Extracting fairly accurate proton range formulas for use in microdosimetry

Abstract

Radiation therapy is a promising treatment for cancer patients. The highest dose of radiation must deliver to tumor and the lowest to the healthy tissues. Since charged particles such as protons have high stopping-power at track-end, these particles can be used to treat tumors close to sensitive tissues. Formulas that commonly used for proton stopping-power in a soft tissue-equivalent material (T.E.) and each of its elements have respectively 48, and 12 constants. Due to the complexity of formulas, high number of constants, high occupancy of computer memory, and rounding error of computer, existing formulas reduces information processing speed. Because of the importance of proton therapy and its applications in dosimetry, microdosimetry, detectors, and computer simulations of these systems, it is necessary to use fast and accurate formulas for the stopping-power and range in the T.E., and its elements. We wrote a computer code in FORTRAN programming language, and used the fitting method and obtained simple and fairly accurate formulas for the proton range in these materials. Our range formula in T.E. have 6 constants, and in elements of T.E. include carbon, nitrogen, and oxygen have 4 and hydrogen have 8 constants. So our formulas greatly reduce the above mentioned errors.