A Mathematical Review for the Analysis of Geometry Factors in X-Ray Medical Imaging

Abstract

Computing ultimately cannot operate in a vacuum: the computer must be used for some problems, generally coming from outside of Computer Science. Often, however, the problem addressed end up requiring background in a number of fields rather just in programming and the application area. A specimen problem taken from X-ray medical imaging ends up requiring in addition classical mechanics, graphics, mathematics, and numerical analysis. Typically, geometrical factors affect the radiographic image produced by X-ray for medical purposes regardless of the format. Each clinical study requires its own acquisition parameters to obtain best quality suitable for the investigation. In spite of over 100 years of the use of x-rays for diagnostics, the choice of technique parameters still relies to a great extent on experience. Scientific efforts to optimize the choice in terms of finding the parameter settings which sufficient image quality at the lowest possible cost in dose are still rare. True optimization requires (1) estimation of the image quality needed to make a correct diagnosis and (2) methods to investigate all possible means of achieving this image quality in order to be able to decide which of them gives the lowest dose. These problems could be approached purely mathematically, as an N-parameter maximization problem. As such it presents a significant challenge, either for a purely mathematical approach or as a minimization problem a successive approximations. This review is based on a mathematical formulation for the analysis of geometry factors in X-ray medical imaging. Calculations are based on the resolution mathematical model in cylindrical coordinates representing the radiation penetration sequence a typical X-ray imaging method. Boundary conditions are involved in the resolution algorithm different stages.