Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Comparison between two different cardiovascular models during a hemorrhagic shock scenario

1 CNR-IRIB BioMatLab (Biomathematics Laboratory), Via Ugo La Malfa 153, 90146 Palermo, Italy
2 CNR-IASI BioMatLab (Biomathematics Laboratory), UCSC Largo A. Gemelli 8, 00168 Rome, Italy
3 Department of Mathematics, King Mongkut’s Institute of Technology Ladkrabang Bangkok, 10520, Thailand

Hemorrhagic shock is a form of hypovolemic shock determined by rapid and large loss of intravascular blood volume and represents the first cause of death in the world, whether on the battlefield or in civilian traumatology. For this, the ability to prevent hemorrhagic shock remains one of the greatest challenges in the medical and engineering fields. The use of mathematical models of the cardiocirculatory system has improved the capacity, on one hand, to predict the risk of hemorrhagic shock and, on the other, to determine efficient treatment strategies. In this paper, a comparison between two mathematical models that simulate several hemorrhagic scenarios is presented. The models considered are the Guyton and the Zenker model. In the vast panorama of existing cardiovascular mathematical models, we decided to compare these two models because they seem to be at the extremes as regards the complexity and the detail of information that they analyze. The Guyton model is a complex and highly structured model that represents a milestone in the study of the cardiovascular system; the Zenker model is a more recent one, developed in 2007, that is relatively simple and easy to implement. The comparison between the two models offers new prospects for the improvement of mathematical models of the cardiovascular system that may prove more effective in the study of hemorrhagic shock.
  Article Metrics

Keywords cardiovascular model; hemodynamics; blood flow simulation; hemorrhage; hemorrhagic shock

Citation: Luciano Curcio, Valerio Cusimano, Laura D’Orsi, Jiraphat Yokrattanasak, Andrea De Gaetano. Comparison between two different cardiovascular models during a hemorrhagic shock scenario. Mathematical Biosciences and Engineering, 2020, 17(5): 5027-5058. doi: 10.3934/mbe.2020272


  • 1. G. Gutierrez, H. D. Reines, M. E. Wulf-Gutierrez, Clinical review: Hemorrhagic shock, Crit. Care, 8 (2004), 373-381.
  • 2. E. Krug, G. K. Sharma, R. Lozano, The global burden of injuries., Am. J. Public Health, 90 (2000), 523-526.
  • 3. J. W. Cannon, Hemorrhagic shock, N. Engl. J. Med., 378 (2018), 370-379.
  • 4. American College of Surgeons, Advanced trauma life support program for doctors: ATLS, 6th edition, Chicago, IL: American College of Surgeons, 1997.
  • 5. G. Becq, S. Charbonnier, L. Bourdon, P. Baconnier, Evaluation of a device scoring classes of emorrhagic shock, Conf. Proc. IEEE Eng. Med. Biol. Soc., 1 (2004), 470-473.
  • 6. J. R. Spaniol, A. R. Knight, J. L. Zebley, J. D. P. Dawn Anderso, J. D. Pierce, Fluid resuscitation therapy for hemorrhagic shock, J. Trauma. Nurs., 14 (2007), 152-160.
  • 7. H. Peng, A. Sweeny, Development of physiologically-based mathematical models for hemostatic resuscitation in trauma, Defence Research and Development Canada, Scientific Report, 2016.
  • 8. K. Sagawa, Critique of a large-scale organ system model: Guytonian cardiovascular model, Ann. Biomed. Eng., 3 (1975), 386-400.
  • 9. A. Guyton, A. Lindsey, B. Kaufmann, Effect of mean circulatory filling pressure and other peripheral circulatory factors on cardiac output, Am. J. Physiol., 180 (1955), 463-468.
  • 10. A. C. Guyton, Venous Return, vol. Ⅱ, 1099-1133, American Physiology Society, 1962.
  • 11. A. Guyton, Circulatory physiology: cardiac output and its regulation, 1st edition, W. B. Saunders Company, 1963.
  • 12. A. C. Guyton, T. G. Coleman, A. W. Cowley Jr., J.-F. Liard, R. A. Norman Jr., R. D. Manning Jr., Systems analysis of arterial pressure regulation and hypertension, Ann. Biomed. Eng., 1 (1972), 254-281.
  • 13. A. C. Guyton, T. G. Coleman, H. J. Granger, Circulation: Overall regulation, Ann. Rev. Physiol., 34 (1972), 13-44.
  • 14. V. Mangourova, J.Ringwood, B. V. Vliet, Graphical simulation environments for modelling and simulation of integrative physiology, Comput. Methods Programs Biomed., 102 (2011), 295-304.
  • 15. J. Kofránek, J. Rusz, S. Matoušek, Guyton's diagram brought to life - from graphic chart to simulation model for teaching physiology, Technical. Comput. Prague, (2007), 978-980.
  • 16. J. Kofránek, J. Rusz, M. Matejak, From Guyton's graphic to multimedia simulators for teaching physiology (resurrection of guyton's chart for educational purpose), Jackson CardiovascularRenal Meeting, 2008.
  • 17. J. R. J. Kofránek, Restoration of Guyton's diagram for regulation of the circulation as a basis for quantitative physiological model development, Physiol. Res., 59 (2010), 897-908.
  • 18. D. A. Beard, K. H. Pettersen, B. E. Carlson, S. W. Omholt, S. M. Bugenhagen, A computational analysis of the long-term regulation of arterial pressure, F1000Research, 2 (2013), 208.
  • 19. D'Ambrosi, A. Quarteroni, G. Rozza (eds.), Modeling of Physiological Flows, vol. 5 of MS&A, Chapter 9, 251-288, Springer, 2012.
  • 20. A. Quarteroni, A. Manzoni, C. Vergara, The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications, Acta Numerica, 26 (2017), 365-590.
  • 21. A. Quarteroni, A. Veneziani, C. Vergara, Geometric multiscale modeling of the cardiovascular system, between theory and practice, Comput. Methods Appl. Mech. Engrg., 302 (2016), 193-252.
  • 22. Y. Zhang, V. Barocas, S. Berceli, C. Clancy, D. Eckmann, M. Garbey et al., Multi-scale modeling of the cardiovascular system: Disease development, progression, and clinical intervention, Ann. Biomed. Eng., 44 (2016), 2642-2660.
  • 23. S. Zenker, J. Rubin, G. Clermont, From inverse problems in mathematical physiology to quantitative differential diagnoses, PLoS Comput. Biol., 3 (2007), 2072-2086.
  • 24. R. L. Ackoff, Systems thinking and thinking systems, Syst. Dyn. Rev., 10 (1994), 175-188.
  • 25. O. Özgün, M. Kuzuoğlu, MATLAB-based Finite Element Programming in Electromagnetic Modeling, Introduction, 2, CRC Press, 2018.
  • 26. A. C. Guyton, Determination of cardiac output by equating venous return curves with cardiac response curves, Physiol. Rev., 35 (1955), 123-129.
  • 27. P. Olmsted, I. H. Page, Hemodynamic changes in trained dogs during experimental renal hypertension, Circ. Res., 16 (1965), 134-139.
  • 28. A. C. Guyton, T. Q. Richardson, Effect of hematocrit on venous return, Circ. Res., 9 (1961), 157-164.
  • 29. D. O. Avellaneda, Multi-resolution physiological modeling for the analysis of cardiovascular pathologies, Signal and image processing, Université Rennes 1, 2013.
  • 30. N. Ikeda, F. Marumo, M. Shirataka, T. Sato, A model of overall regulation of body fluids, Ann. Biomed. Eng., 7 (1979), 135-166.
  • 31. F. S. Grodins, Control Theory and Biological Systems, Columbia University Press, New York, 1963.
  • 32. F. Grodins, J. Buell, A. Bart, Mathematical analysis and digital simulation of the respiratory control system, J. Appl. Physiol., 22 (1967), 260-276.
  • 33. S. Magder, Point: the classical guyton view that mean systemic pressure, right atrial pressure, and venous resistance govern venous return is/is not correct, J. Appl. Physiol., 101 (2006), 1523-1527.
  • 34. J.-P. Montani, B. N. Van Vliet, Understanding the contribution of guyton's large circulatory model to long-term control of arterial pressure, Exp. Physiol., 94 (2009), 382-388.
  • 35. W. R. Henderson, D. E. G. Griesdale, K. R. Walley, A. W. Sheel, Clinical review: Guyton - the role of mean circulatory filling pressure and right atrial pressure in controlling cardiac output, Crit. Care, 14 (2010), 243.
  • 36. L. G. Bongartz, M. J. Cramer, P. A. Doevendans, J. A. Joles, B. Braam, The severe cardiorenal syndrome: 'Guyton revisited', Eur. Heart J., 26 (2005), 11-17.
  • 37. T. Kawada, K. Uemura, K. Kashihara, A. Kamiya, M. Sugimachi, K. Sunagawa, A derivative-sigmoidal model reproduces operating point-dependent baroreflex neural arc transfer characteristics, Am. J.Physiol. Heart Circ. Physiol., 286 (2004), 2272-2279.
  • 38. J. Ringwood, S. Malpas, Slow oscillations in blood pressure via a nonlinear feedback model, Am. J. Physiol. Regul. Integr. Comp. Physiol., 280 (2001), R1105-R1115.
  • 39. D. Glower, J. Spratt, N. Snow, J. Kabas, J. Davis, C. Olsen, et al., Linearity of the frank-starling relationship in the intact heart: the concept of preload recruitable stroke work, Circulation, 71 (1985), 994-1009.
  • 40. N. Kiefer, M. Oremek, A. Hoeft, S. Zenker, Model-Based Quantification of Left Ventricular Diastolic Function in Critically Ill Patients with Atrial Fibrillation from Routine Data: A Feasibility Study. Comput. Math. Methods Med., 2019 (2019), 9682138.
  • 41. A. Fülöp, Z. Turóczi, D. Garbaisz, L. Harsányi, A. Szijártó, Experimental models of hemorrhagic shock: A review, Eur. Surg. Res., 50 (2013), 57-70.
  • 42. A. Guyton, J. Crowell, Dynamics of the heartin shock, Fed Proc., 20 (1961), 51-60.
  • 43. J. E. Hall, A. C. Guyton, Textbook of Medical Physiology Thirteenth ed. Elsevier; 2016.
  • 44. H. Barcroft, O. Edholm, J. Mcmichael, E. Sharpey-Schafer, Posthaemorrhagic fainting study by cardiac output and forearm flow. The Lancet, 243 (1944), 489-491.
  • 45. H. Barcroft, O. Edholm, On the vasodilatation in human skeletal muscle during post-haemorrhagic fainting, J. Physiol., 104 (1945), 161-175.
  • 46. J. P. Hannon, Hemorrhage and Hemorrhagic Shock in Swine: A Review, Letterman Army Insitutute of Research - Presidio of San Francisco, CA; 1989. 449.
  • 47. J. Sondeen, M. Dubick, J. Holcomb, C. Wade, Uncontrolled hemorrhage differs from volume- or pressure- marched controlled hemorrhage in swine, Shock, 28 (2007), 426-433.
  • 48. E. Salomão, Jr, D. Otsuki, A. Correa, D. Tabacchi Fantoni, F. dos Santos, M. Irigoyen, et al., Heart Rate Variability Analysis in an Experimental Model of Hemorrhagic Shock and Resuscitation in Pigs, PLoS ONE, 10 (2015), e0134387.
  • 49. W. Wieling, D. Jardine, F. de Lange, M. Brignole, H. Nielsen, J. Stewart, et al. Cardiac output and vasodilation in the vasovagal response: An analysis of the classic papers, Heart Rhythm., 13 (2016), 798-805.
  • 50. C. Scully, C. Daluwatte, N. Marques, M. Khan, M. Salter, J. Wolf, et al., Effect of hemorrhage rate on early hemodynamic responses in conscious sheep, Physiol. Reports, 4 (2016), e12739.
  • 51. Wiley (ed.), Introduction, vol. 62 of Acta Physiologica Scandinavica, chapter I, 5-12, 1964.
  • 52. E. Starling, On the absorption of fluids from the connective tissue spaces, J. Physiol., 19 (1896), 312-326.
  • 53. A. Guyton, Pressure-volume relationships in the interstitial spaces, Invest. Ophthalmol., 4 (1965), 1075-1084.
  • 54. A. Guyton, J. Hall, The Kidneys and Body Fluids, 264-78, 10th edition, W. B. Saunders, 2000.
  • 55. E. Kirkman, S. Watts, Haemodynamic changes in trauma, Br. J. Anaesth., 113 (2014), 266-275.
  • 56. B. A. Foex, Systemic responses to trauma, Br. Med. Bull., 55 (1999), 726-743.
  • 57. E. Kirkman, Applied cardiovascular physiology, Anaesth. Intensive Care Med., 11 (2010), 165-169.
  • 58. Chapter 2. In: Vodovotz Y, An G, editors. Complex Systems and Computational Biology Approaches to Acute Inflammation. Springer; 2013, 11-28.
  • 59. J. Kofránek, M. Andrlík, T. Kripner, P. Stodulka, From art to industry: Development of biomedical simulators, The IPSI BgD Transactions on Advanced Research,12 (2005), 62-67.


Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved