On inverse reconstruction problems of erythrocyte size distribution in laser diffractometry

In this paper, we have analyzed inverse problems of erythrocyte size distribution reconstruction when laser diffractometry data is given. We consider two geometrical models of erythrocyte — flat disk and biconcave disk. We have found that Tikhonov regularization technique allows one to reconstruct correct erythrocyte size distributions in cases of normal blood, microcytoses and macrocytoses when using a priori information about smoothness, finiteness and positivity of the solution. We also considered the case when the inverse problem is solved assuming the shape of the cells to be flat disks and the diffraction pattern is calculated according to biconcave disk model. In this case, first three statistical moments of the erythrocyte size distributions are obtained with error which is directly proportional to value of flexure in biconcave disk model. In addition, inversion of the corresponding integral equation leads to a solution, which has generally the same shape as the true distribution but is shifted along the horizontal axis. This allows one to calculate true solution by using a priori information about average value of erythrocyte size distribution.