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A Bond Graph Model of the Cardiovascular System

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Abstract

The study of the autonomic nervous system (ANS) function has shown to provide useful indicators for risk stratification and early detection on a variety of cardiovascular pathologies. However, data gathered during different tests of the ANS are difficult to analyse, mainly due to the complex mechanisms involved in the autonomic regulation of the cardiovascular system (CVS). Although model-based analysis of ANS data has been already proposed as a way to cope with this complexity, only a few models coupling the main elements involved have been presented in the literature. In this paper, a new model of the CVS, representing the ventricles, the circulatory system and the regulation of the CVS activity by the ANS, is presented. The models of the vascular system and the ventricular activity have been developed using the Bond Graph formalism, as it proposes a unified representation for all energetic domains, facilitating the integration of mechanic and hydraulic phenomena. In order to take into account the electro-mechanical behaviour of both ventricles, an electrophysiologic model of the cardiac action potential, represented by a set of ordinary differential equations, has been integrated. The short-term ANS regulation of heart rate, cardiac contractility and peripheral vasoconstriction is represented by means of continuous transfer functions. These models, represented in different continuous formalisms, are coupled by using a multi-formalism simulation library. Results are presented for two different autonomic tests, namely the Tilt Test and the Valsalva Manoeuvre, by comparing real and simulated signals.

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References

  • Beeler, G.W. and H. Reuter (1977). Reconstruction of the action potential of ventricular myocardial fibres, Journal of Physiology 268: 177–210.

    Google Scholar 

  • Barbieri, R., A.M. Bianchi, J.K. Triedman, L.T. Mainardi, S. Cerutti and J.P. Saul (1997). Model dependency of multivariate autoregressive spectral analysis. IEEE. Eng. Med. Biol. Mag. 16(5): 74–85.

    Google Scholar 

  • Bestel, J. (2000). Modèle différentiel de la contractrion musculaire contrôlée: Application au système cardiovasculaire, PhD thesis, University Paris 9.

  • Dauphin-Tanguy, et al. (2000). Les Bond Graphs, collection IC2, Hermes.

  • DeBoer, R.W., J.M. Karemaker and H.H. Hara (1987). Hemodynamic fluctuations and baroreflex sensitivity in human: A beat-to-beat model. J. Appl. Physiol. 253: 680–689.

    Google Scholar 

  • Defontaine, A, A. Hernández and G. Carrault (2004). Multi-formalism modelling and simulation: Application to cardiac modelling. Acta Biotheoretica. 52: 273–290.

    Article  Google Scholar 

  • Diaz-Insua, M. and M. Delgado (1996). Modelling and Simulation of the Human Cardiovascular System with Bond Graph: A Basic Development, Computers in Cardiology, IEEE.: pp. 393–396.

  • Diaz-Zuccarini, V.A. (2003). Etude des conditions d'efficacité du ventricule gauche par optimisation téléonomique d'un model de son fonctionnement, PhD thesis, University of Lille.

  • Flessas, A.P., S. Kumar and D.H. Spodick (1970). Effects of the Valsalva manoeuvre on the cardiac systolic intervals: Beat-to-beat versus time analysis. American Heart Journal 80: 522–531.

    Article  Google Scholar 

  • Gabbett, T.J., S.B. Weston, R.S. Barrett and G.C. Gass (2001). Cardiovascular regulation during head-up tilt in healthy 20–30-year-old and 70–75-year-old men, Clinical Science 100: 199–206.

    Article  Google Scholar 

  • Guarini, M., J. Urzua and A. Cipriano (1998). Estimation of cardiac function from computer analysis of the arterial pressure waveform, IEEE Transactions on Biomedical Engineering 45: 1420–1428.

    Article  Google Scholar 

  • Guyton, A.C. and J.E. Hall (1995). Nervous Regulation of the Circulation, and Rapid Control of Arterial Pressure. Textbook of Medical Physiology. Ch 18 9th ed. New York. WB Saunders Co.

  • Heldt, T., E.B Shim, R.D. Kamm and R.G. Mark (2002). Computational modelling of cardiovascular response to orthostatic stress, J. Appl. Physiol. 92(3): 1239–1254.

    Google Scholar 

  • Hernández, A.I., G. Carrault, F. Mora and A. Bardou (2002). Model-based interpretation of cardiac beats by evolutionary algorithms: Signal and model interaction. Artificial Intelligence in Medicine 26(3): 211–235.

    Google Scholar 

  • Hunter, P.J., A.D. McCulloch and H.E.D.J. ter Keurs (1998). Modelling the mechanical properties of cardiac muscle, Progress in Biophysics & Molecular Biology 69: 289–331.

    Google Scholar 

  • Kerckoffs, R.C.P., P.H.M. Bovendeerd and F.W. Prinzen (2003). Intra- and interventricular asynchrony of electromechanics in the ventricularly paced heart. Journal Of Engineering Mathematics 47: 201–216.

    Google Scholar 

  • LeFèvre, J., L. Lefèvre and B Couteiro (1999). A bond graph model of chemo-mechanical transduction in the mammalian left ventricle. Simulation Practice and Theory 7(5–6): 531–552.

    Google Scholar 

  • Linkens, D.A. and H.H. Chen (1995). The design of a Bond-Graph-based controller for muscle relaxant anaesthesia, Proceedings IEEE International Conference on Systems Man and Cybernetics: Intelligent Systems for the 21st Century, Vancouver 4: 3005–3010.

  • Lombardi, F., T.H. Makikallio, R.J. Myerburg, and H.V. Huikuri (2001). Sudden cardiac death: Role of heart rate variability to identify patients at risk, Cardiovasc Res 50: 210–217.

    Article  Google Scholar 

  • Lu, K., J.W. Clark, Jr., F.H. Ghorbel, D.L. Ware and A. Bidani (2001). A human cardiopulmonary system model applied to the analysis of the Valsalva maneuver, Am. J. Physiol. Heart Circ. Physiol. 281(6): H2661–H2679.

    Google Scholar 

  • Malik, M., T. Farrell, T. Cripps and A.J. Camm (1996). Heart rate variability: Standards of measurement, physiological interpretation and clinical use. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, Circulation 93: 1043–1065.

    Google Scholar 

  • Manning, T.S., B.E. Shykoff and J.L. Izzo Jr. (2002) Validity and reliability of diastolic pulse contour analysis (windkessel model) in humans. Hypertension 39(5): 963–968.

    Article  Google Scholar 

  • May-Newman, K. and A.D. McCulloch (1998). Homogenization modelling for the mechanics of perfused myocardium, Progress in Biophysic & Molecular Biology 69: 463–481.

    Google Scholar 

  • McInnis, B.C., Z.W Guo., P.C. Lu and J.C. Wang (1985). Adaptive control of left ventricular bypass assist devices, IEEE Transactions on Automatic Control AC–30(4).

  • Nash, M. (1998). Mechanics and Material Properties of the Heart using an Anatomically Accurate Mathematical Model, PhD thesis, University of Auckland.

  • Olufsen, M.S., J.T. Ottesen, H.T. Tran, L.M. Ellwein, L.A. Lipsitz and V. Novak (2005). Blood pressure and blood flow variation during postural change from sitting to standing: Model development and validation. J Appl Physiol 1523–1537.

  • Palladino, J.L. and A. Noordergraaf (2002). A paradigm for quantifying ventricular contraction, Cell. Mole. Biol., Letters 7(2): 331–335.

    Google Scholar 

  • Rice, J.J., R.L. Winslow and W.C. Hunter (1999). Comparison of putative cooperative mechanisms in cardiac muscle: Length dependence and dynamic responses, Am J Physiol 276: H1734–H1754.

    Google Scholar 

  • Rompelman, O., A.J. Coenen and R.I. Kitney (1977). Measurement of heart-rate variability: Part 1- Comparative study of heart-rate variability analysis methods, Med Biol Eng Comput 15(3): 233–239.

    Google Scholar 

  • Seidel, H. and H. Herzel, (1995). Modelling Heart Rate Variability due to Respiration and Baroreflex, Modelling the Dynamics of Biological Systems. Springer, Berlin 205–229.

    Google Scholar 

  • Smith, N.P., P.J. Mulquiney, M.P. Nash, C.P. Bradley, D.P. Nickerson and P.J.Hunter (2002). Mathematical modelling of the heart: Cell to organ Chaos. Solitons and Fractals 13: 1613– 1621.

    Google Scholar 

  • Suga, H. (2003). Cardiac energetics: From Emax to pressure-volume area, Clinical and Experimental Pharmacology and Physiology 30(8): 580.

    Article  Google Scholar 

  • Tsitlik, J.E., H.R. Halperin, A.S. Popel, A.A. Shoukas, F.C. Yin and N. Westerhof (1992). Modelling the circulation with three-terminal electrical networks containing special nonlinear capacitors, Ann. Biomed. Eng. 20(6): 595–616.

    Google Scholar 

  • Vetter, R.J. and A.D. McCulloch (2000). Three-dimensional stress and strain in passive rabbit left ventricle: A model study. Annals of Biomedical Engineering 28: 781–792.

    Article  Google Scholar 

  • Van Roon, A.M. (1998). Short-term cardiovascular effects of mental tasks, PhD thesis, University of Groningen.

  • Wojcik, L.A. (2003). Modelling of musculoskeletal structure and function using a modular Bond Graph approach, Journal of the Franklin Institute, 340: 63–76.

    Article  Google Scholar 

  • Zeigler, B.P., H. Praehofer and T.G. Kim (2000). Theory of Modelling and Simulation, Second Edition Integrating Discrete Event and Continuous Complex Dynamic Systems. Academic Press.

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Authors and Affiliations

  1. Laboratoire de Traitement du Signal et de l'Image, Inserm U642, Université de Rennes 1 – Campus de Beaulieu, 35042, Rennes Cedex

    V. Le Rolle, A. I. Hernandez & G. Carrault

  2. Supélec IETR, avenue de la Boulaie, B.P. 81127, 35511, Cesson-Sévigné cedex, France

    V. Le Rolle, P. Y. Richard & J. Buisson

Authors
  1. V. Le Rolle
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  2. A. I. Hernandez
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  3. P. Y. Richard
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  4. J. Buisson
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  5. G. Carrault
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Le Rolle, V., Hernandez, A.I., Richard, P.Y. et al. A Bond Graph Model of the Cardiovascular System. Acta Biotheor 53, 295–312 (2005). https://doi.org/10.1007/s10441-005-4881-4

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  • DOI: https://doi.org/10.1007/s10441-005-4881-4

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