Friday, October 30, 2009

Breast Cancer Detection

The Mechanical Engineering Department at Canterbury University has been developing a new method for detecting breast cancer, which has presented interesting and challenging maths problems. The method has been named DIET - Digital Image-based ElastoTomography.

The rationale for the project is this: Incidence of breast cancer among women in NZ is high, and early detection significantly increases the chances of successful treatment. But the standard current method of breast cancer detection using a mammography machine is not only uncomfortable for women (I have sisters who confirmed that for me!), but involves large and expensive equipment. Screening methods which are less invasive (don’t involve radiation) and equipment which is more portable might increase the up-take of screening.

The concept: Cancerous tissue is stiffer than normal tissue. By subjecting the breast to a rapid fine vibration, it should be possible to detect any region of stiffer tissue from the way the surface moves in response to the vibration.

Five cameras are positioned around the breast to take synchronised images while it is vibrating. (The frequency of vibrations is 20 - 50 Hz and amplitude 1 mm.) Now there is the challenging geometry problem of reconstructing a 3-D image of the breast from the digital images. Once the 3-D motion has been reconstructed comes the problem of using the properties of elastic materials to locate the position and size of any regions of greater stiffness.


Richard Brown, now in the Canterbury University Mathematics and Statistics Dept, was working on this projective geometry problem for his PhD in Engineering. Richard is pictured with Thomas Lotz, who is currently on the team working on the DIET project. Thomas (left) is holding a test silicon 'breast' while Richard (right) is holding a calibration cube, which is used to locate the exact position of the cameras before the test is carried out.



My thanks to Richard and Thomas for introducing me to this work when I was visiting Canterbury University in September.

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