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Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. References

Dual-energy X-ray absorptiometry (DXA), using a narrow pencil-shaped X-ray beam coupled to a single detector, has been used extensively. More recently, DXA using a fan-shaped X-ray beam coupled to an array of detectors has been introduced. This new generation of scanners causes an inherent magnification of scanned structures as the distance from the X-ray source decreases. This magnification, which occurs in the medial-lateral direction but not in the craniocaudal direction, does not affect bone mineral density (BMD). There are, however, significant changes of bone mineral content (BMC), bone area, and parameters of hip geometry, with varying distance of the bone scanned from the X-ray source. Variability of soft tissue thickness in vivo, by altering the distance of the skeleton from the scanning table and X-ray source, may cause clinically significant errors of BMC, bone area, and proximal femur geometry when measured using fan-beam densitometers. We analyzed the geometry of Lunar and Hologic fan beam scanners to derive equations expressing the true width of scanned structures in terms of the apparent width and machine dimensions. We also showed mathematically that performing an additional scan, at a different distance from the X-ray source than the first scan, provides simultaneous equations that can be solved to derive the real width of a scanned bone. This hypothesis was tested on the Lunar Expert using aluminium phantoms scanned at different table heights. There was an excellent correlation, r = 0.99 (p < 0.001), between the predicted phantom width and the measured phantom width. In conclusion, this study shows that the magnification error of fan beam DXA can be corrected using a dual scanning technique. This has important implications in the clinical usefulness of BMC and geometrical measurements obtained from these scanners.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. References

Dual-energy X-ray absorptiometry (DXA) using a pencil beam design has been in use for almost a decade. These machines employ a well collimated pencil beam X-ray coupled to a single detector which moves in a raster pattern across the patient, thus obtaining a true projection of the region scanned. This design of pencil beam densitometers does not cause any significant magnification of the scanned bones.1,2 More recently, a new generation of DXA scanners have been introduced based on a multiple detector array design coupled to a fan-shaped X-ray beam. Fan beam densitometers acquire scans by performing a single sweep of the patient with consequent substantially shorter scanning times. These machines, however, due to the shape of the fan beam X-ray, cause an inherent magnification of scanned structures as the distance from the X-ray source, and hence from the apex of the fan beam, decreases.1–3 Therefore, the observed width of scanned bones increases with proximity to the X-ray source. This magnification, which occurs in the medial-lateral direction but not in the craniocaudal direction, does not significantly affect the bone mineral density (BMD).1,3 There are, however, varying degrees of magnification of bone mineral content (BMC) and bone area,1,3 as well as parameters of proximal femur geometry,2,4 with varying distance of the bone scanned from the X-ray source.

We have recently shown2 that variations in soft tissue thickness between patients, by altering the distance of the skeleton from the X-ray source, are sufficiently large to cause significant errors in proximal femur geometry and BMC when measured using fan beam DXA. Therefore, while fan beam DXA provides reliable measurements of BMD, the primary measure used in clinical practice, the magnification caused by these machines presents difficulties in other measurements of bone, including BMC and proximal femur geometry. We present here an examination of the geometry of fan bean DXA scanners and propose a method of correction to overcome the magnification error of these machines.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. References

Geometry of fan beam DXA

We analyzed the geometry of two common fan beam densitomiters, the Lunar Expert (Lunar Corp., Madison, WI, U.S.A.) and the Hologic QDR (Hologic, Inc., Waltham, MA, U.S.A.).

Geometry of the Lunar Expert: Figure 1 shows a schematic diagram of the Lunar Expert. Applying the geometry of similar triangles, we obtain:

  • equation image(1)

Note, X and I are constants, dependent on the dimensions of the scanner, while d and H are patient dependent.

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Figure FIG. 1. Schematic diagram of the Lunar Expert fan beam DXA where X is the distance from X-ray source to the detector surface, d is the width of the scanned object, D is the observed width of the scanned object, H is the height of the scanned object above the scanning table (soft tissue thickness), I is the distance from the upper surface of the scanning table to the detector, and θ is half the angle subtented by the scanned object on the X-ray source.

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Geometry of the Hologic QDR: Figure 2 shows a schematic diagram of the Hologic QDR. Applying the geometry of similar triangles, we obtain:

  • equation image(2)

Note, X and B are constants, dependent on the dimensions of the scanner, while d and H are patient dependent.

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Figure FIG. 2. Schematic diagram of the Hologic QDR fan beam DXA where X is the distance from X-ray source to the detector surface, d is the width of the scanned object, D is the observed width of the scanned object, H is the height of the scanned object above the scanning table (soft tissue thickness), B is the distance from X-ray source to the scanning table, and θ is half the angle subtented by the scanned object on the X-ray source.

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Proposed solution to magnification error

The performance of an additional scan of a patient, at a distance from the X-ray source different from that used in the first scan, would provide a second set of equations involving the variables in Eqs. 1 or 2 above. This second equation could be solved simultaneously with the corresponding first equation to determine the real width (d) of the bone scanned, or alternatively to determine the local soft tissue thickness (H). The hardware and controlling software are already in existence on the Lunar Expert to allow the operator to both accurately and quickly alter the distance of the scanning table from the X-ray source. The mathematics of this solution for the Expert are set out below. A similar solution could easily be derived for the Hologic QDR, although at present this machine does not have the capability to perform scans at different distances from the patient.

Figure 3 shows a schematic diagram of a patient scanned on the Lunar Expert at two heights of the scanning table, I1 and I2, above the detector. (Note I2 = I1 + i where i is the change in table height.) From Eq. 1, we obtain two equations relating to the two observed bone widths, D1 and D2.

  • equation image(3)
  • equation image(4)

Solving the two equations, first to obtain the true width of bone (d) and second to obtain local soft tissue thickness (H) gives

  • equation image(5)
  • equation image(6)

Thus, the real width of a scanned bone (d) or local soft tissue thickness (H) can be determined from two scans performed with a known difference of scanning table heights. The values of X and I1, being hardware-dependent constants, are predeterminable.

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Figure FIG. 3. Schematic diagram showing two scans at different scanning heights on the Lunar Expert fan beam DXA where d is the width of the scanned object, D1 is the observed width of the scanned object at height 1, D2 is the observed width of the scanned object at height 2, I is the distance from the upper surface of the scanning table to the detector, and i is the change in the height of the scanning table.

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RESULTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. References

The effect of varying scanning height differences on the accuracy of a predicted object width

A series of scans of an object of known dimensions was performed. The Lunar Expert was chosen due to the ease of altering the distance between the object being scanned and the X-ray source by altering the scanning table height.

A rectangular aluminimum spine phantom of known width (3.955 ± 0.005 cm, measured by vernier calipers) was positioned on the scanning table parallel to its long axis. A water bath of depth 15 cm was used to simulate soft tissue. Multiple scans of the phantom were performed over the full range of scanning heights available, at 2 cm intervals, from 2 cm below the normal scanning position to 22 cm above this height. The scans were analyzed using the standard Expert software, which automatically defines the phantom margins and calculates observed width. Figure 4 shows the observed width at different scanning heights. As expected, there is a progressive increase of observed width with increasing height of the scanning table, corresponding to increasing proximity to the X-ray source.

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Figure FIG. 4. Observed width of an aluminium phantom (cm) at different heights (cm) of the scanning table, measured relative to the normal scanning position (designated as 0 cm). The equation of the line of best fit is:

  • equation image

The measured width of the phantom (3.955 cm) is shown as a horizontal line.

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To calculate X, Eq. 1 was reformulated to express 1/D as a linear function of H with a slope of −1/dX. Using the known true value of d (3.955 cm), the value of X can be obtained from the slope of the regression. This was necessary since the manufacturer has scaled measurements so that the reported width of D is adjusted to equal the real object width. This correction assumes a soft tissue thickness of approximately 10 cm. As a result of this scaling of measurements, the source detector distance used in the equations must be the value scaled to the machine's calibration, rather than the measured distance. The calculated value of X, for the system as calibrated, was 78.4 cm. This value was then used with the remaining data at different heights from the phantom spine scans to calculate the predicted phantom width over a range of scanning table height separations varying from 2 to 22 cm. The results are shown in Table 1. Apart from the value obtained from scans at only 2 cm apart, the predicted width agreed well with the measured width. There was an improvement in accuracy of the predicted phantom width with increasing difference in the scanning height, with an error of <1% at scanning table height separations >16 cm.

Table Table 1. Predicted Width of an Aluminium Phantom, Calculated from Observed Width in Paired DXA Scans Performed at Different Scanning Table Heights
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The accuracy of predicted width with increasing object size

Four rectangular aluminium phantoms of widths simulating expected clinical lumbar vertebral size variation, 30–60 mm, were prepared, and each was scanned three times at table heights of 0 and 20 cm. The phantoms were positioned on the scanning table with a depth of 15 cm of water to simulate soft tissue. Using the values of observed width obtained and the previously determined value of X, three values for the predicted width of each phantom were calculated. The true width of each phantom was then determined using vernier callipers. Figure 5 shows the mean predicted width at different true phantom widths. There is a correlation of 0.99 and a slope of 1.07. This slope does not differ significantly from unity.

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Figure FIG. 5. Mean predicted width of four aluminium phantoms of different size, calculated from paired DXA scans (×3) at heights of 0 and 20 cm, versus measured width. The line of best fit and the line of identity are shown. The equation is:

  • equation image

a correlation of 0.99 and a slope of 1.07. This slope does not differ significantly from unity.

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DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. References

The inherent magnification of fan beam DXA and its potential effect on BMC, bone area, and hip geometry has been described previously.1–3 The differences in buttock soft tissue thickness that we have previously reported2 would lead to an 8.2% (1.4 SD) increase or 11.4% (1.9 SD) decrease in proximal femur geometry in the largest female measured, compared with the smallest, when measured using the Lunar Expert or Hologic QDR-2000 fan beam densitometers, respectively. Magnification errors of a similar magnitude could be expected to occur for BMC and bone area if measured by fan beam DXA in subjects with the same difference in soft tissue thickness.1,3 Although BMD values, rather than BMC, are the primary measurement used in clinical practice, BMC has important value in some situations, particularly pediatrics and research. Measurement of hip geometry, i.e., hip axis length, when measured using pencil beam DXA, has also been shown to be predictive of the risk of hip fracture independently of BMD.5,6 Therefore, the current inability of fan beam DXA machines to measure reliably these parameters is a significant limitation that does not occur with the pencil beam scanners.

The current study proposes a technique that theoretically should be able to correct the magnification error of fan beam DXA scanners. The results from our phantom studies demonstrate that on the Lunar Expert this technique can correct the magnification error of width measurements with a high degree of accuracy. Our calculations have relied upon a derived value of the source detector difference, obtained from the slope of a regression as outlined above. It is to be expected that this derived value could differ slightly from the true value for the DXA system as calibrated and hence may introduce a small systematic error in the predicted phantom widths. Equation C (above) predicts that this error would be most significant when there are only small differences between the table heights of the two scans. Examination of the data from measurements of the aluminium spine phantom demonstrate a general overestimate in phantom width, most marked at small table height differences, consistent with a small error in the derived value of the source detector distance. A more accurate determination of this value would enable this error to be reduced even further.

In the case of the Lunar Expert, the introduction of this correction technique may be possible with only relatively simple software modifications, removing the need for operator intervention. Similar studies should be performed to validate the theory in the other makes of fan beam DXA instruments. It is noted, however, that for the Hologic fan beam DXA machines, hardware and software modifications would be necessary to allow scanning at different table heights.

In a regional scan, such as the lumbar spine or proximal femur, the local variation in soft tissue thickness will be small. Consequently, a remeasurement at a different scanning height, of a small segment of the region of interest, would be sufficient to calculate local soft tissue thickness, which could then be used to correct the magnification throughout the region. In the case of total body scans, a localized rescan at a different scanning height could not be applied to the whole skeleton due to the obvious differences in soft tissue thickness adjacent to different regions of the skeleton. One possible solution to this problem would be to rescan the whole body using a rapid scanning mode to minimize radiation exposure. The parameters of this second scan could then be used to apply appropriate corrections to bone width for the entire skeleton.

In conclusion, we have demonstrated that the magnification errors of fan beam DXA scanners can be corrected using a dual scanning technique. This has important implications in the reliability, and hence clinical usefulness, of BMC and hip geometry measurements obtained from these machines.

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. References

This work was supported by a grant from Roche Products Pty Ltd.

References

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. References
  • 1
    Blake GM, Parker JC, Buxton FM, Fogelman I 1993 Dual x-ray absorptiometry: A comparison between fan beam and pencil beam scans Br J Radiol 66: 902906.
  • 2
    Pocock NA, Noakes KA, Majerovic Y, Griffiths MR 1997 Magnification error of femoral geometry using fan beam densitometers Calcif Tissue Int 60: 79.
  • 3
    Eiken P, Kolthoff N, Barenholdt, Hermansen F, Pors Nielson S 1994 Switching from DXA pencil-beam to fan-beam. II: Studies in vitro at four centers Bone 15: 667670.
  • 4
    Faulkner KG, Genant HK, Mcclung M 1995 Bilateral comparison of femoral bone density and hip axis length from single and fan beam DXA scans Calcif Tissue Int 56: 2631.
  • 5
    Faulkner KG, Cummings SR, Black D, Palermo L, Gluer CC, Genant HK 1993 Simple measurement of femoral geometry predicts hip fracture: The study of osteoporotic fractures J Bone Miner Res 8: 12111217.
  • 6
    Boonen S, Koutri R, Dequeker J, Aerssens J, Lowet G, Nijs J, Verbeke G, Lesaffre E, Geusens P 1995 Measurement of femoral geometry in type 1 and type 2 osteoporosis: Differences in hip axis length consistent with heterogeneity in the pathogenesis of osteoporostic fractures J Bone Miner Res 10: 19081912.