Conversion relations for quantitative CT bone mineral densities measured with solid and liquid calibration standards

Bone and Mineral, I9 (1992) 145-158 0169-6009/92/%05.00 0 1992 Elsevicr Science Publishers B.V. All rights reserved.

145

BAM 00480

Conversion relations for quantitative bone mineral densities measured with solid and liquid calibration standar

Mitchell M. Good&t Department of Radiology, University of Washington, Seattle, WA, USA

(Received 2 March 1992) (Accepted 8 June 1992)

Summary A vast data base exists for QCT measurements of bone mineral density (BMD) referenced to K2HP04 in water (liquid) standards. To effectively utilize the more stable hydroxyapatite in ;vatel -equivalent plastic (solid) standards that have recently been introduced, it will be necessary to de& conversion relations. A study was performed to investigate the dependence of these relations upon x-ray tube voltage, marrow composition, and patient body size. Test objects included five diverse composition vertebral marrow inserts within three different size lumbar simulators and an Ll vertebra within a Humanoid phantom. The calibration standards were manufactured by Image Analysis, and all data were acquired with a GE 9600 CT scanner operated at 80 kVp and 140 kVp. Least square fits to corresponding liquid versus solid referenced I3MD measurements of the inserts all had r’s >0.999. SEES, ~2 mg/ml, and intercepts of -0. The slopes (BMDK,“Po,/BMDhydrorcyapatilc) for the various body sizes were all about the same with values of 0.86, 0.81, and 0.96 to 1.02 for the single-energy@80 kVp, single-energy@140 kVp, and dual-energy measurements, respectively. Corresponding ratios for the Humanoid vertebra were 0.86, 0.82, and 0.96. The conversion relations were essentially independent of marrow composition and body size but did depend upon kVp. Finally, although the solid standards are more stable, they may still exhibit problems, and these are discussed.

Key words: Computed tomography; Bone density; Calibration; Osteoporosis

Correspondence to: Mitchell M. Goodsitt, Ph.D., University of Michigan, University Hospital, Department of Radiology, 1500 E. Medical Centre Drive, Ann Arbor, MI 48109-0030,USA. Work supported in part by NIH grant # ROl AR39215 * Presented at the 1991 RSNA Meeting. Radiology 1991;18l(P):206-207.

146 Introduction Of all the methods employed to measure bone mineral content, quantitative computed tomography (QCT) has the unique capacity to separately analyze the medullary cavity of the bone. Measurements in this region are desirable because the turnover rate of the trabecular bone in the marrow is about 8 times that of the cortical bone in the outer shell [l]. Thus, the QCT measurements are more sensitive to changes in bone mineral resulting from diseases such as osteoporosis [21. To assess the condition (i.e., risk of fracture) of an individual’s vertebrae with QCT, the measured bone mineral densities (BMDs) of those vertebrae are compared to those of age- and sex-matched normals within a reference population, Vast data bases exist for the BMDs of reference populations [3-81.In nearly all cases these BMDs are in units of mg/ml KzHPQd. KzHP04 has long been used as a calibration standard in bone mineral research [9-l l] because (1) it has x-ray attenuation properties that are very similar to those of true bone mineral (calcium hydroxyapatite) and (2) unlike true bone mineral, it is soluble in water, facilitating the manufacture of a set of mineral standards of known concentrations, which is required for generating calibration curves [9]. Unfortunately, researchers have experienced some problems with these liquid standards. The chief complaint is air bubble formation. Air bubbles arise from (1) the equilibration of the liquid solutions with air dissolved in the plastic material (a phenomenon known as ‘outgassing’) and (2) the evaporation of water through imperfect seals. Outgassing does not change the concentration of the solutions and is therefore of minor importance (C.E. Cann, Univ. of California, San Francisco, pets. commun., 1992). The bubbles form at a rate of about 500 PI/ year, and can be removed from the solutions in phantoms that incorporate bubble traps. The evaporation of water, which is said not to be a problem with the original Cann/Genant phantom (C.E. Cann, pers. commun., 1992),is definitely a problem with many homemade and commercial phantoms. It results in more

811110 (mglcc) F&J.I, Graphical illustration of the effects of air bubble formation in the calibration standards on

the measuredBMD of a vertebra.‘A’ representsthe original calibration line (no air bubbles). When air bubbles form, the conoentrations of the solutions increasecausing a shift to calibrationline lB’. This in turn causes the measuredBMD of a vertebrato decreaseeven when the CT# of that vertebraremainsthe same (no real change in BMD). The changes are exaggeratedin this figure to demonstratethe effect. The true percentagechange in BMD is equal to the percentageof volume occupied by the air bubbles.

147

concentrated solutions. This in turn causes the slope of the calibrationline to increase and hence the BMD to be underestimated (see Fig. 1). The magnitude of the underestimation depends upon the size of the air bubbles relative to the volume of the calibration standards. In fact. it can be shown that the percentage of underestimation is equal to the percentage of volume occupied by the air bubbles. For example, air bubbles as large as 2.5 ml in volume have been observed in each of the -85ml calibration solutions in a reference standard at our institution. This 3% decrease in volume results in a 3% increase in the true concentrations of the standards, which translates into a 3% increase in the slope of the calibration line that is generated assuming the nominal concentrations. Use of this new calibration line results in the underestimation of the true BMD by 3% (note: 82.5 ml/85 ml =0.97) This is an undesirable effect especially in studies geared to detect relatively small (4-6%/year) losses in BMD. Yet, it may not be recognized since the typical reproducibilities of BMD measurements are about 2% [12]. Another undesirable effect of air bubbles is that their presence in a scanned slice may cause artifacts which could affect the accuracy of the measured CT numbers of the calibration standards. Finally, something that is often not recognized is that misleading calibration corrections may be obtained when those corrections are determined from the measured BMD of a KzHP04 in water vertebra within a torso phantom. Specifically, if air bubbles of comparable volume fraction form in both the calibration standard and the torso vertebra, the effects will cancel one another, and no change will be detected in the measured BMD of that vertebra. A solution to the stability problems associated with many of the liquid-based standards is to employ solid standards. These typically are made of known amounts of calcium hydroxyapatite in a water-equivalent plastic. They are presently available from at least four manufacturers: Image Analysis (Irvine, CA), General Electric (Milwaukee, WI) (Image Analysis now makes the GE phantom), Siemens (Erlagen, Germany) [13] and CIRS (Norfolk, VI). To effectively utilize such phantoms, one is faced with two alternatives: either conduct a large study with that phantom to measure the BMDs of a new reference population, or develop conversion relations to translate the new calcium hydroxyapatite (solid) values to the old KzHP04 (liquid) values for comparison with the old database or to derive a solid database. Since KzHP04 and calcium hydroxyapatite have very similar x-ray attenuation properties, the latter approach seems more appropriate. Indeed, one of the manufacturers, Image Analysis, has multiplied the BMD values in the KzHP04-based reference population by 1.15 to obtain a new calcium hydroxyapatite reference data base (B. Arnold, Image Analysis, pers. commun., 1991). The expected conversion relations for the two standards depend upon the degree of similarity between the x-ray attenuation coefficients of K2HP04and calcium hydroxyapatite. The ratio of the mass attenuation coefficients of these standards as a function of x-ray energy is plotted in Fig. 2. (The coefficients were computed with the XCOM computer program which was written by Berger and Hubbell of the National Bureau of Standards.) As shown, this ratio varies by only

148

1

1

1.030

40

-7

so

60

70

00

00

Energy (keV) Pig. 2. The ratio of the mass attenuation coefficient (p/p) of calcium hydroxyapatite a function of x-ray energy.

to that of KzHP04

as

2% over the range of effective x-ray energies employed in CT, Yet, this is not the whole story, as the conversion relations are derived from the CT numbers of the solutions and mixtures which depend upon the concentrations and attenuation coefficients of the mineral, water and water equivalent plastics. The CT numbers are given by the equation: minerill

water x Cwatcr -P(E)watct

x Cmincrul

CT#(E) = 1000x @)wutcr

where p/p represents the mass attenuation coefftcient, fi represents the linear attenuation coefficient and c represents concentration. The water concentrations in the &HP04 solutions are given in a paper by Rao [ 141.Those in the calcium hydroxyapatite mixtures are derived assuming that the mass density of calcium hydroxyapatite is 3.0 g/ml [15], the mass density of solid water is 1 g/ml, and the total volume of the mixture is simply equal to the sum of the partial volumes of the constituents. For example, to determine hater for a mixture containing c mg/ cc of calcium hydroxyapatite (c&, we first assume that the total volume is 1 ml. Then the volume occupied by the calcium hydroxyapatite is CHA x 1 CC/PHA, which leaves I-CHA/JIHA ml of solid water. The concentration of solid water is this value multiplied by the density of solid water (1 g/ml). Hence, we have: Cwater= 1 - CHA/~HA. The above equations were uzed to derive CT# vs BMD (concentration) calibration lines for 0 and 100 mg/ml standards (Cwater= 0.980 g/ml for 100 mg/ml K2HP04 and cwuler= 0.967 g/ml for 100 mg/ml calcium hydroxyapatite). The conversion relation, which is the ratio of the slopes of those calibration lines, was found to vary by about 9% over a typical effective CT x-ray energy range of SOkeV to 85 keV. Specifically, mg Ca/mg K equals 1.Oat 50 keV and 1.09 at 85 keV. Thus, the conversion relations would be expected to be significantly dependent upon the effective energy of the x-ray beam, The purpose of the present study was to determine the dependence of the

149

conversion relations on parameters affecting the effective energy of the x-ray beam at the vertebral location. The particular parameters studied included x-ray tube voltage, patient size. and marrow composition.

Materials and Methods

The ‘patients’ in this study included small, medium and large size lumbar simulators manufactured by CIRS and an Ll vertebra within a Humanoid phantom (Humanoid Systems, Carson, CA). An Image Analysis torso phantom containing a lOO-mg/mlcalcium hydroxyapatite in solid water vertebra was also employed for calibration purposes. An extra thick (t = 4 cm) CIRS lumbar simulator was employed to facilitate positioning and to better mimic the amount of x-ray scatter produced by a subject’s body. The simulator is an anthropomorphic abdominal section phantom. The manufacturer derived the dimensions of the phantom from CT axial slice images of a series of subjects who were being studied for possible demineralization. Compartments that are simulated in the section include subcutaneous fat, the vertebral cortex, paraspinal musculature, and abdominal organs. The phantom is made of epoxy-resin (plastic) based materials that mimic the x-ray attenuation properties of soft tissues, fat, and bone. Two outer ‘fat’ rings can be added to the periphery of the base (small) phantom to simulate medium and large sized patients. The effects of different spongiosa content can be studied by placing a variety of marrow-simulating inserts within a large cavity that is present inside the vertebral cortex. Five marrow inserts having a wide range of compositions were employed in this study. Three of the inserts had compositions typical of those employed in calibrating CT scanners for bone mineral analysis. These included: (1) liquid water within a syringe, (2) 75 mg/ml calcium hydroxyapatite in solid water, and (3) 100mg/ml calcium hydroxyapatite in a plastic simulating a red and yellow marrow mixture containing 30% fat (the 100-F irrsert supplied with the standard lumbar simulator system). The other two inserts had compositions that were closer to those of the spongiosa of normal human subjects. They were: (4) 200 mg/ml ‘bone’ in a red-marrow-simulating plastic (w 36% fat by volume), and (5) 200 mg/ml ‘bone’ mixed with 50% fat by volume in a fat-free red-marrow-simulating plastic. The ‘bone’ in these latter inserts was manufactured to mimic the x-ray attenuation properties of skeletal cortical bone as defined by Woodard and White (e.g. 58% mineral (calcium hydroxyapatite), 24.6% protein, 12.2% water, and 5.2% monosaccharide by mass). According to those authors, ‘trabeculae have the same elementary composition as cortical bone’ [16], so trabecular bone was actually being simulated in the inserts. Inserts 2,4 and 5 were custom manufactured by CIRS. The Image Analysis torso phantom consists of a torso-shaped piece of watersimulating plastic (solid water) in which a cylinder containing 100mg/cc calcium hydroxyapatite in solid water is embedded at the vertebral position. Unlike the CIRS lumbar simulator, the Image Analysis ‘vertebra’ can not be replaced with

150

other ‘vertebrae’ of different compositions and is not surrounded by a simulated cortex. The humanoid phantom, lumbar simulators, and torso phantom were scanned on top of liquid (K2HP04 in water) and solid (calcium hydroxyapatite in solid water) calibration standards manufactured by Image Analysis. Both of these standards consist of cylinders having concentrations of 0 mg/ml, 50 mg/ml, 100 mg/ml and 200 mg/ml mineral in a water background. All scans were performed on a General Electric 9800 Quick CT scanner (Milwaukee, WI) which was equipped with HiLight solid state detectors. The x-ray technique factors employed were: 80 kVp, 70 mA, 2 s, 10 mm, large (48 cm diameter) field of view, and 140kVp, 40 mA, 2 s, 10 mm, large field of view. These are the recommended techniques for single- and dual-energy CT performed on a GE 9800 CT scanner 1171.The region of interest facilities of the scanner were employed to determine the mean CT numbers of the calibration standards in each image, and the data were least-square fi, to derive CT number versus BMD calibration lines. The single-energy (SE) BMD of the inserts and vertebra were then computed by substituting their measured mean CT numbers into the calibration liue equations. This is the conventional Cann-Genant technique Ill], and it was implemented at both 80 kVp and 140 kVp. Dual-energy (DE) measurements of BMD were computed from paired 80 kVp and 140 kVp data according to the method of Cann et al. [18]. The equation employed was: [CT##@OkVp) - CT#( 14OkVp)]- [6 (80kVp) - b (14OkVp)l BMD DE = - -.‘. m (80kVp) --R) (14OkVp) where the mean CT numbers are those of the insert or vertebra, and the 6s are the intercepts and the ms are the slopes of the calibration lines. Three scans were performed of each insert or vertebra at each technique and the corresponding BMDs were averaged in determining the conversion relations. Power calculations using reproducibility data acquired in a previous study [19] showed that three scans should be adequate for detecting 1% changes in SE BMD and about 3% changes in DE BMD with a 90% probability at a significance level (a) of 0.05. Statistics of this order are needed to assess the effect of patient size on the BMD measurements. Solid (calcium hydroxyapatite) to liquid (KzHPOe) conversion relations were computed for each size lumbar simulator. This was accomplished by least-square fitting the measured BMDs of the five inserts in units of calcium hydroxyapatite to the corresponding measured values in units of mg/ml KzHPOd. The resulting conversion relations were of the form: BMD (K) = slope x BMD (Ca) + intercept The ratios of the liquid to solid BMDs of the Ll vertebra in the Humanoid phantom were also computed and compared with the slopes of the above

151

conversion relations. Ideally, a new normative data base should be obtained for the solid standards, This would require a massive study involving hundreds of subjects (e.g., the UCSF data base includes 538 subjects [7]) and taking a year or more to complete. An alternative procedure would be to determine separate solid-toliquid conversion relations for each subject in a study by initially scanning them with both the liquid and solid standards. Subsequent scans would be performed with the solid standards, and the conversion relations would permit employment of the liquid data base, However, the initial scans would be time consuming and involve extra x-ray dose to the subjects. Yet another approach would be to determine a conversion relation for an average size subject or torso phantom and apply that relationship to all other subjects. The errors associated with this approach were assessed in this study. The Image Analysis torso phantom was scanned on top of the solid and liquid calibration standards, yielding a conversion relation of the form estimated BMDk = 2

x measured BMDca + bca - bk mK

where K represents KzHP04, Ca represents calcium hydroxyapatite, and the ms represent the slopes and the bs the intercepts of the calibration lines, This conversion relation was used to estimate the BMDKs of the vertebral inserts within the small, medium and large sized lumbar simulators. The measured BMDcas were introduced into the equation to obtain the estimates, and these were compared with the BMDKs measured with the liquid standard. The error in each case was equal to the measured BMDk minus the estimated BMDk. Errors were also computed when only the slopes were employed in the conversion relation (intercepts assumed to be the same). Results

The SE-80 kVp, SE-140 kVp and DE conversion relations for the small, medium and large lumbar simulators are summarized in Table 1. All of the correlation coefficients were greater than 0.9990, and the standard errors of the estimate were less than 2 mg/ml K2HP04. A plot of one of the conversion equation lines indicating the BMDs of the individual inserts is shown in Fig. 3. The ratios of the KzHP04 to calcium hydroxyapatite BMD values for the Ll vertebra in the Humanoid phantom had values of 0.862 for SE-80 kVp, 0.819 for SE-140 kVp, and 0.962 for DE. These numbers are comparable to the slopes of lumbar simulators. the relations given in Table 1 for the C Table 2 summarizes the errors associated with the alternative approach in which the conversion relations derived for the average size Image Analysis torso phantom were applied to all inserts within the small, medium and large sized lumbar simulators. The single-energy and dual-energy conversion relations were

152

Table 1

Calcium hydroxyapatite to &HP04 conversion relations for the five vertebral inserts within the small, medium, and large sized lumbar simulators. The relations are of the form: BMDK = slope x BMDoa + intercept r

SEB

1.614 1.386 1.806

0.99998 0.99999 0.99996

0.345 0.216 0.464

0.808 0.808 0.812

2.450 3.042 2.568

0.99992 0.99996 a.99995

t-J.682 0.487 0.532

0.975 I.018 0.963

- 1.648 -4.Q23 0.062

0.99906 0.99978 0.99922

I .957 0.948 I.764 us____

Technique

Slope

Intercept

SE-80 kVp Small SE-80 kVp Medium SE-80 kVp Large

0.854 0.864 0.858

SE=140kVp Small SE=140kV;; Medium SE-140 kVp Lar@ BE Small BE Medium DE L.arSe

‘SEE = standarderror of the estimatein mS/ee KzHPOd.

i’s follows: SE-80 BMDx = 0.856 x SE-80 BMDca + 2.858; SE- 140 BMDx = 0.808 x SE-140 BMDcu + 3.788; and DE BMDK = 0.968 x DE BMDeu + 0.684. Errors for the case when the conversion relations only consisted of the ratio of the slopes of the calibration lines are listed in Table 3.

Discussion

The conversion relations listed in Table 1 are essentially independent of body size. It is interesting to note that application of one-way analysis of variance (ANOVA) to the CT number and BMD data (Table 4) shows the CT numbers of the inserts are almost always significantly different for the various body sizes; however, the BMDs are rarely significantly different. This indicates that the use

0

0

20

40

60

20

100 120 140

EMD(mglcc Ca Hydroxyapatlte) Fig. 3. Plot of the SE-80 kVp calciumhydroxyapatiteto KzHP04 conversion relationfor the five vert’ebral insertswithin the small lumbarsimulator.

153

Table 2

Errors in the estimated BMDx of the individual vertebral inserts for the case when those estimates are computed using the measured BMDca and the to BMDx conversion relations derived from the calibration lines obtained when a torso phantom is scanned on top of the solid and liquid standards. Errors are in units of mg/cc &HP04 Hz0

V/O%

100/30%

2OOBJSO% 200B red

Inserts in small lumbar simulator SE-80 kVp SE-140 kVp DE

1.4 0.9 2.6

1.4 2.2 -0.2

I.1 I.5 0.6

1.4 1.2 I.5

2.0 0.8 4.2

0.7 0.9 0.4

0.5 I.3 -1.6

0.8 1.0 0.6

0.3 0.3 0.4

1.4 0.8 2.9

0.4 0.2 1.3

0.6 1.2 -1.2

1.2 1.0 I.5

Inserts in medium lumbar simulator SE-80 kVp SE-140 kVp DE

I.5 0.5 4.2

Inscrlo in large lumbar simulator SE-80 kVp 1.0 SE-140 kVp I.5 DE 0.4

of the calibration standards helps compensate for x-ray beam hardening and scatter errors that are not corrected by the CT scanner algorithm. Furthermore, although significant differences in the BMDs for the different body sizes are sometimes obtained, the magnitudes of these differences are small (typically Table 3

Errors corresponding to those in Table 2 for the case when only the slopes of the calibration lines were employed in the conversion relations (errors are in units of mg/cc KzHP04) 75/O%

IOO/30%

ZOOS/SO%

200B red

Inserts in small lumbar simulator SE-80 kVp -1.5 SE-140 kVp -2.9 DE 2.0

-1.4 -1.6 -0.8

-1.8 -2.2 -0.1

-1.5 -2.6 0.8

-0.9 -3.0 3.5

Inserts in medium lumbar simulator SE-80 kVp -1.3 SE-140 kVp -3.3 DE 3.6

-2.1 -2.9 -0.3

-2.4 -2.5 -2.2

-2.1 -2.8 -0.1

-2.5 -3.5 -0.3

Inserts in large lumbar simulator SE-80 kVp -1.8 SE-140 kVp -2.3 DE -0.3

-1.4 -3.0 2.2

0.4 -3.6 0.6

-2.3 -2.6 - I.9

-1.7 -2.8 0.8

H2Q

154 Table 4

effect of body size on the measured CT numbers and bone mineral densities of the various inserts. Differences that are significant at the 95% level by the Sheffe F-test for one factor ANOVA are indicated. They are specified as SM, SL and ML when the significant differences are between the values in the small and medium bodies, small and large bodies, and medium and large bodies, respectively

The

H20

75/O%

100/30%

200B/50%

Inserts scanned in lumbar simulators on top of liquid calibration standard SM,SL,ML SM,SL,ML SM,SL,ML CT#40 kVp SL SM,SL,ML SM,SL SL CT#.140 kVp SL SL SL SE-80 kVp SE-140 kVp DE Inserts scanned in lumbar simulators on top of solid calibration standard SM,SL,ML SM,SL CT#.IO kVp SM,SL,ML SM,SL,ML SL CT#NO kVp SL,ML SE-80 kVp SL SL SE-140 kVp SL DE

SL,ML SM,SL,ML -

2008 red

SL,ML SM,SL,ML

SL SM,SL,ML -

about 2 mg/ml for SE-80 and SE- 140 versus CT number differences as large as 11 H) and have little effect on the conversion relations. The standard errors of the estimates of the conversion relations are very small, having maximum values for conversions in either direction of 0.54 mg/ml for SE$0 kVp, 0.84 mg/ml for SE-140 kVp, and 2.00 mg/ml for DE. Thus, the relations are essentially independent of the composition of the vertebral insert. That is, other inserts that were not studied such as 50 mg/ml, 100 mg/ml, and 150 mg/ml of calcium hydroxyapatite or bone in red marrow would be expected to have BMDK, BMDca coordinates that would fall on the line generated for the inserts used in the present investigation (e.g. Fig. 3). In general, the slopes of the BMD Ca to BMD K conversion relations for the three size CIRS lumbar simulators and five vertebral inserts have values of 0.86, 0.81, and 0.99 for SE-80 kVp, SE-140 kVp, and DE, respectively. These are the averages of the values in Table 1. The corresponding slopes of the inverse conversion relations (BMD K to BMD Ca) are I .16, 1.24, and 1.Ol. The 1.16 factor at 80 kVp is nearly identical to the 1.I5 factor recommended by Image Analysis for SEQCT. However, the results of this study show such a factor would be inappropriate for other x-ray tube potentials such as 140 kVp where a factor of 1.24 is called for. These experimentally measured factors differ from those that one computes theoretically using the x-ray attenuation coefftcients of calcium hydroxyapatite, WIPO4, and water over an effective energy range of 50 to 85 keV. As previously stated, the latter BMD K to BMD Ca factors range from 1.Oto 1.09. I believe the

155

Theoretical slopes of CT# vs BMD calibration lines as a function of x-ray energy for K2HP04 in water and calcium hydroxyapatite (HA) in solid water standards. The slopes are computed for a range of HA densities. Experimentally measured slopes at 80 kVp and 140 kVp were 1.75 and 1.22 for K2HP04 solutions, and 1.51 and 1.00 for HA in solid water mixtures Energy (keV)

Slope for K?HPOd

Slopes for HA at indicated p 1.9

2.0

2.1

2.5

3.0

55 56 57 58 59 60

1.93 1.88 1.83 1.78 1.73 1.69

1.71 1.65 1.60 1.55 1.50 1.45

1.74 1.68 I .62 1.57 1.52 1.48

1.76 1.70 1.65 1.60 1.55 1.50

1.84 1.78 1.72 1.67 1.62 1.58

1.90 1.85 1.79 1.74 I.69 1.64

73 74 75 76 77 78 79 80

1.29 1.27 1.25 1.23 1.21 1.20 1.18 1.17

1.02 1.00 0.98 0.96 0.94 0.92 0.90 0.88

1.05 1.03 1.00 0.98 0.96 0.94 0.93 0.91

1.07 1.05 1.03 1.01 0.99 0.97 0.95 0.93

1.15 1.13 1.10 1.08 1.06 1.04 1.03 1.01

1.22 1.19 1.17 1.15 1.13 1.11 1.09 1.08

reason for the difference is that when calcium hydroxyapatite is mixed in an epoxy resin, it takes up more volume than would be computed assuming a pure density of 3 g/ml. Further investigations showed that the measured slopes of the K2HP04 in water calibration lines (about 1.75 at 80 kVp and 1.22 at 140 kVp) are the same as those for monoenergetic x-ray beams having energies of about 59 keV at 80 kVp and 76 keV at 140 kVp (see Table 5). Best matches to the corresponding measured slopes of the calcium hydroxyapatite in water calibration lines (about 1.51 and 1.00) occur at about 59 keV and 76 keV when the assumed density of pure calcium hydroxyapatite is -2.0 g/ml (see Table 5). (The slopes of 1.51 and 1.OO.areneeded to match the experimental BMD K to BMD Ca slope ratios of 1.16 and 1.24, respectively). Another possible reason for the differences is that the solid water that is mixed with the calcium hydroxyapatite may not truly be water-equivalent in its x-ray attenuation properties. The entire issue bears further study especially since other researchers have obtained significantly different BMD measurements when using solid phantoms made by different manufacturers [20]. The slopes of the alternative approach conversion relationships (0.86 for SE-80 kVp, 0.81 for SE-140 kVp, and 0.97 for DE) are essentially identical to the average slopes of the conversions for the series of inserts in the three size lumbar simulators (Table 1). The intercepts, however, differ (alternative method inter-

156 Table 6

The effect of kVp on measured BMD kVp standard Measured BMD (mg/ml)for: IA Torso Humanoid 200 mg/ml 100 mg/ml Ll vertebra 200 mg/ml 75 mg/ml HA 100 mg/ml HA 30% fat bone 50% fat bone 36% fat HA in water in water Insert in small lumbar simulator

80 liquid 70.8& 0.6 140 liquid 66.3f 0.4 Biffcwcnce 4.5

83.71 1.1 76.5f 0.2

80 solid 140 solid Difference

95.7 a 0.7

81.1 & 0.7 80,l % 0.6 I .O

7.2

3.9

100.9f 0.6 113.1?:0.9 102.0f 0.3 120.6J-0.5

-1.1

-7.5

116.2 f 1.6 123.0 f 0.8 -6.8

131.1 f 1.5 145.5 f 0.4 - 14.4

90.6& 0.1 118.9 f 1.2 85.2& 0.6 116.9f 0.8

5.4 103.5 f 0.5 101.6 f 0.5 2.0

2.0 137.9 I 0.3 142.7 f 0.6 -4.8

cepts: 2.86 for SE-80 kVp, 3.79 for SE-140 kVp and 0.68; average values for series: 1.60 for SE-80 kVp, 2.69 for SE-140 kVp, and - 1.86 for DE). Use of the alternative conversion relations (Table 2) resulted in rms errors in the estimated BMD (K2HP04) of 1.1 mg/ml for SE-80 kVp and SE-140 kVp, and 2.0 mg/ml for DE. All of these values are less than the precisions of the measurements in phantom studies (w 2 mg/ml for SE and N 3 mg/ml for DE) [21] and are satisfactory. When only the slopes were employed in the conversion relations (Table 3), the rms errors were 1.9 mg/ml for SE-80 kVp, 2.8 mg/ml for SE-140 kVp, and 1.7 mg/ml for DE. These values are comparable to the precisions of the measurements and lend credence to the use of such conversion relations. An important question concerning the use of the SEQCT reference data bases is whether the values generated at 80 kVp are correct for studies performed at 120 kVp or 140 kVp. The data acquired in the present study show the answer is probably no. A comparison of the SE-80 kVp and SE-140 kVp measurements of the various phantoms and inserts is detailed in Table 6. Depending upon the composition of the simulated vertebra, SE measurements at 80 kVp and 140 kVp differed by -7.5 to 7.2 mg/ml for the liquid calibration standard, and - 14.4 to 3.9 mg/ml for the solid calibration standard. These results reflect differences in the energy dependence of the x-ray attenuation coefficients of the materials in the calibration standards and simulated vertebrae. A related question is whether it is correct to employ the UCSF reference data base [7]for BMD measurements made with the Image Analysis liquid calibration standard. The UCSF data were obtained with the Cann/Genant calibration standard which is considerably larger than the Image Analysis calibration standard and therefore results in more x-ray beam hardening. The answer to the question is probably yes; however, differences between measurements obtained with the two liquid standards could be several percent and should be studied further. Finally, several points should be emphasized concerning the applicability of the results of this study. First, experiments were only performed with phantoms;

157

hence, the accuracy of employing the conversion relations for human subject studies depends upon the degree to which the phantoms simulate the x-ra,y attenuation properties of humans. (Concerning this matter, it is reassuring that similar conversion relations were obtained for the Humanoid phantom which contains an actual human skeleton.) Second, the results are CT scanner and calibration standard dependent. Conversion relations could be quite different for CT scanners having different effective x-iay beam energies and different beam hardening and scatter properties and corrections. Also, the relations have already been shown to be different for standards made by the various manufacturers. This presumably is due to differences in composition. Lastly, other problems may exist with the solid standards including possible inhomogeneities as a result of nonuniform mixing, and possible differences in calibration standard samples due to batch-to-batch variations in the compositions of the resin, filler and calcium hy&oxyapatite components.

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