Mammographic features are known to be associated with breast cancer but the magnitude of the effect differs markedly from study to study. Methods to assess mammographic features range from subjective qualitative classifications to computer-automated quantitative measures. We used data from the UK Guernsey prospective studies to examine the relative value of these methods in predicting breast cancer risk. In all, 3,211 women ages z35 years who had a mammogram taken in 1986 to 1989 were followed-up to the end of October 2003, with 111 developing breast cancer during this period. Mammograms were classified using the subjective qualitative Wolfe classification and several quantitative mammographic features measured using computer-based techniques. Breast cancer risk was positively associated with high-grade Wolfe classification, percent breast density and area of dense tissue, and negatively associated with area of lucent tissue, fractal dimension, and lacunarity. Inclusion of the quantitative measures in the same model identified area of dense tissue and lacunarity as the best predictors of breast cancer, with risk increasing by 59% [95% confidence interval (95% CI), 29-94%] per SD increase in total area of dense tissue but declining by 39% (95% CI, 53-22%) per SD increase in lacunarity, after adjusting for each other and for other confounders. Comparison of models that included both the qualitative Wolfe classification and these two quantitative measures to models that included either the qualitative or the two quantitative variables showed that they all made significant contributions to prediction of breast cancer risk. These findings indicate that breast cancer risk is affected not only by the amount of mammographic density but also by the degree of heterogeneity of the parenchymal pattern and, presumably, by other features captured by the Wolfe classification.

SUMMARYIn this paper, it is shown that the symmetric Galerkin boundary element formulation cannot be used in its standard form for multiple connected bodies. This is because the traction integral equation used for boundaries with Neuman boundary condition give non-unique solutions. While this fact is well known from the classical theory of integral equations, the problem has not been fully addressed in the literature related to symmetric Galerkin formulations. In this paper, the problem is reviewed and a general way to deal with it is proposed. The details of the numerical implementation are discussed and an example is solved to demonstrate the e ectiveness of the proposed solution.

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SUMMARYA symmetric Galerkin boundary element formulation is developed for shear deformable plates. A mixed strategy is used for the integration process, i.e. partial regularization using simple solutions followed by a singularity subtraction technique. For the shear equation, full regularization is achieved using new kernel relationships found through a constant shear mode of deformation. Some of the strong singular integrals are avoided altogether by using a modiÿed traction obtained through a very simple variable change; appropriate boundary conditions are deÿned. Details of the implementation are given and several example problems solved to verify the accuracy of the proposed formulation.