On inverse reconstruction problems of the erythrocyte size distribution in laser diffractometry

Abstract

The inverse problems of reconstructing the erythrocyte size distribution when the laser diffractometry data is given for the two erythrocyte geometric models—the flat and biconcave disks—are analyzed. It has turned out that when using each of the models the Tikhonov regularization method taking into account a priori information about the smoothness, finiteness, and the nonnegativity of the solution leads to a correct reconstruction of the unknown size distributions for the cases of normal blood, microcytoses, and macrocytoses, characterized by the presence of the factions’ abnormally small and abnormally large cells. In the case when the inverse problem is solved on the assumption of a flat particle shape, and the diffraction pattern is calculated by the biconcave disk model, the error in the determination of the first three statistical moments are directly proportional to the magnitude of the deepening in the form of a biconcave disk that simulates erythrocytes. In this case the solution qualitatively coincides with the true distribution, but is shifted relatively to it along the horizontal axis, which in principle can be compensated on the basis of a priori information about the average value of the erythrocyte size distribution.