AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 85:339-343 (19911
Technical Note: Calculation of Age at Formation of Radiopaque Transverse Lines STEVE BYERS De artment of Anthropology, University of New Mexico, AEfuquerque, New Mexico 87131
KEY WORDS
Age determination, Harris line formation, Long bone measurement
ABSTRACT A simple method for determining the age of an individual at the time of radiopaque transverse (Harris) line formation is presented. To use this method, only two measurements are required: total bone length and distance of line to nearest bone end; these are put into formulae that calculate the percent of total bone growth when the line appeared. The result of this calculation is compared with tables of percent bone growth per year (one to 16 years in females and one to 18years in males) to arrive at estimations of age at line formation. Since these tables are presented for the femur, tibia, humerus, and radius, this technique can be used on any one of the major long bones exhibiting lines. In studying extinct populations, a number of researchers have used measurements from radio a hs of mature human limb bones to ca cu ate the age of an individual when radiopaque transverse (Harris) lines formed. Unfortunately, the utility of their methods is reduced due to several problems. For example, many are limited to studyin only one (tibia) or two (tibia and femur bones (Clarke, 1982;Hummert and Van Gerven, 1985; Hunt and Hatch, 1981; Maat, 1984; McHenry and Schulz, 1976). Some deal on1 with lines at the distal ends of bones (C arke, 1982;Hummert and Van Gerven, 1985; Maat, 1984; McHenry and Schulz, 1976) while others calculate distances of lines from the rojected center of ossification (Hummert an Van Gerven, 1985; Hunt and Hatch, 1981; Maat, 1984). One imposes a common length of a bone at birth and does not account for the differential growth of a bone at the proximal and distal ends (Allison et al., 1974). Several assume constant owth per year (Allison et al., 1974; EcHenry and Schulz, 1976) while one uses equations that are more complex than necessary (Hunt and Hatch, 1981). Finally, one does not account for the thickness of the epi hyseal areas (Clarke, 1982). Given these pro! Ilems, a techni ue is proposed here that accounts for these s ortcomings and has the
YP
advanta e of requiring only two measurements o a long bone to calculate the age at which lines were formed. Since it requires the calculation of the length of a bone at the time of line deposition, the method is based on three as ects of owth and anatomy. First, since t ey are ormed when normal growth is disrupted (Park, 1964),transverse lines mark the osition of e iphyseal plates at the time of eposition (darke, 1982;Hummert and Van Gerven, 1985; Maat, 1984; Hunt and Hatch, 1981). Therefore, when bone length at the time of line formation is estimated, the thickness of the epiphyseal areas beyond the line(s) must be taken into account. Second, bone growth is well documented in the living and can be used to calculate tables of ercent growth per year. Third, growth at eit er end of a long bone is not equal; this must be accounted for when a line is seen at only one end. These three aspects were determined for the four limb bones most often seen to contain radiopaque lines: femur, tibia, humerus, and radius. To determine the percent of total bone length seen in the ei hyses, data from Maresh (1955)was used. hese show that for
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9
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@ 1991 WILEY-LISS. INC
op
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Received March 26,1990; accepted January 10,1991,
340
S. BI7ERS
the years 10 through 12 (the ages for which these data are available) the percent accounted for by the epiphyses is relatively constant between the sexes in the four bones. In the humerus and radius, approximately 8 percent (sd = .68%) of the total bone length is in the epiphyses while the statistic is 11 percent (sd = .29%) in the femur and 13 percent (sd = .33%)in the tibia. To determine the pattern of growth for these bones, four data sets (Anderson et al., 1963;Anderson and Green, 1948; Gindhart, 1973;Maresh, 1955)were combined to arrive at chronolo 'es of percent bone growth for each year o postpartum life. These chronologies are given in Table 1 for males to 18 years and Table 2 for females to 16 years; greater ages are not needed since the data sets show a levelin off of limb bone growth after these times. he values in the tables are the average percent of mature length that a bone is in each year of life; they are based on the average of mean length per ear divided by the mean mature bone fength in each of the data sets. Although these percents are derived from modern individuals, their use on extinct ou s is warranted because chronologies ase on prehistoric populations (Dewey and Mahler, 1972; Hummert and Van Gerven, 1985; Johnston, 1962) would be incomplete due to deficiencies in samples (Clarke, 1982). Even without this, the determination of the age of a person at death from bone is subject to error similar to differences seen between extinct and extant ou s. To determine t e ifferential between bone growth at the proximal and distal ends, Anderson et al. (1963) and Gill and Abbott (1942)provide data to indicate that approximately 70 percent of femoral growth occurs at the distal end, while approximately 57 percent of tibia1 growth occurs at the proximal end. Gill and Abbott (1942) also give data that shows approximately 81 percent of humeral growth occurs at the proximal end while 75 ercent of radial growth occurs at the dista end. These percents will be used since their variability during growth is unknown at this time. The method for determining a e at line formation proposed here involves t e following operations: 1) calculating the length of the diaphysis when the line was deposited, 2) correcting for epiphyseal thickness, 3) calculating percent of mature bone length, and 4) comparing this percent with the chronology
?
TABLE 1 . Chronology of limb bone growth in males (percent of mature bone length) Age
Humerus
Radius
Femur
Tibia
1
32.3 40.0 45.2 50.0 54.3 58.7 63.0 66.9 70.6 74.1 77.5 80.8 85.3 90.2 94.6 97.8 99.0 100.0
32.7 39.5 44.8 49.5 53.9 58.2 62.2 66.1 69.9 73.5 77.1 80.9 85.0 90.3 95.0 98.0 99.7 100.0
29.6 37.1 43.1 48.5 54.3 59.1 63.7 68.8 73.0 76.9 80.6 84.4 88.8 93.1 96.9 98.9 99.7 100.0
28.8 36.5 42.4 47.6 53.5 57.9 62.3 67.5 71.6 75.7 79.6 83.7 88.5 93.0 96.7 99.0 100.0 100.0
2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17 18
4
r i
P
a
TABLE 2. Chronology of limb bone growth in females (percent of mature bone length) Ape
Humerus
Radius
1
34.5 42.8 48.8 54.0 59.2 63.5 68.5 72.5 76.4 79.8 85.3 90.0 93.8 97.2 99.2 100.0
35.3 42.7 48.8 53.9 59.1 63.5 67.9 72.4 76.4 80.4 85.6 91.0 95.1 97.6 99.5
2 3 4 5 6 7 8 9 10 11 12 13 14
15 16
Femur
Tibia
31.7
31.5 40.1 46.6 52.4 58.6 63.9 69.0 74.3 79.4 83.9 88.8 93.0 96.5 98.3 99.1 100.0
40.2 ~
46.4 52.3 60.0 65.0 70.0 75.2 79.6 ~. 83.9 88.7 93.1 96.9 99.1 99.8 100.0
1nn.n
of bone development. To better understand these operations (and therefore the method), refer to Fi re 1. A radiopa ue line (the position o f t e distal epiphysei late at the time of deposition) is seen at ri i t angles to the major axis of a mature ti ia, approximately three-quarters of the distance down the shaft. The dashed line indicates the hypothetical position of the roximal epiphyseal plate, while the dotted ines indicate the ositions of the ends of the bones when the l n e formed. The length of the diaph sis at deposition (DD)can be obtained by su tracting D (the distance of the distal epi hyseal plate from the distal end) and P (the istance of the proximal epiphyseal plate from the
Y
%
P
r;
a
341
AGE AT FORMATION OF TRANSVERSE LINES
TABLE 3. Formulae for calculating percent of mature bone length at time of radiopaque line formation Bone
Humerus Radius Femur Tibia
End Line Closest to
Formula
Proximal Distal Proximal Distal Proximal Distal Proximal Distal
Pct = 1.09 (T - 1.23P) X 100/T Pct = 1.09 (T - 5.26D) X 100/T Pct = 1.09 (T - 4.00P) X 100/T Pct = 1.09 (T - 1.33D) X 100/T Pct = 1.12 (T - 3.33P) X 100/T Pct = 1.12 (T- 1.43D) X 100/T Pct = 1.15 (T - 1.75P) X 100/T Pct = 1.15 (T - 2.33D) X 100/T
the age at line formation can be found by matching this percent with the proper value in Tables 1or 2. The above involves the calculation of intermediate values (D , TD, Ep, and E D ) which can be eliminated y! combining operations. The formulae presented in Table 3 are the result of such combination and can be used to calculate the percent of mature length of the four bones at the time a radiopaque line was formed at either the distal or proximal end. As can be seen, only two values are needed to use these formulae, the total length (T) from the proximal to the distal end, arallel to the long axis of the bone, and the istance (D or P) from the transverse line to the closest end, Fig. 1. Drawing of bone showin areas of measure- parallel to the long axis. For example, if a ment for determining age when rafiopaque transverse mature tibia from a male that is 430 mm in lines formed. See text for explanation. length has a line 30 mm from the distal end, the percent of mature bone length would be 1.15(430 - 2.33(30)) x 100/430. The result, roximal end) from T (the mature bone 96.3 percent, corresponds to an age between yength). Since P is not known for the bone in 14 and 15 years from Table 1. Similarly, if Figure 1 (and in many x-rays), its value can the line in that same bone was 50 mm from be estimated by 1.33D;D is multiplied by the the proximal end, the percent of mature bone coefficient 1.33 because on the average 57 length would be 1.15(430 - 1.75(50)) x 100/ percent of bone growth occurs at the proxi- 430; the result (91.6 percent) corresponds to mal end (57143 = 1.33) and therefore, the an age between 13 and 14. To determine the efficacy of this method, roximal epiphyseal plate at the time of Pdeposition of the line would be pro ortion- two tests were designed. First, since the ately further from the proximal en$. Thus, distal tibia has been studied most often DD = T - (D + 1.33D) = T - 2.33D. by other workers, its equation from Table 3 Once this is known, the values EP and ED was algebraically manipulated to solve for (the thicknesses of the proximal and distal D = .429(T - (PctA15)). Then the ercents epiphyses, respectively) can be accounted for in Tables 1and 2 were substituted or Pct t o by multiplying DD by the ercent of bone arrive at 34 new e uations, one correspondlen h seen in the epiphysea plates t o arrive ing to each year of ife from 1 to 18 in males at t e total length of the bone at the time of and 1 to 16 in females. Next, using the line deposition (TD). As noted earlier, this ran es given by Maresh (1955) for this bone, value is 13 percent; therefore, TD = the owest value of T (390 mm) was substiDD + .13TD. Throu h algebraic manipula- tuted into the 18 male e uations to enerate tion TD = 1.15DD.d v e n this, the percent of 18 values of D. These va ues of T an D were mature length is merely (T, X 100)l" and then used in the equations of Allison et al.
B
f
P
P
P
s
?
5
342
S. BYERS
(1974), Clarke (1982), Hummert and Van Gerven (1985)and Maat (1984) (after pro er allowances for the thicknesses of the epip yseal plates and/or centers of ossification) and the resultant redicted age at line formation compared wit that given by the technique proposed here. After the comparisons were noted, the value of T was incremented by 10 mm, substituted into the 18 equations, and
offered here underestimated the age of occurrence given by the Hunt and Hatch formulae by approximately one year from ages 8 through 11 in males and 8 through 14 in females while it overestimated by one year for ages 16 through 18in males. For the tibia, the method offered here occasionally overestimated by one year for ages 8 throu h 10 in males and 12 through 16 in femaes and underestimated by one or (rarely) more years for ages 14 through 18 in males. These results are in general agreement with Hunt and Hatch when they observe that the equawith the 16 female formulae startin with tions of Bock et al. (1973), that they used in 350 mm and ending with 420 mm t.e., 8 modified form, overestimate size in middle values of T). This had the result of generat- childhood (6 through 9) and underestimate it ing a set of data comparable to a sample of in late adolescence. The method of this paper 344 distal tibia radiographs with radiopaque ap arently corrects for this problem. lines(i.e., 18 X 12 + 16 x 8 = 344). fn sum, the above technique has several The results of these com arisons were sur- advantages over other published methods. risingly homogeneous. T e method offered First, it is simple to execute in that it re[ere matched perfectly with that of Maat uires only two bone measurements and (1984) for both males and females. This is not use a hypothesized center of ossifireasonable since the data of Anderson and cation. Second, it is useful for incomplete Green (1948) was used to develop that au- burials since it is available for all of the bones thor’s techni ue-data that also was used in seen most often to contain transverse lines. this study. ?he match with Clarke (1982) And last, its accuracy compares well with was less good with the technique offered here other methods and even corrects some of underestimating the occurrence by one year their problems. for ages 1 through 8 and overestimatin by one or (rarely)more years for ages 12 anC f on. LITERATURE CITED This is undoubtedly because that author did not account for the epiphyses in his calculaMJ, Mendoza D, and Pezzia A (1974) A radiotions. The com arison with Allison et al. Allison graphic approach to childhood illness in Precolumbian (1974) was rarey off by more than a year inhabitants of southern Peru. Am. J . Phy. Anthropol. with the method offered here, underestimat40:409-416. ing age of occurrence for all ages in females Anderson M, and Green WT (1948)Lengths of the femur and the tibia. Am. J. Dis. Child. 75:279-290. and underestimating for the younger years M, Green WT, and Messner AMB (1963) (2 through 6) and overestimating for the Anderson Growth and predictions of growth in the lower extremolder years (11through 16)for males. This is ities. J . Bone Joint Surg. 45A(Il:1-14. surprisingly good since those authors used a Bock RD, Wainer H, Petersen A, Thissen D, Murra J , and Roche A (1973) A parameterization for indivikal fixed length at birth (90 mm) and even increhuman growth curves. Hum. Bio. 45:63-80. ments of owth er year from 1to 16. Lastly, SK (1982) The association of early childhood the matc with ummert and Van Gerven Clarke enamel hypo lasias and radiopaque transverse lines (1985) was very close for males (a year unin a culturafiy diverse prehistoric skeletal sample. derestimated for ages 9 through 14) but the Hum. Bio. 54(1):77-84. method presented here underestimated by Dewey JR, and Mahler PE (1972) Bone growth and development in prehistoric populations from as much as three years for all females of ages
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The second test of this method was to compare the growth curves of Hunt and Hatch (1981)for the femur and tibia against values of T generated by the method described above. For the femur, the method
Sudanese Nubia. J. Hum. Evol. 1:89-119. Gill GG, and Abbott LRC (1942) Practical method of predictin the growth of the femur and tibia in the child. Arc%. Surg. 45:286-315. Gindhart,PS (1973) Growth standards for the tibia and radius in children one month through eighteen years. Am. J. Phy. Anthropol. 39:41-48. Hummert JR, and Van Gerven DP (1985) Observations on the formation and ersistence of radiopaque lines. Am. J. Phy. Anthropof66:297-306. Hunt EE, and Hatch JW (1981) Estimation of age a t
AGE AT FORMATION OF TRANSVERSE LINES
death and ages of formation of transverse lines from measurements of human long bones. Am. J. Phy. Anthropol. 54:461469. Johnston FE (1962) Growth of the long bones of infants and young children at Indian Knoll. Am. J. Phy. Anthropol. 20:249-254. Maat GJR (1984)Datingand rating ofHarris’s lines. Am. J. Phy. Anthropol. 63991-299. Maresh MM (1955) Linear growth of long bones of ex-
343
tremities from infancy through adolescence. Am. J. Dis. Child. 89:725-742. McHenry H, and Schulz P (1976) The association between Harris lines and enamel hy oplasias in rehisPhy. Antfiropol. toric California Indians. Am. 44:507-512. Park EA (1964) The imprinting of nutritional disturbances on the growing bone. Pediatrics 33(Suppl): 815-862.
Technical Note: Calculation of Age at Formation of Radiopaque Transverse Lines STEVE BYERS De artment of Anthropology, University of New Mexico, AEfuquerque, New Mexico 87131
KEY WORDS
Age determination, Harris line formation, Long bone measurement
ABSTRACT A simple method for determining the age of an individual at the time of radiopaque transverse (Harris) line formation is presented. To use this method, only two measurements are required: total bone length and distance of line to nearest bone end; these are put into formulae that calculate the percent of total bone growth when the line appeared. The result of this calculation is compared with tables of percent bone growth per year (one to 16 years in females and one to 18years in males) to arrive at estimations of age at line formation. Since these tables are presented for the femur, tibia, humerus, and radius, this technique can be used on any one of the major long bones exhibiting lines. In studying extinct populations, a number of researchers have used measurements from radio a hs of mature human limb bones to ca cu ate the age of an individual when radiopaque transverse (Harris) lines formed. Unfortunately, the utility of their methods is reduced due to several problems. For example, many are limited to studyin only one (tibia) or two (tibia and femur bones (Clarke, 1982;Hummert and Van Gerven, 1985; Hunt and Hatch, 1981; Maat, 1984; McHenry and Schulz, 1976). Some deal on1 with lines at the distal ends of bones (C arke, 1982;Hummert and Van Gerven, 1985; Maat, 1984; McHenry and Schulz, 1976) while others calculate distances of lines from the rojected center of ossification (Hummert an Van Gerven, 1985; Hunt and Hatch, 1981; Maat, 1984). One imposes a common length of a bone at birth and does not account for the differential growth of a bone at the proximal and distal ends (Allison et al., 1974). Several assume constant owth per year (Allison et al., 1974; EcHenry and Schulz, 1976) while one uses equations that are more complex than necessary (Hunt and Hatch, 1981). Finally, one does not account for the thickness of the epi hyseal areas (Clarke, 1982). Given these pro! Ilems, a techni ue is proposed here that accounts for these s ortcomings and has the
YP
advanta e of requiring only two measurements o a long bone to calculate the age at which lines were formed. Since it requires the calculation of the length of a bone at the time of line deposition, the method is based on three as ects of owth and anatomy. First, since t ey are ormed when normal growth is disrupted (Park, 1964),transverse lines mark the osition of e iphyseal plates at the time of eposition (darke, 1982;Hummert and Van Gerven, 1985; Maat, 1984; Hunt and Hatch, 1981). Therefore, when bone length at the time of line formation is estimated, the thickness of the epiphyseal areas beyond the line(s) must be taken into account. Second, bone growth is well documented in the living and can be used to calculate tables of ercent growth per year. Third, growth at eit er end of a long bone is not equal; this must be accounted for when a line is seen at only one end. These three aspects were determined for the four limb bones most often seen to contain radiopaque lines: femur, tibia, humerus, and radius. To determine the percent of total bone length seen in the ei hyses, data from Maresh (1955)was used. hese show that for
B
K
7B
9
B
a
@ 1991 WILEY-LISS. INC
op
R
%
Received March 26,1990; accepted January 10,1991,
340
S. BI7ERS
the years 10 through 12 (the ages for which these data are available) the percent accounted for by the epiphyses is relatively constant between the sexes in the four bones. In the humerus and radius, approximately 8 percent (sd = .68%) of the total bone length is in the epiphyses while the statistic is 11 percent (sd = .29%) in the femur and 13 percent (sd = .33%)in the tibia. To determine the pattern of growth for these bones, four data sets (Anderson et al., 1963;Anderson and Green, 1948; Gindhart, 1973;Maresh, 1955)were combined to arrive at chronolo 'es of percent bone growth for each year o postpartum life. These chronologies are given in Table 1 for males to 18 years and Table 2 for females to 16 years; greater ages are not needed since the data sets show a levelin off of limb bone growth after these times. he values in the tables are the average percent of mature length that a bone is in each year of life; they are based on the average of mean length per ear divided by the mean mature bone fength in each of the data sets. Although these percents are derived from modern individuals, their use on extinct ou s is warranted because chronologies ase on prehistoric populations (Dewey and Mahler, 1972; Hummert and Van Gerven, 1985; Johnston, 1962) would be incomplete due to deficiencies in samples (Clarke, 1982). Even without this, the determination of the age of a person at death from bone is subject to error similar to differences seen between extinct and extant ou s. To determine t e ifferential between bone growth at the proximal and distal ends, Anderson et al. (1963) and Gill and Abbott (1942)provide data to indicate that approximately 70 percent of femoral growth occurs at the distal end, while approximately 57 percent of tibia1 growth occurs at the proximal end. Gill and Abbott (1942) also give data that shows approximately 81 percent of humeral growth occurs at the proximal end while 75 ercent of radial growth occurs at the dista end. These percents will be used since their variability during growth is unknown at this time. The method for determining a e at line formation proposed here involves t e following operations: 1) calculating the length of the diaphysis when the line was deposited, 2) correcting for epiphyseal thickness, 3) calculating percent of mature bone length, and 4) comparing this percent with the chronology
?
TABLE 1 . Chronology of limb bone growth in males (percent of mature bone length) Age
Humerus
Radius
Femur
Tibia
1
32.3 40.0 45.2 50.0 54.3 58.7 63.0 66.9 70.6 74.1 77.5 80.8 85.3 90.2 94.6 97.8 99.0 100.0
32.7 39.5 44.8 49.5 53.9 58.2 62.2 66.1 69.9 73.5 77.1 80.9 85.0 90.3 95.0 98.0 99.7 100.0
29.6 37.1 43.1 48.5 54.3 59.1 63.7 68.8 73.0 76.9 80.6 84.4 88.8 93.1 96.9 98.9 99.7 100.0
28.8 36.5 42.4 47.6 53.5 57.9 62.3 67.5 71.6 75.7 79.6 83.7 88.5 93.0 96.7 99.0 100.0 100.0
2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17 18
4
r i
P
a
TABLE 2. Chronology of limb bone growth in females (percent of mature bone length) Ape
Humerus
Radius
1
34.5 42.8 48.8 54.0 59.2 63.5 68.5 72.5 76.4 79.8 85.3 90.0 93.8 97.2 99.2 100.0
35.3 42.7 48.8 53.9 59.1 63.5 67.9 72.4 76.4 80.4 85.6 91.0 95.1 97.6 99.5
2 3 4 5 6 7 8 9 10 11 12 13 14
15 16
Femur
Tibia
31.7
31.5 40.1 46.6 52.4 58.6 63.9 69.0 74.3 79.4 83.9 88.8 93.0 96.5 98.3 99.1 100.0
40.2 ~
46.4 52.3 60.0 65.0 70.0 75.2 79.6 ~. 83.9 88.7 93.1 96.9 99.1 99.8 100.0
1nn.n
of bone development. To better understand these operations (and therefore the method), refer to Fi re 1. A radiopa ue line (the position o f t e distal epiphysei late at the time of deposition) is seen at ri i t angles to the major axis of a mature ti ia, approximately three-quarters of the distance down the shaft. The dashed line indicates the hypothetical position of the roximal epiphyseal plate, while the dotted ines indicate the ositions of the ends of the bones when the l n e formed. The length of the diaph sis at deposition (DD)can be obtained by su tracting D (the distance of the distal epi hyseal plate from the distal end) and P (the istance of the proximal epiphyseal plate from the
Y
%
P
r;
a
341
AGE AT FORMATION OF TRANSVERSE LINES
TABLE 3. Formulae for calculating percent of mature bone length at time of radiopaque line formation Bone
Humerus Radius Femur Tibia
End Line Closest to
Formula
Proximal Distal Proximal Distal Proximal Distal Proximal Distal
Pct = 1.09 (T - 1.23P) X 100/T Pct = 1.09 (T - 5.26D) X 100/T Pct = 1.09 (T - 4.00P) X 100/T Pct = 1.09 (T - 1.33D) X 100/T Pct = 1.12 (T - 3.33P) X 100/T Pct = 1.12 (T- 1.43D) X 100/T Pct = 1.15 (T - 1.75P) X 100/T Pct = 1.15 (T - 2.33D) X 100/T
the age at line formation can be found by matching this percent with the proper value in Tables 1or 2. The above involves the calculation of intermediate values (D , TD, Ep, and E D ) which can be eliminated y! combining operations. The formulae presented in Table 3 are the result of such combination and can be used to calculate the percent of mature length of the four bones at the time a radiopaque line was formed at either the distal or proximal end. As can be seen, only two values are needed to use these formulae, the total length (T) from the proximal to the distal end, arallel to the long axis of the bone, and the istance (D or P) from the transverse line to the closest end, Fig. 1. Drawing of bone showin areas of measure- parallel to the long axis. For example, if a ment for determining age when rafiopaque transverse mature tibia from a male that is 430 mm in lines formed. See text for explanation. length has a line 30 mm from the distal end, the percent of mature bone length would be 1.15(430 - 2.33(30)) x 100/430. The result, roximal end) from T (the mature bone 96.3 percent, corresponds to an age between yength). Since P is not known for the bone in 14 and 15 years from Table 1. Similarly, if Figure 1 (and in many x-rays), its value can the line in that same bone was 50 mm from be estimated by 1.33D;D is multiplied by the the proximal end, the percent of mature bone coefficient 1.33 because on the average 57 length would be 1.15(430 - 1.75(50)) x 100/ percent of bone growth occurs at the proxi- 430; the result (91.6 percent) corresponds to mal end (57143 = 1.33) and therefore, the an age between 13 and 14. To determine the efficacy of this method, roximal epiphyseal plate at the time of Pdeposition of the line would be pro ortion- two tests were designed. First, since the ately further from the proximal en$. Thus, distal tibia has been studied most often DD = T - (D + 1.33D) = T - 2.33D. by other workers, its equation from Table 3 Once this is known, the values EP and ED was algebraically manipulated to solve for (the thicknesses of the proximal and distal D = .429(T - (PctA15)). Then the ercents epiphyses, respectively) can be accounted for in Tables 1and 2 were substituted or Pct t o by multiplying DD by the ercent of bone arrive at 34 new e uations, one correspondlen h seen in the epiphysea plates t o arrive ing to each year of ife from 1 to 18 in males at t e total length of the bone at the time of and 1 to 16 in females. Next, using the line deposition (TD). As noted earlier, this ran es given by Maresh (1955) for this bone, value is 13 percent; therefore, TD = the owest value of T (390 mm) was substiDD + .13TD. Throu h algebraic manipula- tuted into the 18 male e uations to enerate tion TD = 1.15DD.d v e n this, the percent of 18 values of D. These va ues of T an D were mature length is merely (T, X 100)l" and then used in the equations of Allison et al.
B
f
P
P
P
s
?
5
342
S. BYERS
(1974), Clarke (1982), Hummert and Van Gerven (1985)and Maat (1984) (after pro er allowances for the thicknesses of the epip yseal plates and/or centers of ossification) and the resultant redicted age at line formation compared wit that given by the technique proposed here. After the comparisons were noted, the value of T was incremented by 10 mm, substituted into the 18 equations, and
offered here underestimated the age of occurrence given by the Hunt and Hatch formulae by approximately one year from ages 8 through 11 in males and 8 through 14 in females while it overestimated by one year for ages 16 through 18in males. For the tibia, the method offered here occasionally overestimated by one year for ages 8 throu h 10 in males and 12 through 16 in femaes and underestimated by one or (rarely) more years for ages 14 through 18 in males. These results are in general agreement with Hunt and Hatch when they observe that the equawith the 16 female formulae startin with tions of Bock et al. (1973), that they used in 350 mm and ending with 420 mm t.e., 8 modified form, overestimate size in middle values of T). This had the result of generat- childhood (6 through 9) and underestimate it ing a set of data comparable to a sample of in late adolescence. The method of this paper 344 distal tibia radiographs with radiopaque ap arently corrects for this problem. lines(i.e., 18 X 12 + 16 x 8 = 344). fn sum, the above technique has several The results of these com arisons were sur- advantages over other published methods. risingly homogeneous. T e method offered First, it is simple to execute in that it re[ere matched perfectly with that of Maat uires only two bone measurements and (1984) for both males and females. This is not use a hypothesized center of ossifireasonable since the data of Anderson and cation. Second, it is useful for incomplete Green (1948) was used to develop that au- burials since it is available for all of the bones thor’s techni ue-data that also was used in seen most often to contain transverse lines. this study. ?he match with Clarke (1982) And last, its accuracy compares well with was less good with the technique offered here other methods and even corrects some of underestimating the occurrence by one year their problems. for ages 1 through 8 and overestimatin by one or (rarely)more years for ages 12 anC f on. LITERATURE CITED This is undoubtedly because that author did not account for the epiphyses in his calculaMJ, Mendoza D, and Pezzia A (1974) A radiotions. The com arison with Allison et al. Allison graphic approach to childhood illness in Precolumbian (1974) was rarey off by more than a year inhabitants of southern Peru. Am. J . Phy. Anthropol. with the method offered here, underestimat40:409-416. ing age of occurrence for all ages in females Anderson M, and Green WT (1948)Lengths of the femur and the tibia. Am. J. Dis. Child. 75:279-290. and underestimating for the younger years M, Green WT, and Messner AMB (1963) (2 through 6) and overestimating for the Anderson Growth and predictions of growth in the lower extremolder years (11through 16)for males. This is ities. J . Bone Joint Surg. 45A(Il:1-14. surprisingly good since those authors used a Bock RD, Wainer H, Petersen A, Thissen D, Murra J , and Roche A (1973) A parameterization for indivikal fixed length at birth (90 mm) and even increhuman growth curves. Hum. Bio. 45:63-80. ments of owth er year from 1to 16. Lastly, SK (1982) The association of early childhood the matc with ummert and Van Gerven Clarke enamel hypo lasias and radiopaque transverse lines (1985) was very close for males (a year unin a culturafiy diverse prehistoric skeletal sample. derestimated for ages 9 through 14) but the Hum. Bio. 54(1):77-84. method presented here underestimated by Dewey JR, and Mahler PE (1972) Bone growth and development in prehistoric populations from as much as three years for all females of ages
K
K
f
K
lees
P
f * !b
The second test of this method was to compare the growth curves of Hunt and Hatch (1981)for the femur and tibia against values of T generated by the method described above. For the femur, the method
Sudanese Nubia. J. Hum. Evol. 1:89-119. Gill GG, and Abbott LRC (1942) Practical method of predictin the growth of the femur and tibia in the child. Arc%. Surg. 45:286-315. Gindhart,PS (1973) Growth standards for the tibia and radius in children one month through eighteen years. Am. J. Phy. Anthropol. 39:41-48. Hummert JR, and Van Gerven DP (1985) Observations on the formation and ersistence of radiopaque lines. Am. J. Phy. Anthropof66:297-306. Hunt EE, and Hatch JW (1981) Estimation of age a t
AGE AT FORMATION OF TRANSVERSE LINES
death and ages of formation of transverse lines from measurements of human long bones. Am. J. Phy. Anthropol. 54:461469. Johnston FE (1962) Growth of the long bones of infants and young children at Indian Knoll. Am. J. Phy. Anthropol. 20:249-254. Maat GJR (1984)Datingand rating ofHarris’s lines. Am. J. Phy. Anthropol. 63991-299. Maresh MM (1955) Linear growth of long bones of ex-
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tremities from infancy through adolescence. Am. J. Dis. Child. 89:725-742. McHenry H, and Schulz P (1976) The association between Harris lines and enamel hy oplasias in rehisPhy. Antfiropol. toric California Indians. Am. 44:507-512. Park EA (1964) The imprinting of nutritional disturbances on the growing bone. Pediatrics 33(Suppl): 815-862.
