Several Theoretical and Applied Problems of Human Extreme Physiology: Mathematical Modeling

Grygoryan R.D. (Head of department “Human systems modeling”, Cybernetics Center; Institute of software systems of National Academy of Sciences, Kiev, Ukraine)

Article ID: 4175



Human cardiovascular system (CVS) and hemodynamics are critically sensitive to essential alterations of mechanical inertial forces in directions of head-legs (+Gz) or legs-head (-Gz). Typically, such alterations appear during pilotage maneuvers of modern high maneuverable airspace vehicles (HMAV).The vulnerability of pilots or passengers of HMAV to these altering forces depends on their three main characteristics: amplitude, dynamics, and duration. Special protections, proposed to minimize this vulnerability, should be improved in parallel with the increasing of these hazardous characteristics of HMAVs. Empiric testing of novel protection methods and tools is both expensive and hazardous. Therefore computer simulations are encouraged. Autonomic software (AS) for simulating and theoretical investigating of the main dynamic responses of human CVS to altering Gz is developed. AS is based on a system of quantitative mathematical models (QMM) consisting of about 1300 differential and algebraic equations. QMM describes the dynamics of both CVS (the cardiac pump function, baroreceptor control of parameters of cardiovascular net presented by means of lumped parameter vascular compartments) and non-biological variables (inertial forces, and used protections). The main function of AS is to provide physiologist-researcher by visualizations of calculated additional data concerning characteristics of both external and internal environments under high sustained accelerations and short-time microgravity. Additionally, AS can be useful as an educational tool able to show both researchers and young pilots the main hemodynamic effects caused by accelerations and acute weightlessness with and without use of different protection tools and technics. In this case, AS does help users to optimize training process aimed to ensure optimal-like human tolerance to the altered physical environment. Main physiological events appearing under different scenarios of accelerations and microgravity have been tested.


Cardiovascular system; Hemodynamics; Baroreflexes; Accelerations; Weightlessness; Simulation

Full Text:



[1] Morgan, T.R., 10 October 2000. Physiology of G Exposure & Protection. AFRL.

[2] Scott, J.M., Esch, B.T., Goodman, L.S., et al., 2007. Cardiovascular consequences of high-performance aircraft maneuvers: implications for effective countermeasures and laboratory-based simulations. Appl. Physiol. Nutr. Metab. 32, 332-339. DOI:

[3] Lawley, J.S., Petersen, L.G., Howden, E.J., et al., 2017. Effect of gravity and microgravity on intracranial pressure. J. Physiol. 595, 2115-2127. DOI:

[4] Nicogossian, A.E., Williams, R.S., Huntoon, C.L., et al., 2016. Space Physiology and Medicine: from Evidence to Practice. Springer.

[5] Tanaka, K., Nishimura, N., Kawai, Y., 2017. Adaptation to microgravity, deconditioning, and countermeasures. J Physiol Sci. 67, 271-281. DOI:

[6] Mandsager, K.T., Robertson, D., Diedrich, A., 2016. The function of the autonomic nervous system during spaceflight. Clin. Auton. Res. 25, 141-151. DOI:

[7] Watenpaugh, D.E., 2016. Analogs of microgravity: head-down tilt and water immersion. J. Appl. Physiol. 120, 904-914. DOI: 2015.

[8] Zhang, L.F., Hargens, A.R., 2018. Spaceflight-induced intracranial hypertension and visual impairment: pathophysiology and countermeasures. Physiol. Rev. 98, 59-87. DOI:

[9] Goswami, N., White, O., Blaber, A., Evans, I., et al., 2021. Human physiology adaptation to altered gravity environments. Acta Astronautica. 189, 216-221 DOI:

[10] Demontis, G.C., Germani, M.M., Caiani, E.G., et al., 2017. Human Pathophysiological Adaptations to the Space Environment. Front. Physiol. 02. DOI:

[11] Melchior, F.M., Srinivasan, R.S., Ossard, G., Clère, J.M., 1993. A mathematical model of the cardiovascular response to +Gz acceleration. Physiologist. 36(1 Suppl), S62-3. PMID: 11537428.

[12] Grygoryan, R.D., Kochetenko, E.M., 1996. Informational technology for modeling of fighters medical testing procedures by centrifuge accelerations. Selection &Training Advances in Aviation: AGARD Conference Proceedings 588; Prague, May 25-31, PP3, 1-12.

[13] Grygoryan, R.D., 1999. Development of a hemodynamics computer model of human tolerance to high sustained acceleration exposures. EOARD Contract NoF61708-97-W0253: Final Report. pp. 62.

[14] Grygoryan, R.D., 2002. High sustained G-tolerance model development.STCU#P-078 EOARD# 01-8001 Agreement: Final Report. pp. 66.

[15] Grygoryan, R.D., Hargens, A.R., 2008. A virtual multicellular organism with homeostatic and adaptive properties. In: Adaptation Biology and Medicine: Health Potentials. Ed. L. Lukyanova, N.Takeda, P.K. Singal. - New Delhi: Narosa Publishing House. 5, 261 -282.

[16] Kokalari, I., 2013. Review on lumped parameter method for modeling the blood flow in systemic arteries. Journal of Biomedical Science and Engineering. 06(01), 92-99. DOI:

[17] Shimizu, S., Une, D., Kawada, T., Hayama, Y., Kamiya, A., Shishido, T., Sugimachi, T., 2018. Lumped parameter model for hemodynamic simulation of congenital heart diseases The Journal of Physiological Sciences. 68, 103-111. DOI:

[18] Grigorian, R.D., 1983. Hemodynamics' control under postural changes (mathematical modeling and experimental study). Ph.D thesis. Kiev: Institute of Cybernetics. pp. 214. (in Russian).

[19] Grygoryan, R.D., 2017. Problem-oriented computer simulators for solving theoretical and applied tasks of human physiology. Problems in programming. 3, 161-171. DOI:

[20] Grigorian, R.D., 1990. Modeling the interactions of mechanoreflexes in the zones of high and low pressure. Cybernetics and Computing technology, N.Y. Allerton press. 314, 745-748.

[21] Grigoryan, R.D., 1986. Three-dimensional mathematical model of human hemodynamics”, Cybernetics and Computing Tecnology, N.Y. No.70, pp. 54-58.

[22] Grigoryan, R.D., 1987. A theoretical analysis of some physiological mechanisms of human tolerance to +Gz accelerations, Space Biol. and Airspace Med. (in Russian). 5, 95- 96.

[23] Convertino, V., Hoffler, G.W., 1992. Cardiovascular physiology. Effects of microgravity. J Fla Med Assoc. 79(8), 517-524.

[24] Hargens, A.R., Watenpaugh, D.E., 1996. Cardiovascular adaptation to spaceflight. Med Sci Sports Exerc. 28(8), 977-982.

[25] Buckey, J.C.Jr., Gaffney, F.A., Lane, L.D., et al, 1996. Central venous pressure in space. J Appl Physiol. 81(1), 19-25.

[26] Burton, R.R., Smith, A.H., 1996. Adaptation to aceeleration environments. Capt. 40 In: Environmental physiology. Vol.II Eds. M.J. Fregly and C.M. Blatteis. Oxford Univ.Press. 943-1112.

[27] Jaron, D., Moore, T.W., 1984. A cardiovascular model for studying impairment of cerebral function during +Gz stress. Aviat., Space Environ.Med. 55, 24-31.

[28] Burton, R.R., 1998. Mathematical models for predicting straining G-level tolerances in reclined subjects.J.Grav.Physiol.

[29] Cirovic, S., Walsh, C.D., Fraser, W.D., 2000. A mathematical model of cerebral perfusion subjected to Gz acceleration. Aviation Space and Environmental Medicine. 71(5), 514-521.

[30] Yang, C., Sun, X., Geng, J., Wang, Y., Zhou, Y., Wang, P., 2007. Study on the changes of heart rate during “push-pull effect” simulation using a tilt table combined with a lower body negative pressure device. Chin. J. Aerospace Med. 18, 171-175. DOI: 2007.03.003.

[31] Grygoryan, R.D., Lissov, P.N., Aksenova, T.V., Moroz, A.G., 2009. Specialized software-modeling complex "PhysiolResp". Problems in programming. 2, 140-150.

[32] Grygoryan, R.D., Lissov, P.N., 2004. A software simulator of human cardiovascular system based on its mathematical model. Problems in programming. 4, 100-111.

[33] Goodman, L.S., Banks, R.D., Grissett, J.D., Saunders, P.L., 2000. Heart rate and blood pressure responses to +Gz following varied-duration −Gz. Aviat. Space Environ. Med. 71, 137-141.

[34] Balldin, U.I., Derefeldt, G., Eriksson, L., et al., 2003. Color vision with rapid-onset acceleration. Aviat. Space Environ. Med. 74, 29-36.

[35] Hakeman, A.L., Shepard, J.L., Sheriff, D.D., 2003. Augmentation of the push-pull effect by terminal aortic occlusion during head-down tilt. J. Appl. Physiol. 95, 159-166. DOI: 2002.

[36] Yang, C., 2007. Study of simulation method and protection training of push-pull effect. Ph. D. thesis. Xi’an: Fourth Military Medical University.

[37] Grygoryan, R.D., 2020. Milestones of the modeling of human physiology. Journal of Human Physiology. 2(1), 23-33. DOI:


  • There are currently no refbacks.
Copyright © 2021 Author(s)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.