ИСТИНА

Laser ektacytometry of erythrocytes (ektacytometry) is a fast in vitro diagnostic technique for measuring the deformability of red blood cells - erythrocytes. In ektacytometry [1], the erythrocytes are placed in the so-called Couette flow-chamber in a highly diluted suspension. The shear stress in the flow elongates the cells and orients them in almost the same direction. A laser beam illuminates thousands of the cells in the flow simultaneously, and special CCD sensors measure the diffraction pattern (DP) originated by low angle single scattering of the beam by these cells. In modern ektacytometry, the measured DP is used to calculate an average elongation of particles as a function of stepwisely increasing shear stress values. The problem of finding more detailed characteristics about the shear-induced elongation of cells is of great interest for medical applications (see, e.g., ref. [2]). The main aim of this work is to significantly enhance the capabilities of the ektacytometry. We statistically characterize the ensemble of particles by their distribution in elongations ω (ε), where ε denotes a random value describing the relative elongation of the cells. In the first part of the work, we made several analytical estimates, which relate the shape of a certain iso-intensity curve of the DP with first 3 moments of ε: average value s=<ε>, dispersion µ=<ε2> and asymmetry ν=<ε3>. The estimates are obtained under assumption that size distribution of cells has a negligibly small width; the anomalous diffraction approximation was used for modeling the light scattering by the elongated erythrocytes. The estimates lead to the new algorithm for calculating the parameters s,µ,ν. The algorithm uses second derivatives of the iso-intensity curve in the 4 special characteristic points. We experimentally tested the proposed method using the rat blood samples, which were prepared in a special way such that, in the experiment, the parameters s,µ,ν were known in advance. We recorded the diffraction pattern at a certain shear stress conditions and obtained an iso-intensity curve with level of noise less than 15%. The values of s,µ,ν were calculated using our algorithm and they differed from the corresponding experimentally preset values by less than 15%. One of the estimates on µ was reported by the authors in the ref. [2]. In the second part of the work, we used the assessed parameters s,µ,ν as a priori information to obtain the whole distribution of erythrocytes in elongation ω(ε) by solving corresponding Fredholm integral equation of the first kind. We applied Tikhonov regularization in order to solve the integral equation numerically. We used the general discrepancy principle to obtain an optimal value of the regularization parameter. At the same time, we incorporated the values of s,µ,ν into the numerical procedure in order to achieve somewhat better convergence and accuracy. We conducted numerical tests for different model parameters showing that the erythrocytes distribution in elongation ω(ε) can be calculated with at most 15% error by using the modeled DP with an error level not exceeding 13%. References 1. M. Bessis, N. Mohandas, Blood Cells, 1, 307-313 (1975). 2. S. Yu. Nikitin, A.V. Priezzhev, A. E.Lugovtsov, JQSRT, 121, 1-8 (2013).