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Use of Input Impedance to Determine Changes in the Resistance of Arterial Vessels at Different Levels in Feline Femoral Bed

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Abstract

In many studies, the functional state of vessels of different caliber was determined by fitting the lumped parameters of a mathematical model of the bed in order to fit the vascular input impedance (Z in) data. However, reliability of the results obtained in such a way remains uncertain. In this study, we employed a mathematical model with seven lumped parameters and Z in experimental data to analyze the distribution of resistance across the arterial bed of the hind limb in anesthetized cats, to test reliability of this distribution and to describe the process of ascending arterial dilation followed occlusion of iliac artery. The vascular bed was divided into three segments: large arteries, medium-sized arterial vessels and precapillary resistance vessels together with venous part of the bed. Based on the data of Z in measured in a wide frequency range (from 0 to 150 Hz) we showed that pharmacologically induced constriction and dilation of the arterial microvessels were reflected in the model by the changes in the resistance of distal precapillary vessels only, whereas the local constriction or dilation of femoral and iliac arteries as well as artificial stenosis of the femoral artery resulted exclusively in the changes of the resistance describing the state of large arteries. Using the input impedance method we could demonstrate and quantitatively describe the process of ascending arterial dilation during the post-occlusion (reactive) hyperemia. All these results prove that the model of vascular bed with seven lumped elements used in combination with input hydraulic impedance data can be an effective tool permitted to quantitatively analyze the functional state of arterial vessels of different caliber and to describe the changes in resistance of arterial vessels during vascular reactions.

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References

  1. Balashov, S. A., A. M. Melkumyants, A Yu Naumov, and K. V. Sheptutsolov. Determination of the parameters of hydraulic models of vascular bed by the input impedance method. Fluid Dyn. 36(1):48–56, 2001.

    Article  CAS  Google Scholar 

  2. Bard, Y. Nonlinear Parameter Estimation. New York: Academic Press, 1974. 341 pp.

  3. Bauer, R. D., R. Busse, and A. Schabert. The input impedance of the peripheral vascular termination in skeletal muscle. Pflugers Arch. 403:308–311, 1985.

    Article  CAS  PubMed  Google Scholar 

  4. Bendat, J. S., and A. G. Piersol. Engineering Applications of Correlation and Spectral Analysis. New York, John Wiley & Sons, 1980, 315 pp.

  5. Burattini, R., and P. O. Di Salvia. Development of systemic arterial mechanical properties from infancy to adulthood interpreted by four-element windkessel models. J. Appl. Physiol. 103:66–79, 2006.

    Article  Google Scholar 

  6. Burattini, R., R. Fogliardi, and K. B. Campbell. Lumped model of terminal aortic impedance in the dog. Ann. Biomed. Eng. 22:381–391, 1994.

    Article  CAS  PubMed  Google Scholar 

  7. Burattini, R., and G. Gnudi. Computer identification of models for the arterial tree input impedance: comparison between two new simple models and first experimental results. Med. Biol. Eng. Comput. 20:134–144, 1982.

    Article  CAS  PubMed  Google Scholar 

  8. Draperm, N. R., H. Smith. Applied Regression Analysis. New York: Wiley & Sons, Inc., 2nd ed., 1981, 709 pp.

  9. Fenger-Gron, J., M. J. Mulvany, and K. L. Christensen. Mesenteric blood pressure profile of conscious, freely moving rats. J. Physiol. 488:753–760, 1995.

    CAS  PubMed Central  PubMed  Google Scholar 

  10. Folkow, B., R. R. Sonnenshein, and D. L. Wright. Loci of neurogenic and metabolic effects on precapillary vessels of skeletal muscle. Acta Physiol. Scand. 81(4):459–471, 1971.

    Article  CAS  PubMed  Google Scholar 

  11. Fronek, K., and B. W. Zweifach. Microvascular pressure distribution in skeletal muscle and vasodilatation. Am. J. Physiol. 228:791–796, 1975.

    CAS  PubMed  Google Scholar 

  12. Gessner, U. Vascular input impedance. In: Cardiovascular Fluid Dynamics, edited by D. H. Bergel. London: Academic Press, 1972, Vol. 1, Chap. 10, pp. 315–349.

  13. Kartamyshev, S. P., S. A. Balashov, and A. M. Melkumyants. Role of endothelium sensitivity to shear stress in noradrenaline-induced constriction of feline femoral arterial bed under constant flow and constant pressure perfusions. J. Vasc. Res. 44:1–10, 2007.

    Article  CAS  PubMed  Google Scholar 

  14. Khayutin, V. M., V. P. Nikolsky, A. N. Rogoza, and E. V. Lukoshkova. Endothelium determines stabilization of the pressure drop in arteries. Acta Physiol. Scand. 148:295–304, 1993.

    Article  CAS  PubMed  Google Scholar 

  15. Khayutin, V. M. Active arterial function: prompt adaptation of the vascular lumen to the blood flow and viscosity. In: Contemporary Problems of Biomechanics, edited by G. G. Chernyi and S. A. Regirer. Moscow: Mir Publ. & Boca Raton: CRC Press, 1990, pp. 142–207.

  16. Lutchen, K. R., and A. C. Jackson. Reliability of parameter estimates from models applied to respiratory impedance data. J. Appl. Physiol. 62(2):403–413, 1987.

    CAS  PubMed  Google Scholar 

  17. Marquardt, D. W. An algorithm for least squares estimation of nonlinear parameters –. J. Soc. Ind. Appl. Math. 11:431–441, 1963.

    Article  Google Scholar 

  18. McDonald, D. A. Blood Flow in Arteries. London: Edward Arnold Ltd., 1960.

    Google Scholar 

  19. Melkumyants, A. M., S. A. Balashov, E. S. Veselova, and V. M. Khayutin. Continuous control of the lumen of feline conduit arteries by blood flow rate. Cardiovasc. Res. 21:863–870, 1987.

    Article  CAS  PubMed  Google Scholar 

  20. Olufsen, M. S., and A. Nadim. On deriving lumped models for blood flow and pressure in the systemic arteries. Math. Biosci. Eng. 1(1):61–80, 2004.

  21. O’Rourke, M. F., and M. G. Taylor. Vascular impedance of the femoral bed. Circ. Res. 18:126–139, 1966.

    Article  Google Scholar 

  22. O’Rourke, M. F., and M. G. Taylor. Input impedance of the systemic circulation. Circ. Res. 20:365–380, 1967.

    Article  PubMed  Google Scholar 

  23. Piene, H. Some physical properties of the pulmonary arterial bed deduced from pulsatile arterial flow and pressure. Acta. Physiol. Scand. 98:295–306, 1976.

  24. Piene, H., and A. Hauge. Reduction of pulsatile hydraulic power in the pulmonary circulation caused by moderate vasoconstriction. Cardiovasc. Res. 10:503–513, 1976.

    Article  CAS  PubMed  Google Scholar 

  25. Press W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flann, Numerical recipes in C. In: The Art of Scientific Computing, 2nd ed. Cambridge, UK: Cambridge Univ. Press, 1992.

  26. Rogoza, A. N. A contact transducer for continuous measurement of the diameter of blood vessels. Bull. Exp. Biol. Med. 91:698–701, 1981.

    Article  Google Scholar 

  27. Segal, S. S., and B. R. Duling. Communication between feed arteries and micro vessels in hamster striated muscle: segmental vascular responses are functionally coordinated. Circ. Res. 59:283-290, 1986.

  28. Segers, P., S. Brimioulle, N. Stergiopulos, N. Westerhof, R. Naeije, M. Maggiorini, and P. Verdonck. Pulmonary arterial compliance in dogs and pigs: the three-element windkessel model revisited. Am. J. Physiol. 277(2):H725–H731, 1999.

    CAS  PubMed  Google Scholar 

  29. Stergiopulos, N., B. E. Westerhof, and N. Westerhof. Total arterial inertance as the fourth element of the windkessel model. Am. J. Physiol. 276(1):H81–H88, 1999.

    CAS  PubMed  Google Scholar 

  30. Vanderpool, R., R. Naeije, and N. C. Chesler. Impedance in isolated mouse lungs for the determination of site of action vasoactive agents and disease. Ann. Biomed. Eng. 38(5):1854–1861, 2010.

    Article  PubMed Central  PubMed  Google Scholar 

  31. Westerhof, N., F. Bosman, C. J. De Vries, and A. Noordergraaf. Analog studies of the human systemic arterial tree. J. Biomech. 2:121–143, 1969.

    Article  CAS  PubMed  Google Scholar 

  32. Westerhof, N., G. Elzinga, and P. Sipkema. An artificial arterial system for pumping hearts. J. Appl. Physiol. 31:776–781, 1971.

    CAS  PubMed  Google Scholar 

  33. Westerhof, N., J.-W. Lankhaar, and B. E. Westerhof. The arterial windkessel. Med. Biol. Eng. Comput. 47:131–141, 2009.

    Article  PubMed  Google Scholar 

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Acknowledgments

The work was supported by the Russian Foundation for Basic Research (Grant #13-04-01082). We are grateful to Dr. S. Revenko for valuable discussions and assistance.

Conflict of interest

The authors (A. Naumov, S. Balashov and A. Melkumyants) have no conflicts of interest (financial or otherwise).

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Authors and Affiliations

  1. Institute of Experimental Cardiology, Russian Cardiology Research Center, 121552, 3rd Cherepkovskaya Str. 15A, Moscow, Russia

    Sergey A. Balashov & Arthur M. Melkumyants

  2. Chair of Physics of Living Systems, Moscow Institute of Physics and Technology (State University), Moscow, Russia

    Alexey Yu. Naumov & Arthur M. Melkumyants

Authors
  1. Alexey Yu. Naumov
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  2. Sergey A. Balashov
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  3. Arthur M. Melkumyants
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Correspondence to Arthur M. Melkumyants.

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Associate Editor Scott I Simon oversaw the review of this article.

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Naumov, A.Y., Balashov, S.A. & Melkumyants, A.M. Use of Input Impedance to Determine Changes in the Resistance of Arterial Vessels at Different Levels in Feline Femoral Bed. Ann Biomed Eng 42, 1644–1657 (2014). https://doi.org/10.1007/s10439-014-1016-6

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  • DOI: https://doi.org/10.1007/s10439-014-1016-6

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