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The fractal dimension of red blood cell aggregates in dextran 70 solutions

Bosek M., Szołna-Chodór A., Antonova N., Grzegorzewski B.

Optica Applicata

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2018

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Vol. 48, nr 3

477--488

EN

Fractal dimension of three dimensional red blood cell aggregates were determined by measurement of their size and sedimentation velocity. The sedimentation of the aggregates was investigated with red blood cells suspended in dextran 70 solutions at concentrations from 2 to 5 g/dL, at hematocrit 5% and 10%. The aggregate velocity and size were measured using an image analysis technique. The velocity vs. radius dependence of the aggregates exhibited a scaling behavior. This behavior showed the fractal structure of the aggregates. It is shown that the fractal dimension of the three dimensional red blood cell aggregates depends on the dextran concentration in the suspension. This parameter exhibited a minimum at dextran concentration between 3 and 4 g/dL. Thus the fractal dimensions increased as the aggregation extent decreased. The obtained results show that the sedimentation experiment together with image analysis is a promising technique to determine the fractal dimension of the three dimensional red blood cell aggregates.

2

Fluctuations in settling velocity of red blood cell aggregates

Kempczyński A, Bosek M., Grzegorzewski B.

Optica Applicata

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2014

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Vol. 44, nr 3

365--373

EN

Sedimentation of red blood cell aggregates was experimentally investigated by optical imaging. Suspensions of red blood cell at low hematocrit were obtained from blood of healthy donors. The velocity of three-dimensional red blood cell aggregates was measured using particle image velocimetry. The magnitude and spatial correlation functions of the velocity fluctuations of the settling aggregates were determined. It is shown that the fluctuations in the settling velocity exhibit characteristic correlations in the form of swirls. The formation of 3-D red blood cell aggregates leads to a large initial swirl. The growth of the aggregates and their sedimentation diminishes the swirls size.

3

Optical properties of deposit of red blood cells suspended in dextran solutions

Strzelecka J., Bosek M., Grzegorzewski B.

Optica Applicata

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2010

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Vol. 40, nr 1

177--185

EN

The optical properties of the deposit of red blood cells (RBCs) formed during sedimentation have been investigated. The human blood was obtained from healthy donors. RBCs were suspended in isotonic saline containing Dextran 70 of concentrations 2, 4 and 6 g/dl. Hematocrit of the samples was adjusted to 40%. The intensity of the light scattered by the samples of the RBC suspensions as a function of time and altitude from the bottom of a sample was measured. The region occupied by forming and sedimenting aggregates and the region occupied by deposit of the cells can be found in the sample and the temporal dependence of position of the interface separating both regions, called the deposit formation curve, can be determined. This curve exhibits the growth phase and the packing phase. We have obtained the mean intensity of light scattered by the deposit as a function of time. This intensity exhibits a monotonous decay with time over the growth as well as the packing phase, what shows that packing of the deposit occurs in the same way in both phases. The dependence from time of the mean hematocrit of the deposit was determined. We have introduced an empirical expression describing this dependence. Finally, using this dependence, we have obtained the mean intensity of light scattered by the deposit as a function of hematocrit. We have shown that this intensity follows an exponential decay. The values of an optical parameter of the deposit were found from this dependence.

4

Uncorrelated center of pressure sway of human body

Bosek M., Grzegorzewski B.

Biocybernetics and Biomedical Engineering

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2006

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Vol. 26, no. 4

33-38

EN

Analysis of the human center of pressure (COP) trajectory allows quantification of the state of the postural controI system. In our consideration, as a model of COP sway, Langevin equation has been accepted. Using an analysis based on this equation, the friction coefficient and diffusion matrix have been obtained. The diffusion matrix is analysed using its trace, the angle, of rotation of the coordinate system making this matrix diagonal and the ratio nu of greater eigenvalue of this matrix to its trace. In the rotated coordinate system, with respect to the system defined by anteriorposterior and mediolateral directions, COP displacements, for time intervals shorter than 1 s, are uncorrelated. Eigenvalues of the diffusion matrix are diffusion coefficients in this coordinate system. For different populations, dependences between angle [...] and ratio nu have been found. The values of the diffusion coefficients in both directions of the rotated coordinate system were found to be closer one another, with the greater range of the variability of the angle of this rotation.

5

Langevin equation as a model of COP sway

Bosek M., Grzegorzewski B., Kowalczyk A.

Biocybernetics and Biomedical Engineering

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2005

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Vol. 25, no. 2

53-59

EN

Static posturography is a method of analysis of the human postural control system, in which the center of pressure (COP) sway at quiet standing is investigated. In this study, the Langevin equation is used as a model of the COP sway. The solution of this equation is the probability density function P(r,t/r(t0),t0). For experimental data, it is possible to represent this function in the form of a histogram. In the wave vector space, the probability density function is represented by the characteristic function, containing full information about the distribution of the variable r - r(t0). For young, elderly and parkinsonian populations, for the excluded as well as for the included visual input, for short wave vector k, the experimental functions are shown to be wen approximated by the Gaussian theoretical functions. However, in these cases, for greater wave vectors, non-Gaussian properties of this variable are observed.