Effective radiation attenuation calibration for breast density: compression thickness influences and correction
© Heine et al; licensee BioMed Central Ltd. 2010
Received: 6 May 2010
Accepted: 16 November 2010
Published: 16 November 2010
Calibrating mammograms to produce a standardized breast density measurement for breast cancer risk analysis requires an accurate spatial measure of the compressed breast thickness. Thickness inaccuracies due to the nominal system readout value and compression paddle orientation induce unacceptable errors in the calibration.
A thickness correction was developed and evaluated using a fully specified two-component surrogate breast model. A previously developed calibration approach based on effective radiation attenuation coefficient measurements was used in the analysis. Water and oil were used to construct phantoms to replicate the deformable properties of the breast. Phantoms consisting of measured proportions of water and oil were used to estimate calibration errors without correction, evaluate the thickness correction, and investigate the reproducibility of the various calibration representations under compression thickness variations.
The average thickness uncertainty due to compression paddle warp was characterized to within 0.5 mm. The relative calibration error was reduced to 7% from 48-68% with the correction. The normalized effective radiation attenuation coefficient (planar) representation was reproducible under intra-sample compression thickness variations compared with calibrated volume measures.
Incorporating this thickness correction into the rigid breast tissue equivalent calibration method should improve the calibration accuracy of mammograms for risk assessments using the reproducible planar calibration measure.
Breast density is a significant breast cancer risk factor [1–3]. When estimating breast density from mammograms, the breast is considered as a two-component model consisting of adipose and fibroglandular (abbreviated as glandular hereafter) tissue to varying degrees. One method of measuring breast density uses binary labeling resulting in areas of radiographically dense tissue (glandular tissue) or adipose (non-dense) tissue. Breast density is then estimated as the ratio of the radiographically dense area to the total breast area (dense + adipose) [4–6]. Binary labeling techniques have repeatedly produced a measure that correlates well with breast cancer  without considering inter-image acquisition technique differences.
Recent work has focused on calibration to compensate for differences in the inter-image acquisition technique [7–15]. Calibration produces various standardized data representations by adjusting for variations in the target/filter combination, x-ray tube voltage, radiation exposure, and compressed breast thickness. By reducing measurement variation, calibration should produce a breast density measure that shows a stronger association with breast cancer in comparison with measurements derived without calibration. Moreover if the calibration measures prove viable, breast density assessments can be automated. Additionally, calibration applied at the local level supports the analysis of the calibrated measure's spatial distribution across the breast field of view that is not supported by the binary measure of breast density. In contrast, recent work [16, 17] indicates that calibrated measures of breast density do not produce risk associations stronger than those produced without calibration. We hypothesize, calibration techniques will require further investigation and modification before they prove useful.
We have built our approach [8, 9, 18] upon earlier calibration work  in full field digital mammography (FFDM) to produce a normalized effective radiation attenuation coefficient representation for breast density. This work was developed under the assumption that known phantom heights corresponded with the mammography system compressed breast thickness digital readout value. Preliminary analyses showed that this assumption was not valid. Inaccurate compressed breast thickness represents an ongoing technical challenge in calibrated breast density research [19–21].
This paper addresses compressed breast thickness inaccuracies using deformable phantoms with the following objectives: (1) develop and evaluate a compressed breast thickness correction method that can be incorporated into the rigid breast tissue equivalent phantom calibration model, and (2) compare calibration representation reproducibility under compression thickness variations using known compositions. We used a surrogate breast model because the volumetric compositions were fully specified.
To address the study objectives, a method was derived from the calibration methodology to characterize the compressed sample's spatial thickness variation. This method was evaluated under controlled conditions using modified (rigid) breast tissue equivalent phantoms with known height variations before addressing deformable samples. The rigid phantoms used for this work were purchased from Computerized Imaging References Systems (CIRS, Norfolk VA) and were described in our previous report . These phantoms (non-modified) are standards in calibration research. We coupled this spatial thickness characterization with mechanical measurements of the compression paddle to construct a correction. The correction was evaluated within the calibration application using an alternative two-component deformable phantom model constructed with water and oil filled balloon phantoms that replicated patient imaging. We investigated the compression behavior similarity between mammograms and these deformable phantoms. This alternative model was then used to investigate the calibration representation reproducibility while varying the compression thickness.
Imaging was performed with a General Electric Senographe 2000 D FFDM system, which is used for routine breast cancer screening examinations. The detector specifics were described previously . All phantom images were acquired as left craniocaudal (LCC) views using a Molybdenum/Molybdenum target/filter combination and 26 kV x-ray tube voltage with 160 mAs, where mAs is the system readout value for the generated radiation. An extensive array of acquisition techniques was not required to validate and illustrate the main principles. The image data matrix is 1914 × 2294 pixels. A standard (x, y) positive coordinate system was used with the origin, (0, 0), located at the bottom left hand-corner of the displayed image, where × and y locations are integer valued pixel coordinates ranging from 0-1903 and 0-2293, respectively. The outside detector edge defined the y-axis (vertical direction). The following definitions were used below: xmax = 1903, and ymax = 2293. This system produces both raw and processed image data for display (for presentation) purposes. Raw image data, represented by r(x, y) below, was used for this work. This system is equipped with 15 × 20 cm2 rigid compression paddle. The system compression force changes in 10 N increments with a minimum system readout value of 30 N (the first system readout value above 0.0). The system digital compression thickness readout value, defined as ts below, is cited in cm.
Equations (2) and (5) are planar representations. Spatial averaging [Eq. (2) or Eq. (5)] gives either the average percent glandular, <PG >, composition or equivalently the average effective radiation attenuation coefficient, < μe >, for the sample, respectively.
Inaccurate Compression Thickness
Inaccurate calibration of mammograms stems from applying Eqs. (1-4) to an arbitrary logarithmic response with the incorrect compression thickness. Thickness inaccuracies are due to both the compression paddle deformation/tilt and inaccurate (nominal) system compression thickness digital readout value. There is a rigid/non-rigid misalignment between the non-compressible tissue equivalent phantoms used to generate the height dependent calibration data, which have precise heights and plane surfaces, and the compressed breast thickness determined by the system value. We replicated this misalignment (described below in more detail) with deformable phantoms for the calibration data generation, estimating the compression thickness variation, and evaluating the thickness correction with calibration accuracy comparisons.
Related Calibration Representations
The above expression is equivalent to <PG >/100, which has different dimensionality compared with Eq. (7). A similar [Eq. (8)] breast density representation  results using the total glandular height normalized by the total breast height (approximated by nT above). We compared these representations below.
Thickness Variation Characterization
The logarithmic-intercept was eliminated because it is influenced by height uncertainty. Equation (11) gives the relative height variation from × = x0 to × = x0 +n pixels, orthogonal to the y-axis at a given y location. A one-dimensional profile is determined by letting n become an integer variable defined over a given x-range. The two-dimensional relative height surface
[H(x, y) ] was derived by applying Eq. (11) over an extended y-range. The H(x, y) surface describes the relative height (lower surface) of the compression paddle warp/deformation. We let x0 = 0, which keyed the analysis to x0 = 0 (detector/paddle front-edge). To reduce variation, operations along the × direction were performed using the average of a sliding 10 pixel window, maneuvered without overlap. The approach was applied along the y-direction by substituting y and Δy for × and Δx in the above development.
Thickness Variation Characterization Evaluation Methods
Modified breast tissue equivalent phantom characterization
1 mm slant
2 mm slant
3 mm slant
4 mm slant
Non-rigid Breast Simulating Phantoms
Phantoms were constructed to approximate the shape and deformable behavior of breast tissue. Breast tissue is assumed deformable but non-compressible . We use compress herein to imply the compression paddle operated and the phantom (or breast) deformed accordingly. Thick walled balloons were filled with either distilled water (water), vegetable oil (oil), or water/oil mixtures with known proportions to simulate breast compression.
The breast (CC orientation) is a deformable organ that is relatively pliable. Therefore, the paddle plane was treated as a plate that warps when loaded. The applied compression force is a measure of the sample's resistance (load) to deformation distributed over the contact area transmitted through the strained paddle to the compressor arm. It is the rigidity/elasticity of the paddle plane in combination with that elastic resistive force offered by the compressed sample that determines the final paddle warp (bulge) required for static equilibrium during imaging. Although the breast is a complicated mixture of tissue with varying elastic properties, as an approximation we assume the entire organ behaves as composite deformable body with its own global elastic property. This is supported by earlier work showing that breast compression and mammographic density are unrelated . To show that the deformable phantoms reasonably approximate the resistance offered by the breast undergoing compression, two requirements should hold: (1) the applied force and paddle contact area should be approximately coincident, and (2) the contact area geometry should be similar. Thus, the actual compression thickness similarity is irrelevant for this comparison. If we assume the paddle surface lies in a plane with a given surface area when not stressed, the corresponding warped (stressed) surface will have a slightly greater surface area than that calculated with its x-y dimensions due to the curvature induced by load. In the area calculations, we used the x-y planar dimensions of the paddle, which neglects the increased surface area.
Compression Paddle Measurements
Paddle Deformation Characterization
A set of six water filled phantoms was imaged over a range of compression forces resulting in 35 images. These were used to characterize the compression thickness spatial variation due to the compression paddle plane deformation (bending or warping) by applying the H(x, y) analysis. In this analysis, we used the estimated regression parameters for water (k = w) to estimate the H(x, y) surface [see Eqs. (9-11)] because the phantom conforms to the warped compression paddle surface (the compression thickness surface). These phantoms were filled with arbitrary volumes of water ranging from 500-1200 ml to simulate various breast sizes as shown in Figure 2. The analysis was constrained to the outlined regions to avoid the curvature regions. These regions were 500 ×500 pixels or larger. Phantoms were imaged over a range of compression forces (summarized below). Phantoms were placed on the breast support surface in the central portion of the detector in the y-direction by observation to simulate patient positioning. The effective radiation attenuation coefficient for water was estimated with methods described below using the Eq. (1) form as the regression model. The H(x, y) method was used to locate the maximum bulge heights and positions. Regression analysis was used to determine the relationships between the compression force and the paddle bending characteristics.
The thickness correction was developed using the two forms of measurements outlined above after validating the H(x, y) approach. The paddle bending summaries (from above) were joined with the paddle perimeter measurements. These measures, in combination, were used as boundary conditions to construct the polynomial thickness correction as a function of compression force.
Alternative Calibration Model and Correction Evaluation Methods
Standardized Representations Analysis
We used the alternative two-component system to investigate the various calibration representations and determine their reproducibility under varying compression forces. The 34/66 mixture was calibrated for three system compression readout thicknesses: 5.0 cm, 4.4 cm, and 3.8 cm. This simulated imaging the same patient at different times with varying compression forces. The total glandular volume, average glandular-volume/pixel, and percent glandular representations were calculated using Eqs. (2-8) and compared. The similarity between the effective x-ray attenuation coefficient representation expressed in Eq. (5) and the percent glandular representation expressed in Eq. (2) was demonstrated with regression analysis by calibrating the 34/66 mixture over a range of compression thicknesses. Both the percent glandular and glandular descriptions are used below for consistency with the understanding that they apply to water content for this work only.
Thickness Variation Characterization Validation
was used for comparison, where HT(x, y) is the respective theoretical relative surface generated with the known constant height gradient for a given slant-phantom. The d(x, y) pixel distributions were summarized for all examples in Table 1. The average deviation of d(x, y) was generally less than 0.5 mm and not dependent upon the total phantom height.
Compression Paddle Assessment
Paddle Deformation Characterization
Bulge height and compression force regression analysis
bulge height (hm)
Water filled phantom characteristics
Comp. Force (N)
max x-distance (mm)
Thickness Correction Construction
where the coefficient subscripts include the y dependency for given profile. For fixed y, the coefficients were defined with these boundary conditions: (1) tc(0, y) = tx(0), (2) tc(xmax, y) = tx(xmax), (3) tc(xm, y) = R(xm, y), and (4) ∂tc/∂x = 0 at × = xm. A 20 pixel constant (relative) height margin (x = 0-19) was set equal with tx(0) to approximate the rigidity of the paddle front-edge. This was neglected at the other three perimeter segments due to the large distances from the bulge height position. The corrected compressed sample thickness in cm was expressed as t(x, y) = ts + tc(x, y).
Thickness Correction Evaluation
We evaluated the compressed thickness correction within the calibration application.
Calibration regression parameters
< μ >
< Log-Intercepts >
The 34/66 calibration mixture example # 1
34/66 calibration # 1
The 31/69 mixture calibration example.
The 34/66 calibration mixture example # 2
34/66 calibration # 2
Calibrated Representation Comparison
We compared the percent glandular (PG) and volumetric representations using Eqs. (7-8) with the polynomial correction for three system thickness readout values: 5.0 cm 4.4 cm and 3.8 cm. We retained the usage of glandular for comparison purposes, although water content was determined in various forms. The analysis was applied to the ROI (34/66 mixture) shown in Figure 11 (left) and in Figure 12. Using Eq. (7), the respective average glandular-volume/pixel quantities were estimated as [0.196, 0.175, 0.155] mm3/pixel, whereas the respective total glandular volumes were [101.9, 91.4, 80. 8] ml. These volumetric quantities changed significantly for the selected volume, whereas the PG representation was consistent (Table 5). To emphasize this finding, total fluid volumes for these examples were also estimated as [288.0, 257.9, 227.5] ml respectively. Using Eq. (8), the respective planar spatial summaries are given by: <PG> = 101.9/288.0 × 100 = 35.3, <PG> = 91.4/257.9 × 100 = 35.4, and <PG> = 80.8/227.5 ×100 = 35.5 These examples show the validity of Eq. (8) and that the PG representation is consistent with respect to thickness variations caused by applied compression force variations (Table 5).
The inaccurate compression thickness problem was addressed as two separate components (1) the paddle tilt due to play in the mechanical connection, which was not dependent upon the compressed sample, and (2) the paddle bulge (flex) due its elasticity and the compressed sample's resistance. Serial mechanical measurements of the paddle perimeter were approximately invariant and within ±1.0 mm precision. The H(x, y) analysis was evaluated under known conditions (precision ≤ 0.5 mm), and then used to estimate the paddle bulge. The paddle tilt and bulge assessments were used as boundary conditions for the cubic polynomial thickness correction.
We evaluated the thickness correction using methods that duplicated the rigid/non-rigid misalignment. Figure 10 shows agreement between the compressed behavior of patient mammograms and the deformable (water) phantoms. The overlap in the region between 3-8 dN illustrates the similarity. The relative calibration (average) error was reduced to 7% from 48-68% when applying the thickness correction (Tables 5, 6, 7. The thickness-corrected calibration results were in agreement with the known percent glandular (PG) quantities and within the margin of composition uncertainty. When comparing the static correction findings with those estimated with the surface correction, the latter produced calibration quantities that were closer to the known values. However, the static correction accounted for a greater portion of the overall deviation as gauged by comparing the PG and PGs+5 entries with the PGs entries (Table 5 and Table 6). This is expected because the static correction is embedded within the surface correction. The mechanical correction component was not heavily dependent upon the phantom - breast similarity. To emphasize these overall improvement gains, the average relative difference between the known and measured PG composition quantities is provided parenthetically in the first column for each of the three calibration examples (Tables 5, 6, 7). The accuracy improvements are due to the overall (average) corrected thickness precision, which was approximately within ±1 mm (Table 5). To evaluate the replication properties of both the phantom construction and the correction, the 34/66 mixture was repositioned, imaged, and calibrated, which resulted in similar findings (Table 7). The thickness correction was evaluated further by measuring the calibration parameters over a wide-area in the reference phantoms (Figure 4). The agreement between the wide-area parameters (with the correction) and those parameters measured from the strip regions (Table 4) shows the validity of the correction. In contrast, when there is thickness inaccuracy, the intercepts showed marked variation as demonstrated by comparing corrected quantities (generated from the same wide-area) with the non-corrected quantities (Table 4). We presented these findings in the PG representation because it was reproducible with respect to intra-sample thickness variations, in contrast with other volume measures.
Inaccurate compressed breast thickness is a known source of uncertainty in calibration research. Optical stereoscopic photogrammetry (OSP) methods [20, 21] using stereo triangulation are also under investigation to address this problem. One variation mounted the OSP device on the mammography unit to make compressed breast measurements , which may not be of practical use in the clinical setting . Another variation used OSP measurements of various breast models under compression to generate a thickness correction . Mawdsley et al  found the maximum paddle height occurs at 20 mm from the chest wall (at the y-midpoint) using a system with a specific tilt-paddle. In contrast, our findings (Table 3) show the maximum occurs approximately 57 mm from the chest wall. These findings may not be directly comparable because of the differing paddle connection and operating mechanisms. Varying tilt orthogonal to the chest wall position will impact the maximum paddle height position. If the paddle front edge is fixed while increasing the tilt angle (lowering the paddle at × = xmax), the bulge height maximum position will shift towards the chest-wall position. Moreover, the plane of the paddle used for our work has an upward curvature (about 1 mm crown) when resting with the maximum at approximately 73-75 mm from the chest wall slightly below the y-midpoint. The central portion of the paddle-plane also has slight but noticeable membrane characteristic when flexed with small forces. Our bulge height positions are consistent with the outer breast-paddle contact distance (~81 mm for breast and 86 mm for phantoms) when considering the plane of the paddle behaves as a deformed (bent) thin plate  with the load changing from a distributed load to no-load past the paddle-sample contact area. Our findings agree with Mawdsley et al  in that (1) the linear correction offers improved accuracy because (in this case) the offset with the system readout thickness and paddle tilt induce more variation than the paddle flex, and (2) in general there can be a significant deviation between the system readout value and the actual compressed breast thickness that requires correction. Other researchers investigated thickness inaccuracies using radio-opaque markers and magnification geometry,  which showed negligible deformation parallel to the chest wall and upward tilt from the breast periphery to the chest wall but to a much larger degree than indicated by Eq. (13). Our findings agree, in part, with these researchers  in that the deformation (near × = 0 only) parallel to the chest wall position was small; this related work did not address paddle bulge in the direction orthogonal to the chest wall position.
The calibration representation comparison showed the similarities and differences between percent glandular (PG) and related calibrated volume and height measures. The PG representation is a planar measure that is equivalent to both the normalized volumetric  and the normalized height  measurements in summary, suggesting the definitions used in the literature are not uniform. The total volume representations varied under the assumptions made here, whereas the PG measure was consistent under thickness variations for the same sample. Similar arguments apply to the total glandular height representation  as well.
We developed an alternative model to meet the study objectives because the phantom compositions were known. This eliminated uncertainty but its applicability relies on the similarity of the surrogate phantoms with the original model. When using mammograms to evaluate the various relationships, the compositions are unknown. Some researchers use binary labeled (breast density) mammograms [13, 20] or tissue measures derived from other imaging modalities  in the calibration developmental work, which could introduce uncertainty. In the final validation analysis, the various calibrated measures will require a known cancer/no-cancer (CNC) endpoint to show measurement association. The developmental work could use the CNC endpoint as class separation optimization criterion for making correction adjustments, but this would preclude using the same data for independent association validation. It is less-costly to develop alternative strategies to develop and assess calibration modifications because properly designed databases that include cancer patients are time consuming and expensive to construct. The best approach is still an open ended inquiry because there is little evidence at this time showing that calibrated measurements are efficacious.
The evaluation was performed with phantoms that behaved similar to that of compressed breast deformation, which is a coarse approximation. The effect of skin thickness, (if any) on the calibration accuracy was not addressed because the stretched balloon thickness was negligible compared to skin thickness, which is on the order of ~1-3 mm . The overall analysis could be improved with better phantom construction methods using manufacturing techniques. The paddle bulge assessments provided an empirical (averaged) solution to loaded thin plate problem. Alternatively, the warp of the paddle plane could be estimated using numerical methods derived from plate theory  by (1) considering the paddle plane (thin-plate) loading of each breast separately, and (2) determining the appropriate loading geometry (eroded breast silhouette) and paddle perimeter boundary conditions. Future work includes exploring these more formal techniques of modeling the loaded paddle that could eliminate the need for the deformable breast surrogate models. Nevertheless while the deformable phantoms were less than perfect, the work showed that the thickness correction improved the calibration accuracy dramatically. Our preliminary studies were performed with homogenous phantoms, which are reasonable surrogates for developmental work but are not capable of capturing either the tissue heterogeneity present in mammograms or chest wall compression interaction. The final validation of the percent glandular measure will require a cancer/no-cancer endpoint comparison.
The work was supported by NCI grant #R01 CA114491. The authors would like to thank Autumn Smallwood, Christy Smallwood, Gail Tiffenberg, and all of the staff at the Lifetime Cancer Screening Center at the Moffitt Cancer Center for their support of this experimental work. The authors also thank Drs. Elsie Gross, Ambuj Kumar, and Srinivas Nagaraj for reviewing the manuscript and providing invaluable suggestions that improved the presentation.
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