Mathematical models in the human cardiovascular system. Approaches to the description of 0.1 Hz oscillations of heart rate variability and the magistral blood flow
https://doi.org/10.24884/1682-6655-2018-17-4-11-23
Abstract
The review focuses on the application of methods of mathematical modeling in the study of the mechanisms underlying the formation of low-frequency oscillations in the human cardiovascular system. The main emphasis is put on 0.1 Hz rhythms and related author’s works. New ideas about the fundamental role of the hydrodynamic properties of the vascular bed in the formation of low-frequency oscillations at the frequency of 0.1 Hz are presented and justified.
About the Author
A. A. Grinevich
Institute of Cell Biophysics, Russian Acad. Sci.;
Institute of Theoretical and Experimental Biophysics, Russian Acad. Sci.
Russian Federation
Russian Federation
PhD, senior researcher,
142290, Moscow region, Pushchino, Institutskaya street, 3
References
1. Cohen MA, Taylor JA. Short-term cardiovascular oscillations in man: measuring and modelling the physiologies. The Journal of Physiology. 2002;542(3):669–683. Doi: 10.1113/jphysiol.2002.017483.
2. Kiselev AR, Gridnev VI. Oscillatory processes in vegetative regulation of cardiovascular system. Saratov Journal of Medical Scientific Research. 2011;7(1):34–39. (In Russ.).
3. Draghici AE, Taylor JA. The physiological basis and measurement of heart rate variability in humans. Journal of Physiological Anthropology. 2016;35(1). Doi: 10.1186/ s40101-016-0113-7.
4. Cooke WH, Hoag JB, Crossman AA et al. Human responses to upright tilt: a window on central autonomic integration. The Journal of Physiology. 1999;517(2):617–628. Doi: 10.1111/j.1469-7793.1999.0617t.x.
5. Stefanovska A, Bracic M, Kvernmo HD. Wavelet analysis of oscillations in the peripheral blood circulation measured by laser Doppler technique. IEEE Transactions on Biomedical Engineering. 1999;46(10):1230–1239. Doi: 10.1109/10.790500.
6. Sollers JJ, Sanford TA, Nabors-Oberg R et al. Examining changes in HRV in response to varying ambient temperature. IEEE Engineering in Medicine and Biology Magazine. 2002;21(4):30–34. Doi: 10.1109/memb.2002.1032636.
7. Furlan R, Porta A, Costa F et al. Oscillatory Patterns in Sympathetic Neural Discharge and Cardiovascular Variables During Orthostatic Stimulus. Circulation. 2000;101(8):886– 892. Doi: 10.1161/01.cir.101.8.886.
8. Kamiya A, Hayano J, Kawada T et al. Low-frequency oscillation of sympathetic nerve activity decreases during development of tilt-induced syncope preceding sympathetic withdrawal and bradycardia. American Journal of PhysiologyHeart and Circulatory Physiology. 2005;289(4):H1758– H1769. Doi: 10.1152/ajpheart.01027.2004.
9. Julien C. The enigma of Mayer waves: Facts and models. Cardiovascular Research. 2006;70(1):12–21. Doi: 10.1016/j. cardiores.2005.11.008.
10. Tyurina MY, Krasnikov GV, Tankanag AV. et al. Spectra of heart rate deviations under controlled breath conditions in human. Regionarnoe krovoobrashchenie i mikrotsirkulyatsiya. 2011;10(2):64–70. (In Russ.).
11. Song HS, Lehrer PM. The effects of specific respiratory rates on heart rate and heart rate variability. App. Psychophysiology and Biofeedback. 2003;28:13–23. Doi: 1090-0586/03/0300-0013/0.
12. Lehrer PM, Vaschillo E, Vaschillo B et al. Biofeedback Treatment for Asthma. Chest. 2004;126(2):352–361. Doi: 10.1378/chest.126.2.352.
13. Yucha CB, Tsai P-S, Calderon KS, Tian L. Biofeedbackassisted Relaxation Training for Essential Hypertension. The Journal of Cardiovascular Nursing. 2005;20(3):198–205. Doi: 10.1097/00005082-200505000-00012.
14. Karavidas MK, Lehrer PM, Vaschillo E et al. Preliminary Results of an Open Label Study of Heart Rate Variability Biofeedback for the Treatment of Major Depression. Applied Psychophysiology and Biofeedback. 2007;32(1):19– 30. Doi: 10.1007/s10484-006-9029-z.
15. Hassett AL, Radvanski DC, Vaschillo EG et al. A Pilot Study of the Efficacy of Heart Rate Variability (HRV) Biofeedback in Patients with Fibromyalgia. Applied Psychophysiology and Biofeedback. 2007;32(1):1–10. Doi: 10.1007/s10484-006-9028-0.
16. Horsman HM, Tzeng YC, Galletly DC, Peebles KC. The repeated sit-to-stand maneuver is a superior method for cardiac baroreflex assessment: a comparison with the modified Oxford method and Valsalva maneuver. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology. 2014;307(11):R1345–R1352. Doi: 10.1152/ajpregu.00376.2014.
17. Lehrer PM, Gevirtz R. Heart rate variability biofeedback: how and why does it work? Frontiers in Psychology. 2014;5. Doi: 10.3389/fpsyg.2014.00756.
18. Stamatakos GS. Spotlight on Cancer Informatics. Cancer Informatics. 2006;2:117693510600200. Doi: 10.1177/ 117693510600200029.
19. Karr JR, Sanghvi JC, Macklin DN et al. A Whole-Cell Computational Model Predicts Phenotype from Genotype. Cell. 2012;150(2):389–401. Doi: 10.1016/j.cell.2012.05.044.
20. Berntson GG, Thomas Bigger J, Eckberg DL et al. Heart rate variability: Origins, methods, and interpretive caveats. Psychophysiology. 1997;34(6):623–648. Doi: 10.1111/j.1469- 8986.1997.tb02140.x.
21. Kleiger RE, Stein PK, Bigger JT. Heart Rate Variability: Measurement and Clinical Utility. Annals of Noninvasive Electrocardiology. 2005;10(1):88–101. Doi: 10.1111/j.1542- 474x.2005.10101.x.
22. Angelone A, Coulter NA. Respiratory sinus arrhythmia: a frequency dependent phenomenon. Journal of Applied Physiology. 1964;19(3):479–482. Doi: 10.1152/jappl.1964.19. 3.479.
23. Bernardi L, Porta C, Gabutti A, Spicuzza L, Sleight P. Modulatory effects of respiration. Auton Neurosci. 2001;90(1- 2):47–56. Doi: 10.1016/s1566-0702(01)00267-3.
24. Gang Y, Malik M. Heart rate variability analysis in general medicine. Indian Pacing Electrophysiol. J. 2003;3:34–40.
25. Tripathi KK. Respiration and heart rate variability: a review with special reference to its application in aerospace medicine. Indian J. Aerosp. Med. 2004;48(1):64–75.
26. Taylor JA, Myers CW, Halliwill JR, et al. Sympathetic restraint of respiratory sinus arrhythmia: implications for vagal-cardiac tone assessment in humans. American Journal of Physiology-Heart and Circulatory Physiology. 2001;280(6):H2804–H2814. Doi: 10.1152/ajpheart. 2001.280.6.h2804.
27. Gridnev VI, Kiselev AR, Kotel’nikova EV, et al. Influence of external periodic stimuli on heart rate variability in healthy subjects and in coronary heart disease patients. Human Physiology. 2006;32(5):565–73. (In Russ.)]. Doi: 10.1134/s0362119706050100.
28. Krasnikov GV, Piskunova GM, Tankanag AV et al. Resonant-type interaction of the skin blood flow oscillations at controllable breath in human. Journal of New Medical Technologies. 2010;17(4):15–17. (In Russ.).
29. Tyurina MY, Krasnikov GV, Tankanag AV, et al. Formation of the respiratory-associated blood flow oscillations in the microvascular bed of the human skin under controlled breath conditions. Regionarnoe krovoobrashchenie i mikrotsirkulyatsiya. 2011;10(3):31–37. (In Russ.).
30. Krasnikov GV, Tyurina MY, Tankanag AV et al. Analysis of heart rate variability and skin blood flow oscillations under deep controlled breathing. Respiratory Physiology & Neurobiology. 2013;185(3):562–570. Doi: 10.1016/j.resp. 2012.11.007.
31. Seydnejad SR, Kitney RI. Modeling of Mayer waves generation mechanisms. IEEE Engineering in Medicine and Biology Magazine. 2001;20(2):92–100. Doi: 10.1109/ 51.917729.
32. McSharry PE, McGuinness MJ, Fowler AC. Confronting a cardiovascular system model with heart rate and blood pressure data. Computers in Cardiology. 2005; 32:587−590. Doi: 10.1109/cic.2005.1588169.
33. Magosso E, Ursino M. Cardiovascular response to dynamic aerobic exercise: A methematical model. Medical & Biological Engineering & Computing. 2002;40(6):660–674. Doi: 10.1007/bf02345305.
34. Ursino M, Magosso E. Role of short-term cardiovascular regulation in heart period variability: a modeling study. American Journal of Physiology-Heart and Circulatory Physiology. 2003;284(4):H1479–H1493. Doi: 10.1152/ajpheart. 00850.2002.
35. Kyureghyan SG, Petrosyan TG, Mkhitaryan AL, at al. The mathematical model of the cardiovascular system for physical loads. Izv. NAN RA i GIUA. 2005;18(3):585-592. (in Russ.).
36. Cheng L, Ivanova O, Fan H-H, Khoo MCK. An integrative model of respiratory and cardiovascular control in sleepdisordered breathing. Respiratory Physiology & Neurobiology. 2010;174(1-2):4–28. Doi: 10.1016/j.resp.2010.06.001.
37. Batzel JJ, Kappel F, Timischl-Teschl S. A cardiovascularrespiratory control system model including state delay with application to congestive heart failure in humans. Journal of Mathematical Biology. 2004;50(3):293–335. Doi: 10.1007/ s00285-004-0293-3.
38. Grinchenko VT, Rudnitskii AG. Model’ vzaimodeistviya serdechno-sosudistoi i respiratornoi system. Akustichnii visnik. 2006;9(3):16–26. (In Russ.).
39. Yildiz M, Ider YZ. Model based and experimental investigation of respiratory effect on the HRV power spectrum. Physiological Measurement. 2006;27(10):973–988. Doi: 10.1088/0967-3334/27/10/004.
40. Grinevich AA, Tankanag AV, Chemeris NK. The study of the dependence of the human heart rate from the frequency of controlled breathing. Mathematical biology and bioinformatics. 2013;8(2):537–552. (In Russ.). Doi: 10.17537/2013.8.537.
41. Hoffmann U, Yanar A, Franzeck UK et al. The frequency histogram – A new method for the evaluation of laser doppler flux motion. Microvascular Research. 1990;40(3):293–301. Doi: 10.1016/0026-2862(90)90028-p.
42. Mück-Weymann ME, Albrecht H-P, Hager D, et al. Respiratory-Dependent Laser–Doppler Flux Motion in Different Skin Areas and Its Meaning to Autonomic Nervous Control of the Vessels of the Skin. Microvascular Research. 1996;52(1):69–78. Doi: 10.1006/mvre.1996.0044.
43. Bertuglia S, Colantuoni A, Intaglietta M. Effects of L-NMMA and Indomethacin on Arteriolar Vasomotion in Skeletal Muscle Microcirculation of Conscious and Anesthetized Hamsters. Microvascular Research. 1994;48(1):68–84. Doi: 10.1006/mvre.1994.1039.
44. Landsverk SA, Kvandal P, Kjelstrup T, et al. Human Skin Microcirculation after Brachial Plexus Block Evaluated by Wavelet Transform of the Laser Doppler Flowmetry Signal. Anesthesiology. 2006;105(3):478–84. Doi: 10.1097/00000542- 200609000-00010.
45. Kvandal P, Landsverk SA, Bernjak A et al. Lowfrequency oscillations of the laser Doppler perfusion signal in human skin. Microvascular Research. 2006;72(3):120–127. Doi: 10.1016/j.mvr.2006.05.006.
46. Bernjak A, Clarkson PBM, McClintock PVE, Stefanovska A. Low-frequency blood flow oscillations in congestive heart failure and after β1-blockade treatment. Microvasc. Res. 2008;76(3):224–232. Doi: 10.1016/j.mvr.2008.07.006.
47. Stewart JM, Taneja I, Goligorsky MS, Medow MS. Noninvasive Measure of Microvascular Nitric Oxide Function in Humans Using Very Low-Frequency Cutaneous Laser Doppler Flow Spectra. Microcirculation. 2007;14(3):169– 180. Doi: 10.1080/10739680601139179.
48. Kirilina TV, Krasnikov GV, Tankanag AV et al. Spatial synchronization of the blood flow oscillations in human skin microcirculation. Regionarnoe krovoobrashchenie i mikrotsirkulyatsiya. 2009;8(3):32–36. (In Russ.).
49. Liao F, Jan Y-K. Enhanced phase synchronization of blood flow oscillations between heated and adjacent nonheated sacral skin. Medical & Biological Engineering & Computing. 2012;50(10):1059–1000. Doi: 10.1007/s11517- 012-0948-y.
50. Tankanag AV, Grinevich AA, Kirilina TV et al. Wavelet phase coherence analysis of the skin blood flow oscillations in human. Microvascular Research. 2014;95:53–59. Doi: 10.1016/j.mvr.2014.07.003.
51. Tankanag AV, Grinevich AA, Tikhonova IV et al. Phase synchronization of oscillations in cardiovascular and respiratory systems in humans. Derbov VL, Postnov DE, editors. Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III. 2017. Doi: 10.1117/12.2267492.
52. Tankanag AV, Grinevich AA, Tikhonova IV et al. Phase synchronization of skin blood flow oscillations in humans under asymmetric local heating. Biophysics. 2017;62(4):629–635. Doi: 10.1134/s0006350917040212.
53. Karavaev AS, Prokhorov MD, Ponomarenko VI et al. Synchronization of low-frequency oscillations in the human cardiovascular system. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2009;19(3):033112. Doi: 10. 1063/1.3187794.
54. Prokhorov MD, Ponomarenko VI, Gridnev VI et al. Synchronization between main rhythmic processes in the human cardiovascular system. Physical Review E. 2003;68(4): 041913. Doi: 10.1103/physreve.68.041913.
55. Kiselev AR, Gridnev VI, Prokhorov MD et al. Selection of optimal dose of beta-blocker treatment in myocardial infarction patients based on changes in synchronization between 0.1 Hz oscillations in heart rate and peripheral microcirculation. Journal of Cardiovascular Medicine. 2012;13(8):491–498. Doi: 10.2459/jcm.0b013e3283512199.
56. Grinevich AA, Tankanag AV, Chemeris NK. Role of elasticity of blood vessels in formation of highly amplitude oscillations of a blood flow with frequency of 0.1 Hz. Mathematical biology and bioinformatics. 2014;9(2):341–358. (In Russ.). Doi: 10.17537/2014.9.341.
57. Grinevich AA, Tankanag AV, Chemeris NK. The role of hydrodynamic parameters in the forming of low-frequency oscillations in arterial blood pressure in human. Mathematical Biology and Bioinformatics. 2016;11(2):233–244. Doi. org/10.17537/2016.11.233.
58. Ferrario M, Moissl U, Garzotto F et al. The Forgotten Role of Central Volume in Low Frequency Oscillations of Heart Rate Variability. PLOS ONE. 2015;10(3):e0120167. Doi: 10.1371/journal.pone.0120167.
59. Grinevich AA, Tankanag AV, Safronova VG, Chemeris NK. Role of additive stochastic modulation of the heart activity in the formation of 0.1-Hz blood flow oscillations in the human cardiovascular system. Doklady Biological Sciences. 2016;468(1):106–111. (In Russ.). Doi: 10.7868/ S0869565216150263.
60. Grinevich AA, Tankanag AV, Chemeris NK. Formation of the peak amplitude of blood flow oscillations at a frequency of 0.1 Hz in the human cardiovascular system by the noise effect on the heart. Derbov VL, Postnov DE, editors. Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III. 2017. Doi: 10.1117/12.2267634.
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For citations:
Grinevich A.A. Mathematical models in the human cardiovascular system. Approaches to the description of 0.1 Hz oscillations of heart rate variability and the magistral blood flow. Regional blood circulation and microcirculation. 2018;17(4):11-23. (In Russ.) https://doi.org/10.24884/1682-6655-2018-17-4-11-23
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