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Bony markers at the distal end of the radius for estimating handedness and radial length
= = = = = = = = = =. ANNALS Of ANATOMY = = = = = = = = = =
Bony markers at the distal end of the radius for estimating handedness and radial length Sunil J. Holla, Selvakumar Vettivel, and G. Chandi Department of Anatomy. Christian Medical College, Vellore 632002, India
Summary. Measurements of the size of the bony markers at the distal end of the radius as well as the length of the radius in 61 left and 64 right dry radii were statistically analyzed. Since 90 -951110 of the general population is right-handed, as based on differences in the size of the right sided markers relative to the left, it is proposed that the greater distance between the dorsal tubercle and styloid process and the greater dorsa-palmar diameter of the carpal articular surface opposite the dorsal tubercle are indicative of righthandedness. The length of the radius correlated with: the radio-ulnar transverse diameter at the distal end; the distance between the dorsal tubercle and the styloid process; the dorsa-palmar diameter of the distal end opposite the dorsal tubercle; the dorsa-palmar diameter of the carpal articular surface opposite to the dorsal tubercle; the dorsopalmar diameter of the distal end opposite the medial margin of the groove for the extensor pollicis longus; the dorso-palmar diameter of the distal end opposite the floor of the groove for the extensor pollicis longu s and, finally. the height of the dorsal tubercle in relation LO the posterior margin of the carpal articular surface (P < 0.0(1). Regression equations of the length of the radius for these markers have been derived. Key words: Articular surface - Dorsal tubercle· Groove - Regression
Introduction Handedness, length of long bones and stature are all of medicolegal and anthropological importance. Bony markers at the proximal end of the humerus, such as the dimensions of the intertubercular sulcus (Vettivel et al. 1995), have been found to be useful in estimating handedness and in reconstructing the length of humerus; and those of the proximal Correspondence to: S. J. Halla
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Ann Anat (1996) 178: 191 - 195 Gustav Fischer Verlag Jena
femur, such as neck-shaft angle, neck length, intertrochanteric apical axis length and the vertical diameter of the head, for reconstructing the length of the femur (Prasad et al. 1995). In this study, markers at the distal end of the radius are used to estimate handedness and to reconstruct the maximum length of the radius. These markers can be used when only a fragment of the distal end of the radius is available in a medicolegal case. The markers are (1) radioulnar transverse diameter of the distal end (TD), (2) distance between the dorsal tubercle and the styloid process (DS), (3) dorsa-palmar diameter of the distal end, opposite the dorsal tubercle (DT), (4) dorsa-palmar diameter of the carpal articular surface, opposite the dorsal tubercle (AS), (5) dorsopalmar diameter of the distal end, opposite the medial margin of the groove for the extensor pollicis longus (EPL), (MGEPL) and (6) dorso-palmar diameter of the distal end opposite the floor of the groove for EPL (FGEPL).
Materials and methods One hundred and twenty five dry radii (61 left and 64 right) all devoid of gross pathology, obtained from subjects of the state of Tamilnadu in Southern India, ranging in age from 25 to 55 years, were used for this study. Though the bones were from cadavers dissected in this department, we could not identify the pairs. The bones were a large set of unmatched bones. The markers at the distal end of the radius (Fig. 1) were measured in em with a vernier ~ a liper. The maximum length of the humerus (LENG) was measured in cm with an osteometric board. (1) TD was the straight distance between the tip of the styloid process and the medial margin of the distal end of the radius (2) DS was the straight distance between the medial margin of the dorsal tubercle and the tip of the styloid process. Markers 3, 4, 5 and 6 were measured vertically, including a horizontal glass sheet of a standard thickness of 0.475 cm, on which the anterior surface of the radius was made to rest, but were only recorded after subtracting 0.475 em. This was done to over-
A
the articular surface opposite the dorsal tubercle and the inferior surface of the glass sheet minus the thickness of the glass sheet. (5) MGEPL was the straight distance between the highest point of the medial margin of the groove for the tendon of EPL and the inferior surface of the glass sheet minus the thickness of the glass sheet. (6) FGEPL was the straight distance between the lowest point of the floor of the groove for the tendon ofEPL and the inferior surface of the glass sheet minus the thickness of the glass sheet. (7) LENG was the distance between the most proximal point on the head of the radius and the tip of the styloid process (Singh and Bhasin 1989). DGEPL, the depth of the groove for EPL, was calculated as [(OT + MGEPL)I2] - FGEPL. HOTG, the height of the dorsal tubercle in relation to the groove for EPL, was DT - FGEPL. HOTA , the height of the dorsal tubercle in relation to the posterior margin of the articular surface, was DT - AS. HDTA is inversely proportional to AS. The raw data were statistically analyzed. Ranges, means and standard deviations were determined for the markers and maximum length of the radius. Student's unpaired t-test was applied to find any significant difference in the means between the left and right radii. Correlation coefficients between the maximum length of radius and markers were determined for the radii of the left, right and for both sides. The length of the radius (Y) was regressed on each of the markers (X) and simple regression models at Y '" bX + a were derived, where 'b' was the regression coefficient and 'a' was the intercept, a constant.
B
o
D MM
(
Table 1. Measurements of the markers at the distal end and length of radius (61 left and 64 right unpaired radii)
GLASS
E
Markers
Fig. 1. Markers at distal end of radius. A. TD = The straight distance between the tip of the styloid process and the medial margin of the distal end. DS = The straight distance between the medial margin of the dorsal tubercle and the tip of the styloid process. B. DT = The straight distance between th e top of the dorsal tuber cle and the inferior surface of the glas<, sheet minus the thickness of the glass sheet. MGEPL '" The straight distance bet ween the highest point of the medial margin of the groove for th e tendon of EPL and the inferior surface of the glass sheet minus thickness of the glass sheet. C. AS = The straight distance bet wen the p\lstenor margin of the articular surface opposite the dorsal tubercle and the inferior surface of the glass sheet minus the thickn ess of the glass sheel. The stippled line indicates the orientation of the bone to measure AS when the AS, dorsal tubercle. and center of the upper end are in the plane of the stippled hne. D. FGEPL == The straight distance between \ he lowest poim of the floor of the groove for the tendon of BPL and tbe inferior surface of the glass sheet minus tbe thickne,s 01 i.he glass sheet. E. Occasional radius with MM (medial marpn of the groove for the tendon of EPL) at a higher level than T (Dorsal tubercle), and therefore DT < MGEPL and {OJl MC' EI'L).'21 <. FGEPI . come the difficulty in placing the .iaws or the vernier caliper appropriately on the bone and any error in measuring the height of the dorsal tubercle or depth of the groove l'o r EPL (3) DT was the straight distance between the rop of the dorsal tubercle and the inferior surface o f rhe glas\ sheet minus the thickness of the glass sheet . (4) AS was the straight. distance between the flosterior margin of
TO
OS
DT
AS
Left Right Both Left Right Both Left Right Both Left Right
MGEPL
FGEPL
OGEPL
HDTG
HOTA
LENG
192
Both Left Right Both Left Right Both Left Right Both Left Right Both Left Right Both Left Right Both
Range em
Mean em
SD
2.160 to 3.100 2.095 to 3.215 2.095 to 3.215 1.370 to 2.090 1.385 to 2.320 1.370 to 2.320 1.615 to 2.430 1.545 to 2.505 1.545 to 2.505 0.905 to 1.760 1.155 to 1.720 0.905 to 1.760 1.605 to 2.390 1.355 to 2.495 1.355 to 2.495 1.580 to 2.205 1.380 to 2.300 1.380 to 2.300 -0.060 to 0.320 +0.040 to 0.180 -0.060 to 0.320 -0.020 to 0.310 -0.030 to 0.260 -0.030 to 0.310 1.420 +0.410 to +0.3 to to 0.960 +0.310 to 1.420 20.300 to 27.800 19.500 to 27.100 19.500 to 27.800
2.670 2.610 2.640 1.720 1.780 1.750 2.000 2.000 2.000 1.325 1.385 1.355 2.005 1.995 1.995 1.890 1.900 1.895 0.110 0.100 0.100 0.100 0.100 0.100 0.670 0.620 0.640 23.860 23.930 23.900
0.23 0.25 0.24 0.18 0.20 0.19 0.18 0.19 0.18 0.16 0.14
P
NS
<0.05
NS
<0.05
0.15
0.20 0.20 0.20 0 .17 0.17 0.17 0.05 0.04 0.04 0.D7 0.08 0.07 0.t7 0.13 0.15 1.88 1.91 1.89
NS
NS
NS
NS
<0.06
NS
Results and discussion
the state of Andhra Pradesh in South India (Dronamraju 1975) are right-handed. In the human upper limbs, the majority of the muscles and bones are heavier on the dominant right side (Chhibber and Singh 1972; Dogra and Singh 1970). The radial dorsal tubercle receives a slip from the extensor retinaculum, and is grooved medially (ulnar) by the tendon of the extensor pollicis longus. The wide groove lateral (radial) to the tubercle contains the tendons of the extensor carpi radialis longus and extensor carpi radialis brevis (Williams et al. 1989). In a right-handed individual, the latter two tendons can be expected to be larger. The relative larger size of these tendons and the wider groove for them, compared to those of the extensor pollicis longus, can have the effect of shifting the dorsal tubercle medially (ulnar), away from the styloid process. Thus the DS can be greater in the right radius. In a more active right wrist joint, the right radial articular surface can be expected to be more extensive than the left. Thus the AS can be greater in the right radius. Vettivel et al. (1995) estimated handedness by the presence of differences in the dimensions of the intertubercular sulcus between the left and right humeri. Their argument is that the dimensions of the right intertubercular sulcus, of which the mean values are found to be greater or smaller than the left in a predominantly right-handed sample population, will also be, respectively, greater or smaller in the right sulcus of a right-handed individual. Therefore, in a pair of bones, if those dimensions are respectively greater or smaller as above in the right sulcus, the individual is right-handed or if, in the left sulcus, the individual is lefthanded. In the present study, the mean DS and AS are significantly greater in the right radius (Table 1). Therefore,
Table 1 summarizes the ranges, means and standard deviations of the measurements in cm, of the markers namely, TD, DS, DT, AS, MGFPL, FGEPL, DGEPL, HDTG, HDTA and of the LENG of the left, right and the total number of radii. The DS and AS showed significant difference (P < 0.05) between left and right sides. Table 2 gives the correlation coefficients of the measured variables for the total of 125 radii (correlation matrix). Most of the variables were significantly interdependent, although infrequently with DGEPL and HDTG. Table 3 lists the correlation coefficients of the LENG against the markers of the left, right, and all the radii. In the case of the total number of 125 radii, the LENG correlated significantly (P < 0.001) with all except HDTG. In the 61 left radii, the LENG correlated significantly (P < 0.0011 0.01/0.05) with all except the AS, DGEPL and HDTG; and in the 64 right radii, the LENG correlated significantly (P < 0.00110.01) with all the markers except the HDTG. Table 4 shows the regression analysis of the LENG against the markers of the left, right and total radii. Table 5 gives the regression analysis values needed for those simple regression equations that are derived for the estimation of the LENG from a known value of the correlated markers.
Estimation of Handedness
Ninety to ninety-five percent of the general population (Adams and Victor 1989) and 93 - 950)'0 of the population of
Table 2. Correlation matrix (n = 125)
LENG TD DS DT AS MGEPL FGEPL DGEPL HDTG HDTA
LENG
TD
DS
1.0000 0.5525*** 0.4114*** 0.6206*** 0.3525*** 0.6622*** 0.6558*** 0.2480** 0.0342 0.3964***
0.5525*** 1.0000 0.6740*** 0.7274*** 0.5223*** 0.7627*** 0.7716*** 0.2489** 0.0334 0.3565*** ------.--.--.-
FGEPL
0.4114*** 0.6740*** :.0000 0.6537*** 0.4826*** 0.7092*** 0.7294*** O. J 372 0 . 0531 iI.l07 3*** -
.. -.~-
DGEPL
- _..._--_ _---
HDTC
•...
LENG TD DS DT AS MGEPL FGEPL DGEPL HDTG HDTA n = 125. *p
0.6558*** 0.7716*** 0.7294*** 0.9160*** 0.5946*** 0.9386*** 1.0000 0.1537 -0.0236 0.5115***
0.2480** 0.2489** 0.1372 0.3982** ' O.0()75 0.3373** 0.1537 l.OOOO 0.6377*** 0.4710***
< 0.05, **P < 0.01, ***P
AS
MGEPL
0.6206*** 0.7274*** 0.6537*** 1.0000 0.5987*** 0.8230*** 0.9160*** 0.3982*** 0.3796*** 0.6084***
0.3525*** 0.5253*** 0.4826*** 0.5987*** 1.0000 0.4705*** 0.5946*** 0.0075 0.1207 -0.2715**
0.6622*** 0.7627*** 0.7092*** 0.8239*** 0.4705*** 1.0000 0.9386*** 0.3373** -0.1114 0.5237***
---_._-_..
HDTA
,--_.'.-.. _----_.
0.0342 0.0334 n.OS31 U.3796***
o 12m
0.1114
0.0236 0.637 7***
noon
Ii
DT
1365***
o.O() ,
193
0.3964** 0.3565*** 0.3073*** 0.6084*** -0.2715** 0.5237*** 0.5115*** 0.4710*** 0.3365*** I.()()()O
Table 3. Correlation coefficients between markers at distal end and length of radius (61 left, 64 right, 125 total radii)
TD DS DT AS MGEPL FGEPL DGEPL HDTG HDTA
*P
Table 5. Simple regression analysis values for length of radius (Y) regressed against correlated markers (X), irrespective of sides (n = 125)
left
LENG right
both
Y
0.4850*** 0.3299*** 0.5110*** 0.2456 0.5490*** 0.5505*** 0.1659 0.0031 0.3080*
0.6313*** 0.5021 *** 0.7197*** 0.4807*** 0.7701 *** 0.7520*** 0.3599** 0.0693 0.5371 ***
0.5525*** 0.4114*** 0.6206*** 0.3525*** 0.6622*** 0.6558*** 0.2480** 0.0342 0.3964***
LENG TO OS OT AS MGEPL FGEPL HDTA
< 0.05
** P
< 0.01
*** P
X
b
a
< 0.001
r2 S.E.E.
Table 4. Length of radius (cm) (dependent variable Y) analyzed against markers (cm) at its distal end (independent variables X) using simple regression Y = bX + a
Y
X
b
SE(b) a
SE(a) r2
P
<
S.E. E .
b
a
r2
S.E.E.
4.4 4.1 6.4 4.4 6.3 7.3 4.9
12.3 16.8 11.2 18.0 11.3 10.2 20.8
0.31 0.17 0.39 0.12 0.44 0.43 0.16
1.58 1.73 1.49 1.78 1.42 1.43 1.74
regression coefficient intercept coefficient of determination standard error of estimate
in a pair of radii, if DS and AS are greater in the right radius, the individual is right-handed but if this is so in the left radius, the individual is left-handed.
For left side LENG TD 3.9 3.3 DS 5.3 DT AS 2.9 MGEPL 5.2 FGEPL 6.1 DGEPL 6.3 HDTG -0.1 HDTA 3.4
0.96 1.31 1.16 1.47 1.03 1.21 4.89 3.33 1.35
13.4 18.2 13.3 20.1 13.5 12.3 23.2 23.9 21.6
2.56 2.26 2.32 1.97 2.06 2.30 0.57 0.43 0.93
0.22 0.09 0.26 0.06 0.30 0.30 0.03 0.00 0.09
0.001 0.010 0.001 0.060 0.001 0.001 NS NS 0.016
0.76 1.06 0.89 1.54 0.78 0.92 5.96 3.21 1.58
11.2 15.3 09.4 14.7 09.2 08.2 22.2 23 .8 19.1
2.00 1.89 1.79 2.15 1.56 1.76 0.62 0.40 0.99
0.40 0.25 0.52 0.23 0.59 0.57 0.13 0.00 0.29
0.001 0.001 0.001 0.001 0.001 0.001 NS
0.60 0.81 0.72 1.05 0.64 0.75 3.75 2.30 1.02
12.3 16.8 11.2 18.0 11.3 10.2 22.8 23.8 20.8
1.59 0.31 1.42 0.17 1.45 0.39 1.43 0.12 1.29 0.44 1.43 / 0.43 0.41 0.06 0.29 0.00 0.67 0.16
0.001 0.001 0.001 0.001 0.001 0.001 NS
1.67 1.80 1.63 1.84 1.59 1.59 1.87 1.90 1.81
For right side 4.9 4.8 7.3 6.7 AS MGEPL 7.4 8.3 FGEPL OGEPL 18.1 HDTG 1.8 HDTA 7.9
LENG TO OS OT
1.49 1.66 1.33 1.69 1.23 1.27 1.79 NS 1.92 0.001 1.62
For both sides LENG TO 4.4 4.1 OS 6.4 DT 4.4 AS MGEPL 6.3 FGEPL 7.2 OGEPL 10.7 HDTG 0.9 4.9 HDTA
b SE b
a
SE a r2
P S.E.E.
regression coefficient standard error of regression coefficient intercept standard error of intercept coefficient of determination level of significance standard error of estimate
1.58 1.73 1.49 1.78 1.42 1.43 1.84 NS 1.90 0.001 1.74
Estimation of radial length
Vettivel et a1. (1995) estimated the length of the humerus using the intertubercular sulcus as a marker. Prasad et al. (1996) estimated the length of the femur using markers at the proximal end of the femur. In the present study, the LENG presented a significant correlation with TD, DS, DT, AS, MGEPL, FGEPL and HDTA (Table 3). The significant correlation suggested that these markers are good indicators of length of the radius and can be useful for estimating the length of the radius. These markers can be used when only a fragment of the distal end of the radius is available. It was thought prudent to derive simple regression equations with Y = bX + a to find the estimated length of radius even if one of the markers is known. Table 4 shows regression analysis of the markers for the radius: left, right and both sides. Regression equations can be derived using the value of 'b' and 'a' for a known marker of the left or right side or irrespective of the side. The following are the regression equations that are derived for the estimation of the LENG, irrespective of the side, using the regression analysis values (Table 5) for a known value of a correlated marker: (i) (ii) (iii) (iv) (v) (vi) (vii)
LENG LENG LENG LENG LENG LENG LENG
4.4(TD) + 12.3 cm 4.1(DS) + 16.8 cm = 6.4(DT) + 11.2 cm = 4.4(AS) + 18.0 cm = 6.3(MGEPL) + 11.3 cm = 7.3(FGEPL) + 10.2 cm = 4.9(HDTA) + 20.8 cm
= =
(S. E. E.
= 1.58) (S. E. E. = 1.73) (S. E. E. = 1.49) (S.E.E. = 1.78) (S. E. E. = 1.42) (S. E. E. = 1.43) (S.E.E. = 1.74)
The equations, for which the coefficient of determination (r2) is higher and the standard error of estimate (S. E. E.) is lower (Table 4), can be the equations of choice. The calculated length of the radius can be used to estimate the stature of an individual by referring to the regression equa-
194
tions, tables and multiplication factors (Nat 1931; Siddiqui and Shah 1944; Telkka 1950; Dupertuis and Haddon 1951; Trotter and Gieser 1952, 1958; Athawale 1963; Kolte and Bansal 1974; Pati! et al. 1983) that are available. Such an estimation of handedness, radial length and stature will have potential for application in physical anthropology. medical jurisprudence and forensic identification of an individual. Though the validity of the models was not tried on other populations, the models were significant (P < (l.00 1), the r2 values are over 12070 and the SE of the regression coefficients (b) are small (Table 4). These statistics should guarantee that the models will be robust. Our regression diagnostics have also suggested robustness. Therefore, these models should be applicable to different populations.
References Adams RD, Victor M (1989) Principles of Neurology. 4th edn. McGraw Hill, Singapore, p 380 Athawale MC (1963) Estimation of height from lengths of forearm bones: A study of one hundred Maharashtrian male adults of age between twenty five and thirty years. Am J Phys Arthropol 21: 105-112 Chhibber SR, Singh I (1972) Asymmetry in mw,cle weight in human upper limbs. Acta Anat 81: 462 - 465 Dogra SK, Singh I (1970) Asymmetry in bone weigh I in the human upper limbs. Anat Anz 128: 278 - 280 Oronamraju KR (1975) Frequency of left-handedness among the Andhra Pradesh people. Acta Genet Med Gemellol Roma 24: 161-162 Oupertuis CW, Haddon JA (1951) On reconstruClion of stature from long bones. Am ] Phys Anthropol 9: 15 ,; 1
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01 f, [SSlll"
Kolte PM, Bansal PC (1974) Determination of regression formulae for reconstruction of stature from long bones of upper limbs in Maharashtrians of Marathwada region. 1 Anat Soc India 23: 6-11 Nat BS (1931) Estimation of stature from long bones in Indians of United province: A medicolegal inquiry in anthropometry. Indian 1 Med Res 18: 1245 - 1253 Patil TL, Gawhale KS, Mazumdar RD (1983) Reconstruction of stature from long bones of both upper and lower limbs. 1 Anat Soc India 32: 111 - 118 Prasad R, Vettivel S, Jeyaseelan L, Isaac B, Chandi G (1996) Reconstruction of length of femur from markers of its upper end. Clin Anat 9: 28 - 33 Siddiqui MAH, Shah MA (1944) Estimation of stature from long bones of Punjabis. Indian J Med Res 32: 105 -108 Singh IP, Bhasin MK (1989) A Laboratory Manual of Biological Anthropology: Anthropometry. 1st edn. Kamla-Raj Enterprises, Delhi p 311 Telk ka A (1950) On the prediction of human stature from long bones. Acta Anat 9: 103 - 107 Trotter M, Gieser GC (1952) Estimation of stature from long bones of American Whites and Negroes. Am J Phys Anthropol 10: 453-514 Trotter M, Gieser GC (1958) A re-evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death. Am 1 Phys Anthropol 16: 79 - 123 Vettivel S, Selvaraj KG, Chandi SM, Indrasingh I, Chandi G (1995) Intertubercular sulcus of the humerus as an indicator of handedness and humeral length. Clin Anat 8: 44 - 50 Williams PL, Warwick R, Dyson M, Bannister LH (1989) Osteology. In: Gray's Anatomy, 37th edn. Churchill Livingstone, Edinburgh p 412
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195
Bony markers at the distal end of the radius for estimating handedness and radial length Sunil J. Holla, Selvakumar Vettivel, and G. Chandi Department of Anatomy. Christian Medical College, Vellore 632002, India
Summary. Measurements of the size of the bony markers at the distal end of the radius as well as the length of the radius in 61 left and 64 right dry radii were statistically analyzed. Since 90 -951110 of the general population is right-handed, as based on differences in the size of the right sided markers relative to the left, it is proposed that the greater distance between the dorsal tubercle and styloid process and the greater dorsa-palmar diameter of the carpal articular surface opposite the dorsal tubercle are indicative of righthandedness. The length of the radius correlated with: the radio-ulnar transverse diameter at the distal end; the distance between the dorsal tubercle and the styloid process; the dorsa-palmar diameter of the distal end opposite the dorsal tubercle; the dorsa-palmar diameter of the carpal articular surface opposite to the dorsal tubercle; the dorsopalmar diameter of the distal end opposite the medial margin of the groove for the extensor pollicis longus; the dorso-palmar diameter of the distal end opposite the floor of the groove for the extensor pollicis longu s and, finally. the height of the dorsal tubercle in relation LO the posterior margin of the carpal articular surface (P < 0.0(1). Regression equations of the length of the radius for these markers have been derived. Key words: Articular surface - Dorsal tubercle· Groove - Regression
Introduction Handedness, length of long bones and stature are all of medicolegal and anthropological importance. Bony markers at the proximal end of the humerus, such as the dimensions of the intertubercular sulcus (Vettivel et al. 1995), have been found to be useful in estimating handedness and in reconstructing the length of humerus; and those of the proximal Correspondence to: S. J. Halla
- - - - - - - - - - --
._-_._.......... --
Ann Anat (1996) 178: 191 - 195 Gustav Fischer Verlag Jena
femur, such as neck-shaft angle, neck length, intertrochanteric apical axis length and the vertical diameter of the head, for reconstructing the length of the femur (Prasad et al. 1995). In this study, markers at the distal end of the radius are used to estimate handedness and to reconstruct the maximum length of the radius. These markers can be used when only a fragment of the distal end of the radius is available in a medicolegal case. The markers are (1) radioulnar transverse diameter of the distal end (TD), (2) distance between the dorsal tubercle and the styloid process (DS), (3) dorsa-palmar diameter of the distal end, opposite the dorsal tubercle (DT), (4) dorsa-palmar diameter of the carpal articular surface, opposite the dorsal tubercle (AS), (5) dorsopalmar diameter of the distal end, opposite the medial margin of the groove for the extensor pollicis longus (EPL), (MGEPL) and (6) dorso-palmar diameter of the distal end opposite the floor of the groove for EPL (FGEPL).
Materials and methods One hundred and twenty five dry radii (61 left and 64 right) all devoid of gross pathology, obtained from subjects of the state of Tamilnadu in Southern India, ranging in age from 25 to 55 years, were used for this study. Though the bones were from cadavers dissected in this department, we could not identify the pairs. The bones were a large set of unmatched bones. The markers at the distal end of the radius (Fig. 1) were measured in em with a vernier ~ a liper. The maximum length of the humerus (LENG) was measured in cm with an osteometric board. (1) TD was the straight distance between the tip of the styloid process and the medial margin of the distal end of the radius (2) DS was the straight distance between the medial margin of the dorsal tubercle and the tip of the styloid process. Markers 3, 4, 5 and 6 were measured vertically, including a horizontal glass sheet of a standard thickness of 0.475 cm, on which the anterior surface of the radius was made to rest, but were only recorded after subtracting 0.475 em. This was done to over-
A
the articular surface opposite the dorsal tubercle and the inferior surface of the glass sheet minus the thickness of the glass sheet. (5) MGEPL was the straight distance between the highest point of the medial margin of the groove for the tendon of EPL and the inferior surface of the glass sheet minus the thickness of the glass sheet. (6) FGEPL was the straight distance between the lowest point of the floor of the groove for the tendon ofEPL and the inferior surface of the glass sheet minus the thickness of the glass sheet. (7) LENG was the distance between the most proximal point on the head of the radius and the tip of the styloid process (Singh and Bhasin 1989). DGEPL, the depth of the groove for EPL, was calculated as [(OT + MGEPL)I2] - FGEPL. HOTG, the height of the dorsal tubercle in relation to the groove for EPL, was DT - FGEPL. HOTA , the height of the dorsal tubercle in relation to the posterior margin of the articular surface, was DT - AS. HDTA is inversely proportional to AS. The raw data were statistically analyzed. Ranges, means and standard deviations were determined for the markers and maximum length of the radius. Student's unpaired t-test was applied to find any significant difference in the means between the left and right radii. Correlation coefficients between the maximum length of radius and markers were determined for the radii of the left, right and for both sides. The length of the radius (Y) was regressed on each of the markers (X) and simple regression models at Y '" bX + a were derived, where 'b' was the regression coefficient and 'a' was the intercept, a constant.
B
o
D MM
(
Table 1. Measurements of the markers at the distal end and length of radius (61 left and 64 right unpaired radii)
GLASS
E
Markers
Fig. 1. Markers at distal end of radius. A. TD = The straight distance between the tip of the styloid process and the medial margin of the distal end. DS = The straight distance between the medial margin of the dorsal tubercle and the tip of the styloid process. B. DT = The straight distance between th e top of the dorsal tuber cle and the inferior surface of the glas<, sheet minus the thickness of the glass sheet. MGEPL '" The straight distance bet ween the highest point of the medial margin of the groove for th e tendon of EPL and the inferior surface of the glass sheet minus thickness of the glass sheet. C. AS = The straight distance bet wen the p\lstenor margin of the articular surface opposite the dorsal tubercle and the inferior surface of the glass sheet minus the thickn ess of the glass sheel. The stippled line indicates the orientation of the bone to measure AS when the AS, dorsal tubercle. and center of the upper end are in the plane of the stippled hne. D. FGEPL == The straight distance between \ he lowest poim of the floor of the groove for the tendon of BPL and tbe inferior surface of the glass sheet minus tbe thickne,s 01 i.he glass sheet. E. Occasional radius with MM (medial marpn of the groove for the tendon of EPL) at a higher level than T (Dorsal tubercle), and therefore DT < MGEPL and {OJl MC' EI'L).'21 <. FGEPI . come the difficulty in placing the .iaws or the vernier caliper appropriately on the bone and any error in measuring the height of the dorsal tubercle or depth of the groove l'o r EPL (3) DT was the straight distance between the rop of the dorsal tubercle and the inferior surface o f rhe glas\ sheet minus the thickness of the glass sheet . (4) AS was the straight. distance between the flosterior margin of
TO
OS
DT
AS
Left Right Both Left Right Both Left Right Both Left Right
MGEPL
FGEPL
OGEPL
HDTG
HOTA
LENG
192
Both Left Right Both Left Right Both Left Right Both Left Right Both Left Right Both Left Right Both
Range em
Mean em
SD
2.160 to 3.100 2.095 to 3.215 2.095 to 3.215 1.370 to 2.090 1.385 to 2.320 1.370 to 2.320 1.615 to 2.430 1.545 to 2.505 1.545 to 2.505 0.905 to 1.760 1.155 to 1.720 0.905 to 1.760 1.605 to 2.390 1.355 to 2.495 1.355 to 2.495 1.580 to 2.205 1.380 to 2.300 1.380 to 2.300 -0.060 to 0.320 +0.040 to 0.180 -0.060 to 0.320 -0.020 to 0.310 -0.030 to 0.260 -0.030 to 0.310 1.420 +0.410 to +0.3 to to 0.960 +0.310 to 1.420 20.300 to 27.800 19.500 to 27.100 19.500 to 27.800
2.670 2.610 2.640 1.720 1.780 1.750 2.000 2.000 2.000 1.325 1.385 1.355 2.005 1.995 1.995 1.890 1.900 1.895 0.110 0.100 0.100 0.100 0.100 0.100 0.670 0.620 0.640 23.860 23.930 23.900
0.23 0.25 0.24 0.18 0.20 0.19 0.18 0.19 0.18 0.16 0.14
P
NS
<0.05
NS
<0.05
0.15
0.20 0.20 0.20 0 .17 0.17 0.17 0.05 0.04 0.04 0.D7 0.08 0.07 0.t7 0.13 0.15 1.88 1.91 1.89
NS
NS
NS
NS
<0.06
NS
Results and discussion
the state of Andhra Pradesh in South India (Dronamraju 1975) are right-handed. In the human upper limbs, the majority of the muscles and bones are heavier on the dominant right side (Chhibber and Singh 1972; Dogra and Singh 1970). The radial dorsal tubercle receives a slip from the extensor retinaculum, and is grooved medially (ulnar) by the tendon of the extensor pollicis longus. The wide groove lateral (radial) to the tubercle contains the tendons of the extensor carpi radialis longus and extensor carpi radialis brevis (Williams et al. 1989). In a right-handed individual, the latter two tendons can be expected to be larger. The relative larger size of these tendons and the wider groove for them, compared to those of the extensor pollicis longus, can have the effect of shifting the dorsal tubercle medially (ulnar), away from the styloid process. Thus the DS can be greater in the right radius. In a more active right wrist joint, the right radial articular surface can be expected to be more extensive than the left. Thus the AS can be greater in the right radius. Vettivel et al. (1995) estimated handedness by the presence of differences in the dimensions of the intertubercular sulcus between the left and right humeri. Their argument is that the dimensions of the right intertubercular sulcus, of which the mean values are found to be greater or smaller than the left in a predominantly right-handed sample population, will also be, respectively, greater or smaller in the right sulcus of a right-handed individual. Therefore, in a pair of bones, if those dimensions are respectively greater or smaller as above in the right sulcus, the individual is right-handed or if, in the left sulcus, the individual is lefthanded. In the present study, the mean DS and AS are significantly greater in the right radius (Table 1). Therefore,
Table 1 summarizes the ranges, means and standard deviations of the measurements in cm, of the markers namely, TD, DS, DT, AS, MGFPL, FGEPL, DGEPL, HDTG, HDTA and of the LENG of the left, right and the total number of radii. The DS and AS showed significant difference (P < 0.05) between left and right sides. Table 2 gives the correlation coefficients of the measured variables for the total of 125 radii (correlation matrix). Most of the variables were significantly interdependent, although infrequently with DGEPL and HDTG. Table 3 lists the correlation coefficients of the LENG against the markers of the left, right, and all the radii. In the case of the total number of 125 radii, the LENG correlated significantly (P < 0.001) with all except HDTG. In the 61 left radii, the LENG correlated significantly (P < 0.0011 0.01/0.05) with all except the AS, DGEPL and HDTG; and in the 64 right radii, the LENG correlated significantly (P < 0.00110.01) with all the markers except the HDTG. Table 4 shows the regression analysis of the LENG against the markers of the left, right and total radii. Table 5 gives the regression analysis values needed for those simple regression equations that are derived for the estimation of the LENG from a known value of the correlated markers.
Estimation of Handedness
Ninety to ninety-five percent of the general population (Adams and Victor 1989) and 93 - 950)'0 of the population of
Table 2. Correlation matrix (n = 125)
LENG TD DS DT AS MGEPL FGEPL DGEPL HDTG HDTA
LENG
TD
DS
1.0000 0.5525*** 0.4114*** 0.6206*** 0.3525*** 0.6622*** 0.6558*** 0.2480** 0.0342 0.3964***
0.5525*** 1.0000 0.6740*** 0.7274*** 0.5223*** 0.7627*** 0.7716*** 0.2489** 0.0334 0.3565*** ------.--.--.-
FGEPL
0.4114*** 0.6740*** :.0000 0.6537*** 0.4826*** 0.7092*** 0.7294*** O. J 372 0 . 0531 iI.l07 3*** -
.. -.~-
DGEPL
- _..._--_ _---
HDTC
•...
LENG TD DS DT AS MGEPL FGEPL DGEPL HDTG HDTA n = 125. *p
0.6558*** 0.7716*** 0.7294*** 0.9160*** 0.5946*** 0.9386*** 1.0000 0.1537 -0.0236 0.5115***
0.2480** 0.2489** 0.1372 0.3982** ' O.0()75 0.3373** 0.1537 l.OOOO 0.6377*** 0.4710***
< 0.05, **P < 0.01, ***P
AS
MGEPL
0.6206*** 0.7274*** 0.6537*** 1.0000 0.5987*** 0.8230*** 0.9160*** 0.3982*** 0.3796*** 0.6084***
0.3525*** 0.5253*** 0.4826*** 0.5987*** 1.0000 0.4705*** 0.5946*** 0.0075 0.1207 -0.2715**
0.6622*** 0.7627*** 0.7092*** 0.8239*** 0.4705*** 1.0000 0.9386*** 0.3373** -0.1114 0.5237***
---_._-_..
HDTA
,--_.'.-.. _----_.
0.0342 0.0334 n.OS31 U.3796***
o 12m
0.1114
0.0236 0.637 7***
noon
Ii
DT
1365***
o.O() ,
193
0.3964** 0.3565*** 0.3073*** 0.6084*** -0.2715** 0.5237*** 0.5115*** 0.4710*** 0.3365*** I.()()()O
Table 3. Correlation coefficients between markers at distal end and length of radius (61 left, 64 right, 125 total radii)
TD DS DT AS MGEPL FGEPL DGEPL HDTG HDTA
*P
Table 5. Simple regression analysis values for length of radius (Y) regressed against correlated markers (X), irrespective of sides (n = 125)
left
LENG right
both
Y
0.4850*** 0.3299*** 0.5110*** 0.2456 0.5490*** 0.5505*** 0.1659 0.0031 0.3080*
0.6313*** 0.5021 *** 0.7197*** 0.4807*** 0.7701 *** 0.7520*** 0.3599** 0.0693 0.5371 ***
0.5525*** 0.4114*** 0.6206*** 0.3525*** 0.6622*** 0.6558*** 0.2480** 0.0342 0.3964***
LENG TO OS OT AS MGEPL FGEPL HDTA
< 0.05
** P
< 0.01
*** P
X
b
a
< 0.001
r2 S.E.E.
Table 4. Length of radius (cm) (dependent variable Y) analyzed against markers (cm) at its distal end (independent variables X) using simple regression Y = bX + a
Y
X
b
SE(b) a
SE(a) r2
P
<
S.E. E .
b
a
r2
S.E.E.
4.4 4.1 6.4 4.4 6.3 7.3 4.9
12.3 16.8 11.2 18.0 11.3 10.2 20.8
0.31 0.17 0.39 0.12 0.44 0.43 0.16
1.58 1.73 1.49 1.78 1.42 1.43 1.74
regression coefficient intercept coefficient of determination standard error of estimate
in a pair of radii, if DS and AS are greater in the right radius, the individual is right-handed but if this is so in the left radius, the individual is left-handed.
For left side LENG TD 3.9 3.3 DS 5.3 DT AS 2.9 MGEPL 5.2 FGEPL 6.1 DGEPL 6.3 HDTG -0.1 HDTA 3.4
0.96 1.31 1.16 1.47 1.03 1.21 4.89 3.33 1.35
13.4 18.2 13.3 20.1 13.5 12.3 23.2 23.9 21.6
2.56 2.26 2.32 1.97 2.06 2.30 0.57 0.43 0.93
0.22 0.09 0.26 0.06 0.30 0.30 0.03 0.00 0.09
0.001 0.010 0.001 0.060 0.001 0.001 NS NS 0.016
0.76 1.06 0.89 1.54 0.78 0.92 5.96 3.21 1.58
11.2 15.3 09.4 14.7 09.2 08.2 22.2 23 .8 19.1
2.00 1.89 1.79 2.15 1.56 1.76 0.62 0.40 0.99
0.40 0.25 0.52 0.23 0.59 0.57 0.13 0.00 0.29
0.001 0.001 0.001 0.001 0.001 0.001 NS
0.60 0.81 0.72 1.05 0.64 0.75 3.75 2.30 1.02
12.3 16.8 11.2 18.0 11.3 10.2 22.8 23.8 20.8
1.59 0.31 1.42 0.17 1.45 0.39 1.43 0.12 1.29 0.44 1.43 / 0.43 0.41 0.06 0.29 0.00 0.67 0.16
0.001 0.001 0.001 0.001 0.001 0.001 NS
1.67 1.80 1.63 1.84 1.59 1.59 1.87 1.90 1.81
For right side 4.9 4.8 7.3 6.7 AS MGEPL 7.4 8.3 FGEPL OGEPL 18.1 HDTG 1.8 HDTA 7.9
LENG TO OS OT
1.49 1.66 1.33 1.69 1.23 1.27 1.79 NS 1.92 0.001 1.62
For both sides LENG TO 4.4 4.1 OS 6.4 DT 4.4 AS MGEPL 6.3 FGEPL 7.2 OGEPL 10.7 HDTG 0.9 4.9 HDTA
b SE b
a
SE a r2
P S.E.E.
regression coefficient standard error of regression coefficient intercept standard error of intercept coefficient of determination level of significance standard error of estimate
1.58 1.73 1.49 1.78 1.42 1.43 1.84 NS 1.90 0.001 1.74
Estimation of radial length
Vettivel et a1. (1995) estimated the length of the humerus using the intertubercular sulcus as a marker. Prasad et al. (1996) estimated the length of the femur using markers at the proximal end of the femur. In the present study, the LENG presented a significant correlation with TD, DS, DT, AS, MGEPL, FGEPL and HDTA (Table 3). The significant correlation suggested that these markers are good indicators of length of the radius and can be useful for estimating the length of the radius. These markers can be used when only a fragment of the distal end of the radius is available. It was thought prudent to derive simple regression equations with Y = bX + a to find the estimated length of radius even if one of the markers is known. Table 4 shows regression analysis of the markers for the radius: left, right and both sides. Regression equations can be derived using the value of 'b' and 'a' for a known marker of the left or right side or irrespective of the side. The following are the regression equations that are derived for the estimation of the LENG, irrespective of the side, using the regression analysis values (Table 5) for a known value of a correlated marker: (i) (ii) (iii) (iv) (v) (vi) (vii)
LENG LENG LENG LENG LENG LENG LENG
4.4(TD) + 12.3 cm 4.1(DS) + 16.8 cm = 6.4(DT) + 11.2 cm = 4.4(AS) + 18.0 cm = 6.3(MGEPL) + 11.3 cm = 7.3(FGEPL) + 10.2 cm = 4.9(HDTA) + 20.8 cm
= =
(S. E. E.
= 1.58) (S. E. E. = 1.73) (S. E. E. = 1.49) (S.E.E. = 1.78) (S. E. E. = 1.42) (S. E. E. = 1.43) (S.E.E. = 1.74)
The equations, for which the coefficient of determination (r2) is higher and the standard error of estimate (S. E. E.) is lower (Table 4), can be the equations of choice. The calculated length of the radius can be used to estimate the stature of an individual by referring to the regression equa-
194
tions, tables and multiplication factors (Nat 1931; Siddiqui and Shah 1944; Telkka 1950; Dupertuis and Haddon 1951; Trotter and Gieser 1952, 1958; Athawale 1963; Kolte and Bansal 1974; Pati! et al. 1983) that are available. Such an estimation of handedness, radial length and stature will have potential for application in physical anthropology. medical jurisprudence and forensic identification of an individual. Though the validity of the models was not tried on other populations, the models were significant (P < (l.00 1), the r2 values are over 12070 and the SE of the regression coefficients (b) are small (Table 4). These statistics should guarantee that the models will be robust. Our regression diagnostics have also suggested robustness. Therefore, these models should be applicable to different populations.
References Adams RD, Victor M (1989) Principles of Neurology. 4th edn. McGraw Hill, Singapore, p 380 Athawale MC (1963) Estimation of height from lengths of forearm bones: A study of one hundred Maharashtrian male adults of age between twenty five and thirty years. Am J Phys Arthropol 21: 105-112 Chhibber SR, Singh I (1972) Asymmetry in mw,cle weight in human upper limbs. Acta Anat 81: 462 - 465 Dogra SK, Singh I (1970) Asymmetry in bone weigh I in the human upper limbs. Anat Anz 128: 278 - 280 Oronamraju KR (1975) Frequency of left-handedness among the Andhra Pradesh people. Acta Genet Med Gemellol Roma 24: 161-162 Oupertuis CW, Haddon JA (1951) On reconstruClion of stature from long bones. Am ] Phys Anthropol 9: 15 ,; 1
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01 f, [SSlll"
Kolte PM, Bansal PC (1974) Determination of regression formulae for reconstruction of stature from long bones of upper limbs in Maharashtrians of Marathwada region. 1 Anat Soc India 23: 6-11 Nat BS (1931) Estimation of stature from long bones in Indians of United province: A medicolegal inquiry in anthropometry. Indian 1 Med Res 18: 1245 - 1253 Patil TL, Gawhale KS, Mazumdar RD (1983) Reconstruction of stature from long bones of both upper and lower limbs. 1 Anat Soc India 32: 111 - 118 Prasad R, Vettivel S, Jeyaseelan L, Isaac B, Chandi G (1996) Reconstruction of length of femur from markers of its upper end. Clin Anat 9: 28 - 33 Siddiqui MAH, Shah MA (1944) Estimation of stature from long bones of Punjabis. Indian J Med Res 32: 105 -108 Singh IP, Bhasin MK (1989) A Laboratory Manual of Biological Anthropology: Anthropometry. 1st edn. Kamla-Raj Enterprises, Delhi p 311 Telk ka A (1950) On the prediction of human stature from long bones. Acta Anat 9: 103 - 107 Trotter M, Gieser GC (1952) Estimation of stature from long bones of American Whites and Negroes. Am J Phys Anthropol 10: 453-514 Trotter M, Gieser GC (1958) A re-evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death. Am 1 Phys Anthropol 16: 79 - 123 Vettivel S, Selvaraj KG, Chandi SM, Indrasingh I, Chandi G (1995) Intertubercular sulcus of the humerus as an indicator of handedness and humeral length. Clin Anat 8: 44 - 50 Williams PL, Warwick R, Dyson M, Bannister LH (1989) Osteology. In: Gray's Anatomy, 37th edn. Churchill Livingstone, Edinburgh p 412
Accepted November 9, 1995
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