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Glandular Breast Dose for Monoenergetic and High-Energy X-ray Beams: Monte Carlo Assessment¹

¹ From the Department of Radiology, University of California, Davis, Medical Center, 4701 X St, Radiology Research Laboratories, Sacramento, CA 95817. Received August 26, 1998; revision requested October 23; final revision received January 14, 1999; accepted March 26. Supported in part by grants from the United States Army Breast Cancer Research Program (DAMD17-94-J-4424 and DAMD17-98-1-8176), the California Breast Cancer Research Program (0192), and the National Cancer Institute (R21 CA 82077). Address reprint requests to the author (e-mail: jmboone@ucdavis.edu).

	Abstract

TOP Abstract Introduction MATERIALS AND METHODS RESULTS DISCUSSION Appendix 1 References

 
PURPOSE: To extend the utility of normalized glandular dose (D_gN) calculations to higher x-ray energies (up to 120 keV) and to provide the tools for investigators to calculate D_gN values for arbitrary mammographic and x-ray spectra.

MATERIALS AND METHODS: Validated Monte Carlo methods were used to assess D_gN values. One million x-ray photons (1–120 keV, in 1-keV increments) were input to a semicircular breast geometry of thicknesses from 2 to 12 cm and breast compositions from 0% to 100% glandular. D_gN values for monoenergetic (1–120 keV) x-ray beams, polyenergetic (40–120 kV, tungsten anode) x-ray spectra, and polyenergetic mammographic spectra were computed. Skin thicknesses of 4–5 mm were used.

RESULTS: The calculated D_gN values were in agreement within approximately 1%–6% with previously published data, depending on breast composition. D_gN tables were constructed for a variety of x-ray tube anode-filter combinations, including molybdenum anode–molybdenum filter, molybdenum anode–rhodium filter, rhodium anode–rhodium filter, tungsten anode–rhodium filter, tungsten anode–palladium filter, and tungsten anode–silver filter. D_gN values also were graphed for monoenergetic beams to 120 keV and for general diagnostic x-ray beams to 120 kV.

CONCLUSION: The tables and graphs may be useful for optimizing mammographic procedures. The higher energy data may be useful for investigations of the potential of dual-energy mammography or for calculation of dose in general diagnostic or computed tomographic procedures.

Index terms: Breast radiography, radiation dose, 00.47, 0.99 • Breast radiography, technology, 00.12 • Breast radiography, utilization, 00.99 • Physics

	Introduction

TOP Abstract Introduction MATERIALS AND METHODS RESULTS DISCUSSION Appendix 1 References

 
The assessment of radiation dose to the breast during mammography has been of interest to many investigators (1–19). Over the years, the normalized glandular dose (D_gN) has come to serve as the benchmark parameter, useful for calculating the glandular dose in clinical mammography. The D_gN values are essentially the roentgen-to-rad conversion values, calculated for the "at-risk" glandular component of the breast. Recent efforts to calculate D_gN tables for the mammography community have primarily been focused on clinically relevant spectra (4,5,7) with molybdenum anode–molybdenum filter (Mo-Mo), molybdenum anode–rhodium filter (Mo-Rh), or rhodium anode–rhodium filter (Rh-Rh) combinations in the 20–35-kV range.

In this work, D_gN tables were computed for much thicker breasts than for those in previous reports, with values reported here for breast thicknesses from 2 to 12 cm in 1-cm increments. While the typical compressed breast thickness in the United States is approximately 4.2 cm, there are many women with a compressed breast thickness that ranges to 12 cm or thicker. The tables provided in this article may be useful for these patients.

The motivation to extend D_gN tables to encompass higher energy levels was based on an interest in dual-energy mammography, where the optimal high-energy beam is likely to be very high (>100 keV), well beyond current clinical mammographic x-ray beam energies. In addition, with the recent introduction of full-field digital mammography systems into the clinical environment, it is likely that slightly higher energy x-ray beams may become useful in some instances. This study was intended to extend the utility of D_gN calculations to higher x-ray energies (up to 120 keV) and to provide the tools for investigators to calculate D_gN values for arbitrary x-ray spectra, including monoenergetic x-ray beams (for example, produced by synchrotron sources [20], free-electron lasers [21], or other exotic x-ray sources). To this end, tables of D_gN values have been provided for the x-ray tube anode-filter combinations of Mo-Mo, Mo-Rh, Rh-Rh, tungsten anode–rhodium filter (W-Rh), tungsten anode–palladium filter (W-Pd), and tungsten anode–silver filter (W-Ag). Graphical data also are provided to demonstrate D_gN values for monoenergetic and polyenergetic x-ray beams.

	MATERIALS AND METHODS

TOP Abstract Introduction MATERIALS AND METHODS RESULTS DISCUSSION Appendix 1 References

 
Details of the Monte Carlo Study
Monte Carlo procedures were used to compute the glandular dose to the breast. Although I have developed independent computer code for Monte Carlo studies (22,23), the TART97 Monte Carlo code was purchased from the Radiation Safety Information Computational Center, Oak Ridge National Laboratory (Oak Ridge, Tenn) for use in this study. The TART97 code was developed primarily at Lawrence Livermore National Laboratory (24) in Livermore, Calif, and is a thoroughly verified and mature Monte Carlo program. A full description of the TART97 Monte Carlo program is available in the literature (24); however, a brief description is appropriate here.

In a Monte Carlo simulation, each of the millions of photons traced in computations undergoes absorption or scattering, depending on the outcome of a random number generator. The probabilities of the multiple scattering calculations are weighted by the probability of that event at each x-ray energy studied. The TART97 Monte Carlo routine uses multiple scattering calculations, follows the history of all photons, and includes the photoelectric, Raleigh, and Compton scatter interaction mechanisms in the energy region reported. All photons were followed until they either left the volume of interest, were completely absorbed, or reached an arbitrarily small energy level (0.10 keV).

Monoenergetic x-ray photons at 1-keV intervals were input into a mathematic phantom in each of the simulation runs. Each photon run made use of 1 million photons at each monoenergetic energy level, and these data were used to construct monoenergetic D_gN tables in a procedure described later in this article. The lowest energy simulated was 1 keV, and the highest was 120 keV. For the polyenergetic spectra reported, weighted sums of the monoenergetic D_gN data were computed. The x-ray spectra used for this study were generated by using mathematic spectral models described previously (25,26). The x-ray attenuation coefficients for the filters also were reported previously (27).

Geometry and Composition Issues
The geometry simulated in this study is shown in Figure 1. Instead of a D-shaped semicircular breast shape, as others (4,5) have used, a cylindric breast shape was simulated (Fig 1a). The cone-shaped radiation field emitted from the source was collimated to irradiate half of the breast (a semicircle). The semicircular field geometry was particularly simple to simulate with the TART97 code and was efficient to run. The semicircle of breast tissue that was not in the radiation field was intended to simulate the presence of the torso of the patient (the chest wall). For their geometries, Wu et al (4) and Dance (5) assumed a D-shaped breast (no chest wall). The presence of tissue outside of the radiation field may have a minor influence in terms of backscatter, and this is of particular concern in this study due to the much higher x-ray energies studied here. While the nonirradiated semicircle is not the exact geometry of the chest wall, it was thought that the presence of some tissue behind the breast was slightly more representative of the geometry encountered in mammography, rather than no tissue outside of the radiation field.

View larger version (26K): [in this window] [in a new window]   Figure 1. Diagram shows the geometry used for the Monte Carlo simulations. R1 = radius of breast (including skin layer) in millimeters, R2 = radius of breast (excluding skin layer) in millimeters, SID = source-to-image distance, T = breast thickness, Tskin = skin thickness in millimeters.

For a tissue containing a weight fraction f_g of glandular tissue (and, correspondingly, a weight fraction of 1 - f_g for adipose tissue), it can be shown that the glandular volume fraction v_g is given by

The mass m of each component in the unit volume is simply m_g = _gv_g and m_a = _av_a, where the "g" subscripts refer to glandular tissue and the "a" subscripts refer to adipose tissue. For completeness, the elemental compositions and densities for a variety of glandular fractions are given in the Appendix. By using the above procedure, the linear attenuation coefficients for 0%, 50%, and 100% glandular tissues were compared with those reported by Hammerstein et al (28). These data are shown in Figure 2.

View larger version (25K): [in this window] [in a new window]   Figure 2. Graph shows comparison of the linear attenuation coefficients computed in the present study with those reported by Hammerstein et al (28) for 0%, 50%, and 100% glandular tissue. The data from Hammerstein et al are shown as the symbols, and the coefficients used in the present study are shown as lines. Excellent agreement in terms of attenuation coefficients was observed over the energy range compared.

Conversion of Monte Carlo Results to D_gN Values
For a given breast composition, photon energy, and geometry, the output produced by the TART97 Monte Carlo package that was of interest in this study was the energy deposited (normalized per input photon) in the breast tissue compartment (Fig 1). The average energy to the breast tissue compartment, per incident x-ray photon to the breast, was normalized by means of the energy of the incident photons (all Monte Carlo runs used monoenergetic spectra), such that the fractional energy absorption, f(E), was calculated as follows:

	RESULTS

TOP Abstract Introduction MATERIALS AND METHODS RESULTS DISCUSSION Appendix 1 References

 
Monte Carlo Results for f(E) Values
The Monte Carlo results for 0% and 100% glandular breasts are illustrated in Figure 3. If the breast tissue were not encapsulated in a layer of skin, these curves would be pseudoexponential, f(E) being unity at very low energy levels and decreasing almost exponentially with increasing energy level. However, x-ray photons of the lowest energy are unable to penetrate the relatively thin skin layer to contribute a fraction of their energy to the breast tissues; rather, the energy is deposited in the skin layer. The value of f(E) is, therefore, substantially dampened at the low energy levels because of the effect of skin filtration. As the glandular fraction increases, the f(E) value of the incident x-rays increases slightly, as would be expected due to the changing composition and increasing density.

View larger version (35K): [in this window] [in a new window]   Figure 3a. Graphs show f(E) as a function of incident x-ray energy for (a) 0% glandular tissue and (b) 100% glandular tissue. The curves are shown for 11 tissue thicknesses ranging from 2 to 12 cm in 1-cm increments. The bottom curve represents the data for the 2-cm breast thickness, and the top curve represents the data for the 12-cm-thick breast; intermediate curves are not marked for clarity, but are in order from 3 to 11 cm. Dotted lines = curves for odd-numbered tissue thicknesses (3, 5, 7, 9, and 11 cm), solid lines = curves for even-numbered thicknesses (2, 4, 6, 8, 10, and 12 cm).

View larger version (37K): [in this window] [in a new window]   Figure 3b. Graphs show f(E) as a function of incident x-ray energy for (a) 0% glandular tissue and (b) 100% glandular tissue. The curves are shown for 11 tissue thicknesses ranging from 2 to 12 cm in 1-cm increments. The bottom curve represents the data for the 2-cm breast thickness, and the top curve represents the data for the 12-cm-thick breast; intermediate curves are not marked for clarity, but are in order from 3 to 11 cm. Dotted lines = curves for odd-numbered tissue thicknesses (3, 5, 7, 9, and 11 cm), solid lines = curves for even-numbered thicknesses (2, 4, 6, 8, 10, and 12 cm).

View larger version (38K): [in this window] [in a new window]   Figure 4. Graph shows data for a 50% glandular breast, with f(E) as a function of breast thickness. The f(E) value is almost constant as a function of breast thicknesses. The fact that the 10-keV photon absorption fraction is nonzero implies that 10-keV photons penetrate the skin layer, but the constant behavior as a function of breast thicknesses implies that the absorption kinetics take place principally in the first 2 cm of the breast. Higher energy photons show increased penetration of the skin layer ( f [E] values are higher for the 2-cm breast thickness) and also demonstrate that increased tissue absorption occurs with thicker breasts, as would be expected. Different symbols ( and ) and solid and dotted lines do not represent differences in data but were used for ease of reading.

View larger version (30K): [in this window] [in a new window]   Figure 5. Graph shows f(E) as a function of glandular fraction for various x-ray energies and a 4-cm breast thickness. The f(E) curve is a nearly linear function of glandular fraction, as evidenced by the linearity of the curves. Different symbols ( and ) and solid and dotted lines do not represent differences in data but were used for ease of reading.

View larger version (40K): [in this window] [in a new window]   Figure 6. Graph shows DgN values computed by Dance (5) () in comparison with those computed in the present study () for breast thicknesses of 2, 4, 6, and 8 cm. Dance reported DgN values as a function of the HVL of the x-ray beam, and that approach was adopted here as well. A good qualitative comparison is shown.

View larger version (21K): [in this window] [in a new window]   Figure 7. Graph shows DgN values reported by Wu et al (4) along the y axis in comparison with DgN values from the present study (along the x axis). Individual points represent the data obtained with an energy range of 23-35 kV (in 2-kV increments). The DgN values reported here, averaged over all energy levels and breast thicknesses, differed from those of Wu et al by -6.2% for the 0% glandular breast, -1.9% for the 50% glandular breast, and +0.9% for the 100% glandular breast.

Influence of Skin Thickness
The calculation of glandular dose for a patient has many uncertainties associated with it, and estimation of cancer risk on the basis of the glandular dose has even more uncertainties. The uncertainties in calculating glandular dose include uncertainties not only in the tabulated D_gN values but also practical uncertainties in assessing the thickness of the breast, the breast composition, the precise milliampere-second value used, the differences between the actual mammographic geometry and that used in Monte Carlo simulations, and so on.

Figure 3 illustrates that the highest f(E) of incident x-ray photons occurred in the energy region from about 15 to 25 keV, where the f(E) curves peaked. Not coincidentally, this is the energy region where the vast majority of the x-ray photons in conventional x-ray spectra (eg, Mo-Mo combination at 26 kVp) exist. The fact that there was high absorption in the breast in this energy region also suggests that photons in this energy range are useful for the production of high-contrast images. As mentioned earlier, the left edges of the peaks of the f(E) curves seen in Figure 3 are a consequence of the absorption of incident x-rays by the skin layer. The steep slope of the left edges of the f(E) peaks suggests that a small difference in the assumption of skin thickness may have a large influence on the overall accuracy of the dose calculation.

To examine this in the case of the typical breast, Monte Carlo simulations were performed by using different skin thicknesses. Figure 8 illustrates the calculated D_gN values for a 50% glandular, 4-cm-thick breast. Averaged over the different x-ray spectra (23–35 kV), the change in D_gN values (relative to a 4-mm skin thickness) that resulted from different skin thicknesses was 15.2% (SD, 2.1) for a 2-mm-thick skin layer, 7.1% (SD, 0.9) for a 3-mm-thick skin layer, -6.4% (SD, 0.7) for a 5-mm-thick skin layer, and -11.8% (SD, 1.3) for a 6-mm-thick skin layer.

View larger version (32K): [in this window] [in a new window]   Figure 8. Graph illustrates the influence of skin thickness on the DgN value. In comparison with the 4-mm skin thickness data from the study by Wu et al (4) (•), the DgN values increased, on average, by 7% for a 3-mm skin thickness and by 15% for a 2-mm skin thickness. The DgN values decreased by 6% for a 5-mm skin thickness and by 12% for a 6-mm skin thickness. These simulations used a Mo-Mo spectrum.

Monoenergetic Beams
Figure 9 illustrates the monoenergetic D_gN values expressed in millirad per 10⁶ photons per energy interval. Although the general shapes of these curves are similar to those of the f(E) curves in Figure 3, the influence of tissue thickness is inverted. D_gN values for the same x-ray energy and breast composition increased with decreasing breast thickness, because there is less self shielding in the thinner breast.

View larger version (37K): [in this window] [in a new window]   Figure 9a. Graphs show DgN values normalized per entrant photon instead of per roentgen (as is more typical) for (a) 0% glandular breasts and (b) 100% glandular breasts. Curves are shown for breast thicknesses ranging from 2 to 12 cm in 1-cm increments. The DgN values shown here are higher for thin breasts and lower for thicker breasts, which is the reverse of the trend seen for f(E) in This graph illustrates that, on a per photon basis, photons in the energy region between approximately 12 and 30 keV contribute the most to the DgN value. This is the energy region where most conventional mammographic x-ray spectra are centered.

View larger version (37K): [in this window] [in a new window]   Figure 9b. Graphs show DgN values normalized per entrant photon instead of per roentgen (as is more typical) for (a) 0% glandular breasts and (b) 100% glandular breasts. Curves are shown for breast thicknesses ranging from 2 to 12 cm in 1-cm increments. The DgN values shown here are higher for thin breasts and lower for thicker breasts, which is the reverse of the trend seen for f(E) in This graph illustrates that, on a per photon basis, photons in the energy region between approximately 12 and 30 keV contribute the most to the DgN value. This is the energy region where most conventional mammographic x-ray spectra are centered.

Photons at different energy levels contribute differently to exposure in air, owing to the energy dependence of the mass energy attenuation coefficient of air. As a consequence, D_gN values expressed in the traditional units of millirad per roentgen (vs x-ray energy) (Fig 10) have a different shape than those of the D_gN per photon curves in Figure 9. Figure 10 illustrates the millirad per roentgen D_gN values for 0% (Fig 10a) and 100% (Fig 10b) glandular tissue. Figure 10 is directly useful if one is interested in the D_gN value for a monoenergetic beam of 1-R (0.258-mC/kg) incident exposure to the breast.

View larger version (37K): [in this window] [in a new window]   Figure 10a. Graphs show DgN values for monoenergetic x-ray energies for (a) 0% glandular breasts and (b) 100% glandular breasts. Breast thickness ranged from 2 to 12 cm in 2-cm increments. The DgN values shown in these graphs are plotted in the conventional unit of millirad per roentgen, as opposed to millirad per photon as in The curves in this graph can be read directly when assessing DgN for monoenergetic beams.

View larger version (36K): [in this window] [in a new window]   Figure 10b. Graphs show DgN values for monoenergetic x-ray energies for (a) 0% glandular breasts and (b) 100% glandular breasts. Breast thickness ranged from 2 to 12 cm in 2-cm increments. The DgN values shown in these graphs are plotted in the conventional unit of millirad per roentgen, as opposed to millirad per photon as in The curves in this graph can be read directly when assessing DgN for monoenergetic beams.

High-Energy Polyenergetic Beams
Figure 11 illustrates the D_gN values for polyenergetic x-ray beams in the general diagnostic energy region. Figure 11a shows results for the 0% glandular breast, and Figure 11b shows results for the 100% glandular breast. The x-ray spectra used for these calculations were generated by using a spectral model developed by the author (26). General radiographic (tungsten anode) x-ray spectra were computed from 40 to 120 kV, with the assumption of a 5% kilovoltage ripple (approximating an inverter generator), and with 2.5 mm of added aluminum filtration. The HVL ranged from 1.6 mm aluminum at 40 kV to 5.0 mm aluminum at 120 kV, with an approximately linear relationship (r² = 0.998) between HVL and kilovolt level, where kV = 23.318 x HVL - 0.237. This relationship can be used to convert HVL values to the kilovolt values in Figure 11.

View larger version (35K): [in this window] [in a new window]   Figure 11a. Graphs show DgN values for conventional polyenergetic x-ray beams in which a tungsten anode and 2.5 mm of added aluminum filtration are used. DgN values are shown for (a) 0% glandular breasts and (b) 100% glandular breasts.

View larger version (37K): [in this window] [in a new window]   Figure 11b. Graphs show DgN values for conventional polyenergetic x-ray beams in which a tungsten anode and 2.5 mm of added aluminum filtration are used. DgN values are shown for (a) 0% glandular breasts and (b) 100% glandular breasts.

	DISCUSSION

TOP Abstract Introduction MATERIALS AND METHODS RESULTS DISCUSSION Appendix 1 References

 
In this study, Monte Carlo techniques were used to calculate D_gN values. As validation of the procedures used here, D_gN values for conventional mammographic spectra were compared with the results of the seminal work of Dance (5) and Wu et al (4). The comparison with Dance's results showed agreement within about 1%, and comparisons with the data of Wu et al showed agreement within a range of about 1%–6%, depending upon breast glandularity. The influence of skin thickness was evaluated (Fig 8), and it was seen that a difference of 1 mm in skin thickness (eg, 3-mm instead of 4-mm skin thickness) had an influence of approximately 7% on the D_gN values and that a difference of 2 mm (eg, 2-mm instead of 4-mm skin thickness) had an influence of 15%. As a consequence, the difference between the D_gN values of Wu et al and those in the present study is smaller than typical differences in skin thickness.

Once the results of the present study had been verified against existing results for conventional x-ray spectra, the methods were used to extend D_gN Monte Carlo calculations to 120 keV. A series of tables for possible mammographic spectral candidates has been provided to allow direct calculations of breast dose. Monoenergetic results also were computed and are presented in Figure 10. These data may be useful for computing the D_gN values for arbitrary x-ray spectra, including those that may be useful for dual-energy mammography in the high-energy region.

Mammography as a modality continues to mature, and, at present, there are several digital mammography systems nearing the marketplace. Digital images allow the ability to retrospectively manipulate the displayed contrast. While it is impossible to recover subject contrast that is not recorded by the detector, it is thought that the ability to enhance displayed contrast retrospectively will be useful in improving image contrast in the clinical setting. If this assumption proves to be true after experience, it is likely that some compromises in subject contrast may be appropriate under some circumstances. For example, in women with larger breasts, where dose levels are much higher, a shift to harder x-ray spectra may be effective, and this is one reason why tungsten anodes with higher-atomic-number filtration are under investigation (and why the relevant D_gN values are reported here). At least one design under commercial investigation involves a scanning slot beam of x rays; such a design places high heat-loading demands on the x-ray tube. Tungsten is a remarkable anode material because of its high melting point, and this is another reason why tungsten may become more common in some digital mammography systems. To be fully evaluated, new spectra with unconventional anode and filter materials will be studied for their influence on both image quality and patient dose. The D_gN values reported here may be useful toward that end.

It is likely that alternate spectra will continue to be studied to determine whether further optimization of the mammographic examination can be achieved, given various new technologic developments. Furthermore, there is a small group of women who have a compressed breast thickness exceeding 8 cm; in these cases, D_gN tables were not available, and, for such cases, x-ray spectra have not been optimized.

This study was intended to provide clinical medical physicists, as well as researchers, with the tools needed to calculate glandular breast dose for any arbitrary x-ray spectra in a simple but accurate manner. Efforts to computer fit these curves with adequate precision proved to be unsuccessful; therefore, the raw data in Figures 9 and 10 and in Tables 1–12 will be made available to all interested parties via e-mail request.

	Appendix 1

TOP Abstract Introduction MATERIALS AND METHODS RESULTS DISCUSSION Appendix 1 References

 
The elemental compositions and densities of breasts with different glandular proportions and of skin are given in Table A1.

	Acknowledgments

 
Dermott Cullen, PhD, of the Lawrence Livermore National Laboratory (Livermore, Calif) was most helpful in discussions concerning the use of the TART97 code, and his contribution to this study is gratefully acknowledged.

	Footnotes

 
Abbreviations: D_gN = normalized glandular dose HVL = half-value layer f(E) = fractional energy absorption Mo-Mo = molybdenum anode–molybdenum filter Mo-Rh = molybdenum anode–rhodium filter Rh-Rh = rhodium anode–rhodium filter W-Ag = tungsten anode–silver filter W-Pd = tungsten anode–palladium filter W-Rh = tungsten anode–rhodium filter

See also the editorial by Kimme-Smith (pp 7–10 ) in this issue.

Author contribution: Guarantor of integrity of entire study, J.M.B

	References

TOP Abstract Introduction MATERIALS AND METHODS RESULTS DISCUSSION Appendix 1 References

 

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