Abstract
Arterial blood pressure P(t) and flow V(t) curves measured by ultrasound or other technique exhibit quasi-regular dynamics with clear patterns of the P(V) loops. In this paper, the curves measured in central aorta, upper, and low extremities of young healthy volunteers and patients with cardiovascular disorders are studied. Both quasi-regular and chaotic dynamics of the P(t) and V(t) signals are found. A mathematical model of a series connection of three nonlinear viscoelastic chambers representing central (1) and peripheral arterial (2) and peripheral venous (3) compartments are proposed. The pressure and flow oscillations in each compartment are computed at different model parameters such as resistivity of the microcirculatory bed, elastic and viscous parameters of the arterial and venous walls. It was found the quasi-regular dynamics with different patient-specific patterns of the P(V) attractor are proper to variations of the material parameters within the physiological limits, while the chaotic dynamics appear when wall compliance and/or resistivity of the chambers (2) or (3) are too high. Those variations are proper to deep vein thrombosis, microcirculatory disorders, and age-related degradation of the blood vessel wall.
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References
Nichols, W., O’Rourke, M., Vlachopoulos, C.H. (Eds.): McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles. Hodder Arnold (2011)
Milnor, W.R.: Hemodynamics. Williams & Wilkins, Baltimore (1989)
Kizilova N., Philippova H., Zenin O.: A realistic model of human arterial system: blood flow distribution, pulse wave propagation and modeling of pathology. In: Korzynskiego, M., Cwanka, J. (eds.) Mechanika w Medycynie, vol. 10, pp. 103–118. Rzeszow (2010)
Kizilova, N.: Blood flow in arteries: regular and chaotic dynamics. In: Awrejcewicz, J., Kazmierczak, M., Olejnik, P., Mrozowski, K. (eds) Dynamical Systems. Applications, pp. 69–80. Lodz Politechnical University Press (2013)
Wagner, C.D., Persson, P.B.: Nonlinear chaotic dynamics of arterial blood pressure and renal blood flow. Am. J. Physiol. 268(2), H621–H627 (1995)
Glenny, R.W., Polissar, N.L., Mckinney, S., Robertson, H.T.: Temporal heterogeneity of regional pulmonary perfusion is spatially clustered. J. Appl. Physiol. 79, 986–1001 (1995)
Venegas, J.G., Galletti, G.G.: Low-pass filtering, a new method of fractal analysis: application to PET images of pulmonary blood flow. J. Appl. Physiol. 88, 1365–1373 (2000)
Shirouzu E., Tsuda Y., Sugano H.: Nonlinear analysis of pulse waves measured at brachial artery. In: Proceedings of 1st Joint BMES/EMBS Conference, vol. 2, p. 901 (1999)
Trzeciakowski, J., Chilian, W.: Chaotic behavior of the coronary circulation. Med. Biol. Eng. Comput. 46(5), 433–442 (2008)
Shlesinger, M.F.: Fractal time and 1/f noise in complex systems. Ann. N. Y. Acad. Sci. 504, 214–228 (1987)
Oyama-Higa, M., Miao, T.: Representation of a physio-psychological index through constellation graphs. Lect. Notes Comput. Sci. 2610, 811 (2005)
Li, Ch-M, Du, Y-Ch., Wu, J.-X., et al.: Dynamic analysis with a fractional-order chaotic system for estimation of peripheral arterial disease in diabetic foot. Meas. Sci. Technol. 24(8), 1–11 (2013)
Chen, H.-K., Lee, Ch-I: Anti-control of chaos in rigid body motion. Chaos, Solitons Fractals 21(4), 957–965 (2004)
Hamadiche, M., Kizilova, N.N.: Temporal and spatial instabilities of the flow in the blood vessels as multi-layered compliant tubes. Int. J. Dyn. Fluids 1(1), 1–23 (2005)
Kizilova, N., Hamadiche, M., Gad-el-Hak, M.: Mathematical models of biofluid flows in compliant ducts: a review. Arch. Mech. 64(1), 1–30 (2012)
Kizilova, N.N.: Pulse wave reflections in branching arterial networks and pulse diagnosis methods. J. Chin. Inst. Eng. 26(6), 869–880 (2013)
Tyberg, J.V., Davies, J.E., Wang, Z.h., et al.: Wave intensity analysis and the development of the reservoir–wave approach. Med. Biol. Eng. Comput. 47, 221–232 (2090)
Zenin, O.K., Kizilova, N.N., Philippova, E.N.: Studies on the structure of human coronary vasculature. Biophysics. 52(5), 499–503 (2007)
Kizilova, N.: A detailed digital model of the human arterial system. In: Proceedings of the 1st International Conference on Complex Medical Engineering, pp. 287–292. Japan (2005)
Kizilova, N.: A novel model for explanation the regular and chaotic dynamics in arterial blood flow. In: Dynamical Systems and their Applications, p. 30. Book of abstracts, Kiev (2015)
Alastruey, J., Khir, A.W., Matthys, K.S., et al.: Pulse wave propagation in a model human arterial network: assessment of 1-D visco-elastic simulations against in vitro measurements. J. Biomech. 44, 2250–2258 (2011)
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Kizilova, N. (2016). Three-Chamber Model of Human Vascular System for Explanation the Quasi-Regular and Chaotic Dynamics of the Blood Pressure and Flow Oscillations. In: Awrejcewicz, J. (eds) Dynamical Systems: Modelling. DSTA 2015. Springer Proceedings in Mathematics & Statistics, vol 181. Springer, Cham. https://doi.org/10.1007/978-3-319-42402-6_18
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