A Cephalometric Comparison of Skulls from Different Time

Coll. Antropol. 27 (2003) 2: 789–801UDC 572.72:904"637""312"

Original scientific paper

A Cephalometric Comparison ofSkulls from Different Time Periods –The Bronze Age, the 19th Century andthe Present

Erwin Jonke1, Katrin Schaefer2, Josef W. Freudenthaler1,Hermann Prossinger2 and Fred L. Bookstein2,3

1 Vienna University Clinic of Dentistry, Department of Orthodontics, Vienna, Austria2 Institute for Anthropology, University of Vienna, Vienna, Austria3 Michigan Center for Biological Information, University of Michigan, Ann Arbor, USA

A B S T R A C T

The aim of this study was to evaluate secular trends by means of orthodontic mea-

surements on lateral cephalograms. We use roentgenograms from three populations: 22

Bronze Age skulls from a cemetery near Hainburg/Austria, 140 soldiers who served in

the Hapsburg Imperial Army in the late 19th century, and 154 contemporary recruits of

the Austrian Federal Army. Using conventional morphometric analysis, no statistically

significant differences could be established. But applying geometric morphometrics to

the 2D-coordinates of the pentagon composed of the landmarks Sella, Nasion, Articu-

lare, Gonion and Menton, some biologically interpretable differences were detected, the

size allometry between the 19th- and 20th-century populations being the only notable one.

We conclude that landmarks should be digitised directly (and many more of them) and

that conventional methods used in clinical orthodontics are inappropriate for address-

ing the scientific questions approached here.

Key words: cephalometrics, orthodontics, geometric morphometrics.

Introduction

Human growth patterns with manysecular trends have been evidenced innumerous studies1,2. For example, gener-ational increases in stature have been de-

scribed previously3. The question we areinterested in, and address in this paper,is whether clinical orthodontic measure-ment techniques can contribute to an-

789

Received for publication September 2, 2003

thropological investigations in a corre-sponding manner. As the study of themaxilla, mandible and associated parts ofthe skull is conventionally considered thedomain of orthodontics, we ask: are orth-odontic measurement techniques adequa-tely powerful to detect secular trends?One orthodontic study has dealt with theissue of secular trends in face size4. Asstudies on morphological changes in thecraniofacial skeleton over different timeperiods5,6 are not consistent in their find-ings and also not in their explanations,we think that comparisons among popu-lations from the same region, spanning alarge age range and also environmentalchange (from the Bronze age until thepresent), may contribute to clarifying theexisting results.

We also augment the issue of seculartrends by quantifying other orthodonticfeatures, notably landmark locations de-rived from distance and angle measure-ments. By approaching the study of orth-odontic features in this way, we suspectthat we will find changes on historic andprehistoric time scales, elucidating thepossible existence of such trends in anovel way.

Materials and Methods

This paper analysed lateral cephalo-grams of skulls and of living individualstaken from three collections: 1) 22 skullsfrom the period 6000 BC–400 AD (theskulls of this »Bronze-Age group«, froman excavated cemetery formerly situatednear Hainburg/Donau7, are now housedin the Natural History Museum, Vienna,Austria); 2) 140 skulls of soldiers of vari-ous ethnic origins who had served in theHapsburg Imperial Army and died 120–110 years ago (this »19th-century group«was collected by the anatomist Weisbachand the skulls are now in the NaturalHistory Museum, Vienna, Austria); and3) 154 soldiers conscripted in the present

Austrian Federal Army (this »20th-cen-tury group« consisted of recruits born inthe years 1970 and 1971).

All x-ray images were made in cepha-lostats with a film-lens distance of 152cm. The enlargement factor (107 %) wascalibrated by co-imaging a 10 cm long, 2mm diameter, right-angled wire in themid-sagittal plane. All cephalograms werescanned and digitised with Gamma® Ver-sion 3.2d (Slavicek, Klosterneuburg, Aus-tria) software.

The cephalograms of the 162 skulls(Bronze Age, 19th century) were made af-ter implementing the following procedure:1) the mandible was attached to the ma-xilla in an optimum occlusal fit; in thisposition, it was stabilized with dental flosstied at three suitable points. 2) Blue pe-riphery wax (Surgident® Heraeus KulzerInc., 4315 S. Lafayette Blvd., South Bend,IN 46614, USA) was put between themandibular condyles and the surface ofthe temporomandibular joint for furtherstability and to minimize possible dis-crepancies between dry skulls and livingones. 3) Then the skull was positioned inthe cephalostat. The identification of land-marks in the cephalograms of the in vivo

subjects was done following standard or-thodontic procedures.

The 316 cephalograms were measuredby one cephalometric procedure in termsof distances and angles (Table 1). Theseare a subset of measures that correspondmainly to the McNamara schema of ana-lysis8, a typical tool for diagnosis andmanagement of patients in the contempo-rary orthodontic clinical setting.

Data analysis

Two entirely separate analyses of thesecephalometric data were carried out.

First, conventional orthodontic mea-surements (summary descriptive statis-tics in Table 2) were compared separatelyby Student t-tests and Kruskal-Wallis

790

E. Jonke et al.: Cephalometric Comparison of Skulls, Coll. Antropol. 27 (2003) 2: 789–801

analysis of variance among all three gro-ups (Bronze Age, 19th century, 20th cen-tury) in pairs.

In a second approach, we reconstructeda digitised coordinate data set for a pen-tagon of landmark points involved in some

of the computed measurements. Althoughmany angles and distances relative toother landmarks had been measured, onlythe angles and distances between Nasion,Sella, Articulare, Gonion and Menton al-lowed a triangulation.

In detail, digitised 2D-coordinates weresimulated from the available data as fol-lows (abbreviations are listed in Table 1):Nasion was placed in front of Sella at themeasured distance S-N; Articulare wasplaced at distance S-Ar from Sella alongthe vector at angle Ar-S-N to the Sella--Nasion line; Gonion was placed underArticulare at distance Ar-Go along a vec-tor at angle S-Ar-Go to the Sella-Articu-lare line; and Menton was placed in frontof Gonion at a distance Ar-Go along a vec-tor making the appropriate angle withthe Sella-Nasion line.

We then applied geometric morpho-metrics methods, a statistical toolkit thatis based on Cartesian coordinates of land-mark points. The most widely used strat-egies include Procrustes superimpositi-on9,10, Shape coordinates, Relative Warp

791


TABLE 1LANDMARKS USED CONSTRUCTING THE

CEPHALOMETRIC MEASUREMENTS(AFTER McNAMARA8)

Code Landmark

Se Sella

Ar Articulare

Go Gonion

Me Menton

Na Nasion

Gn Gnathion

A A-point

B B-point

MP Mandibular plane

Uie Upper incisior incisal edge

Uia Upper incisor apex

Lie Lower incisior incisal edge

Lia Lower incisor apex

TABLE 2DESCRIPTIVE STATISTICS OF THE CONVENTIONAL MEASURES OF THE SKULLS FROM THETHREE GROUPS. PAIRWISE COMPARISON YIELDED INSIGNIFICANT DIFFERENCES FOR ALL

MEASURES

MeasurementBronze Age 19th century 20th century

X SD Median X SD Median X SD Median

Distance (mm)

S-N 64.59 4.72 65.5 66.3 3.07 66.5 73.35 3.8 73.35

N-Ar 90.11 5.34 91.2 91.25 3.85 91.3 99.21 4.86 38.5

S-Ar 35.07 3.64 35.4 34.6 3.28 34.4 37.42 3.06 37.25

Ar-Go 48.92 5.30 48.8 54.01 4.49 54.1 54.39 5.3 63.95

Me-N 113.4 6.91 112.1 119.0 6.85 119.2 123.0 6.52 122.8

Angle (°)

GoMe-SN 30.4 6.56 29.3 30.39 6.21 30.0 28.37 6.03 28.2

S-N-A 80.73 4.30 81.0 82.15 4.23 81.8 82.4 3.56 81.7

A-N-B 3.47 2.21 4.0 1.87 2.95 1.6 2.66 2.59 2.85

Ar-Go-Gn 121.5 6.56 120.7 122.5 7.62 122.7 120.9 6.7 121.0

UieUia-SN 97.36 8.30 97.7 100.5 7.51 100.3 104.0 7.55 103.3

LieLia-GoMe 96.49 5.3 95.9 90.56 6.89 89.9 94.6 6.92 94.55

Analysis11, and visualization by Thin Platesplines (see definitions in the Appendix).The analyses and graphics were comput-ed using S-Plus®.

A standard geometric morphometricanalysis12–14 starts with the constructionof Procrustes shape coordinates (the setof vectors connecting the landmarks of aspecimen to corresponding landmarks inthe consensus configuration after a Pro-crustes fit), along with Centroid Size (thefactor divided out in the course of size-standardization). Statistical computationsinclude comparison of group mean shapedifferences, relative warp (principal com-ponents for Procrustes-registered shapeco-ordinates) analyses separately by groupand pooled, and close study of allometry(regressions of the shape coordinates onCentroid Size) by group and pooled.

792


Fig 1. A sagittal section drawing of a lateral

headfilm, illustrating the landmarks used in

this study. Landmark codes as in Table 1.

Fig. 2. Scatters of the Procrustes-fitted points of all the specimens. Landmark codes as in Table 1.

• Bronze Age specimens; + 19th-century sample; � contemporary cases.

Results

Conventional morphometrics

After statistical correction for multi-ple comparisons (Bonferroni correction),no measured quantities were significant-ly different between any pairs of groupsin Table 2.

Geometric morphometrics of five

landmarks

Any geometric morphometric analysisshould begin with a careful scan of the»digitised« data for outliers and atypicalcases. Figure 2 shows the shape coordi-nate scatters for the five landmarks to-gether. All scatters seem well-behaved,

with no obvious outliers. The distributionof Centroid Size (see abscissa, Figure 3) islikewise well-behaved.

Mean differences

Centroid size: mean Centroid Sizes forthe three groups are 55.01 (Bronze Age),55.30 (19th century), and 58.17 (20th cen-tury), with within-group standard devia-tions of around 2.5. The 20th-century pop-ulation is significantly different from theother two, which do not differ from oneanother.

Pentagon shape: mean shapes of thefive-landmark set of shape coordinatesfor the 19th-century and 20th-century pop-ulations differ by permutation test be-

793


Fig. 3. Centroid Size (abscissa) vs. 1st Relative Warp (ordinate) for all 316 configurations.

• Bronze Age specimens; + 19th-century sample; � contemporary cases.

yond the 0.001 level (the observed Pro-crustes distance between group means isnot exceeded in 2,000 random permuta-tions of group label over these 294 cases).The prehistoric group does not differ sig-nificantly from either of these. Figure 4,which collects all our findings as defor-mation grids, begins (at upper left) with

the deformation of the mean 19th-centurypentagonal shape into the mean 20th-cen-tury shape, exaggerated tenfold for visi-bility.

Relative warp analysis

The standard relative warp analysis ofthe full data set of 316 pentagons extracts

794


Fig. 4. Comparison between the 19th- and the 20th-century group, visualised by thin plate spline de-

formation grids to a convenient scale (as labelled). »Group mean difference« shows mean 19th-cen-

tury shape deformed into mean 20th-century shape, exaggerated tenfold for visibility; »First rela-

tive warp« is effectively the same in both groups; »Allometry for the 19th-century group« shows five

times the deformation of the average of the 19th-century specimens of less than average size to the

average of those of greater than average size; »Allometry-free difference« is the allometry-free com-

ponent of the group mean difference.

Group meandifference, � 10

First relativewarp

Allometry (19th-c),5 � interq

Allometry-freedistance � 10

795


Fig. 5 Allometric regressions, landmark by landmark, in terms of the complete pentagon of shape

coordinates (Figure 1 and Figure 2). The second and fourth rows show four times the shift from the

mean location for the smaller half of the subsample to the mean for the larger half.

components with eigenvalues 1.44, 0.27,.... Only the first is likely to have anymeaning. The two larger groups differsignificantly in mean score on this firstrelative warp, but the magnitude of thedifference is less than one-third as greatas for Centroid Size (which we will de-clare to be the factor underlying this rela-tive warp: see below). Figure 3 scattersthe RW1 score against Centroid Size, withgroup coded by plotting symbol. There isclearly a regression here (r = –0.45 in the19th-century subsample, –0.19 in the mo-derns), but most of the variation remainsunexplained. Figure 4 displays this singlerelative warp in the form of a deforma-tion grid to a convenient scale.

Size allometry

There is significant size allometry inthe two larger groups separately. The sec-ond and fourth rows of Figure 5 show theallometric regressions separately by land-mark. In terms of the complete pentagonof shape coordinates, these two allometricpatterns are different between our twolarger groups; but they point in the same

direction of shape space, differing only inthe overall amplitude of this size effect (P~0.40 for the hypothesis of group differ-ences in the directions of these vectors).As is evident from the lengths of the solidversus dashed lines in the figure, theoverall allometric regression is strongerfor the 19th-century sample. (Dotted line:regression for the prehistoric group, whichis less stable owing to its smaller samplesize.)

Evidently, the effect of this shared sizefactor in either of the large samples isoblique to the sample mean difference atmost of the landmarks. The cosine of theangle between pooled within-group sizeallometry and 19th- to 20th-century meandifference is 0.818. (By contrast, that be-tween size allometry and RW 1 is 0.928.)Even so, size allometry explains 0.8182

~

67% of the group mean shape difference.

(In view of these large sample sizes, how-ever, what remains is still statisticallysignificant by permutation test.)

Figure 4 shows all the grids involvedin these comparisons: RW1, group meandifference, size allometry, and allometry-free mean difference. Relative warp 1and size allometry are strikingly similar,both emphasizing change of gonial angleand the ratio of anterior to posterior fa-cial height. The actual group mean differ-ence differs from both in changing thisratio considerably less than a differentratio, facial height to facial depth. Thereis also considerable discrepancy in chan-ges of cranial base shape. The contrast isclarified by the grid at lower right in thefigure, which shows the »allometry-free«component of group mean difference, rep-resenting, more or less, the mandibularhypertrophy without the open bite. Thispattern, combining an opening of the cra-nial base angle with ramal hypertropyand a closing of the gonial angle, seemsnot to correspond to any familiar biologi-cal factor of facial shape.

Discussion

Our discussion of these findings willtouch on three themes: noncomparabilityof the subgroups, inefficiency of conven-tional cephalometric approaches for sci-entific work, and implications for combi-nations of modern and archaic samples ina range of scientific projects.

Comparability of the two large sam-

ples. Our principal finding is the consis-tency of size allometry between these19th-century and 20th-century samples. Itis well-known that contemporary peopleare larger than their ancestors15, presum-ably owing to improved nutrition, bettermedical care, and other socio-economic ef-fects: changes that are sociological, notbiological. Even though the individuals inthe groups studied here may not be repre-sentative of their contemporary popula-

796


tions, the observed size shift is substan-tial, accounting for two-thirds of the groupmean shape difference. There is, how-ever, a difference in the intensity of thisallometry between the samples, for whichsome further explanation might be sought.Further work would require access to pu-tative causes of the mean size differenceor speculations regarding that differencein intensity of size allometry. The remain-ing one-third of empirical shape varia-tion, borne by the inscrutable grid pat-tern at lower right in Figure 4, is perhapsan accumulation of various factors, suchas differences in military recruitmentpractices, ethnicities, age effects, artefactsof cephalometric positioning in dried ma-terials, or orthodontic treatment in themoderns. As it corresponds to no knownbiological factor, we see no useful purposeto be served by its further analysis in soheterogeneous a sample of convenienceas this.

Conventional cephalometric »analysis«

made no useful contribution. This point isnot new with this paper – one of us pub-lished it a quarter of a century ago16, andit has been a provocation to the orthodon-tic literature ever since. Recall that thefindings of the suite of conventional mea-sures, Table 2, were entirely null. Nogroup differences were manifest in thesedata taken one variable at a time. Ananalysis designed for diagnosis and treat-ment of contemporary adolescents has nonecessary relationship to the informationborne in the cephalogram for more funda-mental scientific purposes, like thismulti-century comparison. It is not thatthe »analysis« was noise – the informa-tion it contains was precisely what weused to simulate the digitising of thelandmark »coordinates« that led to thesignificant and successfully interpretableProcrustes analyses here – but that theschema of the measurement, the list of in-dividual distances and angles, is not anappropriate tool for scientific analyses,

because, among other reasons, morpho-metric differences (allometry, size, shape,etc.) are not subtle but rather fundamen-tal effects and have to be captured by themethod applied.

In the present data set, the role of thecephalometric »analysis« was in effect toserve as an indirect digitisation of fivelandmark locations. In that case, therecould have been a great many more thanfive shape coordinate pairs – we couldhave commented on group differences orallometric trends in a variety of dentallandmarks, for example, none of whichcontributed to more than one of the mea-sures like those in Table 1, and hencenone of which could be »digitised« like thelarge pentagon we used.

All the methods exploited here exist inversions for 3D data exactly parallelingthese versions for 2D data. Some land-mark points can be viewed in both lateraland postero-anterior cephalogram. Theresulting analyses, by including informa-tion oblique to the lateral film, wouldgreatly enrich the interpretability of anyfindings that emerge. There are also me-thods available for the Procrustes analy-sis of entire skeletal surfaces, includinglandmark points but also ridge curvesand the smooth shells between17,18. Thesewould greatly enhance the visualizationof large-scale processes such as normalgrowth or evolutionary change, at thecost of somewhat obscuring the small-scale features that are the subject of clin-ical orthodontic attention.

There are implications for prehistoric,

palaeoanthropological and historical stu-

dies. Applications of geometric morpho-metric methods to historical or anthropo-logical questions need to attend morecarefully to issues of sample accrual. Therole of Centroid Size is not limited to theProcrustes scaling it provides. It shapesthe report of findings in at least the twofurther ways reported here: differences ofsize distribution among samples, and the

797


partition of shape differences into its allo-metric and non-allometric parts, with ap-propriate attention paid to both within-group and among-group factors of each(see reference 19). Furthermore, any re-constructed censoring of samples, at thetime of the specimen’s life or the time ofthe study’s execution, can interact withthese size and size allometry effects justas it can with the more familiar range ofpurported findings of Procrustes shapecoordinates per se. The present study, forinstance, might be elucidated by compari-sons between conscription patterns of the19th-century Hapsburg Imperial (Gesetzder Erfüllung der Wehrpflicht, 1868)20 and20th-century Austrian armies (Bundesge-setzblatt Nr. 368, 1975)21.

That is the negative message of thisanalysis. The positive message is that thecontemporary methods of geometric mor-phometrics have progressed far enoughbeyond the standard anthropometrics ofthe applied craniofacial sciences to makea material difference for the strength ofthe associated scientific research find-ings. Within a large suite of familiar dis-tances and angles showing no group dif-ferences whatever, we were able to findenough geometric information that, prop-erly rearranged (into shape coordinates),a signal emerged of strikingly high ampli-tude: a signal, to be sure, dealing withsize, size shift, and size allometry effects,but a signal nonetheless. Analyses of con-ventional cephalometric measures should

be replaced by digitized coordinates oflandmarks (and semilandmarks) 18,22,23

whenever the context is one of a scientificinvestigation. That is not to say that land-mark coordinate data are a panacea. Inthe present study, the Bronze Age samplesize was simply too small for any findingswhatever to be reported, by scalars, shapecoordinates, Centroid Size, or any otherapproach.

In their everyday practice, orthodon-tists will continue to rely on traditionalmeasurements for both diagnosis and in-dividual treatment planning, but wheremultiple explanations are to be combined(here, secular change, size allometry, andprincipal components, as in Figure 4), itis best to turn to the methods that weredeveloped for precisely such scientificcontexts, not the essentially case-by-caseworld of clinical orthodontics.

Acknowledgements

We thank Otto Vyslozil, Klosterneu-burg, and Markus Bernhard, Institut forAnthropology, Vienna, for help with or-ganising the data, Maria Teschler-Nicola,Natural History Museum, Vienna, forpermitting access to those skulls in hercustody that were used in this study, twoanonymous referees for their valuablecomments on an earlier version of this pa-per, and Horst Seidler, Institut for An-thropology, Vienna, for having broughtthis group together.

R E F E R E N C E S

1. WOLANSKI, N., Coll. Antropol., 2 (1978) 69. —2. ULIJASZEK, S. J., F. E. JOHNSTONE, M. A.PREECE (Eds.): The Cambridge encyclopaedia of hu-man growth and development. (Cambridge Univer-sity Press, Cambridge, 1998). — 3. BODZSAR, E. B.,A. ZSAKAI, Coll. Antropol. 26 (2002) 477. — 4. SMITH,G. B., S. M. GARN, W. S. HUNTER, Angle Orthod.,56 (1986) 196. — 5. CARLSON, D. S., Am. J. Phys.Anthropol. 45 (1976) 467.— 6. VARELA, J., Europ. J.Orthod., 14 (1992) 31. — 7. GEYER, E., Skelette ausdem frühbronzezeitlichen Reihengräberfeld bei Hain-

burg a.d. Donau. In: BENINGER, E., F. MÜHLGHO-FER, E. GEYER (Eds.): Das frühbronzezeitliche Reihen-gräberfeld bei Hainburg-Teichtal (Mitt. d. Anthropol.60, 1930). — 8. MCNAMARA, J. A.: An atlas of cra-niofacial growth. Monograph No. 2. (University ofMichigan, Ann Arbor, 1974). — 9. GOODALL, C. R.,J. R. Stat. Soc. B35 (1991) 285. — 10. ROHLF, F. J. J.Classif., 16 (1999) 197. — 11. BOOKSTEIN, F. L.: Mor-phometric tools for landmark data: Geometry and bi-ology. (Cambridge University Press, Cambridge, 1991).— 12. MARCUS, L. F., M. CORTI, A. LOY, G. J. P.

798


NAYLOR, D. E. SLICE (Eds .) : Advances in morpho-metrics. (Plenum Press, New York, 1996). — 13. DRY-DEN, I. L., K. V. MARDIA: Statistical shape analysis.(Wiley, Chichester, 1998). — 14. SCHAEFER, K., H.SEIDLER, F. L. BOOKSTEIN, H. PROSSINGER, D.FALK, G. CONROY, In: FALK, D., K. R. GIBSON,(Eds.): Evolutionary anatomy of the primate cerebralcortex. (Cambridge University Press, Cambridge, 2001).— 15. LINDGREN, G., In: ULIJASZEK, S. J., F. E.JOHNSTONE, M. A PREECE (Eds.): The Cambridgeencyclopaedia of human growth and development.(Cambridge University Press, Cambridge, 1998). — 16.MOYERS, R. E., F. L. BOOKSTEIN, Am. J. Ortho-dont., 75 (1979) 599. — 17. ANDRESEN, P. R., F. L.BOOKSTEIN, K. CONRADSEN, B. ERSB?LL, J.MARSH, S. KREIBORG, IEEE Trans. Med. Imaging,19 (2000) 1053. — 18. MITTEROECKER, P., P. GUNZ,F. L. BOOKSTEIN, Semilandmarks in three dimen-sions. In: SLICE, D. E. (Ed.): Developments in prima-tology: Progress and prospects. (Kluwer Academic/Plenum Press, Dordrecht, 2003). — 19. BERNHARD,M., K. SCHAEFER, P. GUNZ, P. MITTEROECKER,

H. PROSSINGER, F. L. BOOKSTEIN, H. SEIDLER,Am. J. Phys. Anthropol., 120 S36 (2003) 65. — 20. Gesetzvom 5. Dezember 1868, womit für die im Reichsrathevertretenen Königreiche und Länder die Art undWeise der Erfüllung der Wehrpflicht geregelt wird.(Druck und Verlag der k.k. Hof- und Staatsdruckerei,Wien, 1868). — 21. Bundesgesetzblatt Nr. 368; Wehr-gesetz. (Austrian code of law Nr. 368) (1975). — 22.BOOKSTEIN, F., K. SCHAEFER, H. PROSSINGER,H. SEIDLER, M. FIEDER, C. STRINGER, G. W. WE-BER, J.-L. ARSUAGA, D. SLICE, F. J. ROHLF, W.RECHEIS, A. J. MARIAM, L. MARCUS, Anat. Rec.257 (1999) 217. — 23. BOOKSTEIN, F. L., P. GUNZ,P. MITTEROECKER, H. PROSSINGER, K. SCHAE-FER, H. SEIDLER, J. Hum. Evol., 44 (2003) 167. —24. SLICE, D. E., F. L. BOOKSTEIN, L. F. MARCUS,F. J. ROHLF: A glossary for geometric morphome-trics. (http://life.bio.sunysb.edu/morph/bibliographiesand glossary, 1998.) — 25. WEBER, G. W., K. SCHAE-FER, H. PROSSINGER, P. GUNZ, P. MITTER-OECKER, H. SEIDLER, J. Physiol. Anthropol., 20(2001) 69.

E. Jonke

Kieferorthopädische Abteilung, Universitätsklinik für Zahn- Mund- und

Kieferheilkunde, Währingerstrasse 25A, Vienna, Austria

799


KRANIOMETRIJSKA USPOREDBA LUBANJA RAZLIÎTIH VREMENSKIHRAZDOBLJA – BRONÂNO DOBA, 19. STOLJE]E I DANA[NJE VRIJEME

S A @ E T A K

Cilj ove studije bio je procijeniti sekularni trend putem ortodontskih mjerenja late-ralnih kraniograma. Kori{teni su rendgenogrami triju populacija: 22 lubanje iz bron-~anog doba iz groblja blizu Hainburga (Austrija), lubanje 140 vojnika koji su sluìli uvojsci Habsbur{ke monarhije koncem 19. stolje}a, te 154 dana{njih vojnika SavezneAustrijske vojske. Kori{tenjem standardnih morfometrijskih analiza, nisu na|ene sta-tisti~ki zna~ajne razlike me|u uspore|ivanim uzorcima. Primjenom geometrijske mor-fometrije u 2D koordinatama pentagona kojeg sa~injavaju kraniometrijske to~ke: sela,nasion, articulare, gonion i menton, prona|ene su neke biolo{ki interpretabilne razli-ke, pri ~emu se mogla primijetiti samo razlika u veli~ini alometrije me|u populacijama19. i 20. stolje}a. Autori zaklju~uju kako kraniometrijske to~ke trebaju biti direktnodigitalizirane (i puno ve}i broj njih) te da standardne metode koje se koriste u klini~kojortodonciji nisu adekvatne za traènje odgovora na znanstvena pitanja kakva su ovdjepostavljena.

Appendix: Glossary

Explanations below are mainly taken from references 24 and 25.

Superimposition (Procrustes) met-

hods superimpose a sequence of speci-mens so that corresponding landmarksmatch as closely as possible according toan optimality criterion. In this process,size, position and orientation are partia-led out and differences in shape are re-corded as residuals from the referenceshape. The residuals can also be graphedas displacement vectors at each landmark.In numerous software packages there areleast squares and resistant-fit methodsavailable.

Procrustes residuals: The set of vec-tors connecting the landmarks of a speci-men to corresponding landmarks in theconsensus configuration after a Procrus-tes fit. The sum of squared lengths ofthese vectors is approximately the squaredProcrustes distance between the speci-men and the consensus in Kendall's shapespace.

Shape coordinates: In the past, anysystem of distance-ratios and perpendicu-lar projections permitting the exact re-construction of a system of landmarks bya rigid truss. Now, more generally, coordi-nates with respect to any basis for thetangent space to Kendall's shape space inthe vicinity of a mean form: see Procrus-tes residuals.

Centroid Size: One of the fundamen-tal differences between geometric andtraditional morphometrics is the way thesize of objects is computed. In traditionalmethods this is done by using either oneof the original variables or by computing

some multivariate estimate (e.g., PC1,Size Factor). Such estimates are allome-tric size estimates. They are correlatedwith random measurement error (noise)around original shape variables. In con-trast, the size estimate used in GeometricApproach (Centroid Size) is computed us-ing interlandmark distances. Centroid Sizeis the square root of the sum of squareddistances of a set of landmarks from theircentroid, or, equivalently, the square root ofthe sum of the variances of the landmarksabout that centroid in x- and y-directions.Centroid Size is used in geometric mor-phometrics because it is approximatelyuncorrelated with every shape variablewhen landmarks are distributed aroundmean positions by independent noise ofthe same small variance at every land-mark and in every direction. CentroidSize is the size measure used to scale aconfiguration of landmarks so they can beplotted as a point in Kendall's shapespace.

Centroid Size can be used in conjucti-on with shape variables (shape coordi-nates, residuals from procrustes analy-sis). It can be used to 1) measure sizedifferences among specimens or groups,and 2) evaluate allometric patterns.

Relative warp analysis is a modifi-cation of principal component analysis forshape coordinate data. A relative warp isan eigenvector of the matrix of variancesand covariances of the Procrustes shapecoordinates. When principal componentsare computed using covariances in this

800


way, sums of squared differences of scorespreserve the underlying original geome-try of Procrustes distance.

Thin Plate splines compare the shapedifferences between two landmark config-urations. Bookstein (1991)11 proposed thethin-plate spline interpolation formalismto visualize the differences in the posi-tions of the landmarks by modeling thedeformations taking place between thelandmarks; i.e., in all regions withoutlandmark points. Imagine a combinationof landmarks printed on a thin plate andcompare it with a second combination oflandmarks, supposing that the differ-ences in coordinates are taken as verticaldisplacements of this plate perpendicularto itself, one Cartesian coordinate at atime. The energy necessary to deform theplate at each landmark is the so-calledbending energy. And, as the bending en-ergy is highest for the most local defor-mations, its minimization in all the non--landmark areas models their position.Interpolants modeling such plate defor-mations are called thin plate spline func-tions.

They are, first, a convenient solutionto the problem of interpolation by con-structing continuous deformation grids fordata in the form of two landmark configu-rations (which could be the consensusconfigurations of the two populations un-der discussion) and, second, the basis forsophisticated analyses of shape differencelike Relative Warps Analysis of these twoconfigurations.

Eigenvalues: The eigenvalues �i of amatrix A are solutions to the eigenvalue

equation A� �

e ei i i� � . In other words, onelooks at those vectors

�

ei that do not changedirection (but possibly length) when map-ped by the matrix A. If all eigenvaluesare different, the eigenvalue spectrum issaid to be non-degenerate. For a square,nonsingular n � n matrix, there are n

eigenvectors and n eigenvalues, albeit withdegeneracy possible. Of particular inter-est in geometric morphometrics are theeigenvalues and eigenvectors of the co-variance matrix �. Even if all the entriesin a matrix are real, some eigenvaluescan be complex.

801


Documents

A Cephalometric Comparison of Skulls from Different Time