A method based on the Compton scatter theory is derived to compensate the effects of single and double scattering in Tl-201 SPECT.The scatter medium is divided into small volume elements and the scatter counts contributed by such a volume element are obtained by integrating the number of photons scattered by all electrons within the element.The scatter probability from an electron is determined by the Klein-Nishina formula.The counts are then assigned to the detector bin that is the projection point of the center of the element.In this way the singularity in calculating the scatter counts near a point source is eliminated.The main approximation is the finite volume of the element and the limited range of scatter medium included in the calculation.In spite of the approximation,the calculated scatter line source response function and scatter-to-primary ratio agree reasonably with those from Monte Carlo simulation and the computation time is shortened 40 times.

The key technique to differential quadrature method, i. e. the determination of the weighting coefficients, is investigated in this paper. The method of computing different weighting coefficients is developed on the basis of Lagrangian interpolating approximation. This method overcomes the limitation of rigorous restriction in choice of the coordinates of grid points in original method1, and proves favoradble for studies of fluid mechanics problems. Resultes obtained for solving unsteady boundary layers show that the differential quadrature method can achieve rather high accurate solution by using only a few grid points.