THE ANATOMICAL RECORD (PART B: NEW ANAT.

) 289B:195–209, 2006

FEATURE ARTICLE

Damage to the Human Cerebellum from Prenatal

Alcohol Exposure: The Anatomy of a Simple
Biometrical Explanation
FRED L. BOOKSTEIN*, ANN P. STREISSGUTH, PAUL D. CONNOR, AND PAUL D. SAMPSON

Since 1973, it has become clear that exposure of otherwise normal human fetuses to high levels of alcohol damages
a substantial number of the exposed brains in a wide variety of ways nowadays referred to collectively as the fetal
alcohol spectrum disorders (FASDs). Averages of images and measurements of brains with these disorders are
quantitatively different from normal, and the cerebellum is one of the structures at which differences are typically
noted. The present article extends these techniques to a simple, practical, and enlightening detection rule for fetal
alcohol damage in adolescents and adults known to have been heavily exposed. The data arise from 180 clinical MR
brain images (half of adolescents, half of adults; half male, half female; one-third each fetal alcohol syndrome, fetal
alcohol effects, and unexposed). The 180 cerebellums were represented by 328-semilandmark triangulations covering
most of the cerebellar surface. Statistical analysis exploited the now-conventional methods of Procrustes analysis in
three dimensions, along with a recent extension to incorporate size information explicitly. If we reduce the data
complexity even further, to just 23 points along the silhouette of the cerebellum as viewed from above along the
aqueductal axis, the analysis becomes more precise. Now a single multivariate summary score, very strongly
correlated with size, supports a discrimination (diagnosed vs. unexposed) with about 75% accuracy. About one-
quarter of our FASD sample overlaps with the central range of the unexposed in the distribution of this size-based
score, with the other three-quarters distinctly showing cerebellar damage. The finding, which corresponds quite
closely to the fundamental finding of cerebellar hypoplasia in animal experiments, bears implications for fetal alcohol
epidemiology, for geometric morphometrics, and for the geometric complexity of useful data structures derived from
clinical brain imaging. Anat Rec (Part B: New Anat) 289B:195–209, 2006. © 2006 Wiley-Liss, Inc.

KEY WORDS: fetal alcohol spectrum disorders; cerebellum; morphometrics; birth defects; magnetic resonance imaging;
medical image analysis

INTRODUCTION
Since 1973, it has become clear that
Dr. Bookstein is professor of statistics, UW, and clinical director of FADU. He is a
professor of psychiatry and behavioral neuropsychologist with interests in cogni- exposure of otherwise normal human
sciences (PBS), and scientific director of tive, mental health, and neuroimaging as- fetuses to high levels of alcohol dam-
the Fetal Alcohol and Drug Unit (FADU), sessment of individuals with prenatal al-
University of Washington (UW), Seattle, ages a substantial number of the ex-
cohol damage.
Washington, and professor of anthropol- Dr. Sampson is research professor of sta- posed brains in a wide variety of ways
ogy at the University of Vienna, Vienna,
Austria. For a quarter of a century he has
tistics and director of statistical consult- nowadays referred to collectively as
ing for the Department of Statistics, UW.
been identified with the development of the fetal alcohol spectrum disorders
He is a long-time collaborator with Profes-
methods for statistical analysis of data (FASDs). Often this damage can be
from medical images such as these, meth- sor Bookstein on applications of multivar-
ods that seem to be scientifically more iate statistical methods in fetal alcohol re- seen directly in brain images obtained
fruitful in application to issues of fetal al- search; also, he leads a research group on
spatiotemporal modeling in environmet-
much later in life. This assertion actu-
cohol medicine than anywhere else.
Dr. Streissguth, professor emerita of PBS, rics, focusing on air quality data. ally summarizes two of the literature’s
UW, was one author of the original 1973 *Correspondence to: Fred L. Bookstein, claims at the same time: first, that
paper in Lancet announcing the discovery Fetal Alcohol and Drug Unit, Department
there are differences between groups
of fetal alcohol syndrome. Ever since then, of Psychiatry and Behavioral Sciences,
as founding director of FADU, she has University of Washington, Box 359112, Se- of damaged and undamaged people in
been involved in research and clinical attle, WA 98195. Fax: 206-685-2903; the statistical distribution of single or
work on patients with fetal alcohol syn- E-mail: flb@stat.washington.edu
drome and fetal alcohol spectrum disor- multiple measurements of brain im-
ders and hopes that brain studies such as DOI 10.1002/ar.b.20114 ages (e.g., Riley et al., 2004); second,
this will eventually enlighten clinical prac- Published online in Wiley InterScience that decision rules based on these
tice. (www.interscience.wiley.com).
Dr. Connor is assistant professor of PBS, measurements can discriminate be-
tween people with and without FASD

© 2006 Wiley-Liss, Inc.

196 THE ANATOMICAL RECORD (PART B: NEW ANAT.) FEATURE ARTICLE

diagnoses to some clinically useful ex- metric methods, show that the bio- implications for detection of FASDs
tent (e.g., Bookstein et al., 2002a). For metrics of the cerebellum in FASDs with more speculative comments
the first kind of argument, we look at are strongly consistent with the core about the implications of the finding
differences of average or covariance finding, hypoplasia, from the animal for studies in other domains.
structure of vectors of variables be- experiments. An exploratory statisti- In 2002, this journal published our
tween our groups, with the associated cal analysis of allometry (the effect of study (Bookstein et al., 2002a) of a
conventional statistical significance size changes on shape) confirms that different part of the brains of this
tests. To demonstrate the possibility we have captured nearly all of the bio- same 180-subject sample. Those find-
of classification, we examine sensitiv- metric signal by one simple explana- ings have had a substantial impact in
ity, specificity, and accuracy instead. tion based on the typical FASD size domains rather far from the teratolog-
Behind either class of numerical tac- deficit. ical context, including, for instance,
tics lies the broader domain of expla- Thus, the argument of this article the American system of capital pun-
nation. Over the same 30 years, reduc- intermixes some science (the neurot- ishment (Bookstein, 2006). Neverthe-
tionistic animal experiments have eratology of alcohol) with some meth- less, that earlier article does not much
steadily elucidated the pathways that odology (advances in the biometrics overlap with this one (except in the
link the brain damage to the behav- of size and shape, as well as innova- conclusion that fetal alcohol exposure
ioral deficits that are so much easier tions in the simplification of surfaces). can be detected in the brain at much
to observe in a medical context. The sections to follow alternate be- later ages), as the cerebellar findings
In order to study the damage done tween these ingredients. We begin here differ from the callosal findings
by alcohol to one particular part of the with a brief review of what is known of 2002 in several respects. The 2002
human brain, the cerebellum, this ar- about the effect of fetal alcohol expo- study found a difference only of vari-
ticle weaves together the two biomet- sure on the brain in general and the ance; here there is a difference of av-
ric themes, effect estimation and de- cerebellum in particular. After that, erage form as well. The 2002 study did
tection, with the third theme, the we show a method of digitizing the not pursue any hypothesis of allome-
explanatory one. We are working with cerebellar surface with respect to an try, and the data set there was in effect
the same data resource we have axis along the aqueduct that simplifies two-dimensional (a nearly flat curve)
mined for several years: conventional the statistical analyses on which we to begin with. The present report,
magnetic resonance (MR) brain im- will be relying, without weakening based on data from a different part of
ages of 120 diagnosed FASD patients them. Some preliminary findings these brains, exploits a newly three-
compared to those of 60 unexposed about size measures of this structure dimensionalized computer-aided dig-
peers of the same age range and sex. suggest that its shape should be ex- itizing technique, a recently invented
From the images of the 180 cerebel- pressed using silhouettes instead of multivariate statistical tactic, and a
lums, computer-aided hand digitiza- surfaces. When we do so, using the new respect for the virtues of simpli-
tion extracted a biometric surface rep- silhouette in a plane perpendicular to fication not only in the communica-
resentation that can be exploited in the organ’s aqueductal axis, we see tion of quantitative anatomical find-
several ways. In the most conven- that the analysis of alcohol’s effect on ings but in the course of their
tional two-dimensional view, the mid- the size and shape of the cerebellum generation.
sagittal section through vermis, there reduces to a simple and familiar sta-
is hardly any discernible effect of al- tistical model for that view that can be NEUROTERATOLOGY OF
cohol at all. By contrast, statistical interpreted directly in simple biologi-
analysis of a full three-dimensional cal terms and simple two-dimensional
ALCOHOL IN BRIEF
(3D) surface finds clear differences be- diagrams. Returning to the biology of It is well known that alcohol is terato-
tween unexposed and patient samples the problem, we identify the biometri- genic and that the brain is the organ
in both the size and the shape of the cal factor as a direct empirical opera- most vulnerable to its effects (for an
cerebellum. Closer examination of tionalization of the primary observ- overview of what is known in both
this 3D signal suggests the construc- able biological effect of the alcohol animals and humans, see Streissguth,
tion of a new 2D representation that teratogenesis (to wit, hypoplasia of 1997). Documented sites of damage,
conveys most of the information brain tissue). If we pretend we did not besides the cerebellum we study here,
about the alcohol effect without the know about the alcohol diagnosis, the include hippocampus, basal ganglia,
complex visualizations entailed in the FASD cerebellum appears to be just cortex, and corpus callosum. Animal
three-dimensional analysis. This help- an inexplicably small cerebellum hav- studies show specific damage to glial
ful simplification takes the form of a ing the appropriate shape for its small cells and myelin, neurons, apoptotic
visual horizon or silhouette view of size. mechanisms, and dopamine circuits,
the cerebellum, a tactic that was pop- In the context of fetal alcohol stud- and clinical studies, both autopsy and
ular a century ago in anthropometrics ies, this interpretation of our finding in vivo, show many of the same re-
but that has not been used much since bears implications for the nosology of gions and forms of damage in hu-
the onset of 3D computer vision appli- FASDs, for prenatal monitoring, and mans. Clearly the effects are wide-
cations in medical imaging. for endophrenological studies of the spread and can be demonstrated from
The statistics of either the 3D sur- way behavioral deficits arise from the early embryonic days. For a good cur-
face or the 2D silhouette, analyzed by insults to form. Our concluding dis- rent summary of the work on specific
simple and powerful new morpho- cussion draws together some of these neurotoxic mechanisms, including
FEATURE ARTICLE THE ANATOMICAL RECORD (PART B: NEW ANAT.) 197

the implications for prevention or in- velopment and other behavioral se- ropsychological domains known or
tervention, see Chen et al. (2003), and quelae that are seen in humans with suspected to be damaged in the fetal
for a general review of the domain, FASD (Connor et al., 2006). The prin- alcohol spectrum disorders. Prior
up-to-date except in respect of ignor- cipal theme of all the experimental re- analyses of this data record have dealt
ing the publications from our group, sults is specific cell loss, consistent with subcortical landmark point con-
see Riley et al. (2004) or Riley and with the human findings regarding figurations, with the size and shape of
McGee (2005). The majority of teams brain size shortfall and also with the the midline corpus callosum, with the
studying humans with prenatal alco- findings of the present analysis re- prevalence of executive function defi-
hol damage are using MR images, but garding the simple statistical struc- cits in the patient population, and
the only group attempting to convert ture of the group differences. Indeed,
with endophrenology (the correlation
these into a detection protocol seems the current animal research studies,
between behavioral deficits and de-
to be our own (Bookstein et al., which all begin by assuming the facts
tails of the shape of the brain). The
2002a). Other modalities of imaging of cell death and consequent loss of
present report is our first that con-
are under active study at this time mass, generally aim at exploring a va-
riety of reasonable mechanisms by cerns data from the cerebellum.
(fMRI, SPECT, PET, diffusion tensor
imaging), but the grouped effects have which that damage obtains: for in- Data Collection From
likewise not yet been converted into stance, disruption of surface neuro- Cerebellar Surface: An
useful diagnostic protocols. trophin regulators (Light et al., 2002),
Intentional Simplification
Effects on brain function can be de- disruption of the cyclin-dependent ki-
nase system (Li et al., 2002), disrup- The human brain, somebody said re-
tected at lower levels of exposure than
effects on structure. A wide variety of tion of the nitric oxide pathway cently, is “the most complex system in
these neurobehavioral effects, too, are (Bonthius et al., 2004), glial cell mat- the known universe,” and so the sci-
known from experimental animal uration (Gonzáles-Burgos and Alejan- ences trying to understand it have
models, from human studies of diag- dre-Gómez, 2005), or disruption of quite a steep wall to climb. Studies of
nosed patients with FASDs, and from apoptosis-regulating proteins (Siler- congenital insults play the same role
longitudinal prospective studies of Marsiglio et al., 2005). While our work in these pursuits that experimental
human subjects at a range of exposure cannot speak to any of these pathway studies of disordered development
levels. The effects on the typical models, we will confirm the simplicity played in the rise of classic experi-
course of a human life are primarily of the principal experimental finding, mental embryology: understanding
consequences of the behavioral prob- loss of cerebellar mass. the effects of certain specific causes
lems; in modern societies, these ef- may make it easier to describe the or-
fects are devastating. The linkage be- SUBJECTS AND IMAGE-DERIVED igins of other patterns of variability
tween the alcohol-induced brain that we happen to find interesting.
DATA The same excessive complexity that
anomalies and the behavioral deficits
has been demonstrated via correla- Our earlier publication in this journal applies to theories of the brain applies
tional analysis in animals, and MRI (Bookstein et al., 2002a) has already as well to their images, which are the
studies in humans are beginning to reviewed the sample of 180 adoles- most complex structures that medical
explore these possibilities as well cents and adults and the brain images image analysis ever deals with. Such
(Sowell et al., 2001; Bookstein et al., by which we assess the neuroanatomi- complexity, alas, necessarily inter-
2002b). cal damage to the 120 FASD subjects, feres with the far simpler sorts of sta-
and so we can be relatively brief here. tistical processing (mean differences,
From a large registry of persons of all detection rules) through which our
The Cerebellum per se ages diagnosed with fetal alcohol syn- theories must be filtered if they are to
One may choose to investigate the cer- drome (FAS) or fetal alcohol effects be of any medical utility.
ebellum in FASDs for a variety of rea- (FAEs) through the year 1998, we se- Our work here therefore does not
sons: because it is known to be en- lected 15 of each diagnosis for each draw on any of the currently cutting-
tailed in a steadily increasing number sex separately in two age ranges: ado- edge approaches to nonrigid registra-
of cortical pathways, because it is lescents (aged 14 through 17 at the tion of brain images, a topic on which
high on the list of brain parts known time of our data collection) and adults an entire bibliographic essay could
to be affected by prenatal alcohol ex- (aged 18 and older). Each group of 30 well be written (see the special issue
posure (e.g., West, 1986), or just be- diagnosed patients was matched for on biomedical imaging published by
cause it is so easy to see in MR images. age range, sex, and ethnicity to a com- this journal: http://www.wiley.com/
Within the literature of animal exper- parison group of 15 unexposed volun- legacy/products/subject/life/anatomy/
imentation, the cerebellum is unusual teers recruited from the general Seat- bioimage_toc.html). Specifically, the
in the concentration of reports on one tle community. The study combined data to be analyzed below were gath-
single mechanism of teratological two major data collection activities: a ered by computer-aided hand digitiza-
damage, namely, death of Purkinje fairly conventional 3D MR brain im- tion of the visually identifiable cere-
neurons (e.g., Dikranian et al., 2005) age, mildly T1-weighted, at voxel size bellar surfaces of each of the 180
with consequent disruption of cere- 0.85 ⫻ 0.85 ⫻ 1.5 mm3, and 5 hours’ study cerebellums in turn, under the
bellar cortical structure in ways that worth of laboratory testing and inter- guidance of a carefully designed 328-
could explicate the delayed motor de- views tapping a very broad list of neu- point template. Except for one single
198 THE ANATOMICAL RECORD (PART B: NEW ANAT.) FEATURE ARTICLE

relaxation procedure used for the cal-

losal midline analysis in an earlier
phase of this project.
To ease both the construction of a
template and the interpretation of our
results, we designed a convenient
standardized cerebellar Cartesian co-
ordinate system (Figs. 1 and 2) having
a familiar landmark (Tip4V, tip of the
fourth ventricle, intersection of the
crosshairs in Fig. 1) as origin and
aligned with the midsagittal tangent
line to the posterior brain stem as di-
rection of the craniocaudal axis. This
direction, called the axial direction in
the following discussion, is the direc-
tion that will be projected out of the
surface in order to arrive at the curve
called “equator” below. The left-right
direction is taken along the obvious
direction of symmetry for the head as
Figure 1. Template for a simple digitization of the cerebellar surface. Left: View down the
aqueductal axis of the coordinate system, showing the meridians along which semilan-
a whole, and the third coordinate, the
dmarks were set on the template form. Right: View of the midsagittal plane (visible at left anteroposterior, is computed as the
as the yellow line). The single landmark in this construction, Tip4V, is at the intersection perpendicular to the craniocaudal di-
of the crosshairs. The vertical axis is aligned with the apparent posterior boundary of the rection in the midsagittal plane. (Evi-
brain stem in this plane. Beyond the point Tip4V, the vermis is represented by 2 points
dently this is a different direction
where the apparent cerebellar surface cuts the axis (the vertical crosshair) and by 13
other points put down at roughly even spacing on the visibly evident boundary curve. from the more common gravitational
One of these points is taken at farthest right, where it becomes part of the equatorial anteroposterior taken parallel to the
silhouette introduced later. floor or to the Frankfurt horizontal
axis of the skull.) These axes are the
landmark point (Tip4V, tip of the
horizontal and vertical of the panels
fourth ventricle), all of the points col- in Figure 1.
lected are what the literature calls For analysis of the midsagittal sec-
“semilandmarks.” Semilandmarks are tion per se, two semilandmarks are set
locations that convey the biometric on the two intersections of the cere-
variation of a curve or surface by a bellar surface with the craniocaudal
selection of several points lying on the axis of this construction, and a fourth
curve or surface that are individually at the most posterior point of the mid-
nearest to the predetermined points of sagittal cerebellar outline. Twelve fur-
a template under one or another rea- ther points are placed around the
sonable definition of what “nearest” curve of intersection at roughly even
means. This project uses the charac- spacing. See the right panel of Figure
terization of semilandmarks as jointly 1, which is in this midsagittal plane.
minimizing bending energy with re- We are not claiming that the polygon
spect to the template: the relaxation delineated here approximates the cer-
reviewed by Gunz et al. (2004) (for ebellar surface in-between at all accu-
applications to craniofacial bony sur- rately, nor that these points are ana-
faces). This approach approximately tomically homologous in terms of any
preserves the relative spacing of the principled cerebellar atlas (cf. the dis-
points among themselves while cussion of Schmahmann’s below);
Figure 2. Enhancement of the left panel in greatly improving the efficiency of neither assumption is required for the
Figure 1 by a rendering of the simple trian- subsequent statistical analyses and analyses to follow. Likewise, choice of
gulated surface lofted over the meridional the efficacy of visualizations. Our spe- the case used as template is immate-
semilandmarks. The surface is open at the
cific morphometric algorithm is a rial, as long as it is typical in its topol-
left (the peduncles). The equatorial curve
underlying the main analysis of this study is generalization for surfaces of a tech- ogy.
the visible outline of the green rendering nique for curves first published for a We constructed a decimated tem-
between those endpoints. It includes one realistic 2D data analysis right here in plate in the form of intersections of
point on the midplane, the point at the this journal (Bookstein et al., 1999), the same exemplar surface with a pen-
crotch of the notch at center right; this is
also the posteriormost point of the vermis
and the detailed technique to be intro- cil of 16 regularly spaced planes
outline at right and just above the horizontal duced presently is the 3D analogue of through the axis just introduced.
crosshair in the previous figure. the manually managed semilandmark (Here the word “pencil” is a delightful
FEATURE ARTICLE THE ANATOMICAL RECORD (PART B: NEW ANAT.) 199

technical term in geometry. In this teriormost point of the midsagittal otherwise conventional vector of vari-
context, it connotes a one-parameter cerebellar section is located (typically, ables that can be analyzed by stan-
family of planes, a set all having the as in the case here, it is craniad to dard multivariate methods, and any
same equation that involves one free Tip4V in our system), the most lateral patterns unearthed can be visualized
parameter you may take as the angle points left and right in the axial plane (most conveniently, by thin-plate
that the plane through the axis makes through Tip4V, and the two places spline deformation grids) back in the
with the anteroposterior direction of where the axis of the construction space in which they were originally
the head.) The meridional nature of pierces the cerebellar surface above digitized. Statistical significance tests
these locations (a total of 627 triangles and below the registration point. Two, of shape difference are by permuta-
on 328 points) is hinted at in the view the template surface just figured tion testing (Good, 2000) of Pro-
at left in Figure 1, in which the cranio- above is warped into the new subject’s crustes distance between average
caudal (axial) direction of the mid- coordinate system by thin-plate spline shapes taken between groups that
plane image is now perpendicular to using the six points just specified. randomly divide the original collec-
the paper. Notice that the surface here Three, in the midplane and every tion of shapes into two parts instead
is incomplete in the acute angle be- other plane of the warped pencil, the of according with the actual diagnosis
tween the cerebral peduncles; we are points of the warped template are pro- in the data.
not digitizing that part of the surface. jected perpendicularly onto the appar- We attend carefully to the notion of
All three points on the axis of this ent cerebellar outline by the opera- geometrical scaling, centroid size,
construction (Tip4V and the intersec- tor’s hand. Projection does not go into that is built into this toolkit (Book-
tions with the cerebellar surface axi- the depths of sulci, but remains on the stein, 1991). It is this variable that will
ally above and below it) are present in surface (the locally convex comple- ultimately embody the finding of hyp-
all of these sections, but need not be tion) of the visually apparent cerebel- oplasia that links our analyses to the
redigitized. Except at the cut edges, lar cortical tissue edge. Finally, at the experimental animal literature. Cen-
every meridian is bridged to its neigh- conclusion of this operation, when all troid size is the square root of the total
bors by a system of triangles making of the semilandmarks appear to be ly- squared distance of all the landmark
up the “ribbon strips” of Koenderink ing on the visible image surface in the or semilandmark points from their
(1990), a useful way of representing meridional sections through them, common centroid case by case, hence
simply curved surface patches. There they are all relaxed (slid jointly) along the name. This particular measure is
results the polyhedral surface viewed the surface of the tesselation of the strongly correlated with most other
from above in Figure 2. faceted surface they themselves span candidates for a general size measure,
The locating (digitizing) of these 328 to positions of minimum bending en- such as two-dimensional area or
points per cerebellar surface was car- ergy with respect to the template three-dimensional surface area or vol-
ried out interactively via Edgewarp, a form. ume, but it has powerful formal
large package in C⫹⫹ and OpenGL (mathematical) properties as well that
coded over the last decade by MORPHOMETRIC STATISTICAL we will rely on in the course of the
Dr. W.D.K. Green of the Statistics De- multivariate computations here. In
partment at the University of Washing-
METHODS particular, centroid size plays a
ton. The current public release of We analyzed the 328-point data re- unique role in multivariate models of
Edgewarp, which carries out all the source just sketched, and also two of allometry.
computations here using mouse-driven its interesting subsets (the 16 semiland- The reader accustomed to multivar-
operations, is available for free down- marks of the midsagittal section, and iate Gaussian (normal) models may
load as object modules for Linux the 23 semilandmarks of the equator), be less familiar with the allometric
and Mac systems (ftp://brainmap.stat. by the Procrustes methods that have models that are the single most pow-
washington.edu/edgewarp3d/). Instruc- recently become standard for analysis erful explanatory tool in the biometric
tions for using the pulldown menus for of labeled Cartesian locations like style of explanation of form. These
this specific application are available these. That method was reviewed in models have a long history, beginning
from the senior author. our earlier articles (Bookstein et al., with Karl Pearson’s work of the 19th
Once the template was constructed, 1999, 2002a) in this journal, in several century on correlations among suites
by carefully scripted digitizing and tri- textbooks (e.g., Dryden and Mardia, of multiple length measures. Good re-
angulation of a template form, one of 1998), and in many other articles views include Huxley (1932), Gould
the authors (P.D.C.) manually warped strewn over the recent literature of (1965), Blackith and Reyment (1971),
the lofted surface onto every other quantitative morphology. (A Google Reyment and Jöreskög (1993), and
subject in our sample of 180, accord- search on the phrase “Procrustes anal- chapter 4 of Bookstein (1991). Allom-
ing to the following four steps. One, ysis” now brings up about 33,000 re- etry is the statistical study of one spe-
Tip4V is located, and the direction trievals.) The general strategy is to re- cific biological process, the determi-
through it specified that it is parallel duce all the forms to a common nation of shape by growth or size
to the posterior brain stem. (Along coordinate system of deviations from change. When shape is measured by
with the visually obvious axis of bilat- the average shape, by standardization many different variables, as it is in our
eral symmetry, this direction sets the of centroid location, orientation, and tradition of geometric morphomet-
coordinate system we are using.) Then scale in any order. The standardized rics, all those dependencies are usu-
five more points are located: the pos- landmark coordinates turn into an ally modeled jointly in the conven-
200 THE ANATOMICAL RECORD (PART B: NEW ANAT.) FEATURE ARTICLE

of the raw data indicates that this

owes to substantial variability of the
posterior-inferior part of the outline
in this plane.) The size comparisons
involving vermis, shown in Figure 4,
are barely statistically significant for
the two adult samples (for the male,
t ⫽ 2.4; for the female, t ⫽ 2.2), and
not at all for the two adolescent sam-
ples (兩t兩 ⬍ 1). All t values are of n ⫽ 15
unexposed against n ⫽ 30 FASDs. (Be-
cause of differences in variance, the
significance tests associated with the t
Figure 3. Two models of shape allometry. Left: The standard textbook model, in which two ratios would need to be computed by
groups show similar allometric dependence of shape on size with different intercepts and resampling methods, as in Figure 11
different ranges for the size predictor. Right: The finding in this study, in which one single
allometry characterizes the response of shape to size in more than one group of subjects. and its associated discussion.)

Full 328-point surface

tional form of parallel regressions The situation is entirely different for

FINDINGS
the full 328-semilandmark surface
with different predictor ranges (Fig.
Centroid Size data set. The clinical three-group de-
3). These analyses used to proceed by
Cerebellar vermis (midsagittal sign now shows substantial size sig-
extraction of relative warps (principal
nals in all four of our design quad-
components of shape) followed by section) rants (male or female, adults or
group-by-group regressions on size in Analysis of the cerebellar vermis was adolescents), as seen in Figure 5. Note
this manner. by geometric morphometric analysis the excellent separation now, espe-
Only recently (indeed, well after of the 16-point configuration shown at cially for the adult females; note also
publication of our previous article in right in Figure 1. There were no find- that the size distribution for the FAE
this journal) was it recognized that ings here of any shape effect of FASDs subsamples always lies intermediate
there is a better way to carry out the within age-sex classes. (Examination between that for the unexposed and
same modeling: by restoring centroid
size to the shape representations un-
derlying the Procrustes method. In
this new approach (Mitteroecker et
al., 2004), allometry is visualized via
the principal components of an ex-
tended morphometric representation
that includes size information and
shape information simultaneously
and commensurately. The trick is to
add a column to the Procrustes shape
coordinate matrix for the (natural)
logarithm of centroid size, and then
carry out otherwise conventional
principal component analyses in this
newly augmented size-shape space.
This approach incorporates every
classic approach to allometry as one
or another graphical analysis deriving
from the one single computation.
Software for geometric morpho-
metrics is available from a wide range
of purveyors (see, again, the Google
retrieval mentioned above). As the
size-shape computations were still
somewhat experimental when we car-
ried out our analyses, we used Splus, a
Figure 4. Centroid size (square root of total squared distance of all the landmarks from their
commercial statistical programming centroid case by case) for the full data set of 180 midsagittal vermis outlines as schematized
package, as our computing environ- in Figure 1. The vertical axis conveys the design of the study: three diagnostic groups within
ment. four separate categories combining sex with age range.
FEATURE ARTICLE THE ANATOMICAL RECORD (PART B: NEW ANAT.) 201

there is a visual resource near the hor-

izontal sulcus: the apparent outline of
these organs as viewed from a great
distance out along the axis we have
assigned them. The curve in question
has the mathematical characteriza-
tion of a curve on the surface where
the surface tangent plane passes
through the point of viewing. By anal-
ogy with what you see from the top of
a mountain, it is also called the visual
horizon of the surface with respect to
locations a long way away along the
aqueductal axis. We can refer to it less
technically as a silhouette of the cere-
bellum in the direction of the axis or,
even more conveniently, as its equa-
tor.
We thereby recognize in this con-
struction a very old method indeed,
dating back to the dawn of scientific
photography. Curves like these lay at
the foundation of the most well-artic-
ulated classical biometric application,
to the craniofacial skeleton. Volume 2
of Rudolf Martin’s magisterial Lehr-
Figure 5. The same display, centroid size by design group, for the centroid size of the full buch der Anthropologie (1928) incor-
328-point surfaces as digitized. Note the striking differences of distribution by diagnosis porates an enormous range of clever
within the two adult subsamples. extractions of quantities from skulls
viewed in just this way: as outlines of
that for the FAS subsamples. The tion. Axial centroid size (e.g., within- photographs from a sufficient dis-
comparisons show nearly double the subject variance of the axial tance along aligned coordinate direc-
signal-to-noise ratios as those of Fig- coordinate) is correlated with left- tions. The familiar “three ladies of
ure 4: t ratios are 3.97, 4.89, 3.20, and right centroid size for our age-sex the anthropology laboratory” (norma
2.79 for the adult males, adult fe- groups, but anteroposterior centroid lateralis, norma frontalis, and norma
males, adolescent males, and adoles- size is not thus correlated. If we verticalis) produce their outlines as
cent females, respectively. wished to focus our attention on just a just such visual horizons. The curve
There is no paradox here. There is single pair of Cartesian dimensions, it we seek, the one we are calling the
plenty of opportunity for a strong would be the combination of the left- equator of the cerebellum, has in fact
nonmidsagittal morphometric signal right axis with the anteroposterior (in already been shown in Figure 2; it is
to materialize in the size and shape of the outline of the green-tinted surface
other words, omitting the direction of
left and right half-cerebellums. In there. (In this geodetic metaphor, the
the aqueductal axis itself).
fact, we find (in inelegantly detailed “north and south poles” correspond-
displays not shown here) strong sig- Reducing the complexity of the ing to the equator lie on the axis of the
nals in every coordinate direction for coordinate system, the points above
data
the data off the midplane, with many t and below Tip4V in Fig. 1.)
ratios exceeding 5 (corresponding to Hints can be gleaned from the classic Furthermore, the sizes and shapes
effect sizes of greater than 1 standard anatomical monographs on the cere- of these curves are already embedded
deviation). These measures are not di- bellum. We have recourse to that of in our 3D surface representation just
ameters of the form, but specific com- Schmahmann et al. (2000), which as much as were those of the midsag-
ponents of the centroid size formula notes a horizontal sulcus running ittal vermis. To produce the equator
itself in the three Cartesian directions quite near to the widest circuit of from an aqueduct-registered cerebel-
of our coordinate system. The dimen- these organs perpendicular to the lar form, we just discard the axial co-
sion of largest size effect variability is axis. The horizontal sulcus is an ap- ordinate of the points originally digi-
the dimension of bilateral symmetry. proximately planar curve that could tized in 3D at points of their
A simplification would be in order if it well convey much of the information meridians that are, on average, far-
does not do too much damage to the available from the cerebellar surface thest from the axis. There are 23 of
signal strength we are seeking to ex- as a whole, were it only visible in our these points, including the original
ploit. As part of such a simplification, images. Alas, typically it is not visible semilandmark that was most poste-
we would want to minimize redun- in images having the 1 mm3 voxels rior in the midsagittal plane (the un-
dancy of the required data representa- that characterize these MRs. But paired landmark in the figures to fol-
202 THE ANATOMICAL RECORD (PART B: NEW ANAT.) FEATURE ARTICLE

the panel at upper left, we show (by

the dashed line) the projection of the
geometric size axis on these two com-
ponents. Size aligns almost equally
with these first two components and is
almost entirely located within this
plane (more than 92% of its variance
is explained by just these two factors).
We see that there is indeed shape in-
formation available as well as size dif-
ference. Comparing the separate pan-
els of Figure 9 to the corresponding
ranges in Figure 5, we see that there
are more points to the left of the •
symbols in Figure 9 than there were in
Figure 5. The shape analysis sharpens
the size-only discrimination in three
of the four age-sex subgroups, except-
ing only the adolescent female.
The same approach applies in the
simplification of the data to the equa-
tor curve alone. Figure 10 shows the
size-shape relative warp analysis cor-
responding to the size-only displays in
Figure 6. Again, size projects almost
totally onto the first two dimensions
of size-shape space (95% of its varia-
Figure 6. The same again, centroid size by design group, for just the data of the equatorial
silhouette. Separations here, using only 23 points, are nearly as strong as those of Figure 5, tion is captured there), but now the
based on more than 14 times as many data. clustering of the unexposed in the
adult subsamples is quite pro-
low). Properly speaking, these are not ance of shape in the FASD subgroup nounced. The clustering of the adult
plane curves (i.e., outlines from flat that we reported for their callosal out- females in the upper right panel of
slices) but instead places on the sur- lines in 2002. When we draw the av- Figure 10, in particular, is as tight as
face where the implied normal to the erage shapes at their average sizes by what we published in 2002 (for adult
(crudely) digitized surface lies per- age-sex group (Fig. 8), it is gratifying males) by combining behavioral and
pendicular to the axis of the coordi- to see the same display for all four of anatomical data. Here we have ap-
nate system. these design quadrants. The average proached that degree of concentration
effect of having an FASD diagnosis is of the signal of normality by manipu-
Findings for the equator lation of anatomical observations
invariant across our four age-sex
Turning to the 23 points on the equa- groupings. alone.
torial outline, we compute their size
and shape by the usual Procrustes
methods. The centroid sizes for this
Explanatory Finding: Allometry
simplified data set show almost as The information about shape in Fig-
strong a signal as those of the full ure 8 should be considered in light of
328-point surface representation (Fig. the size differences in Figure 6. While
6); t values are 2.75, 4.54, 2.31, and ordinary shape comparisons do not
2.74 for the same four quadrant-spe- find significant differences, there is an
cific comparisons, and the remarkable alternative approach available from
discriminatory power for size for the the geometric toolkit that considers
adult female perseveres. the possibility of correlations between
Beyond the size measure for the shape and size: the allometric model
equatorial curves lie the customary already introduced. The method of
Procrustes shape scatters. Figure 7 size-shape relative warps described
shows these for the adult subsample above can test whether there is infor-
of our study, those who will ultimately mation in the shape domain that can
show the greater signal magnitude in complement classifications based
the final analyses that follow. We see merely on measured size. Figure 9 Figure 7. Procrustes-registered residuals for
the equatorial silhouette, adults only, indi-
here, in the distribution of the ⫻ sym- shows the plot of the first two size- cating the information remaining when
bols on both sides of the central bun- shape relative warps for the full sur- equatorial centroid size, the summary score
dle of • symbols, the same hypervari- face data set of 328 semilandmarks. In of Figure 6, is divided out of the data.
FEATURE ARTICLE THE ANATOMICAL RECORD (PART B: NEW ANAT.) 203

posed one. The form on the left then

sketches the equatorial form expected
for an unrealistically small FASD
case, while the form on the right cor-
responds to the expected form of an
unrealistically large cerebellum from
either diagnostic group. Inside either
deformed outline is the mathemati-
cally smoothest estimate of the field of
tissue deformations (growth excesses
or deficiencies) consistent with the
shift to the outline in question.

Decision Rules
Corresponding to each of these setups
(two size-shape relative warps, plus an
original centroid size variable) is a
discriminant function analysis. The
discrimination is quadratic because
our FASD cerebellums show differ-
ences of variance as well as of aver-
ages compared to those of the unex-
posed subjects. The equator-only
analysis just diagrammed classifies
adult males as unexposed or FASD
with three errors each among the un-
exposed, the FAE, and the FAS, and
Figure 8. Average size and shape of unexposed (solid lines) and pooled FASD (dashed classifies the adult females with the
lines) subsamples for all four quadrants of our main design. This constitutes a fourfold internal
replication of the principal claim of this study. same count of nine errors now distrib-
uted as 4, 3, 2. (Errors are from the
As Figure 10 shows, the main effect phological effect of the size difference full cross-validated analysis in which
of the prenatal alcohol damage on the is not supplemented by any other sys- each subject is classified according to
equator of the cerebellum is to shift tematic effect of the alcohol exposure. the classifier derived from the 44 oth-
not only size, as we already noted, but In the context of our graphical mod- ers in the corresponding study quad-
also the size-correlated parts of shape; els (Fig. 3), we see that the allometric rant. The predictors for the analysis
and size here lies mostly on relative finding does not take on the conven- included centroid size and those two
warp 1 (the one plotted horizontally). tional form of the diagram at left, but dimensions of correlated shape,
Temporarily restricting ourselves to instead manifests the less familiar SSRW1 and SSRW2, separately by
just the adult subsamples, we con- form shown at right. The FASD cere- quadrant.) Analysis for the full surface
sider the effect of alcohol on every bellum differs from the unexposed by data set of 328 points shows about the
single principal component of the a variable extent of the effect of pure same accuracy. The role of the shape
equatorial shape: all 43 of them (an size difference (the horizontal axis representations is to add some redun-
approach that one would never use for here), together with additional varia- dancy and also some biological verisi-
any other statistical purpose). Bear in tion showing no mean tendency to dif- militude and plausibility to the size
mind that the computation here fer between groups in any direction classification as regards FASD versus
makes no reference to the grouping perpendicular to the long axis of the unexposed.
structure of the study design. Figure ellipse shown in the figure. If we restrict ourselves to just one
11 indicates that when appropriately It is instructive to display this first quantity—the horizontal axis in Fig-
corrected for the multiple compari- size-shape relative warp in the form of ure 10, which, recall, was computed
sons, there is no difference between a thin-plate spline deformation grid without reference to diagnostic
the unexposed and the FASD sub- (another component of the standard groupings—we can distinguish the
groups, by nonparametric Wilcoxon geometric toolkit). Figure 12 shows unexposed from the FASD adult cere-
test, on any principal component after the effect of changes (of somewhat bellums with a total of only 22 errors
the first. The FASD subsample (the ⫹ greater amplitude than the data actu- out of the total sample of 90. (The cut
and ⫻ symbols) are vertically centered ally afford) in both directions from corresponding to this discrimination
in the same place as the unexposed the grand mean form over all 180 cer- falls at about 0.05 on the horizontal
(the • symbols) not only in the top row ebellums of this study. The average axis of the panels in the figure; it mis-
of Figure 10 but in every other figure here corresponds to the size and the classifies the 9 of the unexposed to its
corresponding to the other possible shape of either a small unexposed left, along with the 13 exposed to its
vertical axes. In other words, the mor- brain or a relatively large alcohol-ex- right.) This performance, while not as
204 THE ANATOMICAL RECORD (PART B: NEW ANAT.) FEATURE ARTICLE

Figure 9. Plots of the first two size-shape relative warps (principal components) of the 328-point data. Upper left: The complete distribution
over 180 subjects. The dashed line is the projected direction of geometric size (larger forms to the lower right). Other panels are subsets of
the main panel for the four age-sex groups indicated.

solid as the formal quadratic discrimi- clearest in the two-dimensional equa- can show, the entire effect of the pre-
nant analysis, is quite respectable for torial view of Figure 13. At left is natal alcohol exposure (as encoded in
a single size-shape score (the defor- shown the net effect of small centroid the diagnostic grouping) is carried by
mation pattern depicted in Fig. 12). size via a threefold extrapolation of one single mediating variable, the cen-
The corresponding separation purely the mean difference between the troid size of the equatorial silhouette.
by equatorial centroid size, as in Fig- forms larger than the unexposed adult This finding is wholly in keeping with
ure 6, can be set to a nonsignificantly minimum centroid size (about 49; see the simplicity of the animal literature,
lower total count of errors (20, versus the horizontal axis in Fig. 6) and the which finds only one ultimate expres-
the 22 for the analysis including others. This grid is indistinguishable sion of the effect of prenatal alcohol
shape), but omitting mention of the
from the small end of the first size- exposure on the cerebellum that
shape information has the rhetorical
shape relative warp in the preceding might be observed at the gross imag-
effect of blocking the tie to the explan-
figure. But, also, it is indistinguishable ing level: the phenomenon of reduced
atory setting of this finding. Correc-
from the comparison of the FASD cer- cerebellar mass. The different mor-
tion of cerebellar size for net brain
size is not likely to improve this accu- ebellar equators of small size to the phogenetic mechanisms reviewed in
racy, as net brain size is itself known FASD equators of large size (center the current experimental literature
to be reduced in FASD. panel). By comparison (right panel), survey an assortment of pathways
there is no shape difference at all be- that result in that outcome, with an
tween the equatorial form of the un- eye toward possible interventions that
DISCUSSION
exposed cerebellums and that of the might intercept those pathways; but it
In this data set, the effect of the FASD FASD cerebellums that are large for remains the case that net cerebellar
diagnosis is the same as the effect of their diagnosis. size mediates the effect of alcohol
size allometry itself. The graphics are In other words, as far as these data equivalently in the experimental and
FEATURE ARTICLE THE ANATOMICAL RECORD (PART B: NEW ANAT.) 205

Figure 10. The same plots as in Figure 9 for the 23-point equatorial silhouette data. Size allometry is much more effectively aligned with the
horizontal in this morphospace.

the human observational domains. recommending a 2D analysis instead. less extensive cerebellar damage as
While animal studies of behavioral In compensation, so simple a quanti- well; they did not do so for our earlier
deficit are strongly consistent with ob- tative finding articulates very effec- analysis of just the callosal midcurve
servational studies of analogous defi- tively with reductionist explanations (Bookstein et al., 2002a).
cits in humans (Goodlett and West, (such as apoptosis) of that loss of cer- We did not locate or trace any of the
1992), except for the pioneering study ebellar cortical mass. The experimen- cerebellar gyri and sulci (Schmah-
of Sulik et al. (1981) it is much less tal literature, in its centering on one mann et al., 2000). Any additional in-
common to encounter any consilience single trauma (hypoplasia), is a good formation they bear could only add
between morphological investigations match to a statistical exegesis center- power to the analysis here, but the
in the two domains. The finding here ing on just one factor (that size short- strength of the mapping-free finding
of a one-dimensional mediation of the fall). sets a high standard against which to
alcohol effect on the cerebellum in Our finding of a shortfall in size that judge claims of a more supple, adap-
both animals and humans is simple is steeper for the FAS group than the tive, or accurate digitization in view of
and gratifying. FAE group is in keeping with several the considerably greater cost entailed.
Corresponding to so simple a deci- earlier publications (cf. Riley et al., Our standardized coordinate system
sion rule is an equally simple data re- 2004; Riley and McGee, 2005), al- was introduced purely for conve-
source, the equatorial silhouette. In- though we do not confirm earlier find- nience of digitizing: an axis to rotate
tentionally to discard so much of the ings of specific differences in the ver- around. The direction of the central
complexity of the available medical mis (Sowell et al., 1996; Autti-Ramo et axis, evidently set with reference to
image data, as we have done here, is al., 2002; O’Hare et al., 2005). The is- the brain stem, need not be involved
an unusual tactic. We know of no sue remains open as to why the hu- in cerebellar architecture or ontogeny
other research finding beginning with mans with the less extensive facial in any characteristic way. Still, there
a 3D data analysis that has ended up signs seem to show, on average, the is a clear map for future histological
206 THE ANATOMICAL RECORD (PART B: NEW ANAT.) FEATURE ARTICLE

cient to capture the extent of dysmor-

phology in the cerebellum, it ought to
correlate substantially with deficits in
behaviors that involve cerebellar tis-
sue. Such examinations can then be
univariate, not multivariate, which af-
fords them much greater statistical
power (or, equivalently, grants them
adequate power in much smaller sam-
ple sizes). We have such measures in
our current study and have correlated
them with corpus callosum dysmor-
phology in earlier publications (Book-
stein et al., 2002b). Correlations of
cerebellar size with the same mea-
sures will be the topic of a later pub-
lication, but we cannot resist hinting
here that to the variability of size def-
icit within the FASD subgroup do in-
deed correspond strongly correlated
patterns of variability of behavioral
deficits. It is worth noting in this con-
nection that an earlier publication of
ours on brain-behavior correlations in
this sample (Bookstein et al., 2002b)
found a dimension for motor short-
fall, variable in extent, within the
FASD group that was not itself corre-
lated with diagnosis (FAS vs. FAE)
within the FASD category.
Size is the conceptually simplest
quantity to measure in a medical im-
age, and equatorial size is even sim-
pler than most, as the equator falls so
Figure 11. Statistical significance tests of the alcohol effect on all 43 dimensions of size-
shape space for the equator data set in the adult subsample of 90. The leftmost points close to a plane curve. We have re-
plotted correspond to the horizontal and vertical coordinates of the panels at upper center cently had considerable success
and upper right of the preceding figure. The concentration of the group difference in one (Bookstein et al., 2005) in extending
single dimension of the data (which, recall, was rotated to axes in a way making no our adult callosal methodology into
reference to that difference) is quite startling.
the delivery suite by analysis of peri-
natal intracranial ultrasound. Given
or cytoarchitectonic research in the packages. More conventional would the strength of the simple cerebellar
grid patterns of Figures 12 or 13. be an intensified effort to capture the size detection rule shown here, it be-
There is also the matter of the equa- information in the horizontal sulcus, comes equally important to establish
torial curve data acquisition per se, which lies so conveniently near to the a reliable mode of measuring perina-
data that in principle could be ac- curve we have used. But our equator tal cerebellar size. Assessments of this
quired quite independently of the re- is always visible and easy to locate in quantity during the immediate post-
maining information about cerebellar real images once the coordinate sys- natal period could offer both pediatri-
surface form. Wholly automatic algo- tem is set, whereas sulci are often un- cian and parent information about
rithms for analyzing the cerebellar clear, discontinuous, or incomplete. likely brain damage in offspring who
surface, while likely respecting the There is no analogous sulcus going are known to have been alcohol-ex-
landmark properties of Tip4V, might “over the top” of the cerebellum, or we posed, information strongly relevant
well use a quite different heuristic would be recommending more work to the child’s later development.
for assigning preliminary correspon- on digitization of such a structure as Green (2004) argues that classical eye-
dences than the one here, which eased well. blink conditioning will be a particu-
the manual closest-point relaxation de- The finding here simplifies not only larly rich source of findings and mech-
scribed under “Image-Derived Data” the report of the neuroanatomical anisms that relate cerebellar damage
above. We encourage our community dysmorphology but also the subse- to behavioral deficits. Also, informa-
to add the possibility of silhouettes to quent correlational studies of struc- tion gathered before birth might sus-
its usual toolkit of medical image tural damage against functional and tain potential interventions, some of
strategies, and to construct tools for behavioral deficit that are thereby which, such as maternal counseling,
the more widely adopted software suggested. If cerebellar size is suffi- show great promise in other venues.
FEATURE ARTICLE THE ANATOMICAL RECORD (PART B: NEW ANAT.) 207

Figure 12. Grid diagram for the principal allometric finding (equatorial SSRW1, horizontal in Figs. 10 and 11). The computation makes no
reference to diagnostic group.

Fetal alcohol spectrum disorder is verbal summary (“the animal finding (and, it turns out, with behavioral def-
not, of course, the only developmental of cerebellar hypoplasia is confirmed icits as well). The verification of the
disease that involves a growth defi- in humans”), but it is nevertheless a experimental finding in the nonex-
ciency. The role of size shortfall as a good deal more nuanced in its pattern perimental human context thus relies
unitary mediating variable should cer- analyses, and the simple qualitative on a pattern analysis that is much
tainly be considered in animal studies, sentence is not a fair representation of more quantitative than what is re-
which in averaging size differences what has been accomplished here. In- quired for the animal studies them-
over experimental groups evidently stead, a change of rhetoric is neces- selves: a sophisticated technical tool-
must lose power, and in observational sary, a change that is generally neces- kit combining morphometrics and
human studies as well of such prob- sary whenever a finding derived from multivariate statistical analysis, to re-
lems as iron deficiency, prenatal mal- an experimental design in an animal place the machinery of controlled
nutrition, or the intrauterine growth study is to be matched against a non- studies randomizing animals over cal-
retardation due to such causes as ma- experimental set of observations from ibrated conditions of differential dose.
ternal smoking. Causes of variation of a human study. To be as persuasive as We do not so much confirm the con-
the alcohol-induced size deficit within an animal study, an observational sensus of the animal literature, in fact,
experimental or naturally observed data set needs to be a great deal more as we ramify its specification in vari-
groups are manifold and are currently aware of the details of variation. In ous ways that, together, compensate
being studied by a variety of methods the present context, where neither for the absence of experimental con-
(among them, genetic investigations dose nor diagnosis ever was under our trol (see also Bookstein and Sampson,
of the dependence of metabolic path- control, it is much more important 2005). By adopting this explicitly
ways on alleles and correlational anal- than it would be in the analogous an- quantitative pattern-oriented rhetoric,
yses of the timing and mode of expo- imal study that we can assert all of the we modify the description of the phe-
sure). The methodology demonstrated following as fact: cerebellar size is de- nomenon in a genuinely useful way,
here could add information from im- creased in about three-quarters of a one that may lead to the generation of
ages to the biometric reasoning un- sample of human patients with FASD, many additional hypotheses for new
derlying findings in most studies like preferentially in one view geometry studies in animals as well as in hu-
those. more than in others, more in some mans. In a spirit of reductionism,
That methodology is conceptually regions than in others, and in a way these might include investigations of
simple, and simple in one version of a correlated with shape differences morphogenetic dysregulation as a

Figure 13. Threefold magnifications of the shape comparisons summarizing the main teratogenetic finding. Left: The average of the smaller
forms as a deformation of the average of the larger forms, irrespective of diagnostic group. Middle: Comparison of large to small FASD
equatorial silhouettes; this is the same grid as the one above it and also the same as the grid at left in Figure 12. Right: Shape difference
between FASD and unexposed within the size range of the unexposed. There is no alcohol effect without a size effect.
208 THE ANATOMICAL RECORD (PART B: NEW ANAT.) FEATURE ARTICLE

function of position (cf. O’Hare et al., ington and DA-021519 to the Univer- Bookstein FL. 2006. My unexpected jour-
2005); in the other direction, one sity of Michigan. Development of our ney in applied biomathematics. Biol
Theory 1:65–75.
might turn to hypotheses concerning Edgewarp software was supported by
Chen WJA, Maier SE, Parnell SE, West JR.
regional or even global cerebellum- those grants, by National Institutes of 2003. Alcohol and the developing brain:
correlated neuropsychological func- Health grant EB-001957 to the Uni- neuroanatomical studies. Alcohol Res
tion and dysfunction. The logic of versity of Michigan, by Defense Ad- Health 27:174 –180.
morphometric pattern detection ap- vanced Research Projects Agency Connor PD, Sampson PD, Streissguth AP,
Bookstein FL, Barr HM. 2006. Effects of
plies equally to experimental and to (DARPA) contract W81XH-04-2-0012 prenatal alcohol exposure on fine motor
observational studies. to the University of Michigan, and by coordination and balance: a study of
The implications of the present grant P200.093/1-VI/2004 from the two adult samples. Neuropsychologia
finding are thus potentially quite Austrian Council for Science and 44:744 –751.
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