Volumetric Analysis of Mammographic Density

One of the major strengths of the PD method is that it can be employed in retrospective studies, where little information is available about how the mammographic exam is carried out. This eliminates most of the variables in Eqs. (1) and (2); however, it has a significant disadvantage in treating the breast as a binary structure (dense or nondense) and ignoring the variations in thickness of the dense tissue. The previous section illustrated the effect of variation in total breast thickness on estimation of mammographic density. Clearly, this is a three-dimensional problem, which ideally should be treated as such.

Because the radiologist visualizes the information in the mammogram as three-dimensional, this may contribute to the greater risk prediction of subjective classification, compared with PD. The mechanism connecting density to risk is not yet known. It is logical, however, that risk would be more closely associated with the actual amount of dense tissue than with its projected area. A measurement of volume of mammographic density may provide a more relevant characterization of mammographic density in the breast, and potentially a stronger risk prediction.

If all of the variables in Eqs. (1) and (2) were known, or, at least, if a calibration could be achieved for the relationship between tissue composition and optical density, then it should be possible to determine directly the volume of mammo-graphically dense tissue rather than measuring the projected area. In an X-ray procedure, the differential transmission of X-rays through the object of interest results in a range of X-ray intensities reaching the image receptor. The relationship between the X-ray exposure to the image receptor and brightness in the image is summarized by the characteristic curve of the receptor. A characteristic curve typical of mammographic imaging is illustrated in Fig. 11. The relative brightness of structures in the mammographic image can be understood from this relationship. In the uniformly compressed part of the breast, regions having a greater portion of fibroglandular tissue will attenuate the beam more strongly, resulting in fewer X-rays reaching the receptor and a brighter image relative to that of fat. In the margin of the breast, where the thickness is reduced, a greater fraction of the X-rays will reach the receptor and the image will be darker regardless of tissue composition.

In practice the relationship between breast composition and image brightness is further complicated by the fact that the quantity and, on newer equipment, often also the spectral shape of the incident X-ray beam is adjusted depending on the imaging task (composition/thickness of the breast) through automatic exposure control (AEC). The AEC ensures adequate darkening of the film regardless of the composition and thickness of the breast. In a fatty breast, the average brightness value of the image generally represents the attenuation provided by the fatty regions. Fibroglandular tissue may be imaged in the nonlinear low-exposure "toe" of the characteristic curve (Fig. 11a). Conversely, in a dense breast, more radiation is used; the average brightness represents fibrogland-ular tissue and the fatty regions will be imaged in the nonlinear higher-exposure "shoulder" of the characteristic curve (Fig. 11b). Because of this, without specific knowledge of the exposure conditions it is difficult to relate brightness to composition. In addition to the exact exposure conditions (including the shape of the incident spectrum (anode composition, kilovoltage, and beam filter) and the magnitude of the spectrum (AEC)), the brightness in the image will also depend on the film/screen type used and the film processing conditions.

Processing sensitometry is particularly susceptible to temporal variation. Rather than recording and correcting for each of the stages of the imaging process, it is desirable to calibrate the entire system directly for composition and thickness. This is done by including a test object, which allows the direct determination of the relationship between brightness and the thickness and composition of breast tissue. When this object is imaged adjacent to the breast, the empirical relationship obtained incorporates and thereby implicitly corrects for the effect of the X-ray technique and processing variations. Composition at each point in the image can be determined by an inverse lookup of the brightness and thickness at that point in the breast.

A calibration object for this purpose is illustrated in Fig. 12. It consists of steps of different thickness at representative compositions of breast material. Values for intermediate composition and thickness are estimated by interpolation. Practical considerations governing the specification of the

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