Mathematics Meets Medicine : An Alignment Story

Medical imaging has come a long way since 1895, when Wilhelm Conrad Röntgen discovered x-rays. More than a century later, the phrase “going for a scan” can refer to a multitude of different medical imaging techniques that are used for diagnosis and treatment. The “old” x-rays are the backbone of computer tomography (CT) systems. Single photon emission (SPECT) and positron emission tomography (PET) rely on the properties of radioactive isotopes. Magnetic resonance imaging (MRI) exploits the well-known principles of nuclear magnetic resonance; diffusion tensor imaging (DTI) uses magnetic field-gradient pulses to track the movement of water molecules in the brain. These are just a few of the relatively new scanning techniques. Whatever the modality, a typical scan now yields more information than ever before. The various scanners produce gigabyte-size images, often in time series consisting of hundreds or even thousands of images. Clearly, high-performance computing is increasingly important in medical imaging, and mathematics plays a crucial role in this rapidly growing discipline. Activity in this field has been especially intense in the last two decades; see, for example, [1, 5–10] .