have also been
identified which show no age progressivity of
dysmorphology (nasion, intersection of the
greater wings of the sphenoid with planum
sphenoidale, posterior nasal spine, cruciate
eminence) as well as areas that become more
CROUZON AND APERT CRANIOFACIAL MORPHOLOGY
491
5
NO DEFORMATION
Figs. 4, 5. Deformation of 8-year-old normal mean
into age 8 Crouzon mean (Fig. 4 ) and age 8 Apert mean
Fig. 5). Deformation here refers to the two-dimensional
change in shape and size local to each landmark as
calculated from the form change tensor as described in
the text. The craniofacial complex depicted is a Bolton
standard form, age 8. (Broadbent et al., 1975). The principal directions and magnitudes of strain local to each
landmark are plotted. Rigid body motion is not
considered.
normal in size with age (intra dentale superior, constructed point 1, basion). Results of
this analysis agree with Pruzansky’s (1977)
suggestion that parts of the Apert face grow
normally while others do not. I conclude that
this produces localized but not global ageprogressive dysmorphology.
Comparison of my results with those of
Kreiborg and Pruzansky (1981), who state
that the midfacial hypoplasia associated with
Crouzon syndrome grows worse with time,
and of Pruzansky (1977), who characterized
Crouzon syndrome as a n age-progressive disease, reveals basic differences. Excepting
specific biological loci (see Table 91,my analysis has not depicted Crouzon syndrome as
a n age-progressive disease. Method of analysis figures significantly in these contrasting
492
J.T.RICHTSMEIER
results. First, the design used here is crosssectional. The optimal design for studies of
growth is longitudinal (see, for example,
Kreiborg, 1981, 1986). Second, the present
analytical design evaluates Apert and Crouzon morphologies onIy in relation to normal
morphology. This analysis focuses on how
the disease changes morphologically through
time in relation to a normal group which is
changing concurrently. The research design
implemented does not allow conclusions
about whether individuals become “worse”
or “better” with age, but instead, whether
they become morphologically like or unlike
the normal sample with age. It is possible
that conditions associated with Crouzon appear to “worsen” with age without becoming
increasingly different from normal. Finally,
this analysis is limited to morphological differences local to 15 landmarks. Other studies
of age progressivity in these syndromes have
considered the position and shape of the orbits, the mandible, and the facial skeletal
profile as a whole.
I have found evidence that the morphology
associated with Apert syndrome is more homogenous throughout ontogeny than that associated with Crouzon syndrome. The
uniqueness of the Crouzon craniofacial shape
at ages 1 and 2 years (Table 10) might be
explained by variation in the rate of the accelerated cerebral development before 18
months of age. Accelerated brain growth coupled with craniosynostoses which force cranial growth to occur in specific directions
might account for the dissimilarity of cranial
shape of ages 1 and 2 with all other age
groups. This explanation cannot account for
the frequency of significant correlations of
shape of the Crouzon craniofacial complex at
age 6 months with many of the older age
groups, however. Since these latter correlations are frequent (73%), the patterns seen
from age 6 months to 2 years may be due to
the individuals included in these age groups
(ascertainment bias).
The purpose of this study was to determine
localized morphological differences between
normal and abnormal forms. The measures
of shape and size change used derive from a
single component of FES analysis. The mode
of statistical analysis applied here is a single
example of the possible ways in which to test
hypotheses about morphological differences
between groups of forms. Alternate quantities and methods have been used to summarize form change calculated by finite
element and other related methods (Moss et
al., 1985, 1987; Cheverud and Richtsmeier,
1986; Richtsmeier and Cheverud, 1986; Lavelle, 1985; Grayson et al., 1985; Richtsmeier, 1987). Experience will determine the
values and methods which are most appropriate to specific research problems. It is clear
from this analysis, however, that FES analysis provides information pertaining to local
biological form change which was previously
unattainable. Current research must focus
on the development of methodologies for abstracting the most biologically relevant facts
from deformations and the design of efficient
statistical analyses.
ACKNOWLEDGMENTS
I thank Dr. B. Holly Broadbent, Jr., of Case
Western Reserve University for access to the
Bolton collection, and for space at the BoltonBrush Growth Study Center for tracing the
normal sample. I thank members of the Center for Craniofacial Anomalies staff, University of Illinois, especially the late Dr. Samual
Pruzansky, for access to the Apert and Crouzon patient records and for the interest he
showed in this project up until his last days.
Special thanks to Dr. Jim Cheverud for diligent and invaluable instruction and consultation throughout the duration of this project
and for reading varying drafts of the manuscript. His input made the study possible.
Robert Hanmer’s programming skills and Dr.
Jack Lewis’s generous assistance on many
levels were invaluable. I am grateful to
anonymous reviewers for their criticisms,
which pointed out difficulties and helped to
improve my explanation of this research.
This investigation was supported in part by
grants from the Whitaker Foundation to
James Cheverud, and from the National Institutes of Health (DE 02872) and the National Child Service, Department of Health
and Human Services, to the Center for Craniofacial Anomalies, Chicago, IL.
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