The authors have declared that no competing interests exist.
Conceived and designed the experiments: NFB LJM SM. Analyzed the data: QL OM. Contributed reagents/materials/analysis tools: AG GM MJY. Wrote the paper: NFB LJM SM EH. Conceived and executed the present work: NFB LJM SM. Carried out the statistical analysis and prepared the graphs: QL OM. Developed the method used to measure breast density area and volume in mammograms: MJY GM. Prepared images for reads of mammograms and managed the associated measurements: AG. Participated in critically revising the manuscript and gave final approval of the submitted paper: NFB QL OM EH LJM AG GM MJY SM.
Evidence from animal models shows that tissue stiffness increases the invasion and progression of cancers, including mammary cancer. We here use measurements of the volume and the projected area of the compressed breast during mammography to derive estimates of breast tissue stiffness and examine the relationship of stiffness to risk of breast cancer.
Mammograms were used to measure the volume and projected areas of total and radiologically dense breast tissue in the unaffected breasts of 362 women with newly diagnosed breast cancer (cases) and 656 women of the same age who did not have breast cancer (controls). Measures of breast tissue volume and the projected area of the compressed breast during mammography were used to calculate the deformation of the breast during compression and, with the recorded compression force, to estimate the stiffness of breast tissue. Stiffness was compared in cases and controls, and associations with breast cancer risk examined after adjustment for other risk factors.
After adjustment for percent mammographic density by area measurements, and other risk factors, our estimate of breast tissue stiffness was significantly associated with breast cancer (odds ratio = 1.21, 95% confidence interval = 1.03, 1.43, p = 0.02) and improved breast cancer risk prediction in models with percent mammographic density, by both area and volume measurements.
An estimate of breast tissue stiffness was associated with breast cancer risk and improved risk prediction based on mammographic measures and other risk factors. Stiffness may provide an additional mechanism by which breast tissue composition is associated with risk of breast cancer and merits examination using more direct methods of measurement.
Physical forces generated by interactions between cells, and between cells and the extracellular matrix, influence a variety of cell functions including cell growth, survival, motility and differentiation
Radiologically dense breast tissue on mammography, referred to as mammographic density, reflects variations in breast tissue composition. Epithelial and stromal tissues attenuate xrays more than fat and appear dense or white, while fat is more radiolucent and appears dark. Compared to women with little or no density, those with extensive density have a 4–6 fold greater risk of developing breast cancer
We have used measurements of the breast made in a casecontrol study of mammographic density and risk of breast cancer to estimate the extent to which the breast is deformed during compression and derive an estimate of the stiffness of breast tissue. We have compared the estimate of stiffness in cases and controls after adjustment for other breast cancer risk factors.
Details of the recruitment of subjects and of their characteristics, and of the methods used to measure breast tissue volume and area, have been given elsewhere
Written informed consent was obtained from all subjects who authorized the release of their mammograms for the purpose of density measurement and agreed to take part in a telephone interview that asked about factors related to breast cancer risk. Ethics approval for the study was obtained from the University Health Network, Mount Sinai Hospital, Sunnybrook and Women’s College Hospital and from Cancer Care Ontario (for the Ontario Breast Screening Programme).
We have recruited cases and controls that had been examined on mammography units in the clinics of Mount Sinai Hospital, Women’s College Hospital, University Health Network, Sunnybrook Health Sciences Centre, and the North York and Scarborough sites of the Ontario Breast Screening Programme (OBSP), all in Toronto, Canada. The selection of cases and controls was from all subjects having mammography in these sites during the period of 13 March, 2000 and 7 July, 2003. All mammography units in these clinics were calibrated using the methods described below. All subjects examined in OBSP sites were seen for screening mammography, while those seen in hospital sites are likely to have included some for screening and some for evaluation of symptomatic breast disease. OBSP screening sites contributed only 8.2% of the cases and control subjects. The number of cases was small compared to hospital sites and only 1 control could be matched per case.
Potentially eligible cases were all incident cases diagnosed between 13 March, 2000 and 7 July, 2003 in hospitals where the machines had been calibrated and with at least one screenfilm mammogram performed before diagnosis. Cases with bilateral synchronous breast cancer, in which a screenfilm mammogram without radiological signs of cancer was not available, were excluded. Subjects who had breast implants, or reduction mammoplasty were also excluded.
Controls were selected from the same study population as cases. We attempted to identify 2 controls for each case, one examined on the same mammography machine as the case and the other from a different machine. However, some mammography clinics had only one machine and for these we recruited only controls examined on the same machine as the cases. The two types of controls were combined for this analysis.
With the agreement of their physician, potentially eligible case and control subjects were contacted by mail, the study explained and they were asked for consent to the use of their mammogram and to participate in a telephone interview to provide information about risk factors for breast cancer.
After consent had been obtained, screenfilm mammograms for the case and control subjects selected were obtained from the participating mammography units. To “blind” the process of measurement to case or control status, we selected the image of the breast contralateral to the cancer, and the corresponding mammograms in the matched controls. Two methods of measurement that have been described previously
Computerassisted measurement of mammographic density was carried out by one reader (NFB) using
Each mammography machine from which we recruited was calibrated to determine the relationship between the image signal (optical density or blackness of the processed film value) in each pixel, the exposure factors (kilovoltage, milliamp seconds (mAs), tube target and beam filter) and the amount of radiation transmitted by the breast. The latter can then be related to the combination of breast thickness and composition by imaging a “phantom” composed of steps of tissueequivalent plastics of different thicknesses and representing a range of combinations of fat and fibroglandular tissue
Compressed breast thickness is the distance between the compression paddles of a mammography machine and the breast supporting tabletop when the mammogram is obtained. Breast thickness is not constant across the breast area; and we generated a thickness map for each xray image to calculate the total volume and dense volume of the breast. Equations to predict a thickness map for each image were developed from the readout thickness reported by each mammography machine, coordinates in the plane parallel to the breast support table, and the compression force reported by a mammography machine.
A. Estimation of radius (R1) from measure of breast volume B. Estimation of radius (R2) from measure of compressed breast area C. Calculation of breast stiffness from R1, R2 and compression force.
We further assume that the contralateral breast in cases is representative of the subject. It is known that breast tissue composition, assessed by either mammography
We defined the difference between the radius of the mammographic area semicircle, and the radius of the volumetric hemisphere as “deformation”. With the compression force recorded with each mammogram the measure of deformation was used to calculate “stiffness” by the formula: Force/Deformation (N/cm), where N denotes decaNewtons and cm centimetres.
All subjects with available volumetric breast measurements had deformation computed. We excluded from the analysis two subjects with deformation smaller than zero. For selected characteristics of the case and control subjects, we calculated mean and standard deviation (SD) for continuous variables, and proportion for categorical variables. Differences between cases and controls were ascertained by ttest for symmetrically distributed continuous variables, Wilcoxon ranksum test for the nonsymmetrical ones, and chisquare test for categorical variables.
We used linear regression models to examine the association between stiffness and breast cancer status (after adjusting for other risk factors for breast cancer such as age at mammogram, age at birth of first child, weight, height, menopausal status (pre/post), and parity (parous/nonparous), with and without adjustment for breast density measurements. We applied natural log transformation to stiffness, square root transformation to all measurements of breast area, and cube root transformation to all measurements of breast volume to make the distributions more symmetrical with stable variance.
We used logistic regression modeling to examine the association of the area and volume measurements with risk of breast cancer before and after adjustment for deformation or stiffness, in addition to adjustment for the risk factors for breast cancer mentioned above. All pvalues were calculated from twotailed tests of statistical significance.
We imputed the mean value of weight for three subjects, menopausal status (post) for two subjects, and the mean value of age at birth of first child for 280 subjects. For fourteen subjects with force recorded as zero, we used the midpoint value (20) between the machine recording threshold (30) and the minimum force required to produce pressure (10). The results obtained using this imputation were very similar to those from the analysis excluding these 14 subjects. All statistical analyses were carried out using Statistical Analysis Systems (SAS) 9.2 software.
Mean (SD) or %  
Cases ( 
Controls ( 

Height (cm)  162.6 (6.9)  163.2 (6.4)  0.13 (0.05^{W}) 
Weight (kg), 
68.4 (14.3)  68.1 (14.6)  0.75 
Body mass index (kg/m^{2}), 
25.9 (5.2)  25.6 (5.4)  0.35 
Age at mammogram (years)  59.7 (11.0)  59.0 (11.0)  0.37 
Age at menarche (years), 
12.7 (1.4)  12.8 (1.5)  0.65 
Parity (% parous)  71.3  73.2  0.52 
Age at birth of first child (years), 
26.3 (5.0)  26.6 (5.5)  0.60 
Number of live births in parous women, 
2.3 (1.0)  2.3 (1.1)  0.98 
Menopausal status (% post), 
68.4  69.8  0.66 
Age at menopause (years), 
49.0 (6.1)  47.8 (6.3)  0.02 
HRT 
45.0  45.0  0.997 
Years HRT 
8.8 (7.9)  8.9 (8.7)  0.38 
Family history 
21.7  24.8  0.27 
Hormone replacement therapy.
First degree relatives with breast cancer.
Mean (SD)  
Cases ( 
Controls ( 

Compression force (N) 
104.9 (32.0)  103.1 (31.5)  0.52 
Percent dense area  33.1 (20.5)  30.2 (19.8)  0.04 
Dense area (cm^{2})  40.9 (26.9)  37.5 (25.6)  0.05 
Nondense area (cm^{2})  101.2 (64.2)  108.1 (67.7)  0.11 
Total area (cm^{2})  142.1 (60.7)  145.6 (63.8)  0.44 
Percent dense volume  11.3 (16.1)  8.9 (13.9)  0.009 
Dense volume (cm^{3})  58.1 (76.7)  47.0 (76.1)  0.005 
Nondense volume (cm^{3})  669.6 (375.8)  710.7 (420.4)  0.23 
Total volume (cm^{3})  727.7 (360.2)  757.6 (412.2)  0.51 
14 subjects with compression force under minimum detectable threshold was imputed as half of the minimum detectable value. Mean and standard deviation were calculated based on imputed variable.
Pvalue from Wilcoxon ranksum test.
The stiffness measures were natural logarithm transformed. In each plot, the thin vertical line represents the mean of the distribution.
Risk factors include: age at mammogram (linear and quadratic terms), age at birth of first child, weight (kg), height (cm), menopausal status (pre/post) and parity (parous/nonparous). Stiffness (N/cm) was natural logarithm transformed in the analysis. The least square means shown are back transformed to the original scale. Bars show 95% confidence interval. P is the pvalue for the significance of case control difference. When adjusted for percent dense area, square root transformation was used and model includes linear and quadratic terms. When adjusted for percent dense volume, cubic root transformation was used and model includes linear and quadratic terms.
The ORs and 95% CIs for quartiles of stiffness with reference to quartile 1, were 0.94 (0.65, 1.36) for quartile 2, 1.17 (0.81, 1.70) for quartile 3, and 1.35 (0.91, 1.99) for quartile 4.
Breast Density Measure:  Model  
IQOR (95% CI) 
Pvalue 
IQOR (95% CI) 
Pvalue 
AUC 

Risk Factors 
  1.24 (1.05, 1.46)  0.01  0.568  
RF and 
1.58 (1.22, 2.05)  0.0005    0.586  
RF and 
1.54 (1.19, 2.00)  0.001  1.21 (1.03, 1.43)  0.02  0.594 
RF and 
1.22 (1.04, 1.43)  0.01    0.568  
RF and 
1.27 (1.08, 1.49)  0.004  1.29 (1.09, 1.52)  0.003  0.588 
RF and 
1.42 (1.15, 1.75)  0.001    0.581  
RF and 
1.46 (1.18, 1.81)  0.0004  1.27 (1.08, 1.51)  0.004  0.595 
RF and 
1.34 (1.11, 1.62)  0.001    0.582  
RF and 
1.40 (1.16, 1.69)  0.0004  1.29 (1.09, 1.53)  0.004  0.598 
Risk Factors (RF): age at mammogram, age at birth of first child, weight (kg), height (cm), menopausal status (pre/post) and parity (parous/nonparous).
Interquartile odds ratios and 95% confidence intervals were calculated as.
Pvalue corresponds to the change in the likelihood ratio for the addition of the specific variable to a model with all others included.
AUC: area under the curve.
The interquartile odds ratio (IQOR) for stiffness, adjusted for other nonmammographic risk factors was 1.24 (95% confidence interval (CI): 1.05, 1.46), p = 0.01. After adjustment for percent mammographic dense area in addition to other risk factors, the IQOR for stiffness was 1.29 (95% CI: 1.09, 1.52), p = 0.003. After adjustment for percent dense volume, the IQOR for stiffness was 1.27 (95% CI: 1.08, 1.51), p = 0.004.
Before inclusion of the stiffness measure, percent mammographic density, by the area (p = 0.0005) and volume (p = 0.001) measures, and the area (p = 0.01) and volume (p = 0.001) of dense tissue were all significantly and positively associated with risk of breast cancer as separate predictors. After the inclusion in the model of the stiffness measure, the association of percent mammographic density by the area measure was slightly reduced, as shown by the regression coefficient and the interquartile odds ratio, although the area under receiver operating characteristic curve (AUC) increased by 1.4%. For all other mammographic measures the regression coefficients and interquartile odds ratios increased after the inclusion of stiffness, and the associated AUCs increased by between 2.4 and 3.5%.
These results show that estimates of the stiffness of breast tissue during compression are associated with risk of breast cancer after adjustment for other known risk factors including percent mammographic density, which is strongly associated with risk of breast cancer
Strengths of the present study include the relatively large numbers of incident cases and matched controls, with breast images acquired prospectively from calibrated machines. However, stiffness was not measured directly but was based on idealized assumptions about the shape of the breast volume and projected area that are potentially subject to error. For example, calculation of the breast volume measures requires accurate information about the thickness of the compressed breast at each pixel in the image. Yaffe et al have shown elsewhere that the measured percent density by volume is very sensitive to small errors in the measurement of breast thickness
Percent mammographic density, as assessed here in the area measurement, reflects variations in breast tissue composition
There are abundant data to suggest that an association between breast tissue stiffness and breast cancer risk is biologically plausible. Epithelial and stromal cells, collagen, and fat, the tissue components that contribute to variations in mammographic density, are related to each other in several ways. Epithelial and stromal cells communicate with each other by means of paracrine growth factors
Collagen and the stromal matrix are products of stromal cells that may, through their mechanical and other properties, facilitate tumor invasion
To date, there has been limited application of these basic science findings to understanding the association between mammographic density and risk of breast cancer. In addition to having greater amounts of collagen, epithelial and stromal cells, and larger areas that are immunohistochemically positive for Insulinlike growth factorI (IGF1), radiologically dense breast tissue also has greater amounts of the stromal matrix regulatory protein tissue inhibitor metalloproteinase3
Our results suggest that knowledge of both the quantity and stiffness of breast tissue may improve prediction of breast cancer risk in individuals, and facilitate research into the tissue factors that influence breast cancer risk. Stiffness may provide an additional mechanism by which breast tissue composition influences risk of breast cancer and merits examination using more direct methods of measurement such as elastography using ultrasound or magnetic resonance
An estimate of breast tissue stiffness was associated with breast cancer risk, and improved risk prediction based on mammographic measures and other risk factors. Stiffness may provide an additional mechanism by which breast tissue composition is associated with risk of breast cancer and merits examination using more direct methods of measurement.