^{1,a)}, Ke Cao

^{1,b)}and Craig Beam

^{2,c)}

### Abstract

**Purpose:**

Breast density is a significant breast cancer risk factor. Although various methods are used to estimate breast density, there is no standard measurement for this important factor. The authors are developing a breast density standardization method for use in full field digital mammography (FFDM). The approach calibrates for interpatient acquisition technique differences. The calibration produces a normalized breast density pixel value scale. The method relies on first generating a baseline (BL) calibration dataset, which required extensive phantom imaging. Standardizing prospective mammograms with calibration data generated in the past could introduce unanticipated error in the standardized output if the calibration dataset is no longer valid.

**Methods:**

Sample points from the BL calibration dataset were imaged approximately biweekly over an extended timeframe. These serial samples were used to evaluate the BL dataset reproducibility and quantify the serial calibration accuracy. The cumulative sum (Cusum) quality control method was used to evaluate the serial sampling.

**Results:**

There is considerable drift in the serial sample points from the BL calibration dataset that is x-ray beam dependent. Systematic deviation from the BL dataset caused significant calibration errors. This system drift was not captured with routine system quality controlmeasures. Cusum analysis indicated that the drift is a sign of system wear and eventual x-ray tube failure.

**Conclusions:**

The BL calibration dataset must be monitored and periodically updated, when necessary, to account for sustained system variations to maintain the calibration accuracy.

This work was supported by NCI Grant No. R01 CA114491. The authors would like to thank Autumn Smallwood and all of the staff at the Lifetime Cancer Screening Center at the Moffitt Cancer Center for their support of the work.

I. INTRODUCTION

II. METHODS

II.A. Imaging

II.B. Calibration and serial sampling

II.C. Cumulative sum

II.D. Chart constant

II.E. Calibration accuracy

III. RESULTS

III.A. Chart constant estimation

III.B. Decision interval Cusum

III.C. Standard Cusum

III.D. Calibration accuracy

IV. DISCUSSION

V. CONCLUSION

### Key Topics

- Molybdenum
- 80.0
- Calibration
- 65.0
- Medical imaging
- 18.0
- Vacuum tubes
- 16.0
- Mammography
- 8.0

## Figures

The sampling grid to scale. The larger dark rectangle represents the detector. The smaller interior rectangle defines the region where the grid samples were acquired and represents the area that is important for the calibration application. The inner rectangle is centered on the detector in the y-direction with a margin on the left-hand side from the outside of the detector. The smaller sector (smaller squares) numbering is coded (dark light indicates No. 1–8): sector (1, 2, 3) correspond to the top, mid, and bottom samples on the left hand side, sector (4, 5) are the middle top and bottom samples, and sector (6, 7, 8) are on the right hand side from top to bottom, respectively. The individual sector size is .

The sampling grid to scale. The larger dark rectangle represents the detector. The smaller interior rectangle defines the region where the grid samples were acquired and represents the area that is important for the calibration application. The inner rectangle is centered on the detector in the y-direction with a margin on the left-hand side from the outside of the detector. The smaller sector (smaller squares) numbering is coded (dark light indicates No. 1–8): sector (1, 2, 3) correspond to the top, mid, and bottom samples on the left hand side, sector (4, 5) are the middle top and bottom samples, and sector (6, 7, 8) are on the right hand side from top to bottom, respectively. The individual sector size is .

Deviation analysis. This gives the theoretical percent glandular deviation as a function of relative (fractional) logarithmic response (Log-response) shift from the baseline (positive shift) for the adipose tissue equivalent examples: molybdenum/molybdenum (solid), molybdenum/rhodium (cross), and rhodium/rhodium (diamond).

Deviation analysis. This gives the theoretical percent glandular deviation as a function of relative (fractional) logarithmic response (Log-response) shift from the baseline (positive shift) for the adipose tissue equivalent examples: molybdenum/molybdenum (solid), molybdenum/rhodium (cross), and rhodium/rhodium (diamond).

Logarithmic response timelines. These show the logarithmic response (LR) serial samples for the adipose rhodium/rhodium (top) and molybdenum/molybdenum (bottom) timelines. The samples after the x-ray tube replacement start at .

Logarithmic response timelines. These show the logarithmic response (LR) serial samples for the adipose rhodium/rhodium (top) and molybdenum/molybdenum (bottom) timelines. The samples after the x-ray tube replacement start at .

Molybdenum/molybdenum adipose Decision interval (DI) Cusum charts. The top plots show the charts for all regions and the bottom plot shows the charts for all regions. The regions are denoted by these symbols (1) dash, (2) plus sign, (3) asterisk, (4) diamond, (5) triangle, (6) square, (7) multiplication, and (8) circle, respectively, which are also used in the following charts.

Molybdenum/molybdenum adipose Decision interval (DI) Cusum charts. The top plots show the charts for all regions and the bottom plot shows the charts for all regions. The regions are denoted by these symbols (1) dash, (2) plus sign, (3) asterisk, (4) diamond, (5) triangle, (6) square, (7) multiplication, and (8) circle, respectively, which are also used in the following charts.

Molybdenum/molybdenum glandular decision interval Cusum charts.

Molybdenum/molybdenum glandular decision interval Cusum charts.

Rhodium/rhodium adipose decision interval Cusum charts.

Rhodium/rhodium adipose decision interval Cusum charts.

Rhodium/rhodium glandular decision interval Cusum charts.

Rhodium/rhodium glandular decision interval Cusum charts.

Molybdenum/molybdenum adipose standard Cusum charts.

Molybdenum/molybdenum adipose standard Cusum charts.

Molybdenum/molybdenum glandular standard Cusum charts.

Molybdenum/molybdenum glandular standard Cusum charts.

Rhodium/rhodium adipose standard Cusum charts.

Rhodium/rhodium adipose standard Cusum charts.

Rhodium/rhodium glandular standard Cusum charts.

Rhodium/rhodium glandular standard Cusum charts.

Rhodium/rhodium region No. 2 Cusum chart. The chart (diamond) was fitted with quadratic polynomial (solid).

Rhodium/rhodium region No. 2 Cusum chart. The chart (diamond) was fitted with quadratic polynomial (solid).

mixture serial calibration regression examples. These show the percent glandular mapping (diamond) applied to the rhodium/rhodium (top) and molybdenum/molybdenum (bottom) mixtures. Regression lines are solid. The analysis was performed separately for the segments before and after the tube failure/replacement.

mixture serial calibration regression examples. These show the percent glandular mapping (diamond) applied to the rhodium/rhodium (top) and molybdenum/molybdenum (bottom) mixtures. Regression lines are solid. The analysis was performed separately for the segments before and after the tube failure/replacement.

## Tables

Rate of change per relative logarithmic response shift. This shows the fractional deviation for the three examples for both adipose and glandular equivalents for a phantom . The percent glandular (PG) error is given in the bottom row for each tissue equivalent example corresponding to a 1% positive shift in logarithmic response.

Rate of change per relative logarithmic response shift. This shows the fractional deviation for the three examples for both adipose and glandular equivalents for a phantom . The percent glandular (PG) error is given in the bottom row for each tissue equivalent example corresponding to a 1% positive shift in logarithmic response.

The average baseline logarithmic response quantities. Each row (top) entry is the average value, , of the eight regions for a given process. The average percent difference, , between the last serial sample before the x-ray tube failure and the baseline (BL) is provided beneath the respective BL quantities.

The average baseline logarithmic response quantities. Each row (top) entry is the average value, , of the eight regions for a given process. The average percent difference, , between the last serial sample before the x-ray tube failure and the baseline (BL) is provided beneath the respective BL quantities.

Decision interval Cusum control summary. The in-control (IC) behavior is summarized in two segments for before the x-ray tube failure (top) and after the replacement (bottom). Entries cited as intervals represent the range from when at least one chart of a given process was out of control (OC) to the day that all charts of the process were OC. The first segment is measured from the first serial sample (add to adjust to the baseline collection) and the second segment is measured from the day of the second baseline dataset acquisition. Isolated numerical entries indicate that all charts of a given process were OC in unison by the specified day. Processes that were IC over a given segment are labeled as such.

Decision interval Cusum control summary. The in-control (IC) behavior is summarized in two segments for before the x-ray tube failure (top) and after the replacement (bottom). Entries cited as intervals represent the range from when at least one chart of a given process was out of control (OC) to the day that all charts of the process were OC. The first segment is measured from the first serial sample (add to adjust to the baseline collection) and the second segment is measured from the day of the second baseline dataset acquisition. Isolated numerical entries indicate that all charts of a given process were OC in unison by the specified day. Processes that were IC over a given segment are labeled as such.

The molybdenum/molybdenum adipose Cusum regression slopes (logarithmic response per Cusum index) for the first (top) and second (bottom) Cusum segments indicted by S1 and S2, respectively. The lower entries in each row represent the linear correlation coefficient for each fitted line.

The molybdenum/molybdenum adipose Cusum regression slopes (logarithmic response per Cusum index) for the first (top) and second (bottom) Cusum segments indicted by S1 and S2, respectively. The lower entries in each row represent the linear correlation coefficient for each fitted line.

Rhodium/rhodium quadratic coefficients and . This gives the coefficients for the derivative of the fitted second degree polynomial for the rhodium/rhodium Cusum charts averaged (Ave) over the eight regions: , where n is the serial index. The data spans , corresponding to n spanning 1–32. The intraprocess standard deviations (SD) are also provided.

Rhodium/rhodium quadratic coefficients and . This gives the coefficients for the derivative of the fitted second degree polynomial for the rhodium/rhodium Cusum charts averaged (Ave) over the eight regions: , where n is the serial index. The data spans , corresponding to n spanning 1–32. The intraprocess standard deviations (SD) are also provided.

mixture percent glandular (PG) regression analysis. These regression parameters correspond to the plots shown in Fig. 13. The slope is estimated in PG/day units.

mixture percent glandular (PG) regression analysis. These regression parameters correspond to the plots shown in Fig. 13. The slope is estimated in PG/day units.

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