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Abstract

Some studies show that cells are able to penetrate through pores that are smaller than cell size. It concerns especially Red Blood Cells but it also may concern different types of biological cells. Such penetration of small pores is a very significant problem in the filtration process, for example in micro- or ultrafiltration. Deformability of cells allows them to go through the porous membrane and contaminate permeate. This paper shows how cells can penetrate small cylindrical holes and tries to assess mechanical stress in a cell during this process. A new mathematical approach to this phenomenon was presented, based on assumptions that were made during the microscopic observation of Red Blood Cell aspiration into a small capillary. The computational model concerns Red Blood Cell geometry. The mathematical model allows to obtain geometrical relation as well as mechanical stress relations.
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Abstract

This paper presents an analysis of use of ultrasonic standing wave in cell separation from bodily fluids based on the example of erythrocyte separation from plasma. It describes movement of red blood cells in plasma under the influence of the acoustic field (whose forces result from interaction of red blood cells with plasma as the vibrating medium) and under the influence of resistance forces in Stokes’ and Oseen’s approximation. The general properties of solutions of the motion equation are given. The solutions for the parameters of the ultrasonic wave and blood cells which are interesting in terms of practical applications in medical diagnostics are discussed. Time constants of the cell transportation to the regions of stable equilibrium in the field of ultrasonic standing wave are estimated. The formulas which determine the time needed to obtain the assumed concentration increase in plasma in nodes and/or anti-nodes of the standing wave are derived.
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