# Rates of Change in width and length-width ratios of the diaphyses of the hand.

код для вставкиСкачатьRates of Change in Width and Length-Width Ratios of the Diaphyses of the Hand A. F. ROCHE AND R. F. H E R M A " Fels Research Institute, Yellour Springs, Ohio 45387 ABSTRACT The minimum width and the length of each diaphysis of the hand were measured on serial radiographs of 20 boys and 20 girls. These radiographs were taken close to each birthday at ages from 3 to 13 years inclusive. The corresponding length-width ratios were calculated from these parameters. The b values (indicating rates of change) were calculated for width and length-width ratio in each diaphysis in each child. Communality indices (mean T between b values) were calculated for individual diaphyses. These communality indices reflect the associations between each diaphysis and all the other diaphyses of the hand in their rates of change in width and length-width ratio. The sex differences were not statistically significant for mean b values but they were significant for the communality indices for width (boys higher) and length-width ratio (girls higher). Statistically sign5cant neighborhood effects were present in communality indices for widths within rays for the girls and for ratios within rays for both sexes, There were statistically significant marginal effects in communality indices for widths in the girls within rows and for length-width ratios in the boys within rays. It is well known that diaphyses increase sentative diaphyses could provide useful inin width and length at different sites. formation, with less labor than that reThese sites are unlike in their cellular quired to measure all diaphyses. The mechanisms and their genetic and hormonal controls (Ham and Leeson, '65). In some clincal conditions the length and width of bones are affected differentially (Rubin, '64); more frequent usage of measurements of hand radiographs might improve the diagnosis of such conditions. Such usage is infrequent, partly because suitable standards are lacking. The relevant standards are restricted to the width of the second metacarpal and the sum of the widths of the second, third and fourth metacarpals (Smithgall et al., '66; Garn and Rohmann, '66; Bonnard, '68). Lengthwidth ratios of diaphyses in children are lacking. Standard values for length-width ratios in adults have been published (Parish, '60). Necessarily, these values in adults have been based on total length, not diaphyseal length. The present aim was to determine the rates of change in width and length-width ratios of the diaphyses of the hand and the extent to which these rates of change are intercorrelated. These intercorrelations could help to identify the diaphyses that are most representative in their patterns of change in the parameters considered. Measurements restricted to the repreAM. J. PHYS. ANTHROP.,32: 89-96. radiographs used in this study had been employed previously to analyze the rates of total, diaphyseal and epiphyseal elongation (Roche and Hermann, '69). MATEFUAL AND METHODS Measurements were made on serial nonscreened, dorso-palmar radiographs of the left hands of Melbourne children of British ancestry (20 boys, 20 girls). These radiographs were taken near each birthday, from the third to the thirteenth inclusive, with radiographic positioning in accordance with the instructions of Greulich and Pyle ('59) and a tube-film distance of 91.4 cm. The length of each diaphysis was measured in its long axis and the minimum width was recorded at right angles to the long axis. A complete series of radiographs was available for each child. However, diaphyseal length was not measured for distal phalanges in the girls at 13 years because, in ten of the girls, epiphyseo-diaphyseal fusion had occurred in these bones. All measurements were made using a transparent ruler graduated to 0.5 mm; the differences between repeated measurements did not exceed 0.5 mm. 89 90 A. F. ROCHE AND R. F. HERMANN A trend analysis, by the method of Ferguson ('66), showed that plottings of the diaphyseal widths and length-width ratios at successive ages in individuals were linear (table 1). The length-width ratios were derived using lengths that had been recorded directly from the radiographs and widths that were obtained from the regression lines. It has been shown that the age changes in these lengths are linear (Roche and Hermann, '69). Directly recorded widths were not used because even slightly irregular changes in them caused comparatively large fluctuations in the ratios. (Means and standard deviations for width, length and length-width ratios and their annual increments for each diaphysis of the hand are available from The Librarian, Fels Research Institute, Yellow Springs, Ohio 45387.) The b value for each regression line reflects the slope of the line and, consequently, the rate of change in width or length-width ratio. Communality indices were calculated from a complete intercorrelation matrix of the b values for each sex (Garn and Rohmann, '59; Roche and Hermann, '69). These indices (mean r ) reflect the extent to which the rates of change, from 3 to 13 years, in the width TABLE 1 or the length-width ratio of a diaphysis are correlated with corresponding changes in the other diaphyses of the hand. RESULTS Widths There were only slight sex differences in mean b values for corresponding diaphyses, except in the distal phalanges (table 2); even for these diaphyses, considered as a group, the difference was not statistically significant. The rank order correlation between the mean b values in the boys and the girls was statistically significant ( r = 0.877; P. < 0.01). The communality indices between the rates of change in diaphyseal width were higher in the boys than in the girls to a statistically significant extent ( t = 2.895; P. < 0.01). The rank order correlation between the sexes for these communality indices was not statistically significant, partly because of large sex differences between the values for some diaphyses, e.g., middle phalanx 5 (table 3). Mean communality indices were calculated for diaphyses grouped in rows (e.g., metacarpals) or rays (e.g., metacarpal 3 and the phalanges of the third digit). In general, these mean F-ratios for deviations f r o m linear regressions of w i d t h and length-width ratios against age (20 boys; 20 girls) Diaphysis M1 2 3 4 5 PP 1 2 3 4 5 MP2 3 4 5 DP1 2 3 4 5 Boys TABLE 2 Mean b values (slopes) of regression lines for diaphyseal length and length-width ratio (20 boys; 20 girls) Girls ~~ Width Ratio Width Ratio 0.15 0.09 0.09 0.18 0.04 0.12 0.28 0.58 0.32 0.08 0.15 0.44 0.35 0.14 0.31 0.52 0.78 1.56 0.59 0.29 0.54 0.81 0.39 0.33 0.12 0.91 0.64 0.46 0.35 0.48 0.71 0.76 0.16 0.09 0.49 0.20 0.24 0.12 0.19 0.62 0.18 0.35 0.21 0.26 0.12 0.55 0.18 0.35 0.26 0.28 0.17 0.14 0.18 0.72 0.76 0.51 0.49 0.48 0.33 0.24 0.25 0.71 0.61 0.47 0.26 0.59 0.89 0.39 0.43 0.53 0.18 0.07 0.13 0.10 0.14 0.28 M metaca a19 PP proximal phalanx; MP, middle phaianx, and%P: di&al phalanx. None of these F-ratios are statistically significant; therefore the patterns of change against age are linear. Boys Diaphysis M1 2 3 4 5 PP 1 2 3 4 5 MP2 3 4 5 DP 1 2 3 4 5 Girls Width Ratio Width Ratio 0.245 0.275 0.236 0.177 0.198 0.204 0.229 0.225 0.212 0.186 0.174 0.177 0.178 0.160 0.167 0.200 0.200 0.178 0.155 0.520 0.574 0.658 0.608 0.514 0.214 0.224 0.212 0.166 0.207 0.249 0.243 0.223 0.233 0.367 0.270 0.237 0.215 0.245 0.265 0.243 0.158 0.176 0.215 0.222 0.204 0.188 0.182 0.171 0.177 0.160 0.139 0.154 0.167 0.158 0.143 0.130 0.427 0.498 0.590 0.510 0.445 0.216 0.201 0.213 0.180 0.208 0.224 0.227 0.212 0.232 0.307 0.245 0.220 0.206 0.246 0.234 M metac al; PI', proximal phalanx; MP. middle phdanx, an%P, distal phalanx. 91 DIAPHYSES OF THE HAND TABLE 3 Communality indices (mean r ) for rate of change in width and length-width ratio (20 boys; 20 girls) Diaphysis Boys Girls Width Ratio Width Ratio 0.509 0.464 0.515 0.479 0.523 0.531 0.507 0.360 0.444 0.453 0.466 0.481 0.557 0.469 0.256 0.445 0.273 0.218 0.225 0.430 0.224 0.371 0.343 0.428 0.447 0.380 0.409 0.305 0.447 0.388 0.369 0.433 0.501 0.419 0.097 0.184 0.099 0.107 0.065 0.317 0.368 0.298 0.305 0.344 0.336 0.268 0.424 0.430 0.438 0.369 0.433 0.383 0.429 0.092 0.106 0.357 0.278 0.334 0.334 0.333 0.331 0.161 0.397 0.630 0.531 0.319 0.518 0.601 0.597 0.458 0.467 0.483 0.542 0.258 0.181 0.456 0.54 1 0.520 0.483 0.446 M1 2 3 4 5 PP 1 2 3 4 5 MP2 3 4 5 DP 1 2 3 4 5 Mean: all bones M, metacarpal; PP, proximal phalanx; MP, middle phalanx, and DP, distal phalanx. indices for diaphyses within rows or rays were higher than those for the communalities between each diaphysis and all the other diaphyses of the hand. These indices tended to be higher for rows than for rays. However, the mean communality indices were low for the distal phalanges in the boys and the middle phalanges in the girls (table 4). The mean communality indices within rows or rays tended to be higher in the boys than the girls except for the distal phalanges and the fourth ray. The middle phalanges had the highest index of all rows in the boys but the lowest in the girls. In the boys, the indices were high for the first ray and low for the third; in the girls, they were high for the fourth ray and very low for the fifth. There were statistically significant sex differences in the rank order of communality indices within both rows and rays. The hypothesis that the rates of change in width might be more highly correlated between adjacent than non-adjacent diapyses was examined. Almost all comparisons between the correlations of adjacent and non-adjacent pairs of diaphyses showed that the adjacent pairs were more highly correlated (table 5), thus supporting the hypothesis. The hypothesis that correlations between diaphyses of a row or ray in their rates of change in width might be lower for diaphyses on the margin of a row or ray, e.g., metacarpal 5, distal phalanx 2, than for non-marginal diaphyses in the same row or ray was tested (table 6). For both the boys and the girls, the observed tendencies in rows and in rays supported this hypothesis but to an extent that was not statistically significant, except for rows of diaphyses in the girls (t = 2.315; P. < 0.05). Length-width ratios The mean b values were similar for both the boys and the girls (table 2 ) and the rank order correlation between the sexes was statistically significant ( r = 0.935; P. < 0.01). In the boys, the groups of middle and distal phalanges had higher mean b values than in the girls, but to an extent that was not statistically significant. TABLE 4 Communality indices (mean r ) for rate of change in width and in length-width ratio within groups of diaphyses of the hand Girls Boys Rows and rays Width Ratio Width Ratio Metacarpal row Proximal phalanx row Middle phalanx row Distal phalanx row 0.619 0.521 0.678 0.314 0.562 0.581 0.555 0.459 0.475 0.507 0.375 0.361 0.461 0.625 0.444 0.566 Ray I Ray I1 Ray 111 0.608 0.475 0.376 0.440 0.495 0.346 0.280 0.203 0.405 0.351 0.358 0.421 0.320 0.518 0.130 0.353 0.327 0.569 0.746 0.373 Ray IV Ray V 92 A. F. ROCHE AND R. F. HERMANN TABLE 5 Mean correlations between the rates o f change in width and in length-width ratio relevant to possible neighborhood effects Groups of diaphyses Girls Boys Width Ratio Width Ratio Within rows Adjacent Non-adjacent 0.570 0.420 0.696 0.583 0.614 0.482 0.593 0.549 Within rays Adjacent Non-adjacent 0.582 0.409 0.548 0.030 0.430 0.127 0.522 0.300 TABLE 6 Mean correlations between the rates of change i n width and in length-width ratio relevant to possible marginal effects Girls Boys Groups of diaphyses Width Ratio Width Ratio Within rows Marginal Non-marginal 0.555 0.611 0.492 0.696 0.371 0.620 0.456 0.676 Within rays Marginal Non-marginal 0.343 0.574 0.219 0.488 0.387 0.545 0.557 0.599 The communality indices for the rate of change in length-width ratio for each diaphysis (table 3) were higher in the girls than in the boys to a statistically significant extent (t = 2.861; P. < 0.01). This sex difference was particularly marked in the metacarpals. When the indices for these diaphyses were omitted, the sex difference between the mean indices for the remaining diaphyses of the hand was not statistically significant. The rank order correlation of the communality indices between the two sexes was not statistically significant. The mean communality indices for diaphyses grouped in rows tended to be higher than those for each diaphysis with all the other diaphyses of the hand; there was no corresponding difference for the indices between diaphyses grouped in rays (table 4). The mean indices were high for the proximal phalanges in each sex. The row of distal phalanges did not differ markedly from other rows in mean communality index, although each distal phalanx had a low communality index with all the other diaphyses of the hand. The sex differences between the indices for diaphyses grouped in rows or rays were not statistically significant. The corn. munality indices for rows of diaphyses were larger than those for rays with the exception of Rays I11 and IV in the girls. In both the boys and the girls, the communality index for the fourth ray was high and that for the second ray was low. The rank order correlations between the boys and the girls in the communality indices for diaphyses grouped in rows or in rays were not statistically significant. There was a neighborhood effect in most comparisons between adjacent and nonadjacent diaphyses within the rows and the rays of the hand (table 5). The mean diferences beween the communality indices of adjacent and non-adjacent diaphyses were statistically significant for the rays in the boys (t = 5.483; P. < 0.01) but not for the girls. They were not significant in either sex for the rows. The non-marginal diaphyses of the rows were more highly correlated than the corresponding marginal ones to an extent that was statistically significant in the boys ( t = 2.121; P. < 0.05) but not in the girls (table 6). A similar tendency occurred DIAPHYSES OF THE HAND 93 The rates of change in diaphyseal length and width are disassociated in many clinical conditions (Rubin, '64; Caffey, '67). DISCUSSION To assist in the diagnosis of these condiThe rates of diaphyseal elongation in tions, it is desirable to measure only highly the hands of the same children were previ- representative diaphyses. Figure 1 inously analyzed (Roche and Hermann, '69). dicates the five diaphyses in each sex with The communality indices for these rates the highest communality indices with the of diaphyseal elongation, for the hand as other diaphyses of the hand for rate of a whole, were significantly higher in the change in length, width and length-width girls than in the boys (P. < 0.01). The com- ratio. Middle phalanx 4 in each sex and munality indices for rate of change in proximal phalanx 3 in the girls are highly representative. The means and standard width tended to be higher in the boys than deviations for length, width and lengththe girls and the indices for rate of change width ratios in these diaphyses are given in length-width ratio tended to be higher in table 7. It should be noted that the presin the girls; both these tendencies were ent data were derived from the left hands statistically significant (P. < 0.01). of children. In adults, the bones of the With the exception of diaphyseal length right hand exceed those of the left in within rays, the sex differences between width and length-width ratios (Parish, the mean communality indices for rate '60). of change in diaphyseal length, width or Smithgall et al. ('66) and Garn and length-width ratio were not statistically Rohmann ('66) have published standards significant, when the diaphyses were for the width of the second metacarpal. grouped in rows or rays. The TOWS with The present findings would not support relatively high or low mean communality the choice of this bone as representative indices varied between the sexes and be- of the bones of the hand in width. The tween length, width and length-width ratio. communality indices for rate of change in The mean indices tended to be high for width between this diaphysis and the the fourth ray in the boys and for the other diaphyses of the hand ranked fifthird ray in the girls and to be low for the teenth in order of size in the boys and first and fifth rays in each sex. cleventh in order of size in the girls. within rays, but it was not statistically significant in either the boys or the girls. BOYS GIRLS Fig. 1 Diagrams of the hand indicating for each sex the five diaphyses with the highest communality indices, A, length; B, width, and C , length-width ratio. 94 A. F. ROCHE AND R. F. K E R M A " TABLE 7 Means and standard deviations f m the most representative diaphyses Age Diaphysis years 3.0 MP4 4.0 MP4 5.0 MP4 6.0 MP4 7.0 MP 4 8.0 MP4 9.0 MP 4 10.0 MP4 11.0 MP4 12.0 MP4 13.0 MP 4 3.0 PP 3 4.0 PP 3 5.0 PP 3 6.0 PP 3 7.0 PP 3 8.0 PP 3 9.0 PP 3 10.0 PP 3 11.0 PP 3 12.0 PP 3 13.0 PP 3 Girls Boys Length Width mm mm Ratio Length Width mm mm Ratio 13.6 5.4 2.5 13.2 5.3 2.5 ( 0.79) ( 0.44) ( 0.16) ( 0.92) ( 0.30) ( 0.26) 14.5 5.5 ( 0.97) ( 0.45) 2.6 ( 0.17) 2.6 ( 0.17) 2.7 ( 0.18) 2.7 ( 0.18) 2.7 ( 0.22) 2.8 ( 0.18) 2.8 ( 0.20) 2.8 ( 0.19) 2.9 I 0.19) 2.9 ( 0.17) 15.3 5.9 ( 0.92) ( 0.44) 16.1 ( 1.10) 6.0 ( 0.45) 16.8 6.2 ( 1.07) ( 0.45) 17.4 6.4 ( 0.45) 6.5 ( 0.46) 6.8 ( 0.44) 6.9 ( 0.44) 7.0 ( 0.41) 7.3 ( 0.57) ( 1.21) 18.2 ( 1.14) 18.7 ( 1.22) 19.3 ( 1.18) 20.2 ( 1.28) 21.1 ( 1.21) 14.2 5.5 2.6 ( 1.01) ( 0.41) ( 0.15) 14.9 5.7 2.6 ( 1.06) ( 0.35) ( 0.16) 15.5 ( 1.13) 2.7 ( 0.17) 16.4 5.9 2.8 ( 1.10) ( 0.46) ( 0.16) 17.3 6.1 2.8 ( 1.23) ( 0.47) ( 0.18) 17.8 6.3 2.8 ( 1.29) ( 0.53) ( 0.22) 18.5 6.4 2.9 ( 1.56) ( 0.52) ( 0.24) 19.4 6.6 2.9 ( 1.82) ( 0.44) ( 0.26) 20.3 ( 1.73) 20.9 ( 1.38) 22.2 ( 1.52) 23.5 ( 1.59) 25.0 ( 1.72) 26.3 ( 1.76) PP 3 Not representative in the boys 5.8 ( 0.40) 6.8 3.0 ( 0.47) ( 0.22) 6.9 ( 0.44) ( 0.24) 3.1 6.2 3.5 ( 0.50) ( 0.25) 6.6 3.6 ( 0.51) ( 0.29) 6.9 3.7 ( 0.57) ( 0.31) 7.0 3.8 ( 0.55) ( 0.31) 27.7 7.3 3.9 ( 1.71) ( 0.60) ( 0.30) 7.5 3.9 ( 1.89) 29.1 ( 0.53) ( 0.30) 30.3 7.6 ( 0.56) 7.9 ( 0.57) 8.0 ( 0.53) 8.2 ( 0.47) 8.4 ( 0.49) ( 1.92) 31.9 ( 2.05) 33.5 ( 2.45) 35.4 ( 2.36) 36.9 ( 2.10) 4.0 ( 0.32) 4.1 ( 0.30) 4.2 ( 0.35) 4.3 ( 0.36) 4.4 ( 0.39) M P , middle phalanx. PP proximal phalanx. 1 Numbers in parenthesis are the standard deviations of the mean. The communality indices were not particularly low for the metacarpal, proximal phalanx and distal phalanx of the first ray, although this might have been expected because the positioning of this ray is difficult to standardize. In each sex, the lowest indices occurred in middle phalanx 5 and distal phalanx 5 (width) and the fourth proximal phalanx (length-width ratio). Neighborhood and marginal effects were present in the communality indices for length, width and length-width ratio, but the majority were not statistically significant (Roche and Hermann, '69 and present). Significant neighborhood effects were limited to diaphyseal length within rows, diaphyseal width within rays in the girls, and length-width ratios within rays in each sex. Significant marginal effects occurred DIAPHYSES OF THE HAND 95 the age of three months to eleven years. Helv. only for width within rows in the girls and Paediat. Acta, 23: 445-483. for length-width ratios within rays in the Caffey, J. 1967 Pediatric X-ray Diagnosis. 5th boys. Possibly, both neighborhood and ed. Yearbook Medical Publishers, Inc., Chicago. marginal effects are similar in nature and Ferguson, G. A. 1966 Trend analysis. In: Staare due to the presence of nearby diaphtistical Analysis in Psychology and Education. McGraw-Hill Book Co., New York. Chapter 21 yses. The higher communality indices be(pp. 341-353). tween neighboring diaphyses may reflect S. M.,and C. G. Rohmann 1959 Comthe presence of a full complement of Garn, munalities of the ossification centers of the nearby diaphyses; the lower comrnunality hand and wrist. Am. J. Phys. Anthrop., 17: 319indices of marginal diaphyses may be due 323. to an incomplete complement of nearby 1966 The gain and loss of cortical bone in Ohio Whites. Changes in total periosteal diaphyses. There is some supporting eviwidth, medullary cavity width and cortical dence for the view that the presence of thickness in the second metacarpal in 1483 nearby bones is a factor in regulating the male and 1515 female subjects 1.0 through size of a bone (Roche, '67). The com80.0 years. Progress report to Nutrition Secmunality indices of diaphyses that are both tion, Office of International Research, National Institutes of Health. Privately published, The marginal and non-adjacent were compared Pels Research Institute, Yellow Springs, Ohio. with those of diaphyses that are non- Greulich, W. W., and S. I. Pyle 1959 Radio. marginal and adjacent. The directions of graphic Atlas of Skeletal Development of the Hand and Wrist. 2nd ed. Stanford University the differences indicated that these effects Press, Stanford, Calif. (neighborhood plus marginal) were presA. W., and T. S. Leeson 1965 Histology. ent in each sex for length, width and for Ham, 5th ed. J. B. Lippincott Co., Philadelphia. length-width ratio, but to an extent that Parish, J. G. 1960 Skeletal syndromes associ. was statistically significant only for width ated with arachnodactyly. Proc. Roy. SOC.Med., 53: 515-518. in the girls ( t = 3.098, JP. < 0.05). ACKNOWLEDGMENT The present study was supported in part by grants FR-05537 and FR-00222 from the National Institutes of Health, Bethesda, Maryland. LITERATURE CITED Bonnard, G. D. 1968 Cortical thickness and diaphysial diameter of the metacarpal bones from Roche, A. F. 1967 Absence of the lunate. Am. J. Roentgen., ZOO: 523-525. Roche, A. F., and R. F. Hermann 1969 The rates of elongation of the short bones of the hand. Am. J. Phys. Anthrop., i n press. Rubin, P. 1964 Dynamic Classification of Bone Dysplasias. Yearbook Medical Publishers Inc., Chicago. Smithgall, E. B., F. E. Johnston, R. M. Malina and M. A. Galbraith 1966 Developmental changes in compact bone relationships in the second metacarpal. Human Biol., 38: 141-151.

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