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Combined cortical thickness and bone density determination by photon absorptiometry

This content has been downloaded from IOPscience. Please scroll down to see the full text. 1978 Phys. Med. Biol. 23 1101 (http://iopscience.iop.org/0031-9155/23/6/006) View the table of contents for this issue, or go to the journal homepage for more

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PHYS. " E D . BIOL., 1978, Vol. 23, No. 6, 1101-1114.

Printed in Great Britain

Combined Cortical Thickness and Bone Density Determination by Photon Absorptiometry H. W. KRANER Brookhaven National Laboratory, Upton, NY 11973, U.S.A.

J. F. PATTERSOPU' and J. C. SAlITHt Veterans Administration Hospital, Washington, DC 20422, U.S.A. Received 8 August 1977

ABSTRACT. Bone cortical thickness and density were measured in rat femurs in vitro by a photon absorptiometry technique. A scan perpendicular to the long bone axis using photons from highly collimated 108Cd or lZ6Isources yielded the bone wall thickness and attenuation a t mid-shaft. A second scan after the bone was rotated axially 90' was taken to measure the wall or shaft thickness identically responsible for the mid-shaft attenuation of the first scan. The mid-shaft attenuation of the second scan was due to the bone thickness derived from the first scan; thus two complementarymeasurements are derived by this technique.The bone density is then directly calculated with an estimated accuracy of 10% (coefficient of variation) using empirically determined mass attenuation coefficients. Measurements of mass attenuation coefficients of ashed and dried samples were compared with calculated coefficients for estimated bone composition. Results indicate that the mass attenuation coefficient for bone in vivo can be well estimated such that bone density can be accurately derived from this technique.

1. Introduction

Skeletaldemineralisationcanresult from suchdiverse causes as disease, bed rest,nutritional deficiencies, aging,space flight and steroid therapy (Newton-John and Morgan, 1970, Mueller, Mazess and Cameron 1975, Donaldson,Hulley, Vogel, Hattner, Bayers and McMillan 1970, Mack, Lachance, Vose and Vogt 1967). In the past,radiographic assessment has been the major method employed for the assessment of bone mineralisation.However,in general, thistechniquehas lacked thesensitivity necessary for detecting changes in bone mineral content of less than 30% (Boyd, Cameron, McIntosh and Walker 1974). Since the initial report of Cameron and Sorenson (1963), photon absorptiometry has evolved as a sensitive and accurate technique for determining bone mineral content (BMC). The method utilisesthe transmission through bone of a collimated beam of low energy monoenergetic radiation. The amount of transmitted radiation is inversely related to themass of mineral in its path. Usually the results of such measurements have been expressed as bone mineral content (BMC) in grams of bone mineral per unit length. t

Presentaddress:NutritionInstitute,

U.S. Department of Agriculture,Beltsville,

MD 20705, U.S.A. 0031-9155/78/0006-1101 $02.00 @ 1978 The Institute of Physics

1102

H . W . Kraner, J . F. Patterson and J. C. Smith

The present paper describes a technique which measures bone width, cortical thickness andthephotonattenuation thereof.The bone densityincan therefore be derived. Development of the technique was stimulated by the need to measure bone densityin female rats fed an oralcontraceptive oestrogen and/or progestin in diets which were calcium deficient or optimal in calcium content (Smith, Brown, Patterson and Kraner 1976). The well known basic equation of photon transmission is given below where the transmitted intensityfor photons of a specific incident energy a t a position x is I ( x ): W = IoexP - (P/P) h . W ) i l (1)

x i

where Io is the incident intensity and the exponential factors are the mass attenuation coefficient for the species i, incm2g-l, andthearealdensity which contains the density thickness of theith species, (p.t(x))i,in product. The attenuation may be separated so that the individual factors i are either chemical elements or composite materials such as water, bone, fat, etc. In thecase of in vivo measurements using the familiar method introduced by Cameron and Sorenson, theattenuationisduetoboth water (W) and bone (b) and the attenuation factors are written as (p/f)b(f

' t ( X ) ) bf (p/f)w(f

*t(x))w= In (Ib/r(x))*

(2)

The effect of the water on softtissueisdeterminedfrom an off-bone measurement,producing an attenuation factor, CY.The areal density of the bone a t position x is then

In the technique of Cameron and Sorenson, a measurement of total grams of bone intercepted by a scanned photon beam across a long bone is made by integrating (3) on x, the positiontransverse to the long bone axis (giving g/axial length), and calibrating the bone mass per axial length with a comparative standard to yield total bone mass or bone mineral content (BMC) a t a particular position on a representativelong bone. If, however, the physical bulk density p(x) of the bone is desired, a single transmissionmeasurement at any position ( x ) is sufficient if the thickness t ( x )at position x and the mass attenuation coefficient (p/p)b are known:

We go here to the in vitro case with attenuation caused only by bone, excluding its surroundings.Themass attenuation coefficient expressed asthe linear coefficient p divided bythedensity is simply L * a i / A ,Avogadro's number times the attenuation cross-section per atom divided by the atomic weight of p is notinherentlycontainedin the the species. Thedependentvariable expression.

Combined Cortical Thickness andBoneDensityDetermination

1103

I n expression (4),the transmission of photons I(x)/Iocan be easily measured and the mass attenuation coefficients are tabulated (Hubbell 1969, McMaster, Kerr, Del Grande, Mallet and Hubbell 1969) or can be measured for a particular bone. However, the thickness of bone intercepted, t ( x ) ,is not generally known. Therefore, the purpose of this investigation is t o present a technique that gives a reasonable estimate of the combined cortical thickness t ( x ) . The problem of determination of combined cortical thickness may be helpfully illustrated by considering the thickness of a hollow right circular cylinder having outer and inner radii rl and r 2 . If the position x is measured from the circularcentre of the cylinder inany direction, the cylinder thickness perpendicular t o the position x is

t ( x ) = %,{[l - (x/rl)2]1 - (r2/rl)[l - ( ~ / r ~ )for ~ ]r2+> x > 0 and

t ( x ) = 2r1([l- ( x / r J 2 ] + for rl > x > rs.

(5)

The transmission through this geometry as a function of position is the value in eqn (1) for this function t ( x ) . We note that thefirst derivative is not defined sharp behaviourin both t ( x ) and the photon a t x = r2, producingavery attenuation through t(x). This effect is of crucial significance as the position x = r2 is easily discerned in both the hypothetical case of a uniform cylindrical tube and the practical case of a real bone which is less perfectly tubular in geometry. As willbe demonstrated, it is reasonable t o attempt to measure both r2 and r1 from the 'differential' shape of the function I(x)as it reflects t ( x ) . It is then clear that I(x)is measured a t x = 0, the mid-shaft position where t ( x ) is most slowly varyingand isexactly 2 (rl-r2). Archer-Hall, (1973) indeed appreciated the differential Carpenter, Edwards and Francois shape of I(x)and used the height of the absorption at x z r 2 as a measure of BMC .

If the bone to be measured is not well approximated by a right circuhr cylinder, but is irregular or somewhat elliptical, two measurements of wall thickness must be made, one rotated by 90" about the bone axis to the other. The wall thicknessmeasured by the first scanis identically the thickness responsible for the 'mid-shaft' attenuation of the second scan taken a t 90'. Also, the wall thickness found from the second scan is the thickness causing the attenuation at mid-shaft of the first scan. Two values of density from eqn (4)for a given axial position are determined which should be consistent. Lanzl, Cox and Dobben (1970) have used gamma ray attenuation of finger scans taken at 90' t o each other to measure the product pt(x). The cortical thickness is measured radiographically, however, and not from the differential shapes of I(x). Assumptions are not made concerning the mass attenuation coefficient so that only the linear attenuation coefficient p of the compact bone in vivo. is determined forthe subject ; this parameter is often derived in studies Corticalthickness isroutinelymeasuredradiographicallyformanystudies (c.f. Garn, Poznanski and Nagy 1971); however, the precision ofthis technique is sometimes questioned (Garn, Fentz, Colbert and Wagner 1965, Mazess 1970). Borner,Grehn, Boll and Rauk (1969) and Borner, Moll, Rauk and Reiner8

H . W . Kraner, J . F . Patterson and

1104

J . C. Xmith

(1970) also used 90' perpendicular scans of fingers to measure p but derived cortical thicknesses from a (qualitative) comparison of the differential for regularelliptical tubes. attenuationdata, I(x), withcomputedshapes More recently, Elsasser and Ruegsegger (1976) have observed the shape and attenuation of cortical bone inthe distalregion of the forearm by Computerised AxialTomography.Again,linearattenuation coefficients are derived but, in this case, for the entire bone cross-section. It may be re-emphasised here that the linear attenuation coefficient p is the product of the mass attenuation coefficient p / p (element dependent) and dependent), Because the elemental the matrix density p (structurally constituency of the bone cannot be directly verified during in vivo measurements, the ( p / p )( p ) product is not separated. However, for in vitro measurements, the mass attenuation coefficient can (and has been) directly verified and the material density p can be measured, Other techniques for measuring bonedensityhave been described which are basedonComptonscattering Webber 1973, (Clarke and VanDyk 1973, Garnett,Kennett,Kenyonand Webber 1976) or coherent (elastic) photon scattering (Punmalainen, Vimarihuhta, Alhara andOlkkonen 1976); in each case the number of scattered gamma rays is proportional to the product of local electron density and crosssection per electron. Gamma ray absorptiometry of bonedensity for samples in vitro offers several advantages over gravimetric determination in that it is simple and non-destructiveand we shall attempttodemonstrateits accuracy and reproducibility.Additionally we shall consider the extension to in vivo measurementbasedon the assumption that an accurate mass attenuation coefficient can be found to interpret absorptiometric scans from which combined cortical thickness has been derived.

2. Apparatus

The experimental apparatusconsisted generally of the components standard to a transmission geometry gammaray attenuation experiment: source, object, movable stage and detector. The sources of radiation found most convenient for the required range of thicknesses to be scanned were logCd which emits 22 and 25 keV Ag K X-rays and a 88 keV y-ray and 1 2 6 1 filtered to emit substantially only the 27.4 keV Te, K, X-ray(s). Intense sources greater than 1 mCi were used. A high-purity germanium detector was used as the detector in scans with both the 109Cd source and a lZjIsource and a 3.81 cm x 0.62 cm (14 in x in) NaI(T1) detector was used in many scans with the filtered lZ5I source. The high energy resolution of the Ge spectrometer is not a distinct requirement but it does serve to establish easily the spectral lines of interest and mitigate against the inclusion of scattered radiation. For example, the relative intensities of the Ag K, and K, X-rays were found empirically to be 78 : 22 for the source used and both lines were used for the lo9Cdscans. The source-detector geometryand collimators are describedschematicallyin

a

Combined Cortical Thickness and BoneDensityDetermination

1105

fig. 1. The specimen to be scanned was positioned in a 'yoke' (designed to contribute negligible scattering) mounted on a micrometer state dividedin units down to 0.01 mm. The base of the movable stage was held rigidly with respect to the source and detector. The stage could be stepped manually or with a stepping motor. When using the Ge detector, peak regions of interest comprising just the 22 and 25 keV Ag X-rays and 35.4 keV y-ray of the lZ5I 1 2 5 ~or

, ''Cd

xxlrce

r

Directim of bone motion

Source collimator 1.6rnrn thick lead 0.3Lmm dlameter hole

Head of femur in /"paraIlel' orlentat ion

Detector collimator 1.6mm thick lead 0.62mm diameter hole

Fig. 1. Schematic diagram of source, collimators and detectors.

source were distinguished, accumulated and read outon a pulse height analyser for each measurement interval. A less precise 'window' could be used for the output of the NaI(T1) detector. Because only the essentially monoenergetic lz5Isource (27.4 keV) was used, a wide window for the low resolution detector was entirely adequate. The transmission past a sharp thin edge of tantalum sheet provided an estimate of the system (collimator) spatial resolution. It was observed that 90% to 10% reductionintransmission occurred within approximately 0.18 mm for a system of 1.6 mm (hin) thick Pb collimators a t both the source and the detector drilled with very small diameter holes as shown in fig. 1. We will not further characterise the system spatial resolution, but note that for accurate determination of differential absorption data, the system spatial resolution must be smallcompared to the object, but large enough to transmit an adequate photonfluence for a given source activity. 3. Aluminium tube phantomscan An aluminium pipe-like phantom was constructedfromarod of about 6.2 mm diameter type 6061 alloy drilled out with a known inner diameter. This phantom approximated a small bone in vitro with air as the surrounding medium. Watt (1973) and Watt andLogan (1974) have used a phantom of this type to determine errors in BMC which occur in the differential scan due to scan rate and spotsize. Fig. 2 shows the scan using 109Cd and the Ge detector of this phantom in air. The very sharpdiscontinuities are evident presumably at theposition of traversal of inner radius, r2. The inner and outerwall thicknesses and thus the 'cortical' thickness are well defined. Because the phantom is a regular, circular shape, two scans at 90' from each other would be identical and are not required. These data areused in twoways to illustrate the differential scanning method :

1106

I . . W . Kraner, J . F. Patterson and J . C . Smith

( 1 ) By fitting the scan shapes, the total wall thickness is determined t o be 1-74 mm and the transmitted fraction a t mid-shaft traversal of this wall thickness (at 9.5 mm on the x scale) is 111, = 2000/6120 = 0.327. The

weightedmass attenuation coefficient for Ag K X-raysinaluminium (Hubbell 1969) is 2.438 cm2g-l. Using eqn (4)the density of this object is . mass attenuation coefficients were used found to be 2.67 g ~ m - ~Known 6000

!'Lu%

1

6120dverage

'

imrnl

Fig. 2. The attenuation scan of an aluminium tube used to introduce the differential scanning technique. The open circles are a calculated fit to the data assuming a given inner and outer radius of 0.064 in and 0.090 in and an incident intensity I , of 6120 counts per interval.

because a known material (aluminium) was our reference. Similarly, for bone measurements in vitro, the attenuation coefficient is available either by tabulation or direct measurement. The nominal va,lue for the density of aluminium is 2.70 gcm-3 (Hubbell 1969), in excellent agreement with the measured value. (2) Using the known values of the aluminium tube thickness and diameter, one can generate a theoretical attenuation to compare with the observed scan offig. 2. The input values to eqns ( 5 ) and (1) are: rl = 2.39 mm, r2 = 1.52 mm,the mass attenuation coefficient is 2.438 cm2g-l a.nd I , (the incident intensity) is normalised to the observed value off the tube of 6120 counts per interval. The zero of the variable x is the midpoint of the object and is easily determined t o be a t 9.53 mm on the scan scale.A predicted attenuation is thus achieved and shown as the open circles for the left half of the scan (the other side would be identical by symmetry). As shown, predicted and observed attenuation are in excellent agreement and one may be encouraged t o use the differential dat,a to predictwall and cortical thicknesses. The sharp discontinuities at x = r2 given by eqns ( 5 ) are indeed robust and easily measured, Excellent agreement in attenuation at the mid-shaft (9.53 mm) point was observed. 4.

Determination of bone density of rat femurs

This method was used in an animal experiment designed to determine the effect of oral contraceptive hormones and dietary calcium concentration on

Combined Cortical Thickness and BoneDensityDetermination

1107

bone density. After reaching puberty, rats were fed contraceptive steroids ; either an oestrogen, mestranol and/or a progestin, norethindione. Thehormones In were fed at ten times the usual human dose baseduponbodyweight. addition to hormone treatment, the dietarycalcium was varied from a deficient level of 0.2% to anoptimal level of 1.2%. The animals were maintained on the various dietary regimens for 120 days. Then the animals were sacrificed. The bones (femurs)were stripped freeof muscle tissue and driedto a constantweight in a 70 'c vacuum oven. They were not decalcified prior to determination of bone densities. However, the contralateral femur from each animal was fixed and decalcified prior to staining for histological examination. The bones were coded so that the treatment was not known by the investigator determining densities. Over 150 rat femurs were measured in vitro in this study which required a more convenient and simple technique than gravimetric methods. The position of source, collimators, bone and detector is shown in fig. 1 for these measurements. The bone was measured by a scan traverse essentially parallel to the aligned direction with the condoyle as shown in the figure and thena scan with the bone turned 90'. These scans yield typical results shown in fig. 3, where G-l2 l

I

i l

Fig. 3. The attenuation scan of bone No. 2874 G - l 2 in the 'parallel' orientation ( a ) and perpendicular orientation (b). The bone density was found to be 1.50 g cm-3.

( a )is the scan with the condoyle aligned parallel t o the traverse direction and ( b )with the condoyle perpendicular to thetraverse direction. Both the22.1 keV K, and 25.0 keV K, Ag X-rays from the lo9Cdsource were used in the scan of fig. 3 and the result is as shown in Table 1. Table 1

Rat No. 2874 G-12

39

Scan

In (I,,/I)

Combined cortical thickness (mm)

(a)

0.735 1.56

1.41

(a)

0.842

1.13

Density

(e cm-3) ( p = 1.50 k 0.08) 1.44

1108

H . W . Kraner, J . F. Patterson and

J . C . Smith

A value for p / p of 4.158 cm2 8-1 weighted for the K, and K, relative intensities (4) withthe observed was used. Thedensityvalueisfoundthrougheqn attenuation of scan ( a ) and the observed combined corticalthickness from . the attenuation found in scan ( b ) , giving a density of 1.56 g ~ m - ~Similarly, scan ( b ) is due to the cortical thickness found from scan ( a ) and a value of 1.44 g 0111-3 is found. These values do agree with the estimated 10% coefficient of variation (CV) which includes systematic and statistical errors and their average (1.50 g (3111-3) may be quoted for this bone. Scans of bones 2782 G-3 and 7380 G - l are shown in figs 4 and 5, respectively and areincluded to illustrate

131’ 56 I

3533 31

31

32

30

35

31

lmm)

J

33 31

:30

32 immi

Fig. 4. The attenuation scan of bone KO. 2782 G-3 in both parallel ( a )and perpendicular ( b ) orientations. This bone was found to be in the higher range, 1.90 g cm-3.

l

1

1

la)

32 3533

31

3

lnm)

30

!bl 3533 31

32

31

3

(mm1

Fig. 5. The attenuation scan of bone No. 7380 G - l in both parallel ( a )and perpendicular ( b ) orientations. This bone was found to be in the low range, 1.15 g cm-3.

Combined Cortical Thickness and BoneDensityDetermination

1109

qualitatively.therange of bonedensities which were encountered.Bone 2782 G-3 yields densities of 1.91 and 1.88 gcm-3 with p = 1.90 g ~ m - ~Bone . 7380 G - l produces densities of 1.11 and 1-19 gcm-3 with p = 1.15 and is that of an immature rat. The attenuation coefficients were determined empirically for this series of measurements for both the lo9Cdand lZ5I sources using the Ge(HP) detector and NaI(T1) detector. A portion of coarsely ground rat skeleton was further ground to a fine powder and placed in a Lucite holder having 0-25 a in diameter cavity (0.3167 cmz). The weight of the bone sample was 90.2 mg which gave an areal density of 0.285 g cm-2. A linear scan was made across this material as well as across an area of the Lucite holder having no bone. The attenuation coefficient was found to be 4.158 cm2g-l for the lo9Cdsource-Ge(HP) detector system and 1.748 cm2g-l for the lZ5I source-NaI(T1) detector system. It was necessary to takemany points across a sample by scanning because although a sample may appear uniform, it can be inhomogeneous to the extent that a x 2 per point of 2.2 (which implies a probability of reproduction of only 0.02) was found for a set of twelve data points through one rat bone sample. For comparison, the x 2 for the transmission through the adjacent air gap (without the sample) was normal, yielding 1 . 1 per point. The average of several transmission measurements throughvariousportions of the sample was always used to reduce variabilityduetomaterialand bulknon-uniformity.The estimatederrorin the measurementsuggestsastandarddeviation of 5% (including the estimate for the accuracy of the applicability of the particular rat of the attenuation measurement to the bone scans). This technique was used in general for other measurements of attenuation coefficients to be later reported. The precision (reproducibility) of this technique has been tested a t several times in several ways. A good example has been a series of ten measurements madeoveraperiod of five dayswith the lZ5Isource(filtered, 27.4 keV)NaI(T1) detector system in which a single normal rat femur was mounted, measured anddemountedtentimes. Onlycasual attention was paid to to the replacing it a t approximately the sameaxialpositionwithrespect scanningbeam because thedensity measurementis notdependent on the reproducibility of cortical thickness. An average density of 1.96 f 0.07 g cm-3 was determined giving a CV of 4%. To assess the reproducibility further, the variations of the cortical thicknesswere considered not by totalwall thickness, but as thefraction of the full bone width. The total wall thickness divided by full bone width (cortical thickness ‘index’) for ten separate measurements was found to be 0,3944 0.013, having a CV of 3%. On several occasions, a femurhas been remeasured a t different axial positions For example, bone yielding density values within experimental error. 2874 G-l2 found from the data of fig. 3 to have a density of 1.50 gcm-3 was remeasured 2 mm distant on the femur axis and found to have a density of 1.535 g cm-3, easily within an estimated CV of 10% of t h e f i s tmeasurement. Several comparisons of the densities of samples measured by this photon attenuation method and theconventional gravimetric method have been made

1110

H . W . Kraner, J . F . Patterson and

J . C . Smith

t o assess the accuracy of this technique. Four femurs from normal laboratory rats prepared as previouslydescribed were measuredwith the Iz5I-NaI(T1) ~ = 3.4%). systemresultingin an averagedensity of 1.81 f 0.06 g ~ m -(CV The four whole femurs were measured gravimetrically with a result for the average density of 1-84& 0.064 gcm-3, in excellent agreement with the value determined by photon attenuation. However, to be more precise, the femur shanksonly,separated from the epiphysealbone, were remeasuredgravimetrically to yield an average density of 1.97 f 0.12 g cm-2, which is somewhat higher than that observed gravimetrically for the whole femur and by photon attenuation across the shank for femur cortical bone, but within the observed standard deviations. The photon attenuation measurements described above used an empiricallydeterminedmass attenuation coefficient for the 1251NaI(T1) system of 1.718 f 0.06 cm2g-l. Gravimetric determination of the density of large ox bone sampleswere also made and compared with photon attenuation measurements of these samples. Four sampleswithuniform but differentthicknesses were preparedfrom dehydratedmateria'landthe mass attenuation coefficient was measured empirically. The average density from gravimetric measurement was 2.11 f 0.12 gcm-3 which is compared to the value from photon attenuationof 1-97 f 0.10 gcm-3. The gravimetric value is, again, somewhat higher than the value from photon attenuation but the standard deviations as quoted do overlap. These errors include the propagation of the observed standard error of the set of four measurements with an estimated 5% systematic error. 5. Mass attenuationcoefficients

Whereas it is possible readily and conveniently to measurebonedensity

in vitro using empirically derived mass attenuation coefficients, workers using photon attenuation in vivo (op. cit.) report effects in terms of the linear mass attenuation Coefficient, the product of the density and mass attenuation coefficient. Possible variationsinthe mass attenuation coefficients (which cannot be checked experimentally) are therefore included as a factor with the density, usually the variable of interest. It is interesting to raise the question as to how much variability in mass attenuation coefficient one might expect in general (or in a particular kind of experimental system) that would render the separation of ( p / p ) ( p ) imprudent ? For the cases of animal experiments in which the animal may react to large imposed stresses, bone density changes much greater than 10% may be expected (and were indeed observed in vitro in several animals). Over what range of bone constituencies, then, might the mass attenuation coefficient remainconstant of 10% so that variationsin the by greater than 10% could be accurately attributed to changes in bone density ? To address this questionexperimentally,massattenuation coefficients of several bone materials were measured as outlined above by the well-averaged attenuation of finely ground pellets having known areal densities. Measurements were made in this case with a Ge(HP) detector with logCd a t 22.1 and

CombinedCorticalThicknessandBoneDensityDetermination

1111

25.0 keV and with an unfiltered 1251source using the 2 7 4 and 31.0 keV K , , Te X-raysandthe 35.4 keV y-ray. Using these sources, mass attenuation coefficients derived span the energy range of applications ; moreover, the mass attenuation coefficients for a given samplemust display a uniformly decreasing behaviour with energy, an internal consistency. The first requirement for the bone samples which are intercompared is that the 'heavy' constituent is, or bearssome resemblance to, bone mineral, calcium hydroxyapatite which is well known to be represented by Ca,,(PO,),(OH),. Bone samples of human and rat femur were ashed a t 600 'c for two days. Separately, samples of ox bone were ashed in oxygen a t 600 'c for periods of several hours. Very fine powders were obtained and placed in Lucite holders of known weight and area. The areal density of each sample was obtained by weighing to an accuracy of 3%. The resultsof the mass attenuation coefficient measurements are summarised in fig. 6. First, the upper groupof values for the ashed bone samples agree by

1"Cd

0Y

10

'1251

20 30 LO 50 Photon energy l keV1

70

W

Fig. 6. Comparison of measured mass attenuation coefficients with calculated values for calcium hydroxyapatite (upper curve) and for estimated dehydrated bone compositions (lower curve).

no worse than 5"/0 withcalculatedvalues for calcium hydroxyapatite.The generally measured values (which may be fitted to a power function pip E fall on a self-consistent curve. With some assurance, then, themineral portions of samples of human, rat andbovine cortical boneare well described by calcium hydroxyapatite. The lower group of measurements on fig. 6 compares measurements made on dehydrated bone samples (dried a t 70 'c to constant weight) with calculated attenuation coefficients by Kim (1974) for whole human bone and for a human

1112

H.

W.Kraner, J . F.

Patterson and

J. C. Smith

bone system using the relative weight percentages given by Robinson (1975) for bone mineral and collagen, without the component of water. The organic fraction given by Robinson for80%, 86% and fully mineralised bonegoes from the bone a constant 35.56% to 40.8, 39.1 and 35-56%,respectivelywhen systemisdehydrated.Therelative elementaldistribution for boneprotein (collagen)listed by Kim is used: H, 7.14%; C, 42*16y0;N, 16*89y0and 0, 32.27%. The box plotted on fig. 6 represents in vertical extent the range of pip from low values a t 80% mineralisation of rat sample(s) and very nearly the full calculated values of Kim (which considered only 18% femur protein). The measured values for human bone fall somewhat below the 80% mineralisation value but are within 5%of the midpoint of the calculated range. Robinson suggests that most adult bone falls in the range above 80% of full mineralisation. To obtain aworking in vivo absorption coefficient one must add 12 to 9% (by weight,) of wat.er which can be added t'o the calculated values. It does appear when considering observed and calculated dehydrated mass attenuation coefficients that : (a)the variability of mineralisationis reflected in the mass attenuation coefficients by a range which is less than the 10% which could be tolerable for many experimental systems; (b) the measured mass attenuation coefficients for dehydrated samples are in good agreement with both sets of calculated values, lending credence to their estimate. 6. Conclusions Photon attenuation has been found to be a convenient, precise and accurate technique to measure cortical thickness and bone density of animal samples (femurs) in vitro. In this situation, the mass attenuation coefficient for the system is accurately determined empirically. Extension of the method to in vivo measurement requires that anaccurate estimation of the mass attenuation coefficient for the system is determined empirically. Extension of the of the mass method to in vivo measurementrequiresaccurateestimation attenuation coefficient for the bone in question so that the factor in the linear attenuation coefficient p = ( p / p ) p foundbythe mea.surementcan be interpreted. Mass attenuation coefficients calculated including variable amounts of organic component (bone protein) appear to agree with measured dried samples of several species. It is suggested that these p / p are accurate t'o within 10% and may be used in experiments which would tolerate this error.

-

The interest of and helpful discussions with Dm. James Alberi and Stanton Cohn are gratefully acknowledged. We thank Charles Boulin who took much of the scan data, We thank Dr. R. A. Robinson for reading and commenting on the manuscript. Thisresearch was carried out in part under the auspices of the Energy Research and Development Administration: Contract No. EY-76-C-02-0016 and in part under NIH GrantNo. l-HD-2-2783.

Combined Cortical Thickness and BoneDensityDetermination

1113

R~STJM~~: DBtermination combinBe de l’bpaisseur corticale et de la densitb osseuse par absorptiombtrie de photons Au moyen d’une technique d’absorptiombtrie de photons, l’on a mesurb l’irpaisseur et la densite corticales des os dans des fbmurs de rat, in vitro. Un balayage perpendiculaire B l’axe de l’os en longueur, en se servant de photons de source looCdou lZ5IB forte collimation a fourni l’bpaisseur des parois des os et l’atthuation B la moitib. Une deuxieme exploration apres avoir fait tourner l’os axialement de 90’ fut faite pour mesurer l’bpaisseur de la paroi ou de la tige identiquement responsables de l’attbnuation de la premiere exploration L mi-tige. L’attenuation B mi-tige de la seconde exploration btaitdue L l’bpaisseur de l’os dbduite du premier balayage; donc, deux mesures complbmentaires sont obtenues par cette technique. La densitb de l’os est alors calculBe directement, avec une precision bvaluee L 10% (cobfficientde variation)en se servant de coefficient d’attbnuation de masse determinb empiriquement.

ZUSAMMENFASSUNO Kombinierte Bestimmung der Rindenstarke und Knochendichte durch Photonabsorptionmetrie Knochenrindenstarke und -dichte wurden in vitro bei Rattenoberschenkelknochen mit einer Photon-Absorptiometrietechnikgemessen. Eine Abtastung, die lotrecht zu der langen Knochenachse mit Photonen aus stark parallelisierten loOCd- oder lZ5I-Quellen durchgefiihrt wurde, ergab die Knochenwandstarke und die Abschwachung am Mittelstuck. Nachdem der Knochen axial um 90’ gedreht worden war, wurde eine zweite Abtastung durchgefiihrt, urn die Wand- oder Knochenschaftstarke zu messen, dieubereinstimmend fur dieMittelstuckabschwachung der ersten Abtastung verantwortlich ist. Die Mittelstuckabschwachung der zweiten Abtastung beruhte auf der Knochenstarke derersten Abtastung. Somit erhalt man zwei sich erganzende Messungen mit dieser Technik. Die Knochenstarke wird dann direkt berechnet mit einer geschatzten Genauigkeit von 10% (Variationskoeffizient) unter Verwendung empirisch bestimmter Massenabschwachungskoeffizienten.

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