1975, British Journal of Radiology, 48, 471-476
The measurement of sequential changes in cortical bone geometry By A. Horsman, B.A., Ph.D., and M. Simpson, B.Sc. M.R.C. Mineral Metabolism Unit, The General Infirmary, Leeds LS1 3EX {Received May, 1974) ABSTRACT
A method is described whereby the sequential changes occurring in the thickness of the cortices of the metacarpal shafts may be observed. The method utilizes pairs of hand radiographs from which the total bone width and medullary width of the 2nd, 3rd and 4th metacarpals are determined in duplicate using needle-tipped Vernier calipers. The errors are discussed and the precision of the method is shown to compare very favourably with the precision of the most recent densitometric techniques. The rate of loss of bone in post-menopausal women is evaluated, and is shown to be dependent upon the number of years elapsed since the menopause.
1967) and in those longitudinal morphometric studies which have been performed the results have so far been severely limited by measurement error. Most longitudinal studies which have been reported (Atkinson et al., 1970; Borner et al., 1970; Vogel and Friedman, 1970) use the direct photon absorption technique (Reed, 1960; Cameron and Sorenson, 1963), which at sites where the mineral content of the bone does not change rapidly along its length (e.g. femoral shaft) has been claimed to have a precision as high as 2 per cent (West and Reed, 1970). We have developed a simple method of comparable precision, involving morphometric measurements on radiographs of the diaphyses of the metacarpals of both hands, by which sequential changes in bone geometry, and by implication bone mass, may be observed. The method is easily implemented, requiring only conventional diagnostic X-ray facilities and relatively inexpensive measuring calipers.
There is a net loss of bone from the human skeleton with advancing age (Ingalls, 1931; Merz, Trotter and Peterson, 1956; Trotter, Broman and Peterson, 1960). The loss is thought to be a universal phenomenon, varying in magnitude between races, but within any one race starting earlier and progressing more rapidly in women than in men (Nordin, 1965). One important consequence of the age-related reduction in skeletal mass is the progressive weakening of the bones. The skeleton beMETHOD comes less able to withstand trauma with advancing The method utilizes pairs of hand radiographs; age, and the increasing probability of fracture with age in the individual is reflected in the increasing the radiographic procedure and the method by which incidence of fractures with age in the population. the morphometric measurements are performed are For example, almost without exception, in the races described below. for which data are available, the age-specific incidence of fracture of the hip increases with age Radiography (Cave and Nordin, 1972). A postero-anterior contact radiograph of each Studies of the problem of fractures from minimal hand is produced separately. The hand position is trauma, and of metabolic bone diseases in general, standardized; a Perspex plate bearing the outline are dependent upon quantitative measurements of of a right hand is placed over the film cassette and the skeleton. Numerous methods now exist for this the subject's hand fitted to the outline before expurpose. They vary widely in precision and accuracy posure. The plate is inverted for the exposure of the and are often complex and expensive to implement left hand. The cassette contains Kodak autoprocess (Horsman, 1974). One method, morphometry of film which is exposed without screens to 52 kVp tubular bones (Barnett and Nordin, 1960; Virtama radiation for 0-04 seconds at a tube current of 500 and Helela, 1969), perhaps the simplest method mA and a film-focus distance of 100 cm. The films are of all, has been widely used in cross-sectional studies processed for 3 | minutes in Cronex developer at of many populations (Fujita, Orimo and Yoshikawa, 80°C in an automatic processing unit. 1966; Garn, 1970; Nordin, 1965). However, it has only rarely been applied to the evaluation of chan- Marking thefilmsfor measurement ges occurring in individuals (Adams, Davies and Morphometric measurements are performed at Sweetnam, 1970; Garn, Rohmann and Wagner, the midshafts of the 2nd, 3rd and 4th metacarpals 470
JUNE
1975
The measurement of sequential changes in cortical bone geometry
of both hands. (The 5th is omitted due to the comparative irregularity of its endosteal surface.) On the first pair of radiographs only, the midshaft of each metacarpal is found with respect to the metaphyses and pencil marks are drawn at right angles to the long bone axis as illustrated in Fig. 1. The measurement sites on subsequentfilmsare identified by superimposing the later films on the earliest films. Each metacarpal is individually superimposed and marks are drawn on the later film exactly over the marks on the earliest film. It is important that all films are marked using the first film for reference, and care is taken not to draw the marks closer than 1 mm from the outer edge of the bone.
Caliper measurements Needle-tipped Vernier calipers of the type shown in Fig. 2 are used in performing the measurements. The pairs of films are measured in date order, and on each pair the following widths are measured first on the left then on the right hand film: (a) the total widths of metacarpals 2, 3 and 4; (b) repeat (a); (c) the medullary widths of metacarpals 2, 3 and 4; (d) repeat (c). Each caliper reading is rounded to 0-05 mm. It is important not only that all films are measured by the same observer but also that the observer measures all the films within a short space of time. An observer's judgment of the positions of the cortical boundaries can change in the course of time; thus measurements recently performed on the latest films should not be compared with measurements performed in the past on earlier films. CALCULATIONS
Denoting total bone width by TW, medullary width by MW, cortical width by CW, and the first and second observations by subscripts 1 and 2, for each metacarpal the following quantities are evaluated: . . (1) . . (2) CW = TW—MW . . . (3) Then, for each pair of films, the averages over the six metacarpals of TW, MW and CW (TW, MW and CW, the latter being the difference TW —MW) are calculated. Denoting CW at time t by CW(t),_the rate of change of CW between any two pairs of films, cw, is evaluated from the expression _ CW(t 2 )-CW(ti) cw= t 2 —ti
• (4)
ERRORS FIG. 1. Identification of the midshaft measurement site.
The precision of the method is limited by two types of error which may be clearly separated. They are first, intraobserver caliper measurement error, and second, errors
FIG. 2. Calipers used in performing the morphometric measurements.
471
VOL. 48, No. 570
A. Horsmart and M. Simpson arising in the radiography, e.g. incorrect film-focus distance, or rotation of the hand from its standard position. The duplicate observations of total and medullary widths serve three useful purposes. They provide a check against gross errors (such as misreading the calipers); they provide more precise measures of the bone dimensions than would be available from only one measurement; and also they provide a means of assessing the performance of the observer, i.e. a means of evaluating the intra-observer caliper measurement error (observer error). The observer error has been evaluated for each variable using the measurements on 140 women, each with two pairs of films. The measurements were all performed by the same observer (M.S.). Since the method is aimed primarily at the evaluation of differences, the errors, E, have been expressed as the two standard deviation limits on a measured change. For example, denoting by ACW the increase in CW derived from the observed values of CW from pairs of films taken on two different dates, the probability that the real difference lies in the range A C W ^ E is approximately 0-95. Thus changes in excess of E may be regarded as significant (P
The measurement of sequential changes in cortical bone geometry By A. Horsman, B.A., Ph.D., and M. Simpson, B.Sc. M.R.C. Mineral Metabolism Unit, The General Infirmary, Leeds LS1 3EX {Received May, 1974) ABSTRACT
A method is described whereby the sequential changes occurring in the thickness of the cortices of the metacarpal shafts may be observed. The method utilizes pairs of hand radiographs from which the total bone width and medullary width of the 2nd, 3rd and 4th metacarpals are determined in duplicate using needle-tipped Vernier calipers. The errors are discussed and the precision of the method is shown to compare very favourably with the precision of the most recent densitometric techniques. The rate of loss of bone in post-menopausal women is evaluated, and is shown to be dependent upon the number of years elapsed since the menopause.
1967) and in those longitudinal morphometric studies which have been performed the results have so far been severely limited by measurement error. Most longitudinal studies which have been reported (Atkinson et al., 1970; Borner et al., 1970; Vogel and Friedman, 1970) use the direct photon absorption technique (Reed, 1960; Cameron and Sorenson, 1963), which at sites where the mineral content of the bone does not change rapidly along its length (e.g. femoral shaft) has been claimed to have a precision as high as 2 per cent (West and Reed, 1970). We have developed a simple method of comparable precision, involving morphometric measurements on radiographs of the diaphyses of the metacarpals of both hands, by which sequential changes in bone geometry, and by implication bone mass, may be observed. The method is easily implemented, requiring only conventional diagnostic X-ray facilities and relatively inexpensive measuring calipers.
There is a net loss of bone from the human skeleton with advancing age (Ingalls, 1931; Merz, Trotter and Peterson, 1956; Trotter, Broman and Peterson, 1960). The loss is thought to be a universal phenomenon, varying in magnitude between races, but within any one race starting earlier and progressing more rapidly in women than in men (Nordin, 1965). One important consequence of the age-related reduction in skeletal mass is the progressive weakening of the bones. The skeleton beMETHOD comes less able to withstand trauma with advancing The method utilizes pairs of hand radiographs; age, and the increasing probability of fracture with age in the individual is reflected in the increasing the radiographic procedure and the method by which incidence of fractures with age in the population. the morphometric measurements are performed are For example, almost without exception, in the races described below. for which data are available, the age-specific incidence of fracture of the hip increases with age Radiography (Cave and Nordin, 1972). A postero-anterior contact radiograph of each Studies of the problem of fractures from minimal hand is produced separately. The hand position is trauma, and of metabolic bone diseases in general, standardized; a Perspex plate bearing the outline are dependent upon quantitative measurements of of a right hand is placed over the film cassette and the skeleton. Numerous methods now exist for this the subject's hand fitted to the outline before expurpose. They vary widely in precision and accuracy posure. The plate is inverted for the exposure of the and are often complex and expensive to implement left hand. The cassette contains Kodak autoprocess (Horsman, 1974). One method, morphometry of film which is exposed without screens to 52 kVp tubular bones (Barnett and Nordin, 1960; Virtama radiation for 0-04 seconds at a tube current of 500 and Helela, 1969), perhaps the simplest method mA and a film-focus distance of 100 cm. The films are of all, has been widely used in cross-sectional studies processed for 3 | minutes in Cronex developer at of many populations (Fujita, Orimo and Yoshikawa, 80°C in an automatic processing unit. 1966; Garn, 1970; Nordin, 1965). However, it has only rarely been applied to the evaluation of chan- Marking thefilmsfor measurement ges occurring in individuals (Adams, Davies and Morphometric measurements are performed at Sweetnam, 1970; Garn, Rohmann and Wagner, the midshafts of the 2nd, 3rd and 4th metacarpals 470
JUNE
1975
The measurement of sequential changes in cortical bone geometry
of both hands. (The 5th is omitted due to the comparative irregularity of its endosteal surface.) On the first pair of radiographs only, the midshaft of each metacarpal is found with respect to the metaphyses and pencil marks are drawn at right angles to the long bone axis as illustrated in Fig. 1. The measurement sites on subsequentfilmsare identified by superimposing the later films on the earliest films. Each metacarpal is individually superimposed and marks are drawn on the later film exactly over the marks on the earliest film. It is important that all films are marked using the first film for reference, and care is taken not to draw the marks closer than 1 mm from the outer edge of the bone.
Caliper measurements Needle-tipped Vernier calipers of the type shown in Fig. 2 are used in performing the measurements. The pairs of films are measured in date order, and on each pair the following widths are measured first on the left then on the right hand film: (a) the total widths of metacarpals 2, 3 and 4; (b) repeat (a); (c) the medullary widths of metacarpals 2, 3 and 4; (d) repeat (c). Each caliper reading is rounded to 0-05 mm. It is important not only that all films are measured by the same observer but also that the observer measures all the films within a short space of time. An observer's judgment of the positions of the cortical boundaries can change in the course of time; thus measurements recently performed on the latest films should not be compared with measurements performed in the past on earlier films. CALCULATIONS
Denoting total bone width by TW, medullary width by MW, cortical width by CW, and the first and second observations by subscripts 1 and 2, for each metacarpal the following quantities are evaluated: . . (1) . . (2) CW = TW—MW . . . (3) Then, for each pair of films, the averages over the six metacarpals of TW, MW and CW (TW, MW and CW, the latter being the difference TW —MW) are calculated. Denoting CW at time t by CW(t),_the rate of change of CW between any two pairs of films, cw, is evaluated from the expression _ CW(t 2 )-CW(ti) cw= t 2 —ti
• (4)
ERRORS FIG. 1. Identification of the midshaft measurement site.
The precision of the method is limited by two types of error which may be clearly separated. They are first, intraobserver caliper measurement error, and second, errors
FIG. 2. Calipers used in performing the morphometric measurements.
471
VOL. 48, No. 570
A. Horsmart and M. Simpson arising in the radiography, e.g. incorrect film-focus distance, or rotation of the hand from its standard position. The duplicate observations of total and medullary widths serve three useful purposes. They provide a check against gross errors (such as misreading the calipers); they provide more precise measures of the bone dimensions than would be available from only one measurement; and also they provide a means of assessing the performance of the observer, i.e. a means of evaluating the intra-observer caliper measurement error (observer error). The observer error has been evaluated for each variable using the measurements on 140 women, each with two pairs of films. The measurements were all performed by the same observer (M.S.). Since the method is aimed primarily at the evaluation of differences, the errors, E, have been expressed as the two standard deviation limits on a measured change. For example, denoting by ACW the increase in CW derived from the observed values of CW from pairs of films taken on two different dates, the probability that the real difference lies in the range A C W ^ E is approximately 0-95. Thus changes in excess of E may be regarded as significant (P
