Journal of Clinical Monitoring and Computing

, Volume 28, Issue 6, pp 513–523 | Cite as

Simulating physiological interactions in a hybrid system of mathematical models

  • Jörn KretschmerEmail author
  • Thomas Haunsberger
  • Erick Drost
  • Edmund Koch
  • Knut Möller
Original Research


Mathematical models can be deployed to simulate physiological processes of the human organism. Exploiting these simulations, reactions of a patient to changes in the therapy regime can be predicted. Based on these predictions, medical decision support systems (MDSS) can help in optimizing medical therapy. An MDSS designed to support mechanical ventilation in critically ill patients should not only consider respiratory mechanics but should also consider other systems of the human organism such as gas exchange or blood circulation. A specially designed framework allows combining three model families (respiratory mechanics, cardiovascular dynamics and gas exchange) to predict the outcome of a therapy setting. Elements of the three model families are dynamically combined to form a complex model system with interacting submodels. Tests revealed that complex model combinations are not computationally feasible. In most patients, cardiovascular physiology could be simulated by simplified models decreasing computational costs. Thus, a simplified cardiovascular model that is able to reproduce basic physiological behavior is introduced. This model purely consists of difference equations and does not require special algorithms to be solved numerically. The model is based on a beat-to-beat model which has been extended to react to intrathoracic pressure levels that are present during mechanical ventilation. The introduced reaction to intrathoracic pressure levels as found during mechanical ventilation has been tuned to mimic the behavior of a complex 19-compartment model. Tests revealed that the model is able to represent general system behavior comparable to the 19-compartment model closely. Blood pressures were calculated with a maximum deviation of 1.8 % in systolic pressure and 3.5 % in diastolic pressure, leading to a simulation error of 0.3 % in cardiac output. The gas exchange submodel being reactive to changes in cardiac output showed a resulting deviation of less than 0.1 %. Therefore, the proposed model is usable in combinations where cardiovascular simulation does not have to be detailed. Computing costs have been decreased dramatically by a factor 186 compared to a model combination employing the 19-compartment model.


Mathematical models Cardiovascular beat-to-beat model Physiological simulation 


  1. 1.
    The Acute Respiratory Distress Syndrome Network. Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome. N Engl J Med. 2000;342(18):1301–8.CrossRefGoogle Scholar
  2. 2.
    Ricard JD, Dreyfuss D, Saumon G. Ventilator-induced lung injury. Eur Respir J Suppl. 2003;42:2s–9s.CrossRefPubMedGoogle Scholar
  3. 3.
    Slutsky AS. Lung injury caused by mechanical ventilation. Chest. 1999;116(1 Suppl):9S–15S.CrossRefPubMedGoogle Scholar
  4. 4.
    Schranz C, Knöbel C, Kretschmer J, Zhao Z, Möller K. Hierarchical parameter identification in models of respiratory mechanics. IEEE Trans Biomed Eng. 2011;58(11):3234–41.CrossRefPubMedGoogle Scholar
  5. 5.
    Kretschmer J, Wahl A, Möller K. Dynamically generated models for medical decision support systems. Comput Biol Med. 2011;41:899–907.CrossRefPubMedGoogle Scholar
  6. 6.
    Cuellar AA, Lloyd CM, Nielsen PF, Bullivant DP, Nickerson DP, Hunter PJ. An overview of CellML 1.1, a biological model description language. SIMULATION Trans Soc Model Simul Int. 2003;79(12):740–7.CrossRefGoogle Scholar
  7. 7.
    Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, Kitano H, Arkin AP, Bornstein BJ, Bray D, et al. The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics. 2003;19(4):524–31.CrossRefPubMedGoogle Scholar
  8. 8.
    Keating SM, Bornstein BJ, Finney A, Hucka M. SBMLToolbox: an SBML toolbox for MATLAB users. Bioinformatics. 2006;22(10):1275–7.CrossRefPubMedGoogle Scholar
  9. 9.
    Miller A, Marsh J, Reeve A, Garny A, Britten R, Halstead M, Cooper J, Nickerson D, Nielsen P. An overview of the CellML API and its implementation. BMC Bioinformatics. 2010;11(1):178.CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Beard DA, Neal ML, Tabesh-Saleki N, Thompson CT, Bassingthwaighte JB, Shimoyama M, Carlson BE. Multiscale modeling and data integration in the virtual physiological rat project. Ann Biomed Eng. 2012;40(11):2365–78.CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Erson EZ, Cavusoglu MC. Design of a framework for modeling, integration and simulation of physiological models. Comput Methods Programs Biomed. 2012;107(3):524–37.CrossRefPubMedGoogle Scholar
  12. 12.
    Neal ML, Gennari JH, Arts T, Cook DL. Advances in semantic representation for multiscale biosimulation: a case study in merging models. Pac Symp Biocomput. 2009;304–315.Google Scholar
  13. 13.
    Kretschmer J, Möller K. A hierarchical model family of cardiovascular dynamics. In: Jobbágy Á, editors. 5th European conference of the international federation for medical and biological engineering. Vol. 37. Budapest, Hungary: Springer; 2011. p. 295–298.Google Scholar
  14. 14.
    Parlikar T, Verghese G. A simple cycle-averaged model for cardiovascular dynamics. Conf Proc IEEE Eng Med Biol Soc. 2005;5:5490–4.PubMedGoogle Scholar
  15. 15.
    Leaning MS, Pullen HE, Carson ER, Finkelstein L. Modelling a complex biological system: the human cardiovascular system—1. Methodology and model description. T I Meas Control. 1983;5(2):71–86.CrossRefGoogle Scholar
  16. 16.
    Smith BW, Chase JG, Nokes RI, Shaw GM, Wake G. Minimal haemodynamic system model including ventricular interaction and valve dynamics. Med Eng Phys. 2004;26(2):131–9.CrossRefPubMedGoogle Scholar
  17. 17.
    Danielsen M, Ottesen JT. A cardiovascular model. In: Ottesen JT, et al., editors. Applied mathematical models in human physiology. Philadelphia: Society for Industrial and Applied Mathematics; 2004. p. 113–26.Google Scholar
  18. 18.
    Liang F, Liu H. Simulation of hemodynamic responses to the valsalva maneuver: an integrative computational model of the cardiovascular system and the autonomic nervous system. J Physiol Sci. 2006;56(1):45–65.CrossRefPubMedGoogle Scholar
  19. 19.
    Luo C, Ware D, Zwischenberger J, Clark J. Using a Human Cardiopulmonary Model to Study and Predict Normal and Diseased Ventricular Mechanics, Septal Interaction, and Atrio-Ventricular Blood Flow Patterns. Cardiovasc Eng Int J. 2007;7(1):17–31.CrossRefGoogle Scholar
  20. 20.
    Fontecave Jallon J, Abdulhay E, Calabrese P, Baconnier P, Gumery P-Y. A model of mechanical interactions between heart and lungs. Philos Trans A Math Phys Eng Sci. 2009;367(1908):4741–57.CrossRefPubMedGoogle Scholar
  21. 21.
    Beneken JEW, De Wit B. A physical approach to haemodynamic aspects of the human cardiovascular system. In: Reeve EB, Guyton AC, editors. Physical bases of circulatory transport. Philadelphia: W. B. Saunders; 1967.Google Scholar
  22. 22.
    deBoer RW, Karemaker JM, Strackee J. Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model. Am J Physiol. 1987;253(3 Pt 2):H680–9.Google Scholar
  23. 23.
    Salvi P. Pulse waves: how vascular hemodynamics affects blood pressure. Milan: Springer; 2012.CrossRefGoogle Scholar
  24. 24.
    Benallal H, Busso T. Analysis of end-tidal and arterial PCO2 gradients using a breathing model. Eur J Appl Physiol. 2000;83(4–5):402–8.CrossRefPubMedGoogle Scholar
  25. 25.
    Chiari L, Avanzolini G, Ursino M. A comprehensive simulator of the human respiratory system: validation with experimental and simulated data. Ann Biomed Eng. 1997;25(6):985–99.CrossRefPubMedGoogle Scholar
  26. 26.
    Kretschmer J, Schranz C, Knöbel C, Wingender J, Koch E, Möller K. Efficient computation of interacting model systems. J Biomed Inform. 2013;46(3):401–9.CrossRefPubMedGoogle Scholar
  27. 27.
    Lagarias J, Reeds J, Wright M, Wright P. Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J Optim. 1998;9(1):112–47.CrossRefGoogle Scholar
  28. 28.
    Pizov R, Cohen M, Weiss Y, Segal E, Cotev S, Perel A. Positive end-expiratory pressure-induced hemodynamic changes are reflected in the arterial pressure waveform. Crit Care Med. 1996;24(8):1381–7.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Jörn Kretschmer
    • 1
    • 2
    Email author
  • Thomas Haunsberger
    • 1
  • Erick Drost
    • 1
  • Edmund Koch
    • 2
  • Knut Möller
    • 1
  1. 1.Institute of Technical MedicineFurtwangen UniversityVillingen-SchwenningenGermany
  2. 2.Faculty of Medicine Carl Gustav CarusDresden University of TechnologyDresdenGermany

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