ИСТИНА

Laser ektacytometry of red blood cells is a technique in which the cells are put under shear stress forces in some liquid. The forces elongate all the cells along the same fixed direction. A laser beam scattered by the cells is measured in the far field diffraction zone. In conventional ektacytometry, one calculates the average elongation index from given isointensity line distinguished in the diffraction pattern, see publication [1]. This elongation describes ability of cells to deform which is of crucial importance for the vital activity of the organism as the cells permanently have to deform to pass through thin capillaries. Recently several research groups all over the world started to investigate if one can obtain more information about the elongated cells from the corresponding diffraction patterns, see for example paper [2]. In this abstract, the author describes new approach which enables one to obtain distribution of the cells in elongations. Existing approaches such as the one described in [2], provide only average value and width of this function. However in medical applications, knowledge of this function at all points leads to that a doctor can see if there was a tiny fraction of ill cells which is often the case. This relatively small fraction may be the cause of the illness and thus very important in practice. The proposed approach is based on the fact that the unknown distribution is a solution of some Fredholm integral equation of the first kind. In previous work [3], the author showed that applying Tikhonov regularization method one can reconstruct the elongation distribution of cells supposing that all of them has the same surface area. This assumption leads to that the distribution is effectively a function of one variable. The main goal of the present work is to reduce this assumption and consider the cells elongation distribution as a function of two variables. This leads to that the integral equation becomes more physically meaningful although its investigation becomes more complicated. Recent results obtained by the author show that this equation has a unique however not stable solution. Thus, Tikhonov regularization can be applied again to obtain two dimensional elongation distribution of erythrocytes. This work was supported by the grant of the Russian Science Foundation № 18-71-00158. [1] Baskurt O. K., Hardeman M. R., Uyuklu M., Ulker P., Cengiz M., Nemeth N., Shin S., Alexy T., Meiselman H. J. Comparison of three commercially available ektacytometers with different shearing geometries. Biorheology, 2009, 46: 251 – 264. [2] Streekstra, G. J., J. G. G. Dobbe, and A. G. Hoekstra. Quantification of the fraction poorly deformable red blood cells using ektacytometry. Optics express, 2010, 18 (13): 14173-14182. [3] S.Y. Nikitin, A.V. Priezzhev, A.E. Lugovtsov, V.D. Ustinov, A.V. Razgulin. Laser ektacytometry and evaluation of statistical characteristics of inhomogeneous ensembles of red blood cells. Journal of Quantitative Spectroscopy and Radiative Transfer, 2014, 146: 365-375.