Recent mathematical advances may make it easier for doctors to store, transmit, display, share, and catalog mammographic images. Bradley Lucier, Professor of Mathematics and Computer Sciences, is working with researchers at the University of South Carolina and the University of Florida to apply recently developed mathematical techniques to the compression of digitized mammograms. The first reports of this work appeared in the February issue of the Journal of Digital Imaging.
As a public health measure, several groups suggest that all
women over age 40 receive mammographic screenings, which
consist of two X-ray images taken from the top and the side of
each breast. Such screenings can aid in the early detection of
breast cancer. Even if a woman has no symptoms of breast
cancer, the images, kept for many years, can serve as base-line
X-ray images against which later screenings can be compared
for changes.
Large-scale screenings can be difficult in rural and other areas traditionally underserved by health care professionals, where there may not be medical personnel trained to interpret mammograms, or where the logistics of transmitting images to radiologists and the long-term storage and archiving of mammographic images is problematic. It is likely, for example, that mammograms would be stored separately from a patient's other health records.
Digital imaging may prove useful in alleviating these problems. A digitizer scans an X-ray film, divides the film into small squares, and records the brightness of the film in each square as a number, which is stored in a computer. Even though each digitized mammogram requires the space of up to 50 million characters (50 megabytes) of storage, over 100 digitized mammograms can be stored on one 8mm tape as used in hand-held camcorders. The same number of X-ray films, envelopes, etc., would have a volume of well over one cubic foot. Once the image is stored in a computer, it is easier to transmit or share the information over high-speed computer networks than to physically transport X-ray films. Furthermore, doctors can easily blow up parts of a digital image to examine it more closely. Finally, digitized mammograms can be integrated into a patient's completely computerized medical record.
In the future, sophisticated medical centers may contain high speed networks and scientific visualization workstations as a matter of course, but it seems likely that computers in rural clinics will be connected to central medical centers by cheaper, and slower, modems over regular phone lines or perhaps leased lines. It will take too long to transmit digitized mammograms over modems to medical centers for reading (up to 35 hours for a complete screening using today's fastest standard modems). Barring unforeseen advances in communications technologies (and today's telephone networks have severe built-in limits on communications speed), digital imaging may well prove impractical unless techniques of image compression are adopted.
Image compression attempts to reduce the amount of storage needed to represent an image while maintaining all diagnostically relevant information. For mammograms, one must preserve the features that radiologists look for to discover evidence of cancer, and such features occur at all scales. Clusters of small calcium deposits, known as microcalcifications, show up as small, bright dots on the image, and must be preserved. At a middle scale, whether the edges of objects in the breast are smooth or star-shaped (stellated) helps to indicate whether an object is benign (e.g., a cyst) or malignant. Finally, there are large scale features, known as architectural distortions, that may also indicate the presence of cancer. All such features must be preserved.
Professor Lucier worked with Ronald A. DeVore and Bjöšrn Jawerth at the Department of Mathematics of the University of South Carolina to develop a mathematical theory of image compression using objects called wavelets. Applied to images, a wavelet is a pattern of bright and dark. For example, one can start with three such patterns, each the size of the original image. The first is bright on the top of the image and dark on the bottom; the second is bright to the right and dark to the left; and the pattern of light and dark on the third is roughly like a two-by-two checkerboard. One takes each of these patterns and tries to match it with the image.
If the mammogram itself is brighter in the top half than in the bottom, it is a good match with the first pattern, and it is said that the coefficient of the first pattern is large (and positive). If the image is dark at the top and light at the bottom, the coefficient is large (and negative). One then scales the patterns to half their original size and tries to match them against the image in each of the four quadrants of the image. One repeats this after scaling the patterns to one quarter their size, one eighth their size, etc. One builds up the features in the images, like microcalcifications and architectural distortions, from the wavelets at different scales multiplied by their respective coefficients. Compression is achieved by discarding some wavelet coefficients, keeping only those necessary to build up the image features of interest. DeVore, Jawerth, and Lucier developed a theory that tells which wavelets to keep, depending on the scales of the desired features. The result is a compressed image different from the original, but, if done correctly, the difference consists almost solely of random oscillations due to variations in the film or the digitizing technology. Their theory also relates the size and quality of the compressed image to a precise measurement of the smoothness of an image; the smoothness is connected to how cluttered an image looks.
Lucier and DeVore then worked with a group of researchers headed by Laurence Clarke at the Department of Radiology at the Moffit Cancer Center of the University of South Florida to apply these techniques and theories to digital compression of mammograms. Early results, as reported in the Journal of Digital Imaging, indicate that compression rates of about 50 to one may be possible while preserving all features of diagnostic interest. Such compression rates would allow one to transmit a complete mammographic screening from a rural clinic to a medical center in less than 40 minutes over regular phone lines. It would also allow one to store over 5,000 images on one 8mm tape, and would facilitate integrating the mammographic images into a complete computerized medical record.
Full scale clinical testing may begin within the next two years.