Izvestiya of Saratov University.


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Baatyrov R. T., Kalinkin M. Y., Usanov A. D., Dobdin S. Y., Skripal A. V. Estimation of the Value of Reverse Blood Flow in the Artery by the Second Derivative of the Pulse Pressure Wave. Izvestiya of Saratov University. Physics , 2020, vol. 20, iss. 3, pp. 178-182. DOI: 10.18500/1817-3020-2020-20-3-178-182

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Estimation of the Value of Reverse Blood Flow in the Artery by the Second Derivative of the Pulse Pressure Wave

Baatyrov Rakhim Taalaibekovich, Saratov State University
Kalinkin Mikhail Yurievich, Saratov State University
Usanov Andrey Dmitryevich, Saratov State University
Dobdin Sergey Yur'evich, Saratov State University
Skripal Anatoly Vladimirovich, Saratov State University

Background and Objectives: Previously, the diastolic section of the pulse wave was most often analyzed as the result of reflection of a direct wave from the elements of peripheral vessels. However, measurements of the negative linear velocity of blood flow using ultrasound dopplerograms clearly indicate the presence of reverse blood flow in the arteries. The aim of the work was to establish the relationship of the second derivative of the pulse pressure wave with the value of the reverse blood flow in the arterial bed. Materials and Methods: The shape of the pressure pulse wave was calculated based on the two-element windkessel model. The calculation of the second derivative of the pulse pressure wave was performed taking into account the direct and reverse blood flow occurring in the arteries at different values of the reverse blood flow. Results: The linear dependence of the second derivative of the pulse wave on the value of the blood volume of the reverse wave on the diastole is obtained. Conclusions: It is concluded that the second derivative of the pulse pressure wave can be used to estimate the value of the reverse blood flow in the artery, which depends on the state of the peripheral vascular system.

  1. Zhao E., Barber J., Burch M., Unthank J., Arciero J. Modeling acute blood flow responses to a major arterial occlusion. Microcirculation, 2020, vol. 27, iss. 4, pp. e12610. DOI: https://doi.org/10.1111/micc.12610
  2. Hwang J. Y. Doppler ultrasonography of the lower extremity arteries: anatomy and scanning guidelines. Ultrasonography, 2017, vol. 36, no. 2, pp. 111–119.
  3. Zhirnova O. A., Beresten’ N. F., Pestovskaja O. R., Bogdanova E. Ja. Non-invasive diagnosis of disruptions of the elastic properties of arterial vessels. Angiology, 2011, no. 1, pp. 27–42 (in Russian).
  4. Kalakutskiy L. I., Fedotov A. A. Diagnostics of endothelial dysfunction by the method of contour analysis of pulse wave. Izvestiya SFedU. Engineering Sciences, 2009, vol. 98, no. 9, pp. 93–98 (in Russian).
  5. Ivanov S. V., Ryabikov A. N., Malyutina S. K. Arterial stiffness and pulse wave reflection in association with arterial hypertension. Siberian Scientific Medical Journal, 2008, vol. 131, no. 3, pp. 9–12 (in Russian).
  6. Frolov A. V., Sidorenko G. I., Vorob’ev A. P., Mel’nikova O. P., Gul’ L. M. Direct and reflected pulse waves: research methods. Kardiologija v Belarusi [Cardiology in Belarus], 2009, no. 5, pp. 99–108 (in Russian).
  7. Mason D. T., Braunwald E., Ross J. Jr., Morrow A. G. Diagnostic value of the first and second derivatives of the arterial pressure pulse in aortic valve disease and in hypertrophic subaortic stenosis. Circulation, 1964, vol. 30, iss. 1, pp. 90–100. DOI: https://doi.org/10.1161/01.CIR.30.1.90
  8. Hashimoto J., Chonan K., Aoki Y., Nishimura T., Ohkubo T., Hozawa A., Suzuki M., Matsubara M., Michimata M., Araki T., Imai Y. Pulse wave velocity and the second derivative of the finger photoplethysmogram in treated hypertensive patients: their relationship and associating factors. Journal of Hypertension, 2002, vol. 20, iss. 12, pp. 2415–2422. DOI: https://doi.org/10.1097/00004872-200212000-00021
  9. Inoue N., Kawakami H., Yamamoto H., Ito Ch., Fujiwara S., Sasaki H., Kihara Y. Second derivative of the fi nger photoplethysmogram and cardiovascular mortality in middle-aged and elderly Japanese women. Hypertension Research, 2017, vol. 40, iss. 2, pp. 207–211. DOI: https://doi.org/10.1038/hr.2016.123
  10. Munir S., Guilcher A., Kamalesh T., Clapp B., Redwood S., Marber M., Chowienczyk P. Peripheral augmentation index defi nes the relationship between central and peripheral pulse pressure. Hypertension, 2008, vol. 51, iss. 1, pp. 112–118. DOI: https://doi.org/10.1161/HYPERTENSIONAHA.107.096016
  11. Usanov D. A., Skripal A. V., Brilenok N. B., Dobdin S. Yu., Averianov A. P., Bakhmetev A. S., Baatyrov R. T. Functional diagnostics of arterial vessels by pulse wave analysis and equipment for its implementation. Biomedical Engineering, 2020, vol. 54, no. 1, pp. 41–45. DOI: https://doi.org/10.1007/s10527-020-09970-w
  12. Usanov D. A., Skripal A. V., Brilenok N. B., Dobdin S. Yu., Averianov A. P., Bakhmetev A. S., Baatyrov R. T. Diagnostics of functional state of endothelium in athletes by the pulse wave. Proceedings of the 12th International Symposium on Computer Science in Sport (IACSS 2019), 2019, vol. 1028, pp. 176–184. DOI: https://doi.org/10.1007/978-3-030-35048-2_21
  13. Usanov D. A., Protopopov А. А., Skripal А. V., Averyanov А. P., Repin V. F., Rytik А. P., Vagarin А. Yu., Kuznetsov М. А., Petrova М. G. Diagnostics of evolution of risk collapse complications at student group with anomalous cardiovascular reaction. Saratov Journal of Medical Scientific Research, 2010, vol. 6, no. 3, pp. 615–619 (in Russian)
  14. Westerhof N., Lankhaar J., Westerhof B. E. The arterial Windkessel. Med. Biol. Eng. Comput., 2009, vol. 47, iss. 2, pp. 131–141. DOI: https://doi.org/10.1007/s11517-008-0359-2
  15. Hoppensteadt F. C., Peskin Ch. Modeling and simulation in medicine and the life sciences. New York, Springer-Verlag, 2002. 355 p.
  16. Baruch M. C., Warburton D.ER., Bredin S. SD., Cote A., Gerdt D. W., Adkins C. M. Pulse decomposition analysis of the digital arterial pulse during hemorrhage simulation. Nonlinear Biomed. Phys., 2011, vol. 5, no. 1, pp. 1–15.
  17. Magosso E., Cavalcanti S., Ursino M. Theoretical analysis of rest and exercise hemodynamics in patients with total cavopulmonary connection. Am. J. Physiol. Heart Circ. Physiol., 2002, vol. 282, pp. H1018–H1034.
  18. Karavaev A. S., Ishbulatov Yu. M., Ponomarenko V. I., Bezruchko B. P., Kiselev A. R., Prokhorov M. D. Autonomic control is a source of dynamical chaos in the cardiovascular system. CHAOS, 2019, vol. 29, pp. 121101.