Ever since a physicist, Allan Cormack, shared the 1979 Nobel prize in medicine for essentially mathematical research, the value of mathematics in the biomedical field has been universally recognized. It is well known that Cormack's discoveries contributed to the establishment of a subject, nowadays, called computer tomography. However, it is less well known that the basic idea underlying tomography was due to Johann Radon, an Austrian mathematician, who in 1917 supplied a constructive, affirmative, answer to the theoretical question: Is it possible to reconstruct a body of varying density from the knowledge of all line integrals through that body? The essence of reconstructing a cancer tumor from X-ray images is contained in the preceding mathematical problem.
In the same spirit, the work of Flinders’ Biomedical Mathematics research group focusses on problems related to identification cancer tumors and bone structures. Specific projects, currently being investigated include:
Computer-aided early detection of breast cancer in screening mammograms
In Australia, the lifetime risk for a woman to contract breast cancer is 1 in 10 or higher. The rate is even higher in some countries. Breast cancer can be treated better with reduced mortality and morbidity if found early. Accordingly, many countries, including Australia have implemented breast cancer screening programs. Women between the ages of 49 and 69 are encouraged to attend screening every two years. Each visit generates at least four mammographic images; a top (cc) and side view (mlo) for each breast. At least two radiologist “read” these image for signs of breast cancer and a woman is called back for further tests if the radiologists decide that there is sufficient evidence of breast cancer. Reading mammograms by two human experts is time consuming and costly. Accordingly, several groups around the world, including our group at Flinders, have been working toward developing image analysis methods for automating at least part of the process. Although computer algorithms are not yet able to duplicate the cognitive ability of radiologists, methods of pattern recognition can identify some subtle contrast changes and texture patterns that human beings cannot. Research has shown that a human reader working with computer assistance performs as well, both in terms of accuracy and cost as two human readers. The immediate challenge is to improve the contribution of the computers so that computer aided screening clearly reduced the cost and increases the accuracy of screening programs.
Projects within this program include temporal analysis of mammograms, image segmentation methods, graph theoretic methods for image analysis and texture analysis.
Example: Temporal analysis of screening mammograms. (a) shows a current mammogram and (b) is the same breast imaged at the previous visit. An obvious mass has developed during the elapsed time. (c) and (d) show the same images as (a) and (b) but with colored outlines of regions identified and matched automatically by graph based methods. Most of the outlines identify regions that have not changed much since the last visit and are automatically declared as benign. The red outline identifies the cancer because the matching region in the previous mammogram is substantially smaller and of lower contrast than in the current mammogram.
Modeling of structure and changes of structure in cancellous boneBone is living tissue that replenishes itself over time through a process called remodeling. In humans, the entire skeleton is renewed in five to ten years. The remodeling process repairs micro damage and allows the structure of the bone to adapt to changes in loading due to, for example, changes in weight or patterns of activity. The group at Flinders is developing mathematical models for the remodeling process in order to characterize changes in bone volume and structure resulting from disease such as osteoporosis and in response to treatment. The conjecture is that accurate modeling will lead to better understanding of the remodeling process and allow quantitative prediction of bone strength in disease and treatment states.
Projects within the program include characterization of three dimensional structure and modeling changes in bone volume fraction as a function of distance from the growth plate.
Real and simulated bone sections. (a) shows a small section of a micro CT scan of the tibia of a rat. After estrogen deprivation, the bone volume is reduced and the structure has thinned (b). (c) and (d) show the results after simulating the effects of estrogen deprivation using the bone in (a) as the initial state.
Segmenting full body CT scansThis project is in collaboration with Dr. Martin Caon in the Faculty of Medicine, Nursing and Health Sciences at Flinders University. Dr. Caon is developing a method for accurately determining x-ray dosages for children. Currently, most paediatric CT dose calculations utilize the MIRD paediatric computational models of anatomy which are scaled down versions of an adult (Cristy, 1980). These models depict internal anatomy as geometric shapes. They approximately characterise internal organs using geometric volumes such as spheres, cylinders and cones which do not closely resemble the anatomy of children. More accurate anatomy models can be obtained by using real clinical paediatric CT image data. However, this approach has always been hindered by the laborious task of assigning every pixel in the several hundred CT images to the organ/tissue it belongs. As the challenge in automating the above process has not yet been overcome, the identification and labeling of each different tissue and organ (image segmentation) is, to the present time, done manually, one CT image at a time. The process involves identifying the 28 different tissues named by the International Commission of Radiation Protection (ICRP, 2007) as necessary for the calculation of effective dose and may take a year of image processing work to produce one anatomic model. The construction of a series of paediatric anatomy models with an age range from 0 to 14 years, as required for Dr. Caons work, would take a daunting length of time to complete. The biomedical mathematics groups is developing an inherently 3D segmentation method with a human computer interface that will reduce the time needed to label a full body CT scan in a matter of a few hours instead of many months at an accuracy at least equal to fully human segmentation.