Fractal Dimensions in Red Blood Cells

We studied the erythrocyte aggregability for different animals using fractal analysis. Red blood cell aggregation is an important component of whole blood viscosity and is the major cause of the non-Newtonian flow properties of blood. To understand the aggregation process many models have been proposed in the literature. Since aggregates formed by aggregation have a fractal structure, mathematical descriptions of their irregular structure can be obtained using fractal geometry. For this purpose, blood samples were prepared from cows, sheep, rabbits, roosters, horses and humans by diluting 1:200 and mixing for 3 min in adequate reactives. A Turk room, microscope system and computer acquisition system (frame-grabber or video blaster) were used to register and analyse images of cell aggregates. In the case of the blood from cows, sheep, rabbits and roosters no aggregation phenomenon was observed in the microscope slides. However, in the case of horses and humans, erythrocyte aggregates were identified and fractal analysis was carried out by means of a modified box counting method. Higher fractal dimension values were found for horse in comparison to human samples. The results obtained suggest that higher fractal dimensions correspond to higher aggregability, meaning higher complexity of cells’ properties of interaction with each other. These results are concordant with literature data. We conclude that horses and humans have more complex structures of blood cells than the other species in this study.

Fractal Dimensions in Red Blood Cells

We studied the erythrocyte aggregability for different animals using fractal analysis. Red blood cell aggregation is an important component of whole blood viscosity and is the major cause of the non-Newtonian flow properties of blood. To understand the aggregation process many models have been proposed in the literature. Since aggregates formed by aggregation have a fractal structure, mathematical descriptions of their irregular structure can be obtained using fractal geometry. For this purpose, blood samples were prepared from cows, sheep, rabbits, roosters, horses and humans by diluting 1:200 and mixing for 3 min in adequate reactives. A Turk room, microscope system and computer acquisition system (frame-grabber or video blaster) were used to register and analyse images of cell aggregates. In the case of the blood from cows, sheep, rabbits and roosters no aggregation phenomenon was observed in the microscope slides. However, in the case of horses and humans, erythrocyte aggregates were identified and fractal analysis was carried out by means of a modified box counting method. Higher fractal dimension values were found for horse in comparison to human samples. The results obtained suggest that higher fractal dimensions correspond to higher aggregability, meaning higher complexity of cells’ properties of interaction with each other. These results are concordant with literature data. We conclude that horses and humans have more complex structures of blood cells than the other species in this study.

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  • Baskurt, O.K., Kucutakay, M.B., Yalcin O., Meiselman, H.J.: Aggregation behavior and electrophoretic mobility of red blood cells in various mammalian species. Biorheology, 2000; 37: 417- 428. 7. Gudmundsson, M., Oden A., Bjelle, A.: On whole blood viscosity measurements in healthy individuals and in rheumatoid arthritis patients. Biorheology, 1994; 31: 407-416.
  • Nguyen, P.D., O’Rear, E.A.: Temporary aggregate size distributions from simulation of platelet aggregation and disaggregation. Ann. Biomed. Eng., 1990; 18: 427-444.
  • Neelamegham, S., Munn, L.L., Zygourakis, K.A.: Model for the kinetics of homotypic cellular aggregation under static conditions. Biophys. J., 1997; 72: 51-64.
  • Quemada, D.: A non-linear Maxwell model of biofluids: Application to normal blood. Biorheology, 1993; 30: 253-260.
  • Falcó, C., Vayá, A., Iborra, J., Moreno, I., Palanca, S., Aznar, J.: Erythrocyte aggregability and disaggregability in thalassemia trait carriers analyzed by a laser backscattering technique. Clin. Hemorheol. Micro., 2003; 28: 245-249.
  • Oancea, S., Rapa, A., Rusu, V., Cojocaru, N.: A non-Newtonian model of blood for species of athletic mammals. Biorheology, 1999; 36: 129.
  • Rapa, A., Rusu, V., Rotaru, F., Rapa, E., Bejinariu, S., Oancea, S.: Direct evaluation of erythrocyte aggregability in human, sheep and cow blood samples with a computerized image analysis. Rev. Med. Chir. Soc. Med. Nat. Iasi., 1999; 103: 127-130.
  • Nonnenmacher, T.F., Losa, G.A., Weibel, E.R, ed.: Fractals in Biology and Medicine. Boston, USA, 1993.
  • Havlin, S., Buldyrev, S.V., Goldberger, A.L., Mantegna, R.N., Ossadnik, S.M., Peng, C.K., Simons, M., Stanley, H.E.: Fractals in biology and medicine. Chaos Solitons Fractals, 1995; 6: 171-201.
  • Haskell, J.P., Ritchie, M.E., Olff, H.: Fractal geometry predicts varying body size scaling relationships for mammal and bird home ranges. Nature, 2002; 418 (6897): 527-530.
  • Kang, M.Z., Zeng, Y.J., Liu, J.G.: Fractal research on red blood cell aggregation. Clin. Hemorheol. Micro., 2000; 22: 229-236.
  • Bozhokin, S.V.: Quantitative description of the morphological structure of aggregated cellular elements in blood. Biofizika, 1994; 39: 1051-1057.
  • Windberger, U., Ribitsch, V., Resch, K.L., Losert, U.: The viscoelasticity of blood and plasma in pig, horse, dog, ox, and sheep. J. Exp. Anim. Sci. ,1993/1994; 36: 89-95.
  • Weng, X., Cloutier, G., Pibarot, P., Durand, L.G.: Comparison and simulation of different levels of erytrocyte aggregation with pig, horse, sheep, calf and normal human blood. Biorheology, 1996; 33: 365-377.
  • Popel, A., Johnson, P.C., Kameneva, M.V., Wild, M.A.: Capacity for red blood cell aggregation is higher in athletic mammalian species than in sedentary species. J. Appl. Physiol., 1994; 77: 1790-1794.
  • Barshtein, G., Wajnblum, D., Yedgar S.: Kinetics of linear rouleaux formation studied by visual monitoring of red cell dynamic organization. Biophys. J., 2000; 78: 2470-2474.
  • Baumler, H., Neu B., Mitlohner, R., Georgieva, R., Meiselman, H.J., Kiesewetter, H.: Electrophoretic and aggregation behavior of bovine, horse and human red blood cells in plasma and in polymer solutions. Biorheology, 2001; 38: 39-51.
  • Windberger, U., Bartholovitsch, A., Plasenzotti, R., Korak, K.J., Heinze, G.: Whole blood viscosity, plasma viscosity and erythrocyte aggregation in nine mammalian species: reference values and comparison of data. Exp. Physiol., 2003; 88: 431- 440.