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Express Diagnostics of Erythrocytes Size Distribution on the basis of Hyperspectral Holography and Laser Diffractometry Techniques

Andrei LUGOVTSOV1.2, Vladislav USTINOV3, Georgy KALENKOV4,
Sergey KALENKOV5 and Alexander PRIEZZHEV1,2

1Physics Department, Lomonosov Moscow State University, Russia
2International Laser Center, Lomonosov Moscow State University, Russia
3Moscow Center of Fundamental and Applied Mathematics, Lomonosov Moscow State University, Russia
4Institute of Geosphere Dynamics (IDG RAS), Russia
5Moscow Polytechnic University, Russia


Modern medical diagnostics includes blood tests on the first stages that provides very important information allowing to insure the accuracy of further diagnosis. Red cell distribution width (RDW) is known as a crucial parameter in case of blood anemia. RDW is a measure of how much the erythrocytes differ from each other in size. RDW is close to zero, when all cells have similar size, and increases when the sizes are different. RDW has been evaluated for decades, and its application field grows rapidly. Recent investigation performed with more than 8000 people shows that RDW serves as a reliable mortality predictor independent of the disease type [1]. Thus, accurate diagnostic instruments for measuring this parameter are in high demand.
In this work, we developed the approach for diagnostics of erythrocytes size based on the information obtained by laser diffractometry and hyperspectral holography of erythrocytes. In laser diffractometry, erythrocytes are illuminated by a laser beam and a diffraction pattern is observed in the far-field diffraction zone. One can solve an integral equation, in which the diffraction pattern is used as an input data and the solution is the erythrocytes size distribution [2]. Another strategy is to rely on certain features of the diffraction pattern. For example, the visibility of the pattern reflects the shape and size of particles. In [3], it was shown that the visibility of the diffraction pattern monotonically depends on RDW of the cells in the given blood sample. Thus, laser diffractometry allows one to assess the value of RDW. It is possible to illuminate hundreds of thousands of cells within a moment. Calculation of the visibility parameter can also be performed during less than a second using any modern personal computer. This makes the method more preferable to other standards. However, the shape of the cells remains unknown as in the Coulter counter and one has to use some 3D geometrical model of the cells.
In hyperspectral holography (HH), one obtains the phase modulation of the light rays passing through the object with resolution up to half of the incident light wavelength. HH technique has been well developed and successfully tested on biological particles [4]. In the present work, we have applied HH to measure the phase profiles of red blood cells on a glass smear. This enables one to reconstruct the 3D geometrical model of the erythrocytes shape. In this work, we use the specific technique developed in [4].
The main goal of the work is to enhance laser diffractometry of erythrocytes by using the 3D geometrical model of a real cell experimentally obtained using the HH method. The visibility of the diffraction pattern depends not only on RDW value but also on the cells shape. We validate the dependency of the visibility parameter on RDW comparing different theoretical and experimentally obtained cells models.
Geometrical 3D models of human red blood cells in a dry smear were obtained experimentally using the HH method. Corresponding diffraction patterns in the far field diffraction zone were calculated. Visibility values of the diffraction patterns were obtained in cases of low and high red cell size distribution width. The results revealed that the visibility is influenced by the cells shapes. Namely, the visibility is always lower when using the model of real cells shape to compare with the case of ideal symmetric shapes. However, the visibility of the diffraction pattern still can be used to assess the red cell distribution width in clinical practice. The typical visibility value obtained in our calibration experiments was about 7%. Basing on the calculated dependency of the visibility of the diffraction pattern on the spread of cells in size, the relative spread of cells was determined to be 18 ± 4 %. The compact, computerized laser device based on the principles of ektacytometry (diffractometry) designed to measure the width of the distribution of size of erythrocytes has been developed.
Acknowledgement: This work was supported by the Russian Foundation for Basic Research grant №17-29- 03507-ofi-m.
[1] K. V. Patel, L. Ferrucci, W. B. Ershler, D. L. Longo, and J. M. Guralnik, Red blood cell distribution width and the risk of death in middle-aged and older adults, Archives of Internal Medicine 169(5), 515–523, 2009.
[2] D. L. Black, M. Q. McQuay, and M. P. Bonin, Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications, Progress in energy and combustion science 22(3), 267–306, 1996.
[3] S. Yu. Nikitin, A. E. Lugovtsov, A. V. Priezzhev, and V. D. Ustinov, Relation between the diffraction pattern visibility and dispersion of particle sizes in an ektacytometer, Quantum Electronics 41(9), 843–846, 2011.
[4] S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, Hyperspectral holography: an alternative application of the Fourier transform spectrometer, Journal of the Optical Society of America B 34(5), B49–B55, 2017.

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Andrei Lugovtsov
Physics Department and International Laser Center, Lomonosov Moscow State University


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