The study of the dependence of the human heart rate from the frequency of controlled breathing

A. A. Grinevich ; A. V. Tankanag ; N. K. Chemeris

Matematičeskaâ biologiâ i bioinformatika, Tome 8 (2013) no. 2, pp. 537-552.

Résumé

The dependence of heart rate variability from the frequency of controlled breathing was studied by comprehensive mathematical model «PNEUMA». It is shown that the inclusion in the model the frequency dependence of the signal transmission coefficients for the parasympathetic and beta-sympathetic regulation of heart rate leads to the bell-shaped dependence of heart rate variability from frequency of controlled breathing with a peak at a frequency of 0.1 Hz. This is in qualitative agreement with experimental data.

Bibliographie

[1] Baevskii R. M., Berseneva A. P., Otsenka adaptatsionnykh vozmozhnostei organizma i risk razvitiya zabolevanii, Meditsina, M., 1997

[2] “Task Force of the European Society of Cardiology and North American Society of Pacing and Electrophysiology. Heart rate variability. Standards of measurement, physiological interpretation and clinical use”, Circulation, 93 (1996), 1043–1065 ; Vestnik Aritmologii, 11 (1998), 53–78 | DOI

[3] Berntson G. G., Bigger J. T., Eckberg D. L., Grossman P., Kaufmann P. G., Malik M., Nagaraja H. N., Porges S. W., Saul J. P., Stone P. H., van der Molen M. W., “Heart rate variability: origins, methods and interpretive caveats”, Psychophysiology, 34 (1997), 623–648 | DOI

[4] Ryabykina G. V., Sobolev A. V., Variabelnost ritma serdtsa, Star'Ko, M., 1998, 215 pp.

[5] Fleishman A. N., Medlennye kolebaniya gemodinamiki. Teoriya, prakticheskoe primenenie v klinicheskoi meditsine i profilaktike, Nauka, Novosibirsk, 1998, 266 pp.

[6] Kleiger R. E., Stain P. K., Bigger J. T., “Heart rate variability: measurement and clinical utility”, Ann. Nucl. Eng., 10 (2005), 88–101

[7] Angelone A., Coulter N. A. Jr., “Respiratory sinus arrhythemia: a frequency dependent phenomenon”, J. Appl. Physiol., 19 (1964), 479–482

[8] Bernardi L. C., Porta A., Gabutti L., Spicuzza L., Sleight P., “Modulatory effects of respiration”, Auton. Neurosci. Basic and Clin., 90 (2001), 47–56 | DOI

[9] Cohen M. A., Taylor J. A., “Short-term cardiovascular oscillations in man: measuring and modeling the physiologies”, J. Physiol., 542 (2002), 669–683 | DOI

[10] Taylor J. A., Myers C. W., Halliwill J. R., Seidel H., Eckberg D. L., “Sympathetic restraint of respiratory sinus arrhythmia: implications for vagal-cardiac tone assessment in humans”, Am. J. Physiol. Heart Circ. Physiol., 280 (2001), 2804–2814

[11] Song H.-S., Lehrer P. M., “The Effects of Specific Respiratory Rates on Heart Rate and Heart Rate Variability”, App. Psychophysiology and Biofeedback, 28:1 (2003), 13–23 | DOI

[12] Kiselev A. R., Kirichuk V. F., Posnenkova O. M., Gridnev V. I., “Izuchenie prirody periodicheskikh kolebanii serdechnogo ritma na osnove prob s upravlyaemym dykhaniem”, Fiziologiya cheloveka, 31:3 (2005), 76–83

[13] Gridnev V. I., Kiselev A. R., Kotelnikova E. V., Posnenkova O. M., Dovgalevskii P. Ya., Kirichuk V. F., “Vliyanie vneshnikh periodicheskikh stimulov na variabelnost serdechnogo ritma u zdorovykh lits i u patsientov s ishemicheskoi boleznyu serdtsa”, Fiziologiya cheloveka, 32:5 (2006), 74–83

[14] Krasnikov G. V., Piskunova G. M., Tankanag A. V., Tyurina M. I., Chemeris N. K., “Rezonansno-podobnoe vzaimodeistvie kolebanii krovotoka v mikrotsirkulyatornom rusle kozhi cheloveka pri kontroliruemom dykhanii”, Vestnik novykh meditsinskikh tekhnologii, XVII:4 (2010), 15–17

[15] Tyurina M. I., Krasnikov G. V., Tankanag A. V., Piskunova G. M., Chemeris N. K., “Spektry deviatsii chastoty serdechnykh sokraschenii cheloveka pri kontroliruemom dykhanii”, Regionarnoe krovoobraschenie i mikrotsirkulyatsiya, 2011, no. 2, 64–70

[16] Krasnikov G. V., Tyurina M. Y., Tankanag A. V., Piskunova G. M., Chemeris N. K., “Analysis of heart rate variability and skin blood flow oscillations under deep controlled breathing”, Respir. Physiol. Neurobiol., 185:3 (2013), 562–570 | DOI

[17] Kiselev A. R., Gridnev V. I., “Kolebatelnye protsessy v vegetativnoi regulyatsii serdechno-sosudistoi sistemy”, Saratovskii nauchno-meditsinskii zhurnal, 7:1 (2011), 34–39

[18] Lakhno V. D., “Matematicheskaya kletka. Kontseptsii postroeniya matematicheskikh modelei perenosa zaryada v zhivoi kletke”, Vestnik RUDN, Seriya Prikladnaya i kompyuternaya matematika, 2:2 (2003), 77–84 | Zbl

[19] Karr Jonathan R., Sanghvi Jayodita C., Macklin Derek N., Gutschow Miriam V., Jacobs Jared M., Bolival Benjamin, Assad-Garcia Nacyra, Glass John I., Covert Markus W., “A Whole-Cell Computational Model Predicts Phenotype from Genotype”, Cell, 150:2 (2012), 389–401 | DOI

[20] Cheng L., Ivanova O., Fan H.-H., Khoo M. C. K., “An integrative model of respiratory and cardiovascular control in sleep-disordered breathing”, Respiratory Physiology Neurobiology, 174 (2010), 4–28 | DOI

[21] Kiselev I. N., Semisalov B. V., Biberdorf E. A., Sharipov R. N., Blokhin A. M., Kolpakov F. A., “Modulnoe modelirovanie serdechno-sosudistoi sistemy cheloveka”, Matematicheskaya biologiya i bioinformatika, 7:2 (2012), 703–736

[22] Daan S., Beersma D. G., Borbely A. A., “Timing of human sleep: recovery process gated by a circadian pacemaker”, Am. J. Physiol., 246 (1984), R161–R183

[23] Borbely A. A., Achermann P., “Sleep homeostasis and models of sleep regulation”, Principles and Practice of Sleep Medicine, eds. Kogger M. H., Roth T., Dement W. C., Saunders WB, Philadelphia, 2000

[24] Achermann P., Borbely A. A., “Mathematical models of sleep regulation”, Front. Biosci., 8 (2003), s683–s693 | DOI

[25] Riddle W., Younes M., “A model for the relation between respiratory neural and mechanical outputs. II: Methods”, J. Appl. Physiol., 51 (1981), 979–989

[26] Duffin J., Mohan R. M., Vasiliou P., Stephenson R., Mahamed S., “A model of the chemoreflex control of breathing in humans: model parameters measurement”, Respir. Physiol., 120 (2000), 13–26 | DOI

[27] Ursino M., Magosso E., “Acute cardiovascular response to isocapnic hypoxia. I: A mathematical model”, Am. J. Physiol. Heart Circ. Physiol., 279 (2000), H149–H165

[28] Magosso E., Ursino M., “A mathematical model of $\mathrm{CO}_2$ effect on cardiovascular regulation”, Am. J. Physiol. Heart Circ. Physiol., 281 (2001), H2036–H2052

[29] Ursino M., “Interaction between carotid baroregulation and the pulsating heart: a mathematical model”, Am. J. Physiol., 275 (1998), H1733–H1747

[30] Ursino M., Magosso E., “Short-term autonomic control of cardiovascular function: a mini-review with the help of mathematical models”, J. Integr. Neurosci., 2 (2003), 219–247 | DOI

[31] Read D. J., Leigh J., “Blood-brain tissue Pco2 relationships and ventilation during rebreathing”, J. Appl. Physiol., 23 (1967), 53–70

[32] Khoo M. C., “A model-based evaluation of the single-breath $\mathrm{CO}_2$ ventilatory response test”, J. Appl. Physiol., 68 (1990), 393–399

[33] Tankanag A., Chemeris N., “Application of adaptive wavelet transform for analysis of blood flow oscillations in the human skin”, Phys. Med. Biol., 53:21 (2008), 5967–5976 | DOI

[34] Tankanag A. V., Chemeris N. K., “Adaptivnyi veivlet-analiz kolebanii perifericheskogo krovotoka kozhi cheloveka”, Biofizika, 54:3 (2009), 537–544

[35] Tankanag A. V., Chemeris N. K., “A method of adaptive wavelet filtering of the peripheral blood flow oscillations under stationary and non-stationary conditions”, Phys. Med. Biol., 54:19 (2009), 5935–5948 | DOI

[36] Tankanag A. V., “Applications of the Adaptive Wavelet Transform for Analyzing Peripheral Blood Flow Oscillations in the Human Skin”, Medical Physics, ed. Balcerzyk M., Nova Science Publishers, NY, 2013, 85–104