Anatomical differences in the femur and tibia between Negroids and Caucasoids and their effects upon locomotion.код для вставкиСкачать
Anatomical Differences in the Femur and Tibia between Negroids and Caucasoids and Their Effects upon Locomotion M. R. FARRALLY AND W. J. MOORE Departments of Physical Education and Leeds, England KEY WORDS Patellarligament Caucasoid . Negroid. 2 Anatomy, University of Leeds, . Locomotion . Femur . Tibia . ABSTRACT Nine variables of length, width and circumference of the femur and tibia were measured on post-cranial remains of 28 Caucasoids and 45 Negroids. The distance from the point of tibial attachment of the patellar ligament to the head of the tibia (PLID) was also determined. I t was found that the Negroid has a significantly longer and narrower femur and tibia than the Caucasoid, although PLID did not vary between the two groups. Thus PLID, relative to the length of the tibia, was less in Negroids than Caucasoids. A factor analysis was carried out in order to examine the relation between PLID and the other variables. It appeared that the same three factors governed the ten variables in both races. I n Caucasoids, PLID did not load on either the “length” or “width” factors and appeared unique. In Negroids, PLID loaded on Factor I11 with two width measures, and this factor correlated positively with the “width” factor. It is suggested that in Caucasoids PLID does not relate to length or width dimensions of the leg but in Negroids it is related to width rather than length. It is well documented that the inferior limbs of Negroids tend, on average, to be longer than those of Caucasoids, both in absolute terms and relative to total body stature (Dupertuis and Hadden, ’51; Trotter and Gleser, ’58; Graham and Yarbrough, ’68). Assuming that the mechanical characteristics of the human limb are similar to those in other animals, a n increase i n its linear dimensions will give greater potential for jumping and speed of movement (Howell, ’44; Alexander, ’68) provided that the increase in limb segment lengths does not adversely affect leverage about the joint axes. Extension of the knee is brought about by the action of the quadriceps femoris muscle developing tension in the patellar ligament. In this movement, the tibia behaves as a third class lever, rotation occurring about the joint centre in the knee with the point of application of the effort being located at the tibial tuberosity and that of Ann. J. PHYS.ANTHROP., 43: 63-70. the load a t the distal extremity. The centre of rotation is instantaneous (i.e., its position varies with different angles of flexion) since the articular surfaces of the joint are not spherical (Kapandji, ’70). Thus, the effort moment arm (FMA) changes its length during extension. For any particular knee angle the instantaneous centre can be located radiographically and FMA measured (Smidt, ’73) but to do this throughout the range of movement occurring in locomotion would demand a prohibitively large exposure to X-irradiation. Even the radiographic measurement of FMA at a fixed knee angle presents difficulties in the recruitment of suitable subjects (see DISCUSSION). Accordingly, a search was made for a simple measurement on skeletal remains to indicate the magnitude of FMA suitable for comparisons between individuals or groups of individuals. An examination of the morphology of the head of the tibia suggested 63 64 M. R. FARRALLY AND W. J. MOORE that the distance from the point of application of the force generated in the patellar ligament to the most proximal point on the tibia (PLID) would provide such an indication (fig. 1 ) . If the point of application were to be moved distally, for example, FMA would increase because of the sloping anterior face of the head of the tibia. Conversely, movement of the point of application proximally would lead to a reduction of FMA. PLID will not change with the angle of flexion and cannot be used to quantify FMA at various positions of the joint. It should, however, provide an indication of the overall magnitude of FMA suitable for comparative purposes. It might be expected, a priori, that an overall increase in tibia1 length, and therefore in load moment arm, as evidenced in Negroids, will be compensated for by a related increase in PLID, but this expectation involves two assumptions: first, that the Negroid tibia is a scaled-up version of the Caucasoid bone so that an increase in Fig. 1 The knee joint, showing the line of action of the force in the patellar ligament ( F ) , effort moment arm (FMA) and distance from point of application of force generated in patellar ligament to most proximal point in the tibia (PLID) in relation to the instantaneous centre of rotation ( X ) . length will be accompanied by a corresponding increase in PLID and secondly, that increasing the load arm increases the load moment. In this study, these two assumptions have been investigated by an examination of the relationship between PLID and length and width variables of the femur and tibia in male Negroid and Caucasoid skeletal remains. METHODS Specimens The Caucasoid sample was taken from the Scarbrough Collection of the British Museum of Natural History, London (B.M. N.H.). Of the 28 specimens measured, 19 were “complete” - that is, both the femur and tibia were present and in a condition which permitted all the measurements to be recorded. None of the series was sexed. The Negroid sample was taken from five collections : the Ibo and East African series from B.M.N.H. and the Haya, Somali and Jebel Moyan series from the Duckworth Laboratory, Cambridge. Of the 45 subjects measured, 24 were “complete.” All the Negroid specimens were sexed upon excavation except the Jebel Moyan. Where not previously recorded, sex was determined by examination of the pelvic girdle or, if not available, from the characteristics of the femur. In cases of doubt the bones were discarded. Anthropomet y Measurements were recorded using a Harpendon Survey Set, the instruments being calibrated against a steel tape. The measurements taken were as follows: ( 1 ) Maximum length of the f e m u r : the maximum distance from the head of the femur to the most distal point on the medial condyle, after Warren (1897). ( 2 ) Bicondylar length of the f e m u r : the distance from the head of the femur to the horizontal plane of the condyles, termed by Warren ( 1897) the “oblique length.” ( 3 ) Bicondylar width of the f e m u r : the maximum distance across the condyles in the transverse plane. ( 4 ) Anterior-posterior w i d t h of the f e m oral condyles : the maximum distance between the anterior and posterior surfaces of the condyles, measured in the anteriorposterior plane. ETHNIC DIFFERENCES IN FEMUR AND TIBIA ( 5 ) Anterior-posterior w i d t h o f the f e m oral shaft: the minimum width of the shaft in the anterior-posterior plane. (6) Transverse width of the femoral s h a f t : the minimum width of the shaft in the transverse plane. ( 7 ) Minimum circumference of the femoral shaft. ( 8 ) M a x i m u m length o f the tibia: the maximum length of the tibia, from the most proximal point on the intercondylar eminences to the most distal point on the malleolus. ( 9 ) Transverse width o f t h e distal extremity of the tibia: the maximum transverse width of the distal extremity, including the medial malleolus. (10) PLID: the anterior surface of the head of the tibia slopes downwards and forwards (fig. 1 ) . The lower part of this slope produces an eminence termed the tibial tuberosity. On the upper part of the tuberosity is a smooth area which gives attachment to the patellar ligament. PLID was taken as the mean of two measurements from the most proximal point on the intercondylar eminences to: ( a ) the most proximal point on the smooth area of the tibial tuberosity; (b) the most distal point on the smooth area of the tibial tuberosity. Measurements (8) and (10) included the intercondylar eminences and where there were any signs of damage to either of these structures the bone was discarded. Reliability of measurement was tested by taking 20 repeated sets of measurements on a femur and tibia from one individual. The largest coefficient of variation was less than 1.5%. 65 group variability (i.e., between collections) in the Negroid was surprisingly low, only five coefficients were less than 0.999, the lowest being 0.998 recorded between a Jebel Moyan and a Haya. The variability between Negroid and Caucasoid was somewhat greater, well over half the coefficients being below 0.999, the smallest value being 0.996. (2) A one-way ANOVA using the five Negroid collections as treatment levels showed there was no significant difference between collections on nine of the ten variables at the 0.05 level of confidence. On the tenth variable, maximum length of the tibia, a significant difference was recorded at a = 0.05 but not at a = 0.01, and an a posteriori investigation of the difference between means revealed that this difference was in evidence between the Ibo and Somali collections. The difference was only just significant (mean difference bl:b2 = 31.192, HSD at a = 0.05 is 31.982). The high degree of homogeneity revealed by these analyses is in agreement with the findings of Nutter (’58) who found a similarly high level of homogeneity in a large number of measurements taken on both the upper and lower limbs of the Ibo, Haya, Somali and Jebel Moyan series. (See also Mukherjee, Rao and Trevor, ’55.) Differences between Negroids and Caucasoids o n t h e measured variables Mean values for the two samples together with their standard deviations, determined for each variable, are shown in table 1. Homogeneity of variance was tested by an F test and in each of the ten variables the samples were homoscedastic. RESULTS The significance of the difference between Variability within the Negroid sample the two samples was tested by the pooled Since the Negroid sample included sev- variance model of “t.” Significant differeral tribal groups of widely separated geo- ences were recorded at the 0.05 level of graphic location, it was necessary to test its confidence in eight of the ten variables and homogeneity. Two statistical techniques of these only maximum and bicondylar were employed. ( 1 ) A correlation matrix femoral lengths were not significant at a = was drawn up using the Negroid subjects’ 0.01 (table 1). The two variables not exscores on the ten variables in a Pearson’s hibiting significant differences were the Product Moment design. The Caucasoid anterior-posterior width of the femoral consampIe was included to assist the evalu- dyles and PLID. ation of any Negroid between group variT h e relationship o f PLID to ability. The Ibo series contained no “comother measures plete” specimens and consequently could not be included in this analysis. Between In an attempt to discover what factors 66 M. R. FARRALLY AND W. J. MOORE TABLE 1 Numbers, means and standard deviations, homogeneity of variance ( F ) , and student’s t value of the Negroid and Caucasoid samples on the measured variables Negroid Measure Caucasoid N Mean S.D. N Mean S.D. F value Student’s t value 34 476.44 23.95 27 461.42 20.21 1.41 2.56 * 3 Bicondylar width of femur 32 79.50 4.63 27 83.05 4.11 1.27 3.04** 4 Ant.-post. width of femoral condyles 33 62.36 3.89 27 62.88 3.12 1.55 0.55 5 Ant.-post. width of femoral shaft 32 25.84 2.02 26 27.81 2.22 1.20 3.46 ** 6 Transverse width of femoral shaft 32 25.95 1.95 27 28.95 1.53 1.62 6.37** 7 Minimum circumference of femoral shaft 33 84.44 5.62 27 93.61 4.40 1.63 6.80** 8 Maximum length of tibia 33 408.00 24.45 24 373.42 24.56 1.01 5.17* * 9 Transverse width of distal head of tibia 33 47.07 4.48 23 53.23 3.41 1.73 5.47** 35 45.69 5.98 22 45.36 4.96 1.46 0.22 1 Maximumlength of femur 2 Bicondylar length of f emnr 10 PLID *, P 5 0.05. **, PL-0.01. might influence PLID a factor analysis of the ten variables was carried out on the data from the “complete” subjects of both samples (table 2). The variables were subjected to three analyses - principal components, varimax and promax - and factors were extracted separately for each race. The significance level for loadings on each factor was calculated using the BurtBanks Formula (Burt and Banks, ’47). The extraction of factors was terminated at an eigenvalue of 1.OO. Correlation coefficients between factors I and I1 in the promax solution were - 0.54 and - 0.46 respectively for the Negroid and Caucasoid samples (P f0.05 in both cases). In table 2 , factor I1 in the Negroid sample accounts for more percentage variance than factor I and would usually be extracted first. However, in the orthogonal solutions factor I accounted for far more percentage variance than factor I1 and the order of factors thus established was maintained. DISCUSSION The greater length of the Negroid inferior limbs, widely reported by previous authors, was apparent in this study. In width measures, the Negroid exhibited significantly smaller values in all cases except the anterior-posterior width of the femoral condyles. Du Toit (’55) previously reported racial differences in width in the geometry of the knee joint and suggested that the wider distal extremity of the European femur, compared to the Bantu, was due to a splaying of the condyles. This would certainly account for a greater transverse diameter without a corresponding increase in the anterior-posterior width, as recorded in the present data. The lack of a statistically significant difference between the two samples in PLID confounds the initial expectation that a greater tibia1 length would be associated with a related increase in this measure. The findings show that the point of inser- 67 ETHNIC DIFFERENCES IN FEMUR AND TIBIA TABLE 2 Promax analysis of the te n measures. Loadings, significant at p L 0.05 as defined by the Burt-Banks Formula, are indicated by an asterisk Negroid Caucasoid Factor loadings Measurement Factor loadings I I1 I11 Communality I I1 I11 Communality 1 Maximum length of femur 08 103" 01 1.07 10 92" 04 0.86 2 Bicondylar length of femur 08 102' 00 1.05 11 91 ' 05 0.85 3 Bicondylar width of femur 109" 00 29 1.26 99" 10 05 0.99 4 Ant.-post. width of femoral condyles 34 35 16 0.26 81" 11 19 0.71 5 Ant.-post. width of femoral shaft 22 26 49' 0.35 80' 02 33 0.74 6 Transverse width of femoral shaft 42' 04 58" 0.52 54" 25 15 0.38 65* 03 40' 0.59 82' 20 07 0.71 08 95' 18 0.95 11 91' 07 0.85 10 16 1.13 97' 27 12 1.03 100' 19.1 1.05 06 42.1 00 27.1 99' 11.7 0.98 7 Minimum circumference of femoral shaft 8 Maximum length of tibia 9 Transverse width of 104" distal head of tibia 10 PLID % variance 20 31.0 12 32.4 tion of the patellar ligament, relative to tibial length, is more proximal in Negroids than Caucasoids. If PLID is an indicator of FMA, as has been assumed, it would appear that FMA for any given angle of knee flexion is similar in both ethnic groups and therefore smaller as a ratio of tibial length in the Negroid. Initial observations in a radiographic study that we are carrying out for a fixed knee angle support our assumption. Subjects for this type of study are not readily available but so far seven Caucasoids and 12 Negroids have been examined and the mean values of FMA are 4.75 and 4.65 cm respectively ( P > 0.2). This study is being extended as further subjects become available and will form the basis of a subsequent publication. From Newton's second law of motion it can be shown that in knee extension F x FMA =I; where F is the force in the patellar ligament, Of the leg and I is the moment of inertia foot about the & is the angular acceleration knee therefore = F x FMA } I If F and I are the same for both ethnic groups, a decrease in FMA would be associated with a decrease in G. It would thus appear that the greater length of the inferior limb in the Negroid may be at the expense of cadence (i.e., the rate at which the leg can be rotated about the knee). The fact that tibial length is greater in the Negroid suggests not only a greater mass of the leg but also a larger radius of gyration and a greater value of I (since I is a function of mass and radius of gyration, where the radius of gyration is a measure of how far the mass is distributed from the centre 68 M. R. FARRALLY AND W. J. MOORE of rotation). I n contrast, the measures of width are less for Negroids, possibly an indication of a compensating mechanism operating to keep any increase in I as small as possible. This possibility is further s u p ported by the results of the factor analysis (table 2). Length and width variables loaded on separate factors inversely related. The use of three factor analyses was found necessary because neither the direct solution (principal components) nor the orthogonal rotation (varimax) provided factors easy to interpret. I n the principal components analysis some factors were bipolar and some variables loaded on more than one factor. Orthogonal rotation was found to give higher loadings but only oblique rotation of the factors (promax) reduced the number of marginally significant loadings considerably, thus assisting interpretation, In both samples three factors were extracted and the pattern of loadings of the variables in all the analyses was very similar. It would seem not only are these three factors of importance within each sample, but also that the same three factors may be operating in both samples. Factor I would appear to be a width factor. The value to be reached for significance was exceeded by all width variables in the Caucasoid sample, and by all width variables except the anterior-posterior diameters in the Negroid. The low communality (Le., the total amount of common variance shared between the three factors) associated with these two variables in the Negroid suggests a n unreliable measure. Factor I1 seems to be a length factor, significant loadings appearing on the three length measures in each sample. As length and width measures did not load on the same factor in such a way as to make it bipolar, it cannot be directly concluded that length and width are inversely related. However, promax analysis allows oblique rotation of factors such that the factors themselves may be correlated. The correlation coefficients between Factors I and I1 were - 0.54 and - 0.46, respectively, for the Caucasoid and Negroid samples. Both these values are statistically significant ( P 0.05), thus enabling the conclusion to be drawn that the two factors are inversely related. It seems likely that the adaptive mechanisms determining morphological changes to accommodate differences in environmental temperature will have had a profound effect upon both these factors. The above results are in accordance with Allen’s Rule, the long and thin inferior limbs of the Negroid facilitating heat loss. Examination of the loadings on Factor I11 does not evoke a simple explanation of the observed relationships. In the Caucasoid this factor seems unique, although over 11% of the variance was attributed to this factor alone. Also, there was no significant correlation (r < 0.2) with either of the other two factors. It would appear that PLID i n the Caucasoid has little in common with either length or width measures. In the Negroid the same trend was not apparent. Factor I11 accounted for 19% of the variance. It correlated significantly with both Factor I and Factor I1 and was not unique. The presence of loadings from the two width variables of the femoral shaft as well as PLID, and the correlation of r = 0.53 between Factor I and Factor 111, suggests a close link between PLID and width variables. ACKNOWLEDGMENTS We should like to thank Dr. D. Brothwell of the Sub-Department of Physical Anthropology, British Museum (Natural History) and Dr. J. Garlick of the Duckworth Laboratory, Cambridge for permission to examine specimens in their charge. LITERATURE CITED Alexander, R. McNeill 1968 Animal Mechanics. Sidgwick and Jackson, London. Burt, C., and C. Banks 1947 A factor analysis of body measurements for British adult males. Ann. Eugen., 13: 238-256. Child, F. 1973 The Essentials of Factor Analysis. Holt, Rinehart and Winston, New York. Du Toit, G. T. 1955 Internal derangement of the knee. American Academy of Orthopaedic Surgeons, Instructional Course Lectures, Vol. XII, pp. 9-34. Dupertuis, C. W., and J. A. Haddon 1951 On the reconstruction of stature from long bones. Am. J. Phys. Anthrop., 9: 15-53. Graham, T. M., and J. D. Yarbrough 1968 Anthrouometric studies of the lone bones of the ‘‘Shill Mound” Indians. Am. J. Phys. Anthrop., 28: 85-92. ETHNIC DIFFERENCES IN FEMUR AND TIBIA Howell, A. B. 1944 Speed in Animals. University of Chicago Press, Chicago. Kapandji, I. A. 1970 The Physiology of the Joints. Vol. 2 , Lower Limb. E. and S. Livingstone, London. Mukherjee, R., C. R. Rao and J. C. Trevor 1955 The Ancient Inhabitants of Jebel Moya. Cambridge University Press, Cambridge. Nutter, M. C. 1958 A n osteological study of the Hominoidea. Doctoral dissertation, University of Cambridge. 69 Smidt, G. L. 1973 Biomechanical analysis of knee flexion and extension. J. Biomechanics, 6: 79-92. Trotter, M., and G. C. Gleser 1958 A re-evaluation of estimation of stature taken during life and of long bones after death. Am. J. Phys. Anthrop., 16: 79-123. Warren, E. 1897 An investigation on the variability of the human skeleton, with special reference to the Naqada race. Phil. Trans. R. SOC. Ser. B, 189: 135-227.