Breast Cancer: Modelling and Detection

This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection

Shape description and matching using integral invariants on eccentricity transformed images

Matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision. To keep track of changes inside the breast, for example, it is important for a computer aided detection system to establish correspondences between regions of interest. Shape transformations, computed both with integral invariants (II) and with geodesic distance, yield signatures that are invariant to isometric deformations, such as bending and articulations. Integral invariants describe the boundaries of planar shapes. However, they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure. Conversely, eccentricity transforms (Ecc) can match shapes by signatures of geodesic distance histograms based on information from inside the shape; but they ignore the boundary information. We describe a method that combines the boundary signature of a shape obtained from II and structural information from the Ecc to yield results that improve on them separately

Mammographic density, breast cancer risk and risk prediction

In this review, we examine the evidence for mammographic density as an independent risk factor for breast cancer, describe the risk prediction models that have incorporated density, and discuss the current and future implications of using mammographic density in clinical practice. Mammographic density is a consistent and strong risk factor for breast cancer in several populations and across age at mammogram. Recently, this risk factor has been added to existing breast cancer risk prediction models, increasing the discriminatory accuracy with its inclusion, albeit slightly. With validation, these models may replace the existing Gail model for clinical risk assessment. However, absolute risk estimates resulting from these improved models are still limited in their ability to characterize an individual's probability of developing cancer. Promising new measures of mammographic density, including volumetric density, which can be standardized using full-field digital mammography, will likely result in a stronger risk factor and improve accuracy of risk prediction models