When talking about medical imaging, most people know that physics and computer sciences are involved, but few may be aware that mathematics is indispensable. Indeed, many imaging methods are based on mathematical analysis. A scanner produces large amounts of data, but no picture. Complicated mathematical techniques are needed to analyze these data and finally produce pictures or 3D images that aid doctors in diagnostics.
For example, an X-ray beam's strength changes less when it goes through a layer of fat than when it goes through a bone. Mathematicians can use the change to figure out what is inside the patient's body, Peter Kuchment said. "Various medical imaging methods work in this way", the Texas A&M professor explained. "But besides X-rays, we can also use ultrasound, light, electrical currents, microwaves, etc. Instead of one beam or wave, we use a large number of them."
Peter Kuchment has received a grant from the National Science Foundation to work out the mathematical tools for new and more powerful medical imaging methods. "Safety, cost, contrast and resolution are some of the criteria to select good imaging methods", Peter Kuchment added. "But none of the currently available methods is perfect and they all have limitations."
Peter Kuchment sees promise in what he calls "hybrid medical imaging methods", and photo-acoustic imaging, a combination of electromagnetic and ultrasound waves, is one of them. "Microwave or a laser beam can give you perfect contrast so you can easily tell the difference between a tumour and healthy tissue, but you cannot resolve small details", he explained. "Ultrasound, on the other hand, can show small things, but it cannot tell the differences well."
Photo-acoustic imaging combines electromagnetic and ultrasound waves, so doctors will be able to see small details as well as differences between healthy and cancerous tissues, he added. These hybrid imaging methods require complicated mathematical tools, and Peter Kuchment is working on developing them.
As one of the world's leading research institutions, Texas A&M is in the vanguard in making significant contributions to the storehouse of knowledge, including that of science and technology. Research conducted at Texas A&M represents an annual investment of more than $582 million, which ranks third nationally for universities without a medical school, and underwrites approximately 3500 sponsored projects. That research creates new knowledge that provides basic, fundamental and applied contributions resulting in many cases in economic benefits to the state, nation and world.