187© 2006 The Anthropological Society of Nippon

ANTHROPOLOGICAL SCIENCE

Vol. 114, 187–191, 2006

Curvature of the greater sciatic notch in sexing the human pelvis

HIDEO TAKAHASHI1*

1Department of Anatomy, Dokkyo University School of Medicine, 880 Kitakobayashi, Mibu-machi, Shimotuga-gun, Tochigi, 321-0293 Japan

Received 11 November 2005; accepted 26 January 2006

Abstract The maximum curvature of the greater sciatic notch and two standardized indices were cal-culated for use in the sexing of human hip bones. This was done by means of quadratic regression ofthe contour points of the greater sciatic notch. The new variables are not directly affected by the osteo-metric landmarks (e.g. ischial spine, tubercle of the piriformis, and posterior inferior iliac spine) whichdetermine the greatest width of the notch. These landmarks are, however, known to be ill-defined onoccasion, but nevertheless have been used to derive the conventional depth-to-width index and anglesof the sciatic notch. The curvature parameter and its new indices were applied to the sciatic notch of164 Japanese hip bones of known sex (104 males and 61 females). The accuracy of the new variablesin the determination of sex was assessed and compared with that of the conventional indices and anglesof the sciatic notch. The best discriminating variable was found to be the posterior angle with an accu-racy of 91%. The new parameters of the present study that represent localized shape of the sharplycurved edge of the notch diagnosed sex with an accuracy of 88%. In paleoanthropological or forensiccases, using the maximum curvature of the sciatic notch and its indices may be applicable to sexingthe hip bones of specimens with postmortem damage.

Key words: greater sciatic notch, curvature, sexing, hip bone, Japanese

Introduction

Indices and angles of the greater sciatic notch are knownto be highly sexually dimorphic. Consequently, they havebeen considered to be reliable sex discriminators (Caldwelland Moloy, 1932; Lazorthes and Lhez, 1939; Letterman,1941; Genovés, 1959; Jovanovic and Zivanovic, 1965;Jovanovic et al., 1968; Singh and Potturi, 1978; Taylor andDiBennardo, 1984; Novotný, 1986; Patriquin et al., 2005),although they are not the best. The most efficient morpho-logical discriminators of sex relate to the pubic bone(MacLaughlin and Bruce, 1986; Walker, 2005). The pubois-chial index, based on maximum lengths of the ischium andpubis, measured from their acetabular junction, producedaccuracy values of 83.7% and 100.0% for American malesand females. When this was correlated with the angle of thesciatic notch, it was claimed that the sex of 98% of pelvescould be deduced (Washburn, 1949), although the landmarkwithin the acetabulum was ill-defined (Stewart, 1954). Themodified ischiopubic index, using the acetabulum riminstead of the central acetabular point, identified sex with anaccuracy of approximately 95% or greater (Thieme andSchull, 1957; Richman et al., 1979; Kimura, 1982; Novotný,

1986). The acetabulopubic index, which is a variant of themodified ischiopubic index, diagnosed sex with an accuracyof over 90% (Schulter-Ellis et al., 1983). These indices thattake advantage of the greater proportion of the pubis in thefemale pelvis, and are known to be more accurate in thedetermination of sex than the parameters based on the sciaticnotch. However, this highly dimorphic pubic element of thehip bone is especially vulnerable to postmortem damage anddecay, as it is covered by only a thin, fragile shell of corticalbone (MacLaughlin and Bruce, 1986; Bruzek, 2002; Walker,2005).

The greater sciatic notch and acetabulum are located inthe central portion of the hip bone and, consequently, areoften better preserved. Since width and depth of the notch,per se, have been found valueless in determining sex(Williams et al., 1989), width-to-depth indices and angleshave been defined differently (Lazorthes and Lhez, 1939;Martin and Saller, 1957; Singh and Potturi, 1978). Thesevariables are affected substantially by the greatest width ofthe notch, which sometimes cannot be measured. The maindifficulty encountered in the proper measurement of thenotch is the great morphological variability of the area,including the sometimes absence of certain morphologicalstructures and points necessary for defining dimensions ofthe notch; for instance the ischial spine, posterior inferioriliac spine, and tubercle of the piriformis can be variablyexpressed and/or ill-defined (Lazorthes and Lhez, 1939;Jovanovic and Zivanovic, 1965).

For general purposes, visual features can be relied on forsexing the pelvis (Stewart, 1954). Several visual scoringmethods have been proposed (Meindl et al., 1985; Bruzek,

Collected Papers in Honor of Professor Emeritus Banri Endo:Commemoration of His Seventieth Birthday

* Corresponding author. e-mail: htak@dokkyomed.ac.jpphone: +81-282-87-2123; fax: +81-282-86-6229

Published online 1 June 2006in J-STAGE (www.jstage.jst.go.jp) DOI: 10.1537/ase.051111

188 H. TAKAHASHI ANTHROPOLOGICAL SCIENCE

2002; Walker, 2005). These methods are less influenced bythe landmarks of the notch at both ends; however, they tendto be more subjective and may require special osteologicaltraining. The purpose of the present study was to generateand test a new method of sexual discrimination of the greatersciatic notch that is not directly linked with ill-defined land-marks necessary to determine the greatest width of thenotch. In the present study, maximum curvature and relatedindices of notch contour were newly defined. These param-eters were computed from Japanese hip bones, and their sex-ing capabilities were compared with several conventionalindices and notch angles.

Materials and Methods

Hip bones (right side) of 165 Japanese adults (104 malesand 61 females), who had died in early 20th century, wereselected from the medical skeletal collection housed in theUniversity Museum at the University of Tokyo. All speci-mens have their sex documented and show no pathologicalabnormality.

Lateral views of the hip bones were photographed with adigital camera from a distance of 1 m. They were placed ona black background and with a ruler and adjusted to makethe optical axis of the lens orthogonal to the plane of the sci-atic notch. Twelve points were located on each reverseimage (Figure 1). The points A, B, and C are the ischialspine, tubercle of the piriformis, and the most sharply curvedpoint of the notch, respectively. The other eight points on thecontour were determined as follows:

(1) Line CD divides the deep space of the sciatic notchnear point C into two approximately equal parts, where thecontour of this space was assumed to be parabolic. Accord-ing to the procedures outlined in the next two steps (2) and(3), four lines were spaced at roughly even intervals anddrawn orthogonal to line CD, giving rise to eight intersec-tions with the notch contour (Figure 1).

(2) The bottom of the four lines was displaced upwardfrom the position of point B, until the notch contour abovethis line was observed to be parabolic. Line CD was requiredto bisect the bottom line segment of the notch.

(3) The top line was taken where it approached point Cclosely, so that any two adjacent points of the nine intersec-tions of the contour (including point C) were to be approxi-mately equidistant. The other two lines were equally spacedbetween the top and bottom lines. These results were visu-ally checked according to steps (4) and (5), and adjustmentswere made as necessary.

(4) If the bottom line was not bisected by line CD, thenline CD was reconstructed and steps (2) and (3) wererepeated.

(5) If the nine intersections were not scattered evenly, step(3) was repeated by adjusting the top line.

A total of 14 points were digitized on a computer screenwith NIH Image; these were the 12 points defined on eachimage and two additional points on the ruler used for scal-ing. Point C and the six adjacent points were used for quad-ratic regression, by which a parabola was fitted to thecontour of the deep region of the sciatic notch. The regres-

sion curve, which was derived by the least-square method,was in the form of a quadratic equation: y = a2x

2+ a1x + a0.

The maximum curvature at the vertex is given by C0 = 2a2.The minimum radius of curvature is derived as 1/C0

(Figure 2).In geometry, curvature at a point is defined as the deriva-

tive of the inclination of the tangent with respect to arclength. From this definition, the unit of curvature is angle[radian]/length [millimeter]. This implies that curvature isnot dimensionless. The unit of curvature is the reciprocal oflength, because angle is dimensionless. Thus, curvaturedepends on bone size in terms of unit analysis. For a new,dimensionless and size-independent index, curvature shouldbe multiplied by length. Curvature indices 1 (C1) and 2 (C2)are standardized curvatures, which were defined asC1 = C0H and C2 = C0Ac

/2, respectively; morphometrically,C1 is the ratio of the maximum pelvic height (H) to the radiusof the inscribed circle at the vertex (1/C0), and C2 is the ratioof the maximum acetabular diameter (A

c) to the diameter of

the inscribed circle (2/C0) (Figure 2).The angular variables of the sciatic notch were derived by

triangular approximation, as illustrated in Figure 3. Point Ewas defined as the point on the notch contour that is furthestfrom the greatest width AB. The line segment EF is thegreatest depth, which intersects width AB perpendicularly.

Figure 1. Reversed image of a right hip bone (No. 242, male): A,ischial notch; B, tubercle of the piriformis; C, the most sharply curvedpoint of the sciatic notch; D, line CD divides the sciatic notch spacenear point C into two equal parts. Point C and the six adjacent pointswere used in the quadratic regression.

CURVATURE OF THE GREATER SCIATIC NOTCH 189Vol. 114, 2006

Index 1 (I1) of the sciatic notch was defined as the depth-to-width ratio (EF/AB). Index 2 (I2) was set as the ratio of theposterior segment BF to width AB (Lazorthes and Lhez,1939; Letterman, 1941; Genovés, 1959; Jovanovic andZivanovic, 1965; Hager, 1996). The angle BEA (angle of the

sciatic notch) was expressed by θ1 and the angle BEF (poste-rior angle of the notch) by θ2 (Singh and Potturi, 1978).

Basic statistics were computed for the 10 variables listedin Table 1. Sex differences of the means and variances wereexamined by the t-test and F-test, respectively. The male/female cutoff value for a variable is presumed to occurbetween the male and female means. An exploratory proce-dure determined the cutoff value within that range, and min-imized the total misdiagnosed percentage of the two sexes.The average misdiagnosed percentage, which reflects thesex-discriminating capability of the variable, was defined ashalf the total percentage.

Results

The basic statistics (mean, standard deviation, maximum,and minimum) of the 10 variables for each sex are summa-rized in Table 1. The t-tests for all variables verified that sexdifferences were highly significant statistically (P < 0.001 or0.0001), whereas the F-tests showed no significant differ-ences between sex in the variances of all variables except I1

Figure 2. The quadratic regression curve (parabolay = a2x

2+ a1x + a0) and the minimum inscribed circle are superim-

posed: Ac, maximum diameter of acetabulum; 1/C0, minimum radius of

curvature (radius of the circle).

Figure 3. Angles of the greater sciatic notch: A, ischial notch; B,tubercle of the piriformis; E, the furthermost point on the notch con-tour from AB; F, foot of the perpendicular from E to AB; θ1, angleBEA (angle of the sciatic notch); θ2, angle BEF (posterior angle of thesciatic notch).

Figure 4. Histograms of curvature index 2 (C2) and posteriorangle of the sciatic notch (θ2); frequencies are plotted for each sex.

190 H. TAKAHASHI ANTHROPOLOGICAL SCIENCE

(P < 0.01) and C2 (P < 0.05). The percentages of specimensmisidentified using the male/female cutoff values were cal-culated for each sex. The average percentages of misdiag-nosed and correctly predicted pelves of males and femalesare listed in Table 1. The posterior angle (θ2) assigned sexcorrectly in 91% of all specimens. The angle of the notch(θ1) and the curvature indices 1 (C1) and 2 (C2) did so in 88–89%. Histograms for C2 and θ2 are presented in Figure 4.The curvature of the notch (C0) and the maximum diameterof the acetabulum (A

c) correctly identified sex in 85%. The

maximum pelvic height (H), the index of the notch (I1) andthe iliac breadth (W) did so in 81%, 75%, and 64%, respec-tively. These three values were derived from sexually imbal-anced error percentages (Table 1), the causes of which areuncertain but may be due to asymmetry in distribution foreither sex.

Discussion

The four conventional parameters (I1, I2, θ1, θ2) have dif-ferent implications geometrically, as can be seen in Figure 3.Assuming that AB is constant, I1 depends on depth (EF) irre-spective of position (F), whereas the situation with I2 is theopposite (depends on position of F irrespective of depth). Onthe contrary, θ1 and θ2 rely on both depth (EF) and location(F). The relationship of the two angles with point F can beseen by assuming lengths AB and EF to be fixed, uponwhich either of the angles decreases with deviation of thelocation of depth foot (F) from the midpoint of AB. In com-paring the four parameters (Table 1), the accuracy of I1

(75%) tends to be lower than that of any of the other threevariables (87% or more). This implies that the position ofpoint F is a crucial factor for sexing, because only I1 is neu-tral to the foot location of line EF. Of the four parameters,the posterior angle (θ2) was the best sex discriminator,although the length of the posterior segment and index II ofSingh and Potturi (1978) (equivalent to I2 in Table 1) werehighly effective, especially in females (Singh and Potturi,1978). The advantage of θ2 over I2 by 3.8% is rationalized bythe above-outlined geometry. In the meantime, the accuracyof θ2 was 3.3% higher than that of θ1. This indicates that theposterior portion of the sciatic notch is sexually more vari-able than the anterior portion (Lazorthes and Lhez, 1939;Letterman, 1941; Genovés, 1959; Davivongs, 1963; Hager,1996).

The four parameters are principally based on overallshape with triangular approximation; i.e. they are indicesand angles of the sciatic notch as a whole. On the other hand,maximum curvature (C0) is localized at the depth of the con-tour near point C and more precisely fit with a parabola. Not-withstanding a partial and size-dependent indicator of thenotch around the sharply curved region, C0 correctly identi-fied the sex of 85% of the specimens (Table 1). Curvatureindices (C1, C2), which are standardized measures of curva-ture, identified sex more accurately with a frequency of 88–89%.

Sexual dimorphism in C2, which is the ratio of the acetab-ulum to the inscribed circle of the notch (Figure 2), is illus-trated by a histogram in Figure 4. The mean diameter of theacetabulum is 4 times as great as that of the inscribed circle

Table 1. Basic statistics, cutoff values, and accuracy percentages

Variable Sex n Mean SD Min Max F value P > F t value P > |t| Cutoff1Error (%)1

Average (%)2

Error Correct

Max pelvic height (H) F 61 185.89 9.14 155.24 203.43 1.20 0.452 −9.64 <.0001 197.5 3.3 18.9 81.1M 104 200.96 10.00 175.38 224.09 34.6

Iliac breadth (W) F 61 143.80 9.15 117.45 163.50 1.19 0.444 −3.48 <.001 147.9 26.2 36.2 63.8M 104 148.68 8.40 125.49 173.86 46.2

Max diameter of acetabulum

(Ac) F 61 46.36 2.50 39.40 54.66 1.12 0.632 −11.22 <.0001 48.1 19.7 14.6 85.4M 104 51.06 2.65 43.64 57.79 9.6

Curvature of GSN (C0) F 61 0.10 0.03 0.06 0.22 1.41 0.150 −10.57 <.0001 0.13 14.8 15.1 84.9M 104 0.16 0.03 0.09 0.27 15.4

Curvatue index 1 (C1) F 61 19.02 5.49 10.27 43.89 1.50 0.087 −12.46 <.0001 24.5 11.5 11.5 88.5M 104 31.69 6.73 16.89 50.19 11.5

Curvature index 2 (C2) F 61 2.38 0.69 1.29 5.34 1.61 0.046 −13.35 <.0001 2.87 16.4 12.0 88.0M 104 4.03 0.88 2.17 6.94 7.7

Index of GSN (I1) F 61 48.15 6.99 34.95 65.08 1.96 0.005 −7.67 <.0001 56.3 4.9 24.6 75.4M 104 58.22 9.79 35.92 86.09 44.2

Posterior index (I2) F 61 30.81 7.47 5.01 44.23 1.01 0.964 13.76 <.0001 25.1 18.0 12.9 87.1M 104 14.27 7.44 −4.78 35.20 7.7

Angle of GSN (θ1) F 61 87.88 9.03 59.99 104.95 1.31 0.229 13.48 <.0001 81.0 18.0 12.4 87.6M 104 69.79 7.89 54.21 92.22 6.7

Posterior angle (θ2) F 61 32.71 7.92 4.40 46.45 1.31 0.234 15.98 <.0001 23.3 11.5 9.1 90.9M 104 13.87 6.93 −4.51 30.55 6.7

1 Optimal male/female cutoff values and percentages of misclassified bones for each sex.2 Average percentages of misdiagnosed and correctly identified pelves between males and females.

CURVATURE OF THE GREATER SCIATIC NOTCH 191Vol. 114, 2006

in the male, whereas it is 2.5 times greater in the female(Table 1). In geometric morphometrics, thin-plate splineinterpolation was applied to the sciatic notch (Steyn et al.,2004). Since the method is based on cubic equations insteadof the quadratic ones used in the present study, curvaturederived by spline function may yield a better accuracy rate insexing.

The pubic bone, which proved to be the most efficientmorphological discriminator in sexing (MacLaughlin andBruce, 1986), is more fragile than the central portion of thepelvis, including the greater sciatic notch and acetabulum(Taylor and DiBennardo, 1984). Practically, the generallybetter preserved sciatic notch should be more useful in pale-oanthropology and forensics. Conventional indices (I1, I2)and angles (θ1, θ2) of the notch were verified with high accu-racy, but all these parameters essentially are based on thegreatest width of the sciatic notch (AB), where point A is theischial spine and point B is the tubercle of the piriformis.The former is vulnerable to damage and the latter is some-times absent, especially in females (Jovanovic et al., 1968).The advantage of the newly defined curvature (C0) and itsrelevant indices (C1, C2) over the conventional indices andangles of the sciatic notch is that they are not affected by theosteological landmarks A and B, and are essentially fracture-resistant.

Sex differences in bones inevitably are linked to function;while the primary pelvic function in both sexes is locomotor-associated, the pelvis is adapted to parturition in females,particularly the lesser pelvis (Williams et al., 1989; Hager,1996). It has been hypothesized that, owing to opposingselection pressures on pelvic morphology in females, i.e.efficiency in locomotion and obstetric adequacy, female pel-vic morphology is less variable than that of males (Tague,1989). Although this was not statistically proven by Tague(1989), the hypothesis was partially supported by the twoparameters, C2 and θ1, in the present study, by means of anF-test.

Acknowledgments

I am indebted to G. Suwa for access to the materials, C.Yoshizawa for capturing and digitizing bone images and twoanonymous reviewers for invaluable comments. The presentstudy was supported by a Grant-in-Aid for ScientificResearch from the Japanese Ministry of Education(#11304059).

References

Bruzek J. (2002) A method for visual determination of sex, usingthe human hip bone. American Journal of Physical Anthro-pology, 117: 157–168.

Caldwell W.E. and Moloy H.C. (1932) Sexual variations in thepelvis. Science, 76: 37–40.

Davivongs V. (1963) The pelvic girdle of the Australian Aborig-ine; sex differences and sex determination. American Journalof Physical Anthropology, 21: 443–455.

Genovés S. (1959) L’estimation des différences sexuelles dans l’oscoxal; différences métriques et différences morphologiques.

Bulletins et Mémoires de la Société d’Anthropologie de Paris,Série 10, 10: 3–95.

Hager L.D. (1996) Sex differences in the sciatic notch of greatapes and modern humans. American Journal of PhysicalAnthropology, 99: 287–300.

Jovanovic S. and Zivanovic S. (1965) The establishment of the sexby the great schiatic notch. Acta Anatomica, 61: 101–107.

Jovanovic S., Zivanovic S., and Lotric N. (1968) The upper part ofthe great sciatic notch in sex determination of pathologicallydeformed hip bones. Acta Anatomica, 69: 229–238.

Kimura K. (1982) Sex differences of the hip bone among severalpopulations. Okajimas Folia Anatomica Japonica, 58: 265–276.

Lazorthes G. and Lhez A. (1939) La grande échancrure sciatique:étude de la morphologie et de ses caractères sexuels. Archivesd’Anatomie, d’Histologie et d’Embryologie, 27: 143–170.

Letterman G.S. (1941) The greater sciatic notch in Americanwhites and negroes. American Journal of Physical Anthropol-ogy, 28: 99–116.

MacLaughlin S.M. and Bruce M.F. (1986) The sciatic notch/ace-tabular index as a discriminator of sex in European skeletalremains. Journal of Forensic Sciences, 31: 1380–1390.

Martin R. and Saller K. (1957) 1. Methodik (Becken). In:Lehrbuch der Anthropologie, Band 1, Gustav Fischer, Stutt-gart, pp 554–561.

Meindl R.S., Lovejoy C.O., Mensforth R.P., and Don Carlos L.(1985) Accuracy and direction of error in the sexing of theskeleton: implications for paleodemography. American Jour-nal of Physical Anthropology, 68: 79–85.

Novotný V. (1986) Sex determination of the pelvic bone: a systemsapproach. Anthropologie, 24: 197–206.

Patriquin M.L., Steyn M., and Loth S.R. (2005) Metric analysis ofsex differences in South African black and white pelves.Forensic Science International, 147: 119–127.

Richman E.A., Michel M.E., Schulter-Ellis F.P., and CorrucciniR.S. (1979) Determination of sex by discriminant functionanalysis of postcranial skeletal measurements. Journal ofForensic Sciences, 24: 159–167.

Schulter-Ellis F.P., Schmidt D.J., Hayek L.A., and Craig J. (1983)Determination of sex with a discriminant analysis of new pel-vic bone measurements: part 1. Journal of Forensic Sciences,28: 169–180.

Singh S. and Potturi B.R. (1978) Greater sciatic notch in sex deter-mination. Journal of Anatomy, 125: 619–624.

Stewart T.D. (1954) Sex determination of the skeleton by guessand by measurement. American Journal of Physical Anthro-pology, 12: 385–389.

Steyn M., Pretorius E., and Hutten L. (2004) Geometric morpho-metric analysis of the greater sciatic notch in South Africans.Homo, 54: 197–206.

Tague R.G. (1989) Variation in pelvic size between males andfemales. American Journal of Physical Anthropology, 80: 59–71.

Taylor J.V. and DiBennardo R. (1984) Discriminant function anal-ysis of the central portion of the innominate. American Jour-nal of Physical Anthropology, 64: 315–320.

Thieme F.P. and Schull W.J. (1957) Sex determination from theskeleton. Human Biology, 29: 242–273.

Walker P.L. (2005) Greater sciatic notch morphology: sex, age,and population differences. American Journal of PhysicalAnthropology, 127: 385–391.

Washburn S.L. (1949) Sex differences in the pubic bone of Bantuand Bushman. American Journal of Physical Anthropology,7: 425–432.

Williams P.L., Warwick R., Dyson M., and Bannister L.H. (1989)The skeleton of the lower limb. In: Gray’s Anatomy,Churchill Livingstone, London, pp. 422–434.