Evaluation of Compton attenuation and photoelectric absorption coefficients by convolution of scattering and primary functions and counts ratio on energy spectra

PURPOSE: Estimation of Compton attenuation and the photoelectric absorption coefficients were explored at various depths. METHODS: A new method was proposed for estimating the depth based on the convolution of two exponential functions, namely convolution of scattering and primary functions (CSPF), which the convolved result will conform to the photopeak region of energy spectrum with the variable energy-window widths (EWWs) and a theory on the scattering cross-section. The triple energy-windows (TEW) and extended triple energy-windows scatter correction (ETEW) methods were used to estimate the scattered and primary photons according to the energy spectra at various depths due to a better performance than the other methods in nuclear medicine. For this purpose, the energy spectra were employed, and a distinct phantom along with a technetium-99 m source was simulated by Monte Carlo method. RESULTS: The simulated results indicate that the EWW, used to calculate the scattered and primary counts in terms of the integral operators on the functions, was proportional to the depth as an exponential function. The depth will be calculated by the combination of either TEW or ETEW and proposed method resulting in the distinct energy-window. The EWWs for primary photons were in good agreement with those of scattered photons at the same as depths. The average errors between these windows for both methods TEW, and ETEW were 7.25% and 6.03% at different depths, respectively. The EWW value for functions of scattered and primary photons was reduced by increasing the depth in the CSPF method. CONCLUSIONS: This coefficient may be an index for the scattering cross-section.