Geometric Morphometrics of CorpusCallosum and Subcortical Structures in theFetal-Alcohol-Affected BrainFRED L. BOOKSTEIN,1* PAUL D. SAMPSON,2 ANN P. STREISSGUTH,3 AND

PAUL D. CONNOR3

1Institute of Gerontology, University of Michigan, Ann Arbor, Michigan 481092Department of Statistics, University of Washington, Seattle, Washington 981953Department of Psychiatry and Behavioral Sciences, University of Washington School of Medicine,Seattle, Washington 98195

ABSTRACT

Background: Although experienced clinicians havebeen diagnosing fetal alcohol syndrome (FAS) fornearly 30 years, the rest of the spectrum of fetalalcohol damage is not being classified effectively. Thisarticle describes a quantification of neuroanatomicalstructure that may supply a useful discriminator ofprenatal brain damage from alcohol. It is demonstratedin a data set of adults of both sexes.

Methods: Ninety adults (45 males) were examined bymagnetic resonance imaging (MRI). These subjectswere group-matched for age and ethnicity across threediagnoses: FAS, fetal alcohol effects (FAE), and nor-mals. All FAS and FAE were heavily alcohol-exposed inutero; normals were not. From T1-weighted MR brainimages, we extracted 3D morphometric representa-tions of shape for 33-landmark point configurations and40-point outlines of the corpus callosum along its mid-line (a slightly nonplanar structure).

Results: There are striking differences between ex-posed and unexposed in the statistical distributions ofthese two shapes. The differences are better charac-terized by excess variance in the exposed groupthan by any change in average landmark or outlineshape. For each sex, combining the callosal outlinedata with the landmark data leads to a powerfulquadratic discriminator of exposed from unexposed.The discriminating features include the relationshipof brain stem to diencephalon, and localized variabil-ities of callosal outline shape, but not diagnosis (FASvs. FAE).Conclusions: Statistical analysis of brain shape is apowerful new source of information relevant to fetalalcohol spectrum nosology and etiology. Patientswith FAS and FAE do not differ in these brain shapefeatures, but both differ from the unexposed. Theaspects of brain shape that are especially variablemay be entailed in the underlying neuroteratogeneticmechanisms.Teratology 64:4–32, 2001. © 2001 Wiley-Liss, Inc.

INTRODUCTIONThe teratogenic properties of alcohol were suspected

when children with unusual faces, growth deficiency,and a variety of abnormalities were observed amongthe offspring of alcoholic women (Rouquette, ’57; Le-moine et al., ’68; Jones et al., ’73). Jones and Smith (’73)coined the term “fetal alcohol syndrome” (FAS). Soonafterward, additional groups of children with this di-agnosis were reported from France (Dehaene et al.,’77), Germany (Majewski et al., ’76), Sweden (Olegårdet al., ’79), and elsewhere. By 1978, after more than 250published case reports (Clarren and Smith, ’78), it wasclear that FAS was only one identifiable form of anextended range of disorders associated with maternalalcohol abuse. By 1980, the teratogenic properties ofalcohol had been clearly established in animal models(cf. Randall, ’77), and neurobehavioral consequences ofprenatal alcohol exposure were being discovered thatwere not necessarily associated with morphologic ab-normality or even growth deficiency (Martin et al., ’77;Ouelette et al., ’77; Sander et al., ’77; Landesman-Dwyer et al., ’78; Streissguth, ’78; Streissguth et al.,’80a, b). By the mid-1980s, there was a large body ofliterature from both animal and human data congruentwith the principles of teratology as set out by Wilsonand Fraser (’77), showing multiple central nervous sys-tem (CNS) effects of prenatal alcohol exposure (West,’86) that depend on the dose, timing, and condition ofexposure. Related literature (Riley and Voorhees, ’86)enumerated teratogens in addition to alcohol for whichbrain damage was not necessarily accompanied bymorphological abnormalities or growth deficiency.

Yet throughout this period, clinical diagnosis re-mained focused on FAS. The non-FAS range of thespectrum of fetal alcohol damage has been variously

Grant sponsor: National Institutes of Health; Grant number: AA-10836; Grant number: GM-37251.

*Correspondence to Fred L. Bookstein, Institute of Gerontology, Uni-versity of Michigan, 300 North Ingalls Building, Ann Arbor, MI48109-2007. E-mail: fred@brainmap.med.umich.edu

Received 10 August 2000; Accepted 30 December 2000

TERATOLOGY 64:4–32 (2001)

© 2001 WILEY-LISS, INC.

labeled fetal alcohol effects (FAE) (Clarren and Smith,’78; Hanson et al., ’78), expanded FAS (Shaywitz et al.,’80), alcohol-related birth defects (NIAAA, ’83), prena-tal exposure to alcohol (Riley et al., ’95), partial FASand alcohol-related neurodevelopmental disorder(ARND) (Stratton et al., ’96), or atypical FAS and alco-hol encephalopathy (Astley and Clarren, ’00). For 20years, until just recently, there were few clinical pro-tocols for diagnosis within this range in the individualcase, despite the overwhelming evidence that alcohol isteratogenic throughout pregnancy (Guerri, ’98) atdoses and timings of exposure that may not produceobservable dysmorphology or growth deficiency. Thewidespread abuse of alcohol in our society, combinedwith this persistent nosological confusion regarding“partial manifestations” of the syndrome, have led tomajor problems identifying and meeting the therapeu-tic needs of individuals prenatally damaged by alcoholover this extended range of effects.

A quantitative evaluation of brain morphology mightimprove this diagnostic process. This article is one in aseries examining brain morphology and neuropsycho-logical deficit in a balanced sample of 180 subjectsequally divided by age (adults and adolescents), sex,and diagnosis (FAS, FAE, and normals for compari-son). The present article examines alcohol-relatedbrain damage using data from three-dimensional (3D)analysis of magnetic resonance images (MRI) for thefull sample of 90 adult subjects but defers analysis ofadolescents and of neuropsychological sequelae at allages to later manuscripts.

In studies of other severe childhood disorders, suchas schizophrenia or autism, subjects are characterizedby typical behaviors of unknown etiology. By contrast,in studies of FAS/FAE, patients have all been damagedby a known teratogen, prenatal exposure to ethanol:they represent the spectrum of consequences of a bio-logical process the cause of which is known. Exploitingthis knowledge of etiological homogeneity, in recentyears several investigators using MRI have reportedmorphologic abnormalities in patients with FAS/FAE(Mattson et al., ’96: diencephalon, cerebellum, andbasal ganglia; Riley et al., ’95: corpus callosum; Swayzeet al., ’97: corpus callosum) that arise from the commonembryological challenges confronting these patients’brains. The present article shares this thrust, as wellas the rich data resources of contemporary MRI, but

exploits a considerably more sophisticated analyticstrategy for neuroanatomic data.

The methodology we exploit in this study is land-mark-based, as discussed in the section, MR Imagesand Derived Data. In its handling of size differences,the method is demonstrably more powerful than earlierattempts (e.g., Mattson et al., ’96) to “adjust” the size ofneuroanatomical components for the microencephalythat is often found to characterize those with the diag-nosis of FAS or FAE. The principal sample filter ap-plied in the present study is simply the requirementthat the subjects be able to negotiate both the MRIsession and the 5-hr neurobehavioral battery. (Theneurobehavioral findings will be reported and corre-lated to the neuroanatomical data in subsequent pub-lications.) The resulting study is the first, we believe, ofsufficient sample size and richness of neuroanatomicaldata structure to develop strategies for individual clas-sification and detection. It is to this elusive questionthat the present work is addressed, toward the resolu-tion of the conundrum that has driven the entire re-search program of our group: the prognostically andtherapeutically valid classification of patients withbrain damage from prenatal alcohol exposure over thefull range of forms of damage. Only a broad-spectrumnosology can be expected to drive appropriate servicedelivery protocols.

SAMPLE

We studied 90 Seattle-area subjects aged 18–37years, comprising 30 unexposed normals and 60 cases.For brevity, we refer to the pool of all 60 cases as “theexposed,” although, of course, each was not only ex-posed to alcohol prenatally, but also affected, as evi-denced by their alcohol-related diagnoses. Thirty hadbeen diagnosed as FAS by a dysmorphologist, 30 asFAE. All groups of 30 were divided equally betweenmales and females, and the subgroups of 15 weregroup-matched by age and, as far as possible, by eth-nicity (Table 1). After giving informed consent, all sub-jects were examined by the identical protocol. Patientascertainment was from the Seattle FAS Follow-upDatabase, accrued over nearly three decades from re-ferrals from dysmorphologists. The diagnosis wasmade by David W. Smith or one of his fellows or train-ees (usually Sterling K. Clarren) after a clinical dys-

TABLE 1. Age, race, and IQ by sex and diagnosis

White Nat. Am. Black Mean age Age range Mean IQ IQ range

MalesNormals 10 3 2 24.2 19.1–36.9 113 85–137FAE 9 4 2 23.6 18.6–32.4 87 67–107FAS 9 6 0 23.9 18.5–36.9 84 65–113

FemalesNormals 9 5 1 23.1 19.0–36.2 114 93–136FAE 11 4 0 24.9 18.0–37.4 83 75–106FAS 10 4 1 25.1 18.2–35.9 82 66–102

Nat. Am., Native American; FAE, fetal alcohol effects; FAS, fetal alcohol syndrome.

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 5

morphology examination (Aase, ’90). Patients were di-agnosed according to the clinical guidelines of the time,for the most part (Jones and Smith, ’75; Smith, ’76;Clarren and Smith, ’78; Smith, ’83), before the recentdiagnostic changes suggested by the Institute of Med-icine (Stratton et al., ’96). Those without the full fea-tures of FAS were usually classified as FAE, oftenprefixed by “possible” or “probable.” In many ways,they could now be diagnosed as ARND (Stratton et al.,’96); however, we have retained the original terminol-ogy in this study. Normal subjects were recruited fromemployees and their children at local health care facil-ities and educational institutions to match approxi-mately the age and ethnic composition of the exposedgroup. Potential normal subjects were excluded whohad alcohol or drug problems, neurological problems,birth defects, cancer, or human immunodeficiency vi-rus/acquired immunodeficiency syndrome (HIV/AIDS),who were legally blind, who did not have English astheir first language, who had undergone psychologicaltesting during the last year, who had braces, or whosebiological mothers had a history of alcohol or drugproblems or had ever binged (five drinks or more on anoccasion) while pregnant with the subject. Potentialexposed subjects were excluded for AIDS, blindness,brain tumor, neurotoxic medications for cancer, or anative language other than English. Exposed subjectswere not screened for alcohol abuse, other substanceabuse, or multisubstance abuse, as these are knownrisks secondary to fetal alcohol exposure (Streissguthet al., ’96).

The six groups defined by sex and diagnostic cate-gory averaged 23–25 years of age (Table 1). The racial/ethnic composition of the sample approximates thecomposition of the alcohol-affected patient pool. Ourneuroradiologist noted two occurrences of “severe cal-losal abnormality” (one an FAS male, one an FAEmale). Although our sample design did not refer to IQin any explicit way, lowered full-scale IQ is a knownconsequence of the brain damage that follows fetalalcohol exposure. The exposed fall short of normalmean IQ by almost 2 standard deviations (SD), onaverage.

MR IMAGES AND DERIVED DATA

T1-weighted sagittal SPGR images were acquiredover a period of 12 min in a GE 1.5T Signa scanner atthe University of Washington: TE, 8 msec; TR, 29 msec;and flip angle, 45 degrees. The resulting 2562 3 124arrays of 0.852 3 1.14 mm3 voxels were processed byEdgewarp 3D software (Bookstein and Green, ’98).

Most neuroanatomic studies have been based on nowconventional volumetric analyses derived typicallyfrom detailed manual (possibly computer-aided) iden-tification of neuroanatomic structures and the compu-tation of their volumes. Tissue classification algo-rithms have also led to analyses of gray and whitematter volume. Measurement protocols are being de-veloped for volumetric analyses that we will carry out

later. The current article focuses on biological land-marks, which are named, biologically homologous loca-tions that can be associated with Cartesian coordi-nates. When landmarks can be identified tocharacterize structures of interest, the most efficientstatistical analyses, as well as the most informativegeometric diagrams and biological interpretations ofdifferences or variations in shape, will be based onanalyses of landmarks by the best current methods, asreviewed below.

The notion of a landmark is a general one, referringto any geometric locus that might be the target of alabel in a textbook illustration. Among the types oflandmarks are ordinary geometric points in two orthree dimensions, curves in a plane or in space, and 2Dsurfaces. In this article, we exploit the first two of thesetypes: points and curves.

Landmark points

We began this study believing that other researchershad developed protocols for identification of neuroana-tomic landmarks. In particular, we had intended tobegin with landmarks suggested by Evans et al. (’91).However, we were unable to find literature citations toany suitable operational definitions for any list of land-marks. (Indeed, many of the points originally proposedby other researchers, including those we proposed touse from the Evans group in Montreal, were not trulypoint landmarks for which operational definitionscould be promulgated.) We therefore conducted an in-vestigation to determine a set of point landmarks thatcould be reliably identified over a sample of normal ornear-normal adult brain images.

To this end, we used the 3D visualization and digi-tization facilities of the Edgewarp software packagefrom the University of Michigan (Bookstein and Green,’98) to explore operational definitions of landmarkssuch as those presented in Table 2. In consultationwith neuroradiologist David Haynor, University ofWashington, we carried out three rounds of trainingand comparison of digitizations of the point landmarksin Table 2 by our neuropsychologist (P.D.C.) and by anundergraduate research aide. Average inter-observerdifferences in digitized landmarks (averaging over 5randomly selected subjects) ranged from ;0.5 mm to,2.0 mm for most landmarks. It was determined, how-ever, that despite generally good agreement, occasionaloutliers resulting from misidentification of difficult-to-locate landmarks could not be avoided. To ensure reli-able landmark location, we adopted the protocol ofhaving all digitizations by the research aide reviewedand adjusted by our neuropsychologist. Our interestwas not in establishing reliability levels for identifica-tion of these landmarks by other researchers (for whichfurther inter-observer reliability studies would need tobe conducted), but simply to provide reliably identifiedlandmarks suitable for analysis in this study.

This investigation resulted in surprisingly few iden-tifiable 3D point landmarks in the human brain, andthose mainly subcortical. Table 2 reviews the set of 33

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MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 7

we ultimately came to use. Twelve are subcortical mid-line points, 16 come as 8 pairs of bilateral points, and 5are “extremal landmarks” (Bookstein, ’91) at the outerboundary of the cortex with the cranium.

Callosal outlines

There is a small but persuasive literature of alcoholeffects on the corpus callosum (e.g., prenatal alcoholexposure seems to be the principal known cause ofpartial or total callosal agenesis; Riley et al., ’95). Wetherefore determined to represent it more richly thancould be managed by its four unpaired landmarks:genu, internal genu, splenium, and rostrum (Table 2).Beginning with the landmark point rostrum alreadylocated, we digitized the rest of the callosal midlineoutline as a 39-point sequence of semilandmarks (land-

marks “slipped” along the outline; see below). Tracingwas carried out by one of the authors (F.L.B.), who wasblind to the diagnostic group. A typical set of digitizedlocations, totaling 40 points, is at left in Figure 1. Theseare spaced roughly inverse to curvature on a referenceform (the first one digitized). At right is a typical digi-tizing scene: a perpendicular section through a candi-date point along the lower border of isthmus. Eachdigitized point lies precisely on the “vertical” (axis ofsymmetry) of an image like this at the apparent bound-ary of callosum. The word “vertical” is in inverted com-mas because anatomically it is oriented perpendicularto the callosal outline, and so lies truly vertically onlyat a few scattered points (top and bottom of the arch,bottom of the splenium). The cross-hairs in this panelindicate how within any such plane, a plane containing

Fig. 1. Aspects of digitizing the corpus callosum in 3D. (left) Fulloutline, one subject, as projected onto a near-parasagittal plane. (Thesemilandmarks 1 do not actually lie precisely within this plane or anysingle plane.) Except for rostrum, all of the points on the outline havebeen allowed to slip to minimize bending energy with respect to atemplate form. Other landmarks: anterior commissure, posterior com-missure, tip of fourth ventricle, and left and right brain boundaries(not shown) at posterior commissure. (right) A typical point of the

outline (semilandmark 28, the one used in later figures) for onesubject, showing how approximate symmetry is used to determine thepoint digitized. The section here is perpendicular to the estimatedtangent line of the outline in its vicinity. The point digitized is slippedperpendicular to that tangent line until it lies at midgray voxel valueon the “midline” located visually by evidence of symmetry, and then ismoved along the tangent direction to minimize bending energy of theconfiguration as a whole.

8 BOOKSTEIN ET AL.

the normal to the callosal midline somewhere, the par-ticular point we seek is taken by its mediolateral posi-tion and its location on the grayscale gradient of theneural tissue. The third coordinate, pointing out of thispage, is the coordinate that passes tangentially aroundthe callosum in the left-hand image; it is computed bythe sliding algorithm reviewed above, rather than be-ing selected by the digitizing technician.

Even in the normal subgroup, these curves are dis-tinctly nonplanar: they do not lie in any possible “mid-sagittal plane.” For purposes of the statistical analysisto follow, the mediolateral (out-of-plane) coordinate hasbeen suppressed; its distribution shows no differencesamong the diagnostic subgroups in either mean or vari-ance. Reliability of these outlines over a random sub-sample of six digitized independently several monthsapart showed a reproducibility of ,0.6 mm in thetrajectory of the curve averaged over the whole out-line. This is comparable to the standard error of thebetter landmark points and is considerably smallerthan the magnitude of the effects reported in thepresent analyses (reported in units of Procrustes dis-tance, not mm).

MORPHOMETRIC METHODS

After inspection for errors, the configurations of neu-roanatomical landmarks or callosal semilandmarkswere analyzed by standard methods of the morphomet-ric synthesis. The entire subcortical region is quanti-fied in a single multivariate analysis that considers notonly differences in average size or volume, but alsodeviations from normal shapes and spatial relations ofthe different parts of the brain, whether the pattern ofdamage be found to be gross or localized. The modernstatistical toolkit underlying this work has been thesubject of a recent textbook (Dryden and Mardia, ’98)and several recent review articles (Bookstein, ’96, ’97a,’98). There is one statistical space for the variation ofthe shape of the landmark set and another for thevariation of the shape of the callosal outline. Thus, intheir geometry the landmark data and the callosaloutline data have been kept separate. In either of thesespaces, the shape of the geometric object in question (alandmark set, or an outline) is represented by onesingle “observation” per specimen—a rather compli-cated observation, yes, but one that is treated as a

Figure 1. (Continued.)

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 9

single algebraic entity for statistical purposes—regard-less of the number of points in the original digitizedrepresentation. When the spaces are combined (to pro-duce the findings displayed in Fig. 12), it is by statis-tical, not geometrical, procedures.

Getting from Cartesian coordinates to shape

The construction of a statistical shape space for out-line data is a special case of the construction thatapplies to landmark data. This section provides a quicksketch of the standard method for landmark points andthen indicates the nature of the extension to handlesmoothly curving forms such as the callosum. The Ap-pendix at the end of this article reviews the standardlandmark methods in considerably greater detail.

Shape is the information about landmark configura-tions that remains unchanged under adjustments ofposition, orientation, or scale. One straightforward wayof representing this information for statistical pur-poses begins by considering a shape distance betweenany pair of landmark configurations, and then con-structing a useful set of geometric coordinates, shapecoordinates, for which this shape distance is the appro-priate “Euclidean” sum of squares. Since the great orig-inal paper by Kendall (’84), the distance used for thesespaces has always been one or another modification ofthe following definition of Procrustes distance. It isconvenient to begin by removing location and size in-formation from each configuration separately, by cen-tering each at its own center of gravity and scaling eachto a fixed sum of squares around that center. Thescaling factor divided out in this step, called centroidsize, remains available as a size measure for use at anysubsequent stage of analysis. If all forms are standard-ized in this way, the Procrustes distance between anytwo is simply the sum of squares of the ordinary Eu-clidean distances between the matching landmarks ofthe two landmark configurations when one of them isfreely rotated (around the common center of gravity)until this sum of squares is minimized.

Shape averages and shape coordinates

From the shape distance formulation, the rest of thestatistical scheme follows very directly. One can definethe average shape of a set of landmark configurationsas the shape from which they have, taken together, theleast summed squared Procrustes distance. (This isprecisely analogous to the least-squares property ofordinary arithmetic averages: the average of any set ofnumbers is the value that has the least summedsquared difference from the numbers actually beingaveraged.) After that average has been computed, eachoriginal shape of the data set can be superimposedupon it by the rotation described in the preceding para-graph—the rotation that supplies the actual minimumsum of squares serving for its Procrustes distance tothe average. The locations at which the original land-marks arrive after this rotation serve us as the shapecoordinates of the original landmark configurationswith respect to the sample as a whole. For k land-

marks, there are 2k of these coordinates for 2D data, or3k for three-dimensional data. (But four dimensions oftheir space (for 2D data) or seven dimensions (for 3Ddata) necessarily have no variance; instead, they ex-press the constraints on position, orientation, and scalethat were imposed during the course of the construc-tion.) These coordinates serve as the set of variablesthat make possible an analysis of shape by otherwisefamiliar multivariate procedures. For instance, in Fig-ure 7, each point shown stands for two shape vari-ables—its x-coordinate and its y-coordinate—withgroup comparisons going forward in terms of the aver-ages, the variances, and the covariances of those vari-ables. (For a general discussion of the relationshipbetween shape coordinates and shape variables, in-cluding the most familiar shape variables such as an-gles or ratios of distances, see Bookstein, ’91). All theformulas entailed in this sequence of steps are avail-able in the Dryden textbook and the Bookstein reviews;software is available free of charge, to carry out thecomputations on most scientific research computerplatforms (see the website http://life.bio.sunysb.edu/morph/ maintained by F.J. Rohlf at the State Uni-versity of New York at Stony Brook). Our analyseswere carried out in the Splus statistical system, usingfunctions written by the authors.

Shape coordinates for outline data

A corresponding analysis for the callosal outline datatakes into account the indeterminacy of “homologous”points along extended curves like this midline. Book-stein (’97b) suggested that, beginning from any plausi-ble sampling of points along the curves of the sample, aProcrustes average in the sense just reviewed for land-marks alternate with a “sliding” operation that redis-tributes the semilandmarks of each outline along thatoutline in such a way as to minimize the “bendingenergy,” quantified in one specific algebraic way, thatcharacterizes the relation of the outline to the fullsample average. This approach is preferable to evenspacing of points, in permitting coordination of infor-mation between top and bottom of the arch, and ispreferable to approaches that assign coordinates out ofa “center” for the reasons reviewed in Bookstein (’91).For a justification of the relevance of bending energy tothis context, see Bookstein (’99). In the callosal dataset, our bending energy computation (for sliding) alsotook account of four conventional landmark points: thecommissures, the tip of the fourth ventricle, and therostrum, the only good point landmark actually locatedon the callosum. At the convergence of this alternatingalgorithm, one arrives at a sample average shape and aset of shape coordinates just as before. Points gener-ated by this algorithm are called semilandmarks.

Principal components analysis for shape

Once shape coordinates are in hand, a variety ofmultivariate statistical tools become available that cor-respond to those that apply to more typical biostatisti-cal data sets. This analysis exploits two of these tools:

10 BOOKSTEIN ET AL.

principal components analysis and testing statisticalsignificance of group differences in average shape or inthe variability of shape.

Whether for landmark data (points) or for semilan-dmark data (outlines), principal components analysisof shape is carried out by ordinary principal compo-nents analysis of the shape coordinates just described.The analysis uses their covariance matrix, not theircorrelation matrix, in order to preserve the Procrustesgeometry through subsequent steps. Within the con-text of shape analysis, these components are often di-agrammed as deformations (warps) of a grand mean(see Fig. 5), and are thus called relative warps. (In thisarticle, “deformation” is used only in its mathematicalsense, a smooth map from one picture to another.)

For ordinary sets of variables, the first principalcomponent is characterized as the linear compositethat has the greatest variance among the set of allpossible composites whose coefficients sum in square to1. Similarly, the first relative warp is the compositeshape variable (pattern of joint landmark rearrange-ment) having the largest variance among all the shapevariables of a given Procrustes length. If the concept ofthe Procrustes length of a variable seems forbidding,there is an exact equivalent that may be more accessi-ble: the Procrustes length of a shape variable is pro-portional to its variance on a model of “pure digitizingnoise,” the same small variance in every direction atevery landmark. Biological data can often be modeledeffectively by this noise distribution, perhaps after sys-tematic factors (e.g., prenatal exposure) have been con-trolled. The second relative warp is the compositeshape variable having greatest variance (per unit Pro-crustes length) of all those that are uncorrelated withthe first relative warp of the sample, and so on. Everysubject in the data set has a score (projection) on everyrelative warp of the data set, and these scores can bescattered to look for patterns or clusters, tested formean difference between groups, correlated with osten-sible causes or effects of shape, and generally treatedjust like any other set of principal component scores inany other application of multivariate statistics.

Testing statistical hypotheses about shape

Although this morphometric version of principalcomponents analysis is only slightly modified from thestandard approach, the way in which one tests hypoth-eses of mean shape difference changes considerably. Inmost morphometric data sets, there are more of theseshape coordinates (variables) than subjects. Hence oursignificance tests will usually be permutation tests(Good, ’94). In a permutation test, a quantity is selectedthat captures a scientific question about the relationbetween two aspects of the data structure. For in-stance, in studying the association between diagnosisand callosal outline in our 45 males, we might selectthe Procrustes distance between the average callosaloutline shapes of exposed and unexposed as an inter-esting measure of the scientific signal we are examin-ing. Then the distribution of this quantity is computed

over a very large collection of “pseudo datasets” inwhich diagnosis (FAS vs. FAE vs. normal) is randomlyreassigned over the 45 adult male callosal outlines. Thesignificance level of the empirical association betweendiagnosis and callosal outline, for the chosen quantity(the mean difference), equals the probability that arandom permutation of this type results in a Pro-crustes difference between averages at least as great asthe value actually observed. It was Ronald Fisher him-self (the “F” of the F-test) who first noted that this iswhat we actually mean by a statistical significancelevel, to which any other quantity deriving from text-book formulas, including his own, merely approxi-mates. For data sets large enough to preclude lookingat “all possible permutations” (about 340 billion, for oursample of 30 exposed vs. 15 unexposed males), onelooks at an adequately large random sample, here, afew hundred to a thousand or so. Permutation tests areeasily performed in any of the standard statistical soft-ware packages and, for landmark data such as these,are built into Rohlf’s TPSregr program, available freeof charge for Windows PCs from the Stony Brook, NewYork, site.

In the landmark data set, the feature underlying thetest for mean shift is Procrustes distance. In the outlinedata set, it is Procrustes distance in the direction nor-mal to the outline. For demonstrations of hypervari-ability, it is the ratio of the sum of variances of the firstthree principal components of shape for the exposed tothat for the unexposed.

MAIN MORPHOMETRIC COMPARISONS, BYDIAGNOSIS AND SEX

Our morphometric analyses involve comparisons ofboth kinds of shape by diagnostic group and sex andprincipal components of both kinds by sex. There arefindings of four different types: size differences, meansand principal components of landmark shape, meansand principal components of callosal outline shape, andthe combined pattern of the two shape components. Inthis section, each of these is recounted separately, lead-ing to a total of six distinct findings. In general, groupdifferences in shape variability far outweigh group dif-ferences in average shape or average size, allowing astartlingly powerful discrimination of the exposed fromthe unexposed by shape alone, whereas the two ex-posed subgroups (FAS and FAE) differ in shape hardlyat all. The reader who does not wish to wade deeplyinto the details may choose at this point to turn directlyto the section, Summary of the Findings, which high-lights the six main findings separately from the sup-porting computations.

Size

A morphometric analysis of either landmarks orsemilandmarks should begin by considering centroidsize, the scaling factor divided out in the course ofproducing shape coordinates. Means and standard de-viations of this descriptor are presented in Table 3 for

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 11

the two different data structures of this study, thelandmark configuration and the callosal outline config-uration. For the landmark data in the males, bothexposed groups differ by about 4% from the normalmean. The females diagnosed with FAE differ from thenormal females by about the same amount, but theFAS females were about 8% in deficit. Student’s t-testsfor these comparisons are all significant at P , 0.01.For this landmark configuration, centroid size is ap-proximately proportional to “shoebox size,” the diago-nal of a rectangular shoebox around the landmark con-figuration as a whole. For the centroid size of thecallosal outline, the difference of 7% between the nor-mal mean and the average for the exposed pool issignificant at P , 0.002 by t-test. For forms that arethis long and narrow, centroid size is approximatelyproportional to the diameter of the callosum itself, thedistance from genu to splenium. For the females, theFAS mean is clearly different from both of the others.In terms of callosal area, the conventional alternativeto centroid size, the male diagnostic groups likewiseshow a 7% shortfall for the exposed pool, but none ofthese differences is significant, as the within-groupcoefficient of variation for area is far greater than thatfor length. For the females, mean callosal area in theFAS subgroup is again clearly and significantly differ-ent from the other two (P , 0.002).

Our shape findings are reviewed in three subsec-tions: landmark shape variation, callosal outline shapevariation, and the combination.

Landmark shape variability

Figure 2 illustrates the mean landmark shape con-figurations according to their three cardinal views(from the front, the top, and the side). The axes are inunits of Procrustes coordinates, which are dimension-less. In the top row, the landmarks are named at theirgrand mean locations; in the bottom row, the sex- anddiagnosis-specific means are shown, exaggerated five-fold away from the grand means for visibility. TheProcrustes distances among these six means are shownabove the diagonal in Table 4, and their significancelevels (by permutation test using 500 permutations)below the diagonal. In general, no differences attribut-able to syndrome are as large as the difference betweenthe male and female normals, and within sex no meandifference between any pair of the three diagnosticgroupings is significant. Male and female normals, as

well as male and female FAE, are very significantlydifferent, whereas male and female FAS are not toodifferent. However, such contrasts are not the primaryinterest of this study. Although the groups are knownto differ in centroid size, and although centroid size isa covariate of shape variation in general human popu-lations, it is not appropriate to “correct” any of thesecomparisons for size difference, as brain size is deter-mined by the same prenatal dose that led to the diag-nostic assignments of these subjects in the first place.

We learn a great deal more from the examination ofrelative warps than we could glean from these meancomparisons alone. Figure 3 shows the scatter of thefirst two relative warps separately by sex. Recall thatthese are the patterns of relatively greatest shape vari-ation, each one standing for a set of correlated shifts ofall the landmarks jointly. Like any other principal com-ponent, the pattern they delineate pertains to the poolof all the male subjects, or all the females, and not toany single subject. In either sex, the scatter of thenormal sample (filled circles) is much less than that ofthe 1 and 3 symbols standing for the exposed. Theoriginal analysis was of the first three relative warps,and tests were carried out using that slightly largersubspace. For the males, the significance level of theextra variance in the exposed subsample, summed overthe first three relative warps, is P , 0.01; for thefemales, it is P , 0.025. Most of the excess of variancein the relative warps can be captured by projecting ontothe directions shown (separately by sex) in Figure 3.The short axes of the normal subsamples after outliers(one for the males, two for the females) are seques-tered. (That is, once those outliers are sequestered, thecenter of gravity of the remaining control data in eachpanel is the midpoint of the little segment there, andthe best-fitting ellipse to the covariance pattern ofthese points has the direction indicated as its shortestdiameter.) Separately by sex, these patterns of jointlandmark rearrangement have considerably more vari-ance in the alcohol-exposed subsample than in the un-exposed sample.

Visualization of systematic aspects of 3D shape vari-ation, such as these particular linear combinations,goes forward best via dynamic (tumbling) 3D displays.For publication, one selects a number of still imagesfrom these displays. Figure 4 shows the effect of anarbitrary multiple of these changes at all landmarkssimultaneously, in the usual three views. In both sexes,

TABLE 3. Size measures by diagnosis and sex*

Group Landmark CS Callosal CS Callosal area

Normal M 248.9 6 4.8 26.25 6 1.72 1159 6 155FAE M 238.2 6 9.1 24.22 6 1.67 1057 6 216FAS M 240.5 6 7.7 24.63 6 1.99 1103 6 227

Normal F 241.7 6 7.3 25.52 6 1.80 1199 6 165FAE F 233.8 6 6.9 24.73 6 1.29 1154 6 181FAS F 224.6 6 9.4 23.15 6 1.10 928 6 162

CS, centroid size; M, male; F, female; FAE, fetal alcohol effects; FAS, fetal alcohol syndrome.*Means 6 SD in digitizing units of mm, except for area, which is in units of mm2.

12 BOOKSTEIN ET AL.

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MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 13

very little of this correlated hypervariation lies in themediolateral direction; thus, we can profitably restrictour attention to the lateral view, which nullifies thisdimension. In that view, Figure 5 demonstrates theeffect of an arbitrary amount of change in the trans-versal dimensions of Figure 3 by displacement vectors(top) and by splined deformations (bottom). The land-mark key is repeated for convenience at lower right.The thin-plate spline, a standard tool of the new mor-phometrics, depicts a landmark rearrangement as adeformation of the diagram plane in which the land-marks lie. Of all the grids that could be drawn for this

purpose, the spline is the smoothest—the one that hasthe least extent of local bending in one specific alge-braic sense. For an extended explanation and justifica-tion, see Bookstein (’96, ’97a, ’98).

Each scene divides into two regions: structures on oradjacent to the pons, and rearrangements in the vicin-ity of the corpus callosum. In both sexes, the segmentconnecting fornix (Fx) to bottom of pons (BtP) is rotatedstrikingly, in accord with the realignment of grid linesfrom vertical throughout the middle of both grids. Thefeature in question varies bidirectionally; for example,the rotation of that vertical grid line could have just as

TABLE 4. Procrustes distances between diagnostic groups: landmark pointdata*

Male Female

Normal FAE FAS Normal FAE FAS

Normal M — 61 72 138 104 58FAE M 0.222 — 18 194 129 64FAS M 0.176 .0.5 — 206 149 71

Normal F 0.002 — — — 77 94FAE F — 0.002 — 0.052 — 50FAS F — — 0.295 0.323 .0.5 —

M, male; F, female; FAE, fetal alcohol effects; FAS, fetal alcohol syndrome.*Entries above upper left–lower right diagonal: squared Procrustes distances between groupmean shapes, multiplied by 105. Below diagonal: significance levels, according to 500 per-mutations of diagnostic label over landmark configuration.

Fig. 3. Relative warps analysis (principal components analysis of shape coordinates) for the landmarkdata set. Left, males; right, females. Scatters of relative warp scores 1 versus 2 are in units of Procrustesdistance. Short segments in each panel, indicating the dimension of least variance of the normals, aretaken along the shorter principal axis for the subscatters of the apparently typical normals (14 males or13 females). Outliers excluded for this purpose (but included in all statistical testing): for the males, therightmost normal point; for the females, the leftmost and rightmost normal points.

14 BOOKSTEIN ET AL.

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MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 15

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16 BOOKSTEIN ET AL.

well been drawn as counterclockwise, by reversing allthe vectors in the top panels. In the males, this factor ofhypervariability moves BtP, Obex, Tip4, and TpPstrongly anteriorly (respectively posteriorly) with re-spect to the commissures, whereas all the points of thecallosum shift posteriorly (respectively anteriorly) ex-cept for Spl, the posteriormost point itself. In the fe-males, this brain stem shift is rather more upward(respectively downward) than forward (respectivelybackward), the principal shift in the posterior callosumis at the fornices, and the front of the callosum shiftsdownward (respectively upward) rather than backward(respectively forward) with respect to the commissures.Also in both sexes, the central cerebellar sulcus (CCS)has moved distinctly anterior (respectively posterior)with respect to the occipital pole OcPo. Keep in mindthat each of these is to be read as a pattern of coordi-nated shifts in all landmarks, and that what we arelooking at is not the shift of an average shape amongthe diagnostic groups (none of those was significant),but rather the extra variation apparent in the pool ofdiagnostic groups by comparison with the normals,separately by sex.

These patterns supply tantalizing hints of localiza-tion of the excess variation for confirmation in othersamples. For example, as shown in Figure 6, the with-in-sample variance of the vector from “midpons” (BtP,Obex, Tip4, and TpP) to fornix is 0.00049 in the maleexposed pool and 0.00051 in the female, versus 0.00020in the normal males and 0.00032 in the normal fe-males; this variance ratio is significant at P , .005 for

the males, and at 0.07 for the females, by ordinaryF-test. (The variance of a vector is the sum of thevariances of its two components separately; this sum isindependent of the orientation of the coordinate systemin which the components are specified.) The vector maybe imagined as a sort of axis for the relationship ofbrain stem to diencephalon. (In particular, the notionof a “midpons” has no biological reality but is just aconvenient way of summarizing the common shift pat-tern of the four points in its vicinity with respect to theshifts of the two fornix points, which go the other wayaccording to this same pattern.) In this sense, there isconsiderably more variance in the exposed than in thenormals in the angle between brain stem and dienceph-alon; the hypervariation factors of Figure 4 show thisvariation along with the displacements of other land-marks, such as those near genu, that happen to beassociated with it.

Callosal outline shape variability

The data set of callosal outline shape offers the richerfindings here. Figure 7 (left) shows the complete sam-ple scatter of 40 points (39 semilandmarks, togetherwith rostrum) for the complete data set of 90 adults.This variability is commensurate with that of the land-mark points analyzed in the previous section. Figure 7(right) shows the six diagnosis- and sex-specific means.In pairwise mean comparisons (by permutation test),none of the differences among the male diagnostic sub-groups is significant, but all pairwise comparisonsamong averages for the females are nominally signifi-

Fig. 6. Interpretation of landmark hypervariance factors by localization to a vector from midpons tomidfornix in the lateral view. The vectors are plotted as if all images were registered to a commonmidpons point, as shown. Legend: F, normals; 1, FAE; 3, FAS. “Midpons” is the centroid of thequadrilateral TpP, BtP, Obex, and Tip4.

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 17

cant. Distances and significance levels (by permutationtests of 500 runs) are presented in Table 5. Figure 8sets out their shape differences pairwise as thin-platesplines, exaggerated threefold for legibility. The nor-mal mean clearly bears a differently shaped spleniumfrom either diagnostic group, and a thicker genu. Theisthmus is thinner in the FAS subgroup, with the archrelatively higher in the FAE subgroup. As the top rowof Figure 8 suggests, the splenium anomaly for bothexposed groups is similar to the representation of themean shape for normal males as a deformation of thatfor the normal females.

Even more than the landmarks, our callosal databespeak a strong excess variability in the exposed sub-sample. Figure 9 shows the subscatter of its 45 outlineshapes for each sex (as in Fig. 7). When the normal

subsamples are indicated by connecting the dots, itbecomes apparent that the semilandmarks of the syn-dromal subsample lie well outside the envelope of theoutlines for the normal subsamples at several sites. Wecan test this impression rigorously by applying thesame permutation test (variance of relative warps be-tween exposed and unexposed) that was used for thelandmark data. Summed over the three callosal shapedimensions of largest Procrustes variance, the netshape variability within the exposed pool is signifi-cantly larger than that within the normal pool at P ,0.01 for the males, P , 0.025 for the females. Figure10 localizes this difference by ordinary F-tests (Bart-lett’s test for difference of variances) at each semilan-dmark separately. Because variation along the direc-tion of the average curve has already been adjusted out

Fig. 7. Procrustes shape coordinates for the projected callosal outlines. Left, complete sample scatter ofrostrum and 39 semilandmarks for all 90 subjects. Right, means by diagnosis and sex.

TABLE 5. Procrustes distances between diagnostic groups:callosal outline data*

Male Female

Normal FAE FAS Normal FAE FAS

Normal M — 53 34 65 162 63FAE M 0.425 — 20 71 99 77FAS M .0.5 .0.5 — 58 108 57

Normal F 0.126 — — — 157 102FAE F — 0.120 — 0.006 — 118FAS F — — 0.323 0.040 0.044 —

M, male; F, female; FAE, fetal alcohol effects; FAS, fetal alcohol syndrome.*Entries above upper left–lower right diagonal: squared Procrustes distances between groupmean shapes, multiplied by 105. Below diagonal: significance levels, according to 500 per-mutations of diagnostic label over callosal shape.

18 BOOKSTEIN ET AL.

during the course of producing these Procrustes coor-dinates (see section, MR Images and Derived Data), thetest is of variance in one direction only, perpendicularto the average curves of Figure 7. For at least onesemilandmark in each sex, the significance of this vari-ance discrepancy is P , 0.05/39 ; 0.001, so that the setof multiple comparisons is significant according to theconventional (Bonferroni-corrected) inference as well.The arcs of greatest discrepancy are quite differentlysituated in the two sexes: for males, anterocaudal toisthmus; for females, in the arch.

Figure 11 focuses on the best three of these points,for each sex, to illustrate what the F-test is detecting.Point by point, the normals’ semilandmark coordinatesconcentrate themselves about the average outline atleast as well as did the relative warp scores for thewhole set of landmarks (Fig. 3). We thus harvest awhole new discriminator to augment the pair sug-gested in Figure 3. For the males, the point of greatestapparent information content, semilandmark 28, isconcentrated indeed, and so we take its coordinate

perpendicular to the outline as the simplest usefulscalar for adducing the hypervariance of the exposed.For the females, the semilandmarks atop the archshow the greatest variance ratios. A summary scorethat weights upper and lower arcs equally takes theaverage vertical coordinate of the set of all four.

Combining the shape spaces

Figure 12 combines the findings for landmarks andcallosal outlines in one composite display. Separatelyby sex, the dimension of sharpest increase in variancefrom the landmark relative warp analysis (Fig. 4) isplotted against the shape coordinate of greatest hyper-variance from the outline analysis (Fig. 11). Clearly,the two analyses, by landmark and by callosal outline,are complementary. If, as shown, boxes are takentightly around the cores of the scatters for the normals,a classification rule emerges that calls subjects alcohol-affected just when they lie outside the boxes. The rulehas putative sensitivity and specificity of 0.90 and 0.93for males, 0.97 and 0.87 for females—enormously

Fig. 8. Thin-plate splines for comparison of normal males and females and also for all pairwisecomparisons of the female averages from Fig. 7. Each difference is exaggerated threefold for legibility.

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 19

greater than anything hitherto reported from neuro-anatomical data, with or without knowledge of size.These classifiers are uncorrelated; thus, each channelof measurement detects some exposed cases as hyper-variant that are not detected by the other. But, ofcourse, as the findings are not homologous between thesexes, each needs to be replicated in its own additionalsample. Replications using 45 male and 45 female ad-olescents are in progress.

As the earliest FAS patients were often mentallyretarded, it is important to think about IQ as a relevantdimension of these subject populations; nevertheless,because lowered IQ is itself a consequence of the braindamage that is our primary dependent variable, we didnot impose any IQ selection criterion during the courseof assembling our samples. Figure 13 annotates Figure12 with the full-scale IQ scores of the alcohol-affectedsubgroup. The plot is entirely consistent with ouremerging awareness that facial stigmata, intellectualdeficit, and actual neuroanatomical abnormalities arefairly independent within the relatively high-perform-ing end of the exposed range. There is no apparentpattern of full-scale IQ deficit by position in this plot ineither sex, nor is the FAE subgroup “intermediate” inany useful sense between the normal subsample andthe subjects diagnosed with the full FAS. As this is animportant finding, albeit a negative one, we present itmore explicitly in Figure 14, which makes explicit howIQ varies with “net severity” of brain damage, mea-sured as distance from the average of the typical nor-mal subgroups boxed in Figure 12. The line on each

graph is a standard scatterplot smoother applied to theexposed subsample only. Clearly, there is no tendencyfor IQ to decrease with distance from the neuroana-tomically normal in this composite shape space. Withinthe exposed group there is also no association of theseshape discriminators with centroid size.

SUMMARY OF THE FINDINGSThe preceding discussion was a lengthy recount of

analyses that are likely to be relatively unfamiliar tothe reader. It may be helpful to summarize these find-ings before discussing their implications. We analyzedvariations of shape, by sex, among normal subjects andsubjects diagnosed with an alcohol-related disorder,either FAS or FAE. Two data structures were extractedfrom the same MRI: one of 33-point landmark locationsand the other of 40-point representations of a callosalmidline curve. Our principal findings are the following:

1. For both sexes, and for both shape representations,the exposed group has distinctly more shape vari-ability than the normal group.

2. In the landmark point data, the excess variabilityseems to involve the brain-stem-to-diencephalonaxis.

3. In the callosal outline data, both sexes have morevariance among the exposed than among the nor-mals, but the site of particular hypervariation dif-fers by sex. The additional variance seems concen-trated under the isthmus in males, but in the heightof the arch for females.

Fig. 9. Procrustes shape coordinates for the outlines shown in Fig. 7, separately by sex, with the outlinesof the normal subjects connected. The variation of the exposed shapes outside the range of the normal isclear at several arcs around the circumference. The overall ratio of within-group variances, exposed vs.unexposed, is significant by the permutation test described in the text.

20 BOOKSTEIN ET AL.

4. The combination of these two localizations of vari-ability supports a discrimination between the nor-mals and the alcohol-affected with startlingly highsensitivity and specificity.

5. For both sexes, FAS and FAE each differ from thenormal mean, but in neither sex do they differ muchfrom each other. In particular, the discrimination ofnormals from exposed is not improved by knowledgeof subdiagnosis.

6. Nor is the discrimination of normals from exposedimproved by knowledge of IQ within this samplepopulation.

DISCUSSION

Our alcohol-exposed subjects had been diagnosed be-fore the onset of the study. Each was assigned either adiagnosis of FAS or what was then called FAE afterexamination by a dysmorphologist experienced in FAS.We combined these historical diagnostic records withdata collected under a new methodology for quantify-ing brain differences between groups. Two types ofdata were involved: (1) landmark point configurations,restricted to brain regions where landmarks could eas-ily be located (i.e., subcortical structures); and (2)closed curves in space, required for the analysis of thecorpus callosum. The statistical analysis of their vari-ability went forward separately, using closely relatedalgebraic tools, and was then fused at the final stage ofthe analysis, the discrimination step.

The methodology weaving these data together in-volves three separate strategic decisions, each more or

less unusual within our literature. The principal find-ings (as reviewed above) are expressed in terms ofvariances, not mean differences; they refer to shapevariables instead of size variables; and the scientificgoal they pursue is a discrimination, not a description.Interrelations among these thrusts are built into themethodology of shape coordinate analysis on which wehave relied. For instance, the initial decision to exam-ine shape variables more intensively than size vari-ables made possible the important finding of the excessvariability among the exposed—the shape features in-volved are not easily summarized in conventional mea-sures of distance or area within parts of the form. Inturn, the strength of the hypervariation underlies thesurprisingly effective separation of affected subjectsfrom normals conveyed in Figure 12, the sensitivityand specificity of which are so unexpected. Using eitherlandmark point shape or outline shape, whichever ismore practical for the tissue(s) at hand, the new toolkitsupports studies of the affected parts of the brain andof the relationship among those parts at the same timeand in the same computations. And however widelydistributed the data in space, their statistical summaryremains a unitary multivariate computation. We high-light the implications of these findings under five head-ings: the biotheoretical meaning of findings dealingwith variability, the corpus callosum in ethanol terato-genesis, the literature of dysregulated brain stem/dien-cephalon relationships, the growing suspicion that FASand FAE are the same clinical entities, and some meth-odological details.

Fig. 10. P-values of F-tests for excess variance in the exposed subsample perpendicular to the averageoutline, semilandmark by semilandmark. For the males, the signal shown concentrates in the isthmus;for the females, in the arch.

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 21

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22 BOOKSTEIN ET AL.

Variability as a finding

It is not that the idea of considering differences ofvariance instead of differences in mean is unfamiliar tothe quantitative biologist. It is present in most appliedstatistics texts under the heading of “verifying the as-sumptions” (of equal variances) required for conven-tional analyses of variance. In its essentials the com-parison of two variances is a matter of the sameF-ratios (variance ratios) that already underlie theusual tests for mean differences. What makes themunusually apposite for teratological applications suchas these is their direct application to a specific high-dimensional vector of shape coordinates. In teratology,it is the malformations of shape, not those of size, thatare inherently of greatest interest, and so a differencein variances need not be considered a nuisance inter-fering with inferences about means, but rather can bea powerful finding in its own right.

This finding is in accord with the now rather oldliterature concerning the origins of normal variation,the denominators of all the variance ratios we havebeen finding significant in the present study. For aclassic overview of this topic, see Chapter 3, “Anatom-ical Variations—Significance,” in Williams (’56). Thischapter reviews the literature (through 1956) on quan-titative and qualitative variations of structure in ani-mals and humans, concluding, unsurprisingly, thatgreat variation from one normal individual to anothercan be found in structures in all of the body’s physio-logical systems, and that, in particular, “the brain isextremely variable in every character that has been

subject to measurement” (an observation the authorattributes originally to Karl Lashley). Williams goeson: “Few studies are available concerning the struc-tural variations in human brain tissue, considering thepossible importance of their relation to behavior. Vir-tually nothing is known about disharmonies of devel-opment in the central nervous system except for verygross deficiencies.” We know of no review over theintervening 44 years that would substantially alterthis summary; the last monograph on methods for themultivariate study of such variations as might arise,Olson and Miller’s Morphological Integration (’58), alsodates from the 1950s. Regarding current methodologi-cal fashions, it is worth noting that the index of onepopular current reference on psychopathology (Harris,’98) does not include any citations to the use of the term“variability” at all.

All the more startling, therefore, that our study ofone abnormal developmental pathway, having theknown cause of alcohol teratogenesis, has uncoveredtwo distinct neuroanatomical configurations—thebrain stem/diencephalon axis and the quantitativeshape of the midline corpus callosum—for which the“disharmonies of development” prove so spatially spe-cific. The finding is a variance ratio; thus, the signal itbetokens might pertain either to its denominator (un-usual invariance of form in the normally developingembryo) or to its numerator (a disregulation of thenormal process in the same embryo that has been al-cohol-affected). The former interpretation, the narrow-ing of range of the most crucial aspects of embryogen-

Fig. 12. Scatter of the most hypervariant landmark shape dimension against the selected hypervariantcallosal shape coordinate, separately by sex. The great concentration of the normal subgroups (filledcircles) is evident. 1, FAE; 3, FAS.

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 23

esis, is the more fruitful theoretically, as it correspondsto Waddington’s classic notion of developmental canal-ization, whereby individuals attain a common endpointof anatomical form despite variation in ontogeneticconditions. The callosum finding has precisely the log-ical structure of a disrupted canalization. Rhetorically,a “disruption” lacks the implication of a polarity thatwould otherwise be borne in words such as “deficit”;indeed, in the hypervariation characterizing thepresent findings, there is no particular direction inwhich the exposed group has been substantially shiftedwith respect to the controls—no “direction of deficit,”such as would underlie a linear discriminant function;instead, there is a calibration of similarity versus dis-similarity to the normal, a contrast of typical withatypical in all directions of potential shape defect, notjust one preferred direction.

The corpus callosum finding

Development of the human corpus callosum beginson about the 39th postconception day with differentia-tion of the commissural plate, and callosal fibers dif-ferentiate from that plate at about the 74th day,achieving adult morphology by day 115 (Loeser andAlvord, ’68). It is therefore reasonable, that damagesecondary to prenatal alcohol exposure would resultprincipally from exposure within the first trimester ofpregnancy, as is the case for the general “latent braindamage” observed by detailed measurement of behav-ior in large human samples (Streissguth et al., ’93).Indeed, partial or total agenesis of the corpus callosumhas been noted before in subjects diagnosed with FAS

(Riley et al., ’95; Swayze et al., ’97)—this observationwas the reason we chose to measure callosal outline forthe purposes of the present study. We had no cases ofdiagnosable agenesis in this adult sample. If agenesisitself is a direct consequence of exposure, it is likely tobe engendered only at levels of exposure that arehigher than those that typify the subjects of thepresent study (who, the reader will recall, had to becapable of undergoing a 5-hr battery of neurobehav-ioral tests in addition to the MR acquisition generatingthe data analyzed in the present study). The callosumtypically develops in a rostrocaudal direction (Schaeferet al., ’90), and partial agenesis is usually observedposteriorly, but we do not see any concentration of sizedifference or of variance differences at either end of thecallosum (cf. Fig. 7).

Inasmuch as all the patients in this study were di-agnosed with alcohol damage, the data set affords nocontrasts speaking to any specificity of the findings.Indeed, more serious prenatal insults, such as spinabifida, can entail partial callosal agenesis at consider-ably greater rates than are found in fetal alcohol pop-ulations. But the literature suggests no reason to sus-pect hypervariance of callosal form in any mildersyndrome. We would welcome comparative studies onthis theme, especially in other patient groups charac-terized by attention disorders (cf. Banich, ’98).

Although Riley et al. (’95) make no explicit referenceto callosal shape variability per se, their Figure 4 in-cludes standard deviations of “proportional area” (ar-eas of five sectors of the callosal outline as a percentageof their total), and thus lets us interpret their data set

Fig. 13. Enhancement of Fig. 12 by full-scale IQ for the exposed subsamples. NA, score missing(unobtainable).

24 BOOKSTEIN ET AL.

in the light of our present findings. The coefficient ofvariation of all five of the proportional areas is obvi-ously significantly larger in their exposed subgroupthan their unexposed subgroup, “preconfirming” ouranalysis. Apparently more discrepant is one recentstudy reporting an increase in callosal size consequentto exposure. Using a binge model in macaques, Milleret al. (’99) found that the rostral half (only) of theexposed callosa increased in size by comparison withunexposed controls. Operationally, the separation be-tween rostral and caudal halves of the callosum is atthe divergence of the fornix. This is perhaps an unfor-tunate strategy for group comparisons in which thatpoint itself may have shifted along the callosal outline.In our human sample, hypervariance is concentratedat that point, especially in females (Fig. 4). Note alsothat, according to Table 3 of their publication, callosalsize is clearly hypervariable in the exposed groups.Hence the Miller finding, based as it is on a total of only15 animals over three groups, could well be an expres-sion of hypervariance rather than the mean shift re-ported by those authors.

The brain stem/diencephalon finding

Brain stem anomalies have been found in a numberof developmental syndromes, often teratogenetic. Inone autopsy of an autistic patient, a shortening of thebrain stem was noted, an outcome arising in animalmodels including Hoxa-I gene knockout and exposureto antimitotics or to thalidomide (Rodier et al., ’96, ’97).

A mouse model of holoprosencephaly (Lanoue et al.,’97) shows abnormalities of mid- and hindbrain struc-ture. Retinoic acid early in pregnancy in mice producesArnold-Chiari malformations (Alles and Sulik, ’92), in-cluding herniation of the hindbrain, owing to the pri-mary damage to the neural crest and rhombencepha-lon. Similar brain stem dysmorphology is oftenobserved after alcohol exposure in laboratory animals(Maier et al., ’99; Thomas et al., ’96). Studies of prena-tally alcohol-exposed rats have linked brain stem dam-age of this sort to some of the behavioral deficits thatcharacterize FAS/FAE in humans: decreased brainstem weight with motor deficits (Thomas et al., ’96), orbrain stem damage with auditory processing (Churchet al., ’96)—for the human analogue, see Pettigrew andHutchinson (’84). But these studies did not pursue theissue of geometric shape as it has been formalized inthe analyses presented in this article.

FAS and FAE do not seem to differneurologically

Studies of neurobehavioral teratology in animalshave demonstrated repeatedly that both brain dysmor-phogenesis and behavioral dysfunction occur in off-spring prenatally exposed to alcohol even in the ab-sence of dysmorphic facial features, limb anomalies, orgrowth deficiency (Goodlett and West, ’91; Riley et al.,’90; Means et al., ’88). For more than a decade, firstqualitative and, recently, quantitative evidence for theabsence of clear behavioral distinctions between pa-

Fig. 14. Within this sample of exposed subjects, none profoundly retarded, atypicality of neuroanatomi-cal form greatly distinguishes them from the normal subgroup but nevertheless is not associated witheither the facial features of the full FAS syndrome or the measured full-scale IQ. Broken line, lowessscatterplot smoother (for the exposed subsample only). F, normals; 1, FAE; 3, FAS.

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 25

tients with FAS and those with FAE has been accruingfrom several research sites (Streissguth et al., ’91; Ko-dituwakku et al., ’95; Aronson, ’97; Mattson et al., ’97;’98; Mattson et al., ’99; Autti-Ramo, ’00). Previous ef-forts to detect brain anomalies in patients with FAScompared with FAE (Clark et al., ’00; Mattson et al.,’97) have been straitjacketed by their reliance on sizeand volume assessments, which are irrevocably con-founded with IQ levels, and thus with diagnosis. (Alco-hol-exposed children who are mentally retarded are farmore likely to be diagnosed with FAS than are thosewho are not; see Sampson et al., ’00). The sharp focuson shape variation here more effectively quantitatesthe intricacies of brain maldevelopment observed qual-itatively by teratologists and embryologists for de-cades. That the diagnosis of FAS cannot be distin-guished from that of FAE from solid brain MRI (asquantified in the way we have done in the presentstudy) bears enormous implications for the clinicalcourse of these patients, inasmuch as brain dysmor-phology is the center of the prenatal teratogenetic ef-fect of alcohol. Diagnoses that can take these into con-sideration are thus likely to improve the delivery ofappropriate social services, as they will be more closelytailored to the actual neuroteratological basis for prog-nosis in this class of patients.

Morphometric data

Of the two morphometric data channels combined inthis article, that of landmark point locations is the lessunfamiliar. The general issue of homology amongpoints of the cortex proper (e.g., points on gyri or sulci,points on the gray–white boundary) is currently thesubject of intense debate among many research groups(see, e.g., Toga, ’99). Thus far there is no methodologyfor judging the comparative merits or demerits of sug-gestions from this class: for instance, there is not yetany general agreement that Talairach’s (’88) originalclinical suggestion of an AC–PC registration is demon-strably wrong on scientific grounds, let alone agree-ment on the reasons why it should be considered wrong(cf. Toga, ’99). The registration here, using the machin-ery of Procrustes shape coordinates, arises from a jus-tification that is mathematical, not necessarily empir-ical: it is the optimal way of visualizing shapevariations of landmark configurations in general. Inempirical applications, analyses that assign correspon-dences to points stand or fall on the covariations of theensuing shapes or sizes with known causes or conse-quences of form, such as the fetal alcohol spectrumdiagnoses in the present study.

In this connection, we had originally included, verytentatively, three other landmarks that did not make itinto the final list of 33 (Table 2). The “bottom of the topof the cingulate sulcus”—a midline landmark locatingthe base of the cingulate sulcus where it turns laterallyalong the superior aspect of the brain—proved intoler-ably unreliable across raters. It is typical, we nowbelieve, of landmark structures that are truly curves inspace, to be represented as such for statistical pur-

poses, but we restricted the present investigation tojust one such curve, the callosum, because of the clearimplication of prenatal alcohol in callosal anomaliesalready noted in the literature.

The posterior analogues of landmarks Fr–r and Fr–l,tips of the frontal horns of the ventricle, would be thetwo matching tips of the occipital horns. These couldindeed be localized reliably on the individual subject,usually by following the narrow crevices of CSF poste-riorly to some extent. However, the points thus arrivedat appear to be bimodally distributed, with one tenta-tive location about 2 cm posterior to the other. Theappearance of the landmark in one or the other of thesepositions proved not to be associated with diagnosis,sex, or, in many cases, the contralateral position. Infact, this “tip” is a pair of landmarks, one of which wasmissing on each side for each subject. We omitted theselandmarks because, taken individually, they were sys-tematically missing in this way. Otherwise, the readermay have noted (by the absence of a footnote to thecontrary in Table 2) that there are no missing land-mark data across the full collection of 33 points here for90 subjects. We would welcome the attempts of othersto extend Table 2 to include cortical points that couldbe characterized on the same principles.

The corpus callosum outline data set here, whichfollows the midline of that structure as it gently twistsin the vicinity of the putative midsagittal plane, is notitself a plane curve. As compared with the more usualtechnique of callosal visualization, which extracts anoutline from one single image plane, the twistingleaves measures of area, both total and sectoral, rela-tively unaltered, but greatly affects the assessment ofvariability of actual locations at small scale. As wehave seen, the areal finding is weaker than that forcurving outline shape as regards mean differences bydiagnosis, and offers no equivalent of the techniquesfor localizing shape hypervariability that constitute theprincipal signal we have found. (For more on contem-porary strategies for callosal morphometrics, see Book-stein, ’00.)

ACKNOWLEDGMENTS

The authors have been generously supported by NIHgrants AA-10836 (to A.P.S.) for the project as a wholeand GM-37251 (to F.L.B.) for the development of ana-lytical methods. Malay Chan digitized thousands oflandmark points with extraordinary care. DavidHaynor, M.D., University of Washington, supplied theclinical reviews of all the subjects’ MR images. JuliaKogan and Lisette Austin managed the assembly of abalanced set of six study groups subject to constraintson imaging and testing staff and facilities. Data weredigitized in Edgewarp, a flexible package for navigat-ing solid medical images. A manual can be found atftp://brainmap.med.umich.edu/pub/EWSH3.1. HelenBarr has supported us enthusiastically throughout theresearch that led to this article, and has helped greatlyto clarify several underlying points of exposition.

26 BOOKSTEIN ET AL.

APPENDIX:MORE ON PROCRUSTES METHODS

This Appendix expands on the terse summary ofmultivariate morphometric tools sketched under theMorphometric Methods section. Four main notions areexplained in detail: Procrustes shape distance, Pro-crustes shape averages, Procrustes shape coordinates,and relative warps. The presentation is limited to thesimplest case, landmark points in two dimensions, butthe extensions to 3D data and to semilandmarks(points on curves) are straightforward. Sources thattreat all this material at greater length include Book-stein (’96, ’97a, ’98) and Dryden and Mardia (’98).These particular characterizations of the main techni-cal terms were worked out during the mid-1990s. Auseful on-line glossary (Slice et al., ’95) expands ontheir interrelationships, which represent a consensusamong a community of several toolbuilders, along witha variety of other terms central to earlier applicationsof these methods.

Procrustes shape distance

To carry out multivariate analysis of the “shape” of adata set of k-landmark point configurations, it is suffi-cient to have a distance measure between the twoshapes that obeys the usual rules. Suppose we havetwo landmark configurations, that is to say, two setsX1, X2 of k points with coordinates ( x1i, y1i), i 51, . . . , k, for the first form and ( x2i, y2i) for the second.If we were talking about “location” rather than shape,a reasonable notion of squared distance between thetwo would just be the usual Pythagorean sum

Oi 5 1

k

@~x1i 2 x2i!2 1 ~y1i 2 y2i!

2#

of all squared coordinate differences between the posi-tions of corresponding landmarks in the two forms.

We need to adapt this formula so that it gives thesame answer whenever either of the two shapes ismoved, rotated, or rescaled: then it will be talkingabout shape, as we want it to, rather than merely aboutlocations in the original digitizing planes. It turns outbest if we reformulate the problem in a way that turnsout to reduce to just this Euclidean formula undercertain conditions. We circumvent the problem ofchange of position by not allowing position to vary.Each form X1 or X2 has to be put down with its coor-dinates centered at (0, 0)—that is, we subtract ¥i 5 1

k x1i/kfrom each x1i, and similarly for y1i, x2i, and y2i. Geo-metrically, the effect of this is just a shift of the originof coordinates of each form, leaving its shape, as well asits size, alone. Also, we circumvent change of scale bylikewise not allowing scale to vary: replacing each setof centered coordinates with a new set chosen so thatthe sum of their squared distances from the origin (0, 0)of coordinates, which is now also their centroid, isexactly 1. We do this by dividing each centered form bya suitable scale factor, namely, the square root of what-

ever that sum of squares was before this operation.This factor, called centroid size, is examined by groupin Table 3 (see text).

With position and scale both standardized, thatleaves rotation. Just as we have repositioned each formindependently, and rescaled each form independently,we could imagine having to rotate each form indepen-dently to some arbitrary horizontal or vertical. Butthat is not the way the method actually goes. It turnsout a much better idea to state instead that we wouldlike the result of adjusting rotation to give us back theEuclidean sum of squares corresponding to the rotatedpoints. When two sets of points are both rotated by thesame angle, the sum of squared distances doesn’tchange at all, and so what is needed is the relativerotation of one form with respect to the other that leadsto the least Euclidean sum of squares out of all possiblerelative rotations. One version of Procrustes shape dis-tance is then defined as the square root of this sum ofsquares when the relative rotation is chosen appropri-ately. Other versions of the definition differ from thisone only by inconsequential adjustments, like usingthe arcsine of a small number in place of the number.

The steps in this computation follow down the rowsof Figure A1. At the top are two quadrilaterals of land-marks presumed to arise from real images. Erasewhatever outline information goes with these land-marks, but treat them purely as configurations of dis-connected points. Then connect each landmark to thecentroid of its own form. Its centroid size is the squareroot of the sum of squares of these lengths. For eachform, rescale the sum of squares of the distances shownto unity (second row) by dividing by this centroid size.Next (third row, left) translate one of the forms so thatits centroid directly overlies the centroid of the otherform. Finally, identify the rotation (third row right)that minimizes the sum of squares of the residual dis-tances between matched landmarks. The squared Pro-crustes distance between the forms (fourth row, re-drawn with their own outlines back in) is (to a verygood approximation) the sum of squares of those resid-uals at this minimum: total area of the circles at lowerright, divided by p.

Procrustes average shape

To this point, there is now a formalism for computinga shape distance measure between any two landmarkconfigurations, but not, as yet, any way to add or sub-tract them, so that we can’t define the average of ashape data set as its sum divided by its count, the waywe do for vectors—at least, not yet. Turn instead to adifferent characterization of the same idea: the averageshape as the shape about which the specimens of a dataset have the least sum of squared Procrustes distances.Although it may seem to you that this definition issomehow both vacuous and circular, in fact it is per-fectly rigorous mathematically. Furthermore, for anylandmark data set you will ever encounter in practice,the (unique) average shape can be computed by the

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 27

iterative algorithm sketched in Figure A2 for a sampleof four four-landmark shapes.

The top row displays some “raw data”: four quadri-laterals of similar but not identical shapes. Guess atthe value of the average shape—not a wild guess, butsomething in the vicinity of the real data: for instance,

guess that the average shape is the same as the shapeof the first specimen. Then (second row) superimposeeach of the original forms (including this form) overthis guessed average in exactly the posture implied byFigure A1—the position in which that Euclidean sumof squared distances is smallest.

The next guess for the average shape is made up ofthe averages of the positions of the landmarks, one byone, after they are superimposed over the previousguess in this way. The third row of Figure A2 showswhat happens when you update the candidate for av-erage shape and go through the cycle of fits again: youget the same average, to the accuracy of the printer’sdots in Figure A2. In nearly every real data set, thisstraightforward iterative algorithm converges to ade-quate precision by the end of the second iteration. Tokeep the figures from getting smaller row after row, itis also customary to rescale each candidate average tocentroid size 1 before diving back into the second row,the refitting procedure.

Procrustes shape coordinates

The last panel in Figure A2 shows two concepts: the“Procrustes average shape” we sought, and copies of allthe original forms scattered around it, each Procrustes-fitted to their common average. This composite imageis the crux of the value of the whole Procrustes toolkit.By definition of Procrustes distance, the sum ofsquared distances of the shape coordinates of each orig-inal shape from those of the Procrustes average shapeis its squared Procrustes distance from that average.But also, the sum of squared distances between thefinal positions of the landmarks of any two of the orig-inal forms is also their squared Procrustes distance.

For Figure A3, erase everything except the littlescatters around the average at lower right in FigureA2, and put a separate coordinate system down cen-tered at each averaged landmark position in turn. Wethereby arrive at an exact analogue of one of the twogreat customary ways of setting up a multivariate sta-tistical analysis, the approach usually called principalcoordinates analysis, beginning with sums of squareddistances instead of values of variables. Readers famil-iar with factor analysis will recognize this under thename of R-mode analysis. Beginning with distances,we have arrived (in an essentially unique way) at anequivalent set of 2k ordinary variables.

These are the Procrustes shape coordinates, whichrepresent all the information in the shape of the orig-inal sets of landmarks for any linear multivariate sta-tistical purpose. Any question about the correlation ofshape with its causes or effects can be answered byusing this single set of coordinates as a “vector of shapevariables” in the corresponding standard multivariateprocedure. For instance, to talk about averages of thesecoordinates by subgroups of the sample (e.g., the threediagnostic groups of this paper), it is sufficient to aver-age their Procrustes shape coordinates, which pro-duced the locations plotted in Figures 2 and 7. Ourpermutation tests for significance of these differences

Fig. A1. The Procrustes superposition for a pair of forms. (top row)Two forms of four homologous landmarks. (second row) Each form isrescaled so that the sum of squares of the distances to the centroid ofits four landmarks is 1. This is the sum of squares of the four linesshown. (third row) The centroids are superposed, and then one formis rotated over the other so that the sum of squared distances betweencorresponding landmarks is a minimum. (fourth row) With the con-struction lines erased, the squared Procrustes distance between thepair of forms is that sum of squared distances. It is proportional to thetotal area of the circles drawn at lower right.

28 BOOKSTEIN ET AL.

computed exactly analogous averages over pseu-dogroups rather than real groups. Correlations ofshape with its causes or consequences, such as IQ,likewise proceed coordinate by coordinate in this rep-resentation, and are tested by permutation proceduresusing explained and unexplained squared Procrustesdistances just as for variables arrived at by direct ob-servation in the ordinary way.

Relative warps

Finally, a useful factor analysis of shapes is oneversion of ordinary principal components of these sameProcrustes shape coordinates. Instead of starting fromtheir correlation matrix, the usual procedure in mostbranches of applied biometrics, one works with theircovariance matrix (an option available under the name

“unscaled” in most packages). The reason for this is, atroot, a magnificent mathematical elegance underlyingthe entire Procrustes toolkit. When data arise on amodel of wholly random digitizing error around thesame true landmark locations—digitizing error that isthe same at every landmark and in every direction,what is called isotropic noise—the resulting distribu-tion of Procrustes shape coordinates has extraordinarysymmetries, regardless of what that average form was.Specifically, under that strong isotropic assumption(which is not far from applying to many real data setsonce systematic factors of form are regressed out), thetheoretical distribution of Procrustes shape coordi-nates necessarily has 2k 2 4 dimensions of exactlythe same variance, and a final 4 dimensions of novariance at all, regardless of the average shape.

Fig. A2. Procrustes averaging and Procrustes shape coordinates. Top row: four forms of four land-marks. Middle row: Procrustes fit of each (X’s) to an arbitrary starting guess (dots: the first form).Bottom left: the next estimate of the average (dots) is the average of the fitted locations from theprevious step. Bottom right: a second round of fits and averages changes it hardly at all—the algorithmseems to have converged already.

MORPHOMETRICS OF FETAL ALCOHOL DISORDERS 29

Because this is important, we say it another way aswell. No matter what the average form looks like, ifdata arise from it by uninformative noise, the proba-bility distribution of all those Procrustes shape coordi-nates is pretty much proportional to e 2 cPD2

, where c isa suitable precision-like constant that takes into ac-count the centroid size of the “true picture” as well asthe amplitude of digitizing noise, and PD2 is thesquared Procrustes distance of any digitized form fromthe true average. If a spherical covariance matrixstands for no information, one that is not sphericalstands for exactly the kind of information at which aprincipal components analysis is aimed. Principal com-ponents of Procrustes shape coordinates (under thecovariance-matrix option) represent precisely the di-mensions of shape variability that have the highest

variance “per unit Procrustes distance” just as princi-pal components of ordinary lists of variables have thehighest variance “for unit sum of squared coefficients,”and those dimensions of extra variance help us ordi-nate data distributions with the greatest efficiency justas do scatterplots of factor scores in most other appli-cations.

You are probably used to seeing such componentsemerge from packages only in tabular form—columnsof coefficients, one for each component, headed by itseigenvalue (“explained variance”). For shape coordi-nates, the corresponding tables are immediately con-verted to geometric diagrams showing how the pointsmove away from the average shape, landmark by land-mark, in strongly or weakly correlated ways (depend-ing on the magnitude of the analogous eigenvalues).Specialized principal components of this sort, re-stricted to the covariance matrix of shape coordinates,are called relative warps because these displacementsare usually drawn out in turn by images of deformed(warped) Cartesian grids. Each of these graphicalstyles is exploited in Figure 5.

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