Automated Percentage of Breast Density Measurements for Full-field Digital Mammography Applications

Rationale and Objectives

Increased mammographic breast density is a significant risk factor for breast cancer. A reproducible, accurate, and automated breast density measurement is required for full-field digital mammography (FFDM) to support clinical applications. We evaluated a novel automated percentage of breast density measure (PD a ) and made comparisons with the standard operator-assisted measure (PD) using FFDM data.

Methods

We used a nested breast cancer case–control study matched on age, year of mammogram and diagnosis with images acquired from a specific direct x-ray conversion FFDM technology. PD a was applied to the raw and clinical display (or processed) representation images. We evaluated the transformation (pixel mapping) of the raw image, giving a third representation (raw-transformed), to improve the PD a performance using differential evolution optimization. We applied PD to the raw and clinical display images as a standard for measurement comparison. Conditional logistic regression was used to estimate the odd ratios (ORs) for breast cancer with 95% confidence intervals (CI) for all measurements; analyses were adjusted for body mass index. PD a operates by evaluating signal-dependent noise (SDN), captured as local signal variation. Therefore, we characterized the SDN relationship to understand the PD a performance as a function of data representation and investigated a variation analysis of the transformation.

Results

The associations of the quartiles of operator-assisted PD with breast cancer were similar for the raw (OR: 1.00 [ref.]; 1.59 [95% CI, 0.93–2.70]; 1.70 [95% CI, 0.95–3.04]; 2.04 [95% CI, 1.13–3.67]) and clinical display (OR: 1.00 [ref.]; 1.31 [95% CI, 0.79–2.18]; 1.14 [95% CI, 0.65–1.98]; 1.95 [95% CI, 1.09–3.47]) images. PD a could not be assessed on the raw images without preprocessing. However, PD a had similar associations with breast cancer when assessed on 1) raw-transformed (OR: 1.00 [ref.]; 1.27 [95% CI, 0.74–2.19]; 1.86 [95% CI, 1.05–3.28]; 3.00 [95% CI, 1.67–5.38]) and 2) clinical display (OR: 1.00 [ref.]; 1.79 [95% CI, 1.04–3.11]; 1.61 [95% CI, 0.90–2.88]; 2.94 [95% CI, 1.66–5.19]) images. The SDN analysis showed that a nonlinear relationship between the mammographic signal and its variation (ie, the biomarker for the breast density) is required for PD a . Although variability in the transform influenced the respective PD a distribution, it did not affect the measurement’s association with breast cancer.

Conclusions

PD a assessed on either raw-transformed or clinical display images is a valid automated breast density measurement for a specific FFDM technology and compares well against PD. Further work is required for measurement generalization.

Mammographic breast density is a significant breast cancer risk factor . Many of the breast density research studies to date have been based on an operator-assisted measure (PD) to estimate the percentage of breast density within a mammogram. There are various methods under development to automate the estimation of breast density . Developing a fully automated and standardized breast density measurement has proven somewhat difficult, but at least two commercial standardized measures are available for raw full-field digital mammography (FFDM) images: Volpara and Quantra . However, these have not been shown to be associated with breast cancer risk to date.

Although there are various FFDM manufacturers, the two predominant FFDM technologies used today consist of direct and indirect x-ray conversion systems that produce images with different characteristics. The data representation produced by FFDM systems may vary because of the x-ray detection technology, x-ray generation, or postacquisition processing. FFDM systems produce both raw and clinical display (ie, processed) representation mammograms. A given clinical display, or processed image, is derived from its respective raw image with methods developed by the unit’s manufacturer. The raw images are normally not considered in the clinical evaluation. When applying automated methods, it is not clear if both representations result in similar breast density measurements, if there is a preferred representation, or what impact the technology plays.

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Methods

Study Population and Mammography

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Statistical Analysis

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Operator-assisted Percentage of Density

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Automated Percentage of Breast Density

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r0i=d1+f1. r

In Equation 1, the subscript, i , defines the three data representations: i = r for raw image, i = t for the raw-transformed image, and i = p for the processed clinical display image. The d 1 and f 1 images are complementary high and low half-band filtered versions (filter outputs) of r 0 i . When the raw image dimension is n x × n y pixels (in the x and y direction), the expansion images have the same dimension.

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Preprocessing

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r0t=a0[(m0×r0r)+1]k, r

[

(

)

]

where a 0 and k are parameters determined with the optimization procedure. The pixel values of r 0 r were first linearly mapped between (0, 1) before applying Equation 2 . The m 0 factor is an empirically determined scaling constant ≈101 that constrains the pixel values to the allowable dynamic range and was derived by generalizing the normalization method used in our calibration research work . The m 0 factor is the average current × time (milliampere-second) system readout from a random sample of mammograms. The form of the denominator (addition of one) prevents pixel values in r 0 t from reaching infinity. Equation 2 defines the raw-transformed image representation. We used this 30-image data set to determine these two unknown parameters using an evolutionary optimization strategy .

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Signal-dependent Noise Analysis

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y=c0+c1x+c2x2+c3x3+c4exp(−z)2, y

exp

(

−

)

where y is the local noise variance, x is corresponding local signal, z=x−c5c6 z

−

6 , and the c__i are the fit coefficients. Equation 3 is a general expression that was tailored to each representation by initial observation using the 30-image data set discussed previously. For the raw data ( i = r ), we set c 3 = c 4 = c 5 = c 6 = 0; for the raw-transformed data ( i = t ), we set c 4 = c 5 = c 6 = 0; and for the processed data ( i = p ), we set c 3 = 0. Both the signal and noise values were mapped between (0, 1) before applying the curve-fitting analysis. Representative examples are provided to show the differences. We also summarized each representation’s fit-coefficient distributions with the mean (taken over all images) and 95% CIs. For our purpose, c 0 is a bias term used as degree of freedom or flexibility in the fitting processes, and is not discussed in detail.

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Results

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Table 1

Patient Characteristics: Distribution of Relevant Patient Characteristics (Variable) and Breast Density Measures for the Cases, Controls, and Overall

Variable Case ( n ) Mean SD Control ( n ) Mean SD Total ( n ) Mean SD_P_ Value Age (years) 192 64.2 10.6 358 64.3 10.6 550 64.3 10.7 — BMI (kg/m 2 ) 188 29.0 6.4 335 28.8 6.2 523 28.9 6.3 .81 PD a (trans) 192 21.0 7.3 358 19.1 7.3 550 19.8 7.4 .002 PD a (proc) 192 19.1 7.9 358 16.9 7.5 550 17.6 7.7 .0005 PD (raw) 192 15.0 12.1 358 13.6 12.5 550 14.1 12.4 .17 PD (proc) 192 18.1 10.3 358 16.9 10.0 550 17.4 10.1 .15

BMI, body mass index.

The breast density measures include 1) the automated percentage of breast density measure (PD a ) applied to the raw-transformed images (trans); 2) PD a applied to the clinical display processed images (proc); 3) operator-assisted percentage of breast density measure (PD) applied to the raw images (raw); and 4) PD applied to the clinical display processed images. The mean and standard deviation (SD) are provided for each characteristic. Breast density quantities are percentages. The respective case–control quantities were compared using conditional logistic regression (Wald test).

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Table 2

Percentage of Breast Density Associations with Breast Cancer

Control ( N ) Case ( N ) Unadjusted Adjusted with BMI PD a raw-transformed Quartile 1 [3.98–13.41] 89 30 1.00 1.00 Quartile 2 [13.41–18.14] 90 40 1.26 (0.73–2.18) 1.27 (0.74–2.19) Quartile 3 [18.14–23.82] 89 50 1.85 (1.05–3.26) 1.86 (1.05–3.28) Quartile 4 [23.82–38.47] 90 72 2.93 (1.64–5.22) 3.00 (1.67–5.38) Az 0.605 (0.569-0.643) 0.606 (0.549-0.654) Per 1 SD increase 1.39 (1.13–1.70) 1.40 (1.14–1.71) Az 0.606 (0.559-0.648) 0.597 (0.550-0.647) PD a processed Quartile 1 [2.99–10.72] 89 27 1.00 1.00 Quartile 2 [10.72–15.80] 90 50 1.80 (1.04–3.12) 1.79 (1.04–3.11) Quartile 3 [15.80–22.14] 89 44 1.61 (0.90–2.88) 1.61 (0.90–2.88) Quartile 4 [22.14–35.37] 90 71 2.89 (1.64–5.09) 2.94 (1.66–5.19) Az 0.602 (0.553-0.647) 0.610 (0.565-0.655) Per 1 SD increase 1.42 (1.16–1.72) 1.43 (1.17–1.74) Az 0.603 (0.560-0.652) 0.600 (0.548-0.649) PD raw Quartile 1 [0.00–4.81] 89 35 1.00 1.00 Quartile 2 [4.81–10.09] 90 50 1.48 (0.88–2.49) 1.59 (0.93–2.70) Quartile 3 [10.09–18.69] 89 49 1.46 (0.85–2.51) 1.70 (0.95–3.04) Quartile 4 [18.69–76.84] 90 58 1.70 (1.00–2.87) 2.04 (1.13–3.67) Az 0.553 (0.520-0.599) 0.575 (0.523-0.624) Per 1 SD increase 1.14 (0.94–1.39) 1.21 (0.97–1.51) Az 0.567 (0.508-0.624) 0.566 (0.507-0.619) PD processed Quartile 1 [1.11–9.63] 89 39 1.00 1.00 Quartile 2 [9.63–15.07] 90 51 1.28 (0.77–2.13) 1.31 (0.79–2.18) Quartile 3 [15.07–21.39] 89 40 1.04 (0.61–1.76) 1.14 (0.65–1.98) Quartile 4 [21.39–67.10] 90 62 1.68 (1.00–2.83) 1.95 (1.09–3.47) Az 0.563 (0.523-0.601) 0.573 (0.526-0.622) Per 1 SD increase 1.15 (0.95–1.38) 1.22 (0.98–1.51) Az 0.551 (0.502-0.599) 0.551 (0.500-0.603)

BMI, body mass index; CI, confidence interval; SD, standard deviation.

This table provides the quartile and continuous breast density associations with breast cancer for 1) the automated measure (PD a ) applied to the raw-transformed ( top left ) and processed clinical display ( bottom left ) representation images and 2) the operator-assisted measure (PD) applied to the raw ( top right ) and processed clinical display ( bottom right ) representations images. Breast density quantities are percentages. Odds ratios are given with 95% CIs parenthetically and the area under the receiver operating characteristic curve (Az) is provided for each model with 95% CIs. Az was calculated within matched case–control pairs to use the design. SD is calculated from the control distribution.

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Table 3

Correlation Coefficients

Measurement PD raw PD proc PD a raw-trans PD a proc PD raw 1.00 0.73 0.37 0.46 PD proc 0.73 1.00 0.38 0.43 PD a raw-trans 0.37 0.38 1.00 0.87 PD a proc 0.46 0.43 0.87 1.00

PDa, automated percentage of breast density measure; PD, the operator-assisted measure.

This table lists the inter- and intra-measure Pearson correlation coefficients for PD and PD a . PD was applied to the raw and clinical display processed images (proc), whereas PD a was applied to the raw-transformed (raw-trans) and processed (proc) images.

Table 4

Signal-dependent Noise Model Coefficients

Coefficients Image Representation raw raw-trans proc c 0 0.140 (0.130–0.150) 0.019 (0.017–0.021) −0.111 (−0.116 - −0.106) c 1 0.455 (0.410–0.501) 0.274 (0.255–0.293) 3.001 (2.926–3.076) c 2 0.131 (0.098–0.164) 0.339 (0.265–0.414) −2.265 (−2.390 - −2.141) c 3 — 0.106 (0.047–0.165) — c 4 — — −0.433 (−0.538 - −0.328) c 5 — — 1.038 (1.016–1.060) c 6 — — 0.083 (0.064–0.102)

The table provides the summarized signal-dependent noise modeling coefficients for the three data representations modeled with Equation 3 : raw; raw-transformed (raw-trans); and processed clinical display (proc). For each coefficient, the mean over the entire data set is provided. Confidence intervals are provided with each quantity parenthetically. Terms not included in the modeling are marked with dashes in the respective columns.

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Discussion

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Conclusions

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Acknowledgments

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Appendix

Repeated Optimization

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Table 1A

Percentage of Breast Density Associations with Breast Cancer from the Repeated Optimization Trials

PD a Raw Transformed (Min) Control ( N ) Case ( N ) Unadjusted Adjusted with BMI PD a Raw Transformed (Mean) Control ( N ) Case ( N ) Unadjusted Adjusted with BMI PD a Raw Transformed (Max) Control ( N ) Case ( N ) Unadjusted Adjusted with BMI Quartile 1 [1.56–7.25] 89 32 1.00 1.00 Quartile 1 [2.62–10.91] 89 35 1.00 1.00 Quartile 1 [4.06–15.10] 89 35 1.00 1.00 Quartile 2 [7.25–10.94] 90 45 1.42 (0.82–2.46) 1.44 (0.83–2.49) Quartile 2 [10.91–15.61] 90 40 1.13 (0.65–1.98) 1.14 (0.65–2.00) Quartile 2 [15.10–20.85) 90 43 1.19 (0.69–2.06) 1.20 (0.69–2.07) Quartile 3 [10.94–16.08] 89 47 1.52 (0.88–2.64) 1.53 (0.88–2.67) Quartile 3 [15.61–20.79] 89 43 1.29 (0.75–2.24) 1.31 (0.76–2.28) Quartile 3 [20.85–25.02] 89 47 1.36 (0.79–2.34) 1.38 (0.80–2.38) Quartile 4 [16.08–31.94] 90 68 2.45 (1.39–4.32) 2.55 (1.44–4.54) Quartile 4 [20.79–34.42] 90 74 2.35 (1.36–4.06) 2.45 (1.41–4.27) Quartile 4 [25.02–34.98] 90 67 2.05 (1.19–3.54) 2.10 (1.21–3.66) Az 0.58 (0.54–0.63) 0.60 (0.55–0.64) Az 0.59 (0.54–0.63) 0.60 (0.55–0.65) Az 0.59 (0.53–0.62) 0.59 (0.53–0.63) Per 1 SD increase 1.40 (1.15–1.72) 1.44 (1.17–1.77) Per 1 SD increase 1.37 (1.12–1.67) 1.39 (1.13–1.70) Per 1 SD increase 1.26 (1.03–1.53) 1.27 (1.04–1.55) Az 0.62 (0.57–0.66) 0.60 (0.56–0.65) Az 0.60 (0.55–0.64) 0.59 (0.55–0.65) Az 0.59 (0.53–0.64) 0.60 (0.54–0.64)

BMI, body mass index; CI, confidence interval; SD, standard deviation.

This table provides the breast cancer quartile and continuous breast density associations with breast cancer for the automated measure (PDa) applied to the raw-transformed data using the parameter set with the minimum value of k (Min) on the left , parameter set comprised of the distribution averages of both parameters ( middle ), and the set containing the maximum value of k (Max) on the right . Breast density quantities are percentages. Odds ratios are given with 95% CIs parenthetically, and the area under the receiver operating characteristic curve (Az) is provided for each model with 95% CIs. Az was calculated within matched case–control pairs to use the design. SD is calculated from the control distribution.

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Automated Percentage of Breast Density Measurements for Full-field Digital Mammography Applications

Rationale and Objectives

Methods

Results

Conclusions

Methods

Study Population and Mammography

Statistical Analysis

Operator-assisted Percentage of Density

Automated Percentage of Breast Density

Preprocessing

Signal-dependent Noise Analysis

Results

Discussion

Conclusions

Acknowledgments

Appendix

Repeated Optimization

References

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