Curvature of the Greater Sciatic Notch in Sexing the Human Pelvis HIDEO TAKAHASHI1*

Home , Hip bone, Ischial spine, Ischium, Pubis (bone)

ANTHROPOLOGICAL SCIENCE Vol. 000, 000–000, 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 of the 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) which determine the greatest width of the notch. These landmarks are, however, known to be ill-defined on occasion, but nevertheless have been used to derive the conventional depth-to-width index and angles of the sciatic notch. The curvature parameter and its new indices were applied to the sciatic notch of 164 Japanese hip bones of known sex (104 males and 61 females). The accuracy of the new variables in the determination of sex was assessed and compared with that of the conventional indices and angles of the sciatic notch. The best discriminating variable was found to be the posterior angle with an accuracy of 91%. The new parameters of the present study that represent localized shape of the sharply curved edge of the notch diagnosed sex with an accuracy of 88%. In paleoanthropological or forensic cases, using the maximum curvature of the sciatic notch and its indices may be applicable to sexing the hip bones of specimens with postmortem damage.

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

Introduction 1986). The acetabulopubic index, which is a variant of the modified ischiopubic index, diagnosed sex with an accuracy Indices and angles of the greater sciatic notch are known of over 90% (Schulter-Ellis et al., 1983). These indices that to be highly sexually dimorphic. Consequently, they have take advantage of the greater proportion of the pubis in the been considered to be reliable sex discriminators (Caldwell female pelvis, and are known to be more accurate in the and Moloy, 1932; Lazorthes and Lhez, 1939; Letterman, determination of sex than the parameters based on the sciatic 1941; Genovés, 1959; Jovanovic and Zivanovic, 1965; notch. However, this highly dimorphic pubic element of the Jovanovic et al., 1968; Singh and Potturi, 1978; Taylor and hip bone is especially vulnerable to postmortem damage and DiBennardo, 1984; Novotný, 1986; Patriquin et al., 2005), decay, as it is covered by only a thin, fragile shell of cortical although they are not the best. The most efficient morpho- bone (MacLaughlin and Bruce, 1986; Bruzek, 2002; Walker, logical discriminators of sex relate to the pubic bone 2005). (MacLaughlin and Bruce, 1986; Walker, 2005). The pubois- The greater sciatic notch and acetabulum are located in chial index, based on maximum lengths of the ischium and the central portion of the hip bone and, consequently, are pubis, measured from their acetabular junction, produced often better preserved. Since width and depth of the notch, accuracy values of 83.7% and 100.0% for American males per se, have been found valueless in determining sex and females. When this was correlated with the angle of the (Williams et al., 1989), width-to-depth indices and angles sciatic notch, it was claimed that the sex of 98% of pelves have been defined differently (Lazorthes and Lhez, 1939; could be deduced (Washburn, 1949), although the landmark Martin and Saller, 1957; Singh and Potturi, 1978). These within the acetabulum was ill-defined (Stewart, 1954). The variables are affected substantially by the greatest width of modified ischiopubic index, using the acetabulum rim the notch, which sometimes cannot be measured. The main instead of the central acetabular point, identified sex with an difficulty encountered in the proper measurement of the accuracy of approximately 95% or greater (Thieme and notch is the great morphological variability of the area, Schull, 1957; Richman et al., 1979; Kimura, 1982; Novotný, including the sometimes absence of certain morphological structures and points necessary for defining dimensions of the notch; for instance the ischial spine, posterior inferior Collected Papers in Honor of Professor Emeritus Banri Endo: iliac spine, and tubercle of the piriformis can be variably Commemoration of His Seventieth Birthday expressed and/or ill-defined (Lazorthes and Lhez, 1939; * Corresponding author. e-mail: [email protected] Jovanovic and Zivanovic, 1965). phone: +81-282-87-2123; fax: +81-282-86-6229 For general purposes, visual features can be relied on for Published online 1 June 2006 sexing the pelvis (Stewart, 1954). Several visual scoring in J-STAGE (www.jstage.jst.go.jp) DOI: 10.1537/ase.051111 methods have been proposed (Meindl et al., 1985; Bruzek,

2002; Walker, 2005). These methods are less influenced by the landmarks of the notch at both ends; however, they tend to be more subjective and may require special osteological training. The purpose of the present study was to generate and test a new method of sexual discrimination of the greater sciatic notch that is not directly linked with ill-defined landmarks necessary to determine the greatest width of the notch. In the present study, maximum curvature and related indices of notch contour were newly defined. These parameters were computed from Japanese hip bones, and their sexing capabilities were compared with several conventional indices and notch angles.

Materials and Methods Hip bones (right side) of 165 Japanese adults (104 males and 61 females), who had died in early 20th century, were selected from the medical skeletal collection housed in the University Museum at the University of Tokyo. All specimens have their sex documented and show no pathological abnormality. Lateral views of the hip bones were photographed with a digital camera from a distance of 1 m. They were placed on a black background and with a ruler and adjusted to make the optical axis of the lens orthogonal to the plane of the sciatic notch. Twelve points were located on each reverse image (Figure 1). The points A, B, and C are the ischial spine, tubercle of the piriformis, and the most sharply curved point of the notch, respectively. The other eight points on the Figure 1. Reversed image of a right hip bone (No. 242, male): A, contour were determined as follows: ischial notch; B, tubercle of the piriformis; C, the most sharply curved (1) Line CD divides the deep space of the sciatic notch point of the sciatic notch; D, line CD divides the sciatic notch space near point C into two approximately equal parts, where the near point C into two equal parts. Point C and the six adjacent points contour of this space was assumed to be parabolic. Accord- were used in the quadratic regression. ing to the procedures outlined in the next two steps (2) and (3), four lines were spaced at roughly even intervals and drawn orthogonal to line CD, giving rise to eight intersec- sion curve, which was derived by the least-square method, 2 tions with the notch contour (Figure 1). was in the form of a quadratic equation: y = a2x + a1x + a0. (2) The bottom of the four lines was displaced upward The maximum curvature at the vertex is given by C0 = 2a2. from the position of point B, until the notch contour above The minimum radius of curvature is derived as 1/C0 this line was observed to be parabolic. Line CD was required (Figure 2). to bisect the bottom line segment of the notch. In geometry, curvature at a point is defined as the deriva- (3) The top line was taken where it approached point C tive of the inclination of the tangent with respect to arc closely, so that any two adjacent points of the nine intersec- length. From this definition, the unit of curvature is angle tions of the contour (including point C) were to be approxi- [radian]/length [millimeter]. This implies that curvature is mately equidistant. The other two lines were equally spaced not dimensionless. The unit of curvature is the reciprocal of between the top and bottom lines. These results were visu- length, because angle is dimensionless. Thus, curvature ally checked according to steps (4) and (5), and adjustments depends on bone size in terms of unit analysis. For a new, were made as necessary. dimensionless and size-independent index, curvature should (4) If the bottom line was not bisected by line CD, then be multiplied by length. Curvature indices 1 (C1) and 2 (C2) line CD was reconstructed and steps (2) and (3) were are standardized curvatures, which were defined as repeated. C1 = C0H and C2 = C0Ac/2, respectively; morphometrically, (5) If the nine intersections were not scattered evenly, step C1 is the ratio of the maximum pelvic height (H) to the radius (3) was repeated by adjusting the top line. of the inscribed circle at the vertex (1/C0), and C2 is the ratio of the maximum acetabular diameter (Ac) to the diameter of A total of 14 points were digitized on a computer screen the inscribed circle (2/C0) (Figure 2). with NIH Image; these were the 12 points defined on each The angular variables of the sciatic notch were derived by image and two additional points on the ruler used for scal- triangular approximation, as illustrated in Figure 3. Point E ing. Point C and the six adjacent points were used for quad- was defined as the point on the notch contour that is furthest ratic regression, by which a parabola was fitted to the from the greatest width AB. The line segment EF is the contour of the deep region of the sciatic notch. The regres- greatest depth, which intersects width AB perpendicularly. Vol. 114, 2006 CURVATURE OF THE GREATER SCIATIC NOTCH 3

Figure 2. The quadratic regression curve (parabola 2 y = a2x + 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 4. Histograms of curvature index 2 (C2) and posterior angle of the sciatic notch (θ2); frequencies are plotted for each sex.

sciatic notch) was expressed by θ1 and the angle BEF (posterior angle of the notch) by θ2 (Singh and Potturi, 1978). Basic statistics were computed for the 10 variables listed in Table 1. Sex differences of the means and variances were examined by the t-test and F-test, respectively. The male/ female cutoff value for a variable is presumed to occur between 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. Figure 3. Angles of the greater sciatic notch: A, ischial notch; B, The average misdiagnosed percentage, which reflects the tubercle of the piriformis; E, the furthermost point on the notch con- sex-discriminating capability of the variable, was defined as θ tour from AB; F, foot of the perpendicular from E to AB; 1, angle half the total percentage. BEA (angle of the sciatic notch); θ2, angle BEF (posterior angle of the sciatic notch). Results The basic statistics (mean, standard deviation, maximum, Index 1 (I1) of the sciatic notch was defined as the depth-to- and minimum) of the 10 variables for each sex are summa- width ratio (EF/AB). Index 2 (I2) was set as the ratio of the rized in Table 1. The t-tests for all variables verified that sex posterior segment BF to width AB (Lazorthes and Lhez, differences were highly significant statistically (P < 0.001 or 1939; Letterman, 1941; Genovés, 1959; Jovanovic and 0.0001), whereas the F-tests showed no significant differ- Zivanovic, 1965; Hager, 1996). The angle BEA (angle of the ences between sex in the variances of all variables except I1 4 H. TAKAHASHI ANTHROPOLOGICAL SCIENCE

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

2 1 Error Average (%) Variable Sex n Mean SD Min Max F value P > Ft value P > |t|Cutoff 1 (%) 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 81.1 M 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 63.8 M 104 148.68 8.40 125.49 173.86 46.2

Max diameter of (Ac) F 61 46.36 2.50 39.40 54.66 1.12 0.632 −11.22 <.0001 48.1 19.7 14.6 85.4 acetabulum M 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 84.9 M 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 88.5 M 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 88.0 M 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 75.4 M 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 87.1 M 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 87.6 M 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 90.9 M 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.

(P < 0.01) and C2 (P < 0.05). The percentages of specimens (75%) tends to be lower than that of any of the other three misidentified using the male/female cutoff values were cal- variables (87% or more). This implies that the position of culated for each sex. The average percentages of misdiag- point F is a crucial factor for sexing, because only I1 is neu- nosed and correctly predicted pelves of males and females tral to the foot location of line EF. Of the four parameters, are listed in Table 1. The posterior angle (θ2) assigned sex the posterior angle (θ2) was the best sex discriminator, correctly in 91% of all specimens. The angle of the notch although the length of the posterior segment and index II of (θ1) and the curvature indices 1 (C1) and 2 (C2) did so in 88– Singh and Potturi (1978) (equivalent to I2 in Table 1) were 89%. Histograms for C2 and θ2 are presented in Figure 4. highly effective, especially in females (Singh and Potturi, The curvature of the notch (C0) and the maximum diameter 1978). The advantage of θ2 over I2 by 3.8% is rationalized by of the acetabulum (Ac) correctly identified sex in 85%. The the above-outlined geometry. In the meantime, the accuracy maximum pelvic height (H), the index of the notch (I1) and of θ2 was 3.3% higher than that of θ1. This indicates that the the iliac breadth (W) did so in 81%, 75%, and 64%, respec- posterior portion of the sciatic notch is sexually more vari- tively. These three values were derived from sexually imbal- able than the anterior portion (Lazorthes and Lhez, 1939; anced error percentages (Table 1), the causes of which are Letterman, 1941; Genovés, 1959; Davivongs, 1963; Hager, uncertain but may be due to asymmetry in distribution for 1996). either sex. The four parameters are principally based on overall shape with triangular approximation; i.e. they are indices Discussion and angles of the sciatic notch as a whole. On the other hand, maximum curvature (C0) is localized at the depth of the con- The four conventional parameters (I1, I2, θ1, θ2) have dif- tour near point C and more precisely fit with a parabola. Not- ferent implications geometrically, as can be seen in Figure 3. withstanding a partial and size-dependent indicator of the Assuming that AB is constant, I1 depends on depth (EF) irre- notch around the sharply curved region, C0 correctly identi- spective of position (F), whereas the situation with I2 is the fied the sex of 85% of the specimens (Table 1). Curvature opposite (depends on position of F irrespective of depth). On indices (C1, C2), which are standardized measures of curva- the contrary, θ1 and θ2 rely on both depth (EF) and location ture, identified sex more accurately with a frequency of 88– (F). The relationship of the two angles with point F can be 89%. seen by assuming lengths AB and EF to be fixed, upon Sexual dimorphism in C2, which is the ratio of the acetab- which either of the angles decreases with deviation of the ulum to the inscribed circle of the notch (Figure 2), is illus- location of depth foot (F) from the midpoint of AB. In com- trated by a histogram in Figure 4. The mean diameter of the paring the four parameters (Table 1), the accuracy of I1 acetabulum is 4 times as great as that of the inscribed circle Vol. 114, 2006 CURVATURE OF THE GREATER SCIATIC NOTCH 5 in the male, whereas it is 2.5 times greater in the female Bulletins et Mémoires de la Société d’Anthropologie de Paris, (Table 1). In geometric morphometrics, thin-plate spline Série 10, 10: 3–95. interpolation was applied to the sciatic notch (Steyn et al., Hager L.D. (1996) Sex differences in the sciatic notch of great apes and modern humans. American Journal of Physical 2004). 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