A picture is worth a thousand words.
This truism captures the reason medical imaging is so important for health and medical research. But medical images hold far more information than even the best doctors can extract. It is through computational mathematics that doctors are able reap the full benefits of today's technology.
Take, for example, functional magnetic resonance imaging (fMRI). This technology can provide clear, detailed pictures of the brain by projecting radio waves through a magnetic field. fMRI images are used to determine which brain regions a person uses to accomplish a cognitive task. Active regions show up slightly brighter than inactive regions because of increased blood flow. However, the measured changes in brightness are too subtle for the human eye to detect and are degraded because of random measurement uncertainties. For this reason, scientists use sophisticated statistical methods on a computer to distinguish the active from the inactive brain regions.
Functional MRI is having an immense impact in the medical world, being used by doctors and psychologists to study everything from drug addiction to how humans understand jokes. All made possible by computational mathematics.
Mathematics and computers are the indispensable tools that join technology to medical science. As the power of computers continues to increase, and as the installation of fMRI scanners in hospitals and clinics grows, the need for sophisticated mathematical and statistical algorithms to handle the ocean of data will skyrocket. Computational mathematics can be used to tackle these number-crunching tasks and pave the way for future advances in the exciting field of medical imaging.