Presented under the auspices of the Special Year on Mathematical Support for Molecular Biology . Computer technologies have been widely used in medical research. While the methodology of continuous mathematics is used in most research on medical computing, discrete algorithmic techniques have also played an important role in developing various medical applications. For example, graph optimization algorithms have been used in developing virtual endoscopy and dynamic programming techniques have been used in finding an optimal radiosurgical treatment plan.
Many medical applications call for solutions to various discrete algorithmic problems.
For instance, in radiosurgical treatment planning, it is important to find the best positions to place radiation doses within a target image. In gamma unit treatment planning, the dose delivery is based on the unit shot, which is approximately a spherical dose distribution in 3D space. For irregularly shaped target volumes, it is a challenging task to pack a set of shots together to yield an acceptable cumulative dose distribution. This is a discrete optimization problem, in which the location, collimator size, and relative weight of each shot, and the total shots being used are optimized at the same time. The study of computing in medical applications has opened many challenging issues and problems for both the medical computing community and the algorithm community.