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Modeling the Dynamics of the Cardiovascular-respiratory System (CVRS) in Humans, a Survey

Published online by Cambridge University Press:  17 October 2012

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Abstract

In this paper we give a survey on modeling efforts concerning the CVRS. The material we discuss is organized in accordance with modeling goals and stresses control and transport issues. We also address basic modeling approaches and discuss some of the challenges for mathematical modeling methodologies in the context of parameter estimation and model validation.

Keywords

cardiovascular-respiratory systemblood flowparameter estimation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 5: Immunology , 2012 , pp. 65 - 77
Copyright
© EDP Sciences, 2012

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Références

Agoshkov, V., Quarteroni, A., Rozza, G.. Shape design in aorto-coronaric bypass anastomoses using perturbation theory. SIAM Journal on Numerical Analysis, 44 (2006), 367–384. CrossRefGoogle Scholar
Alastruey, J., Parker, K. H., Peiró, J., Sherwin, S.. Lumped parameter outflow models for 1-D blood flow simulations : Effect on pulsewaves and parameter estimation. Communications in Computational Physics, 4 (2008), 2–19. Google Scholar
Alfon, J., Royo, T., Garcia-Moll, X., Badimon, L.. Platelet deposition on eroded vessel walls at a stenotic shear rate is inhibited by lipid-lowering treatment with atorvastatin. Arterioscler. Thromb. Vasc. Biol., 19 (1999), 1812–1817. CrossRefGoogle Scholar
A. Attarian, J. Batzel, B. Matzuka, H. T. Tran. Application of the unscented Kalman filtering to parameter estimation. Mathematical Model Development and Validation in Physiology : Application to the Cardiovascular and Respiratory Systems, J. J. Batzel, M. Bachar, and F. Kappel, eds., vol. 2064 of Lecture Notes in Mathematics, Berlin, 2012, Springer-Verlag.to appear.
Attinger, E. O.. The physics of pulsatile blood flow with particular reference to small vessels. Investigative Ophthalmology, 4 (1965), 973–987. Google Scholar
H. T. Banks, A. Cintrón-Arias, F. Kappel. Parameter selection methods in inverse problem formulation. Mathematical Modeling and Validation in Physiology : Application to the Cardiovascular and Respiratory Systems, J. J. Batzel, M. Bachar, F. Kappel, eds., vol. 2064 of Lecture Notes in Mathematics, Berlin, 2012, Springer-Verlag.to appear.
Banks, H. T., Dediu, S., Ernstberger, S., Kappel, F.. Generalized sensitivities and optimal experimental design. J. Inverse and Ill-Posed Problems, 18 (2010), 25–83. CrossRefGoogle Scholar
Banks, H.T., Holm, K., Kappel, F.. Comparison of optimal design methods in inverse problems. Inverse Problems, 27 (2011).
Banks, H. T., Holm, K., Kappel, F.. A Monte Carlo based analysis of optimal design criteria. J. Inverse and Ill-Posed Problems, 20 (2012), 1–38. CrossRefGoogle Scholar
J. Batzel, M. Fink, F. Kappel. Modeling the human cardiovascular-respiratory control response to blood volume loss due to hemorrhage. Positive Systems. C. Commault, N. Marchand, eds., vol. 341 of Lecture Notes in Control and Information Sciences, Berlin, 2006, Springer-Verlag, 145–152.
J. J. Batzel, M. Bachar, V. Bhalani, F. Kappel, P. Kotanko, J. Raiman. Haemodynamics, Chapter 10, “Mathematical Physiology” (A. De Gaetano and P. Palumbo, Eds.), Encyclopedia of Life Support Systems (EOLSS), Eolss Publishers, Oxford, UK, 2008.
J. J. Batzel, M. Bachar, F. Kappel.The Circulatory System. Chapter 9, “Mathematical Physiology” (A. De Gaetano and P. Palumbo, Eds.), Encyclopedia of Life Support Systems (EOLSS), Eolss Publishers, Oxford, UK, 2008.
J. J. Batzel, M. Bachar, F. Kappel. Respiration and Gas Exchange, Chapter 12, “Mathematical Physiology” (A. De Gaetano and P. Palumbo, Eds), Encyclopedia of Life Support Systems (EOLSS), Eolss Publishers, Oxford, UK, 2008.
Batzel, J. J., Goswami, N., Lackner, H. K., Roessler, A., Bachar, M., Kappel, F., Hinghofer-Szalkay, H.. Patterns of cardiovascular control during repeated tests of orthostatic loading. Cardiovascular Engineering : An international Journal, 9 (2009), 134–143. CrossRefGoogle ScholarPubMed
J. J. Batzel, F. Kappel, D. Schneditz, H. T. Tran.Cardiovascular and Respiratory Systems : Modeling, Analysis and Control. vol. 34 of Frontiers in Applied Mathematics, SIAM, Philadelphia, 2007.
M. P. F. Berger, W. K. Wong, eds., Applied Optimal Designs, John Wiley & Sons, Chichester, UK, 2005.
Bishop, M. J., Plank, G., Vigmond, E.. Investigating the role of the coronary vasculature in the mechanisms of defibrillation. Circ Arrhythm Electrophysiol, 5 (2012), 210–219. CrossRefGoogle ScholarPubMed
Brunberg, A., Heinke, S., Spillner, J., Autschbach, R., Abel, D., Leonhardt, S.. Modeling and simulation of the cardiovascular system : a review of applications, methods, and potentials. Biomed. Tech., 54 (2009), 233–244. CrossRefGoogle Scholar
Cavalcanti, S., Cavani, S., Ciandrini, A., Avanzolini, G.. Mathematical modeling of arterial pressure response to hemodialysis-induced hypovolemia. Computers in Biology and Medicine, 36 (2006), 128–144. CrossRefGoogle ScholarPubMed
Cavalcanti, S., Cavani, S., Santoro, A.. Role of short-term regulatory mechanisms on pressure response to hemodialysis-induced hypovolemia. Kidney International, 61 (2002), 228–238. CrossRefGoogle ScholarPubMed
Cavalcanti, S., Ciandrini, A., Severi, S., Badiali, F., Bini, S., Gattiani, A., Cagnoli, L., Santoro, A.. Model-based study of the effects of the hemodialysis technique on the compensatory response to hypovolemia, Kidney International, 65 (2004), 1499–1510. CrossRefGoogle ScholarPubMed
Cavalcanti, S., Di Marco, L. Y.. Numerical simulation of the hemodynamic response to hemodialysis-induced hypovolemia. Artif. Organs, 23 (1999), 1063–1073. CrossRefGoogle Scholar
Cavani, S., Cavalcanti, S., Avanzolini, G.. Model based sensitivity analysis of arterial pressure response to hemodialysis-induced hypovolemia. ASAIO Journal, 2001 (2001), 377–388. CrossRefGoogle Scholar
Crosetto, P., Deparis, S., Fourestey, G., Quarteroni, A.. Parallel algorithms for fluid-structure interaction problems in haemodynamics. SIAM Journal on Scientific Computing, 33 (2011), 1598–1622. CrossRefGoogle Scholar
D’Angelo, C., Quarteroni, A.. On the coupling of 1d and 3d diffusion-reaction equations : Application to tissue perfusion problems. Mathematical Models and Methods in Applied Sciences, 18 (2008), 1481–1504. CrossRefGoogle Scholar
M. Danielsen, J. T. Ottesen. A dynamical approach to the baroreceptor regulation of the cardiovascular system. Proceeding to the 5th International Symposium, Symbiosis ’97, 1997, 25 – 29.
Danielsen, M., Ottesen, J. T.. Describing the pumping heart as a pressure source. J. Theor. Biol., 212 (2001), 71–81. CrossRefGoogle ScholarPubMed
de los Reyes V, A., Kappel, F.. Modeling pulsatility in the human cardiovascular system. Mathematica Balcanica, New Series, 24 (2010), 229–242. Google Scholar
A. A. de los Reyes V. A mathematical model for the cardiovascular system with a measurable pulsatile pressure output. PhD thesis, University of Graz, Graz (Austria), March 2010.
Fåhræus, R., Lindqvist, T.. The viscosity of blood in narrow capillary tubes. Am. J. Physiol., 96 (1931), 562–568. Google Scholar
V. V. Fedorov, P. Hackel. Model-Oriented Design of Experiments. Springer-Verlag, New York, NY, 1997.
Fink, G. D.. Hypothesis : the systemic circulation as a regulated free-market economy. A new approach for understanding the long-term control of blood pressure. Clin. Exp. Pharmacol. Physiol., 32 (2005), 377–383. CrossRefGoogle Scholar
Fink, M., Attarian, A., Tran, H. T.. Subset selection for parameter estimation in an hiv model. Proc. Applied Math. and Mechanics, 7 (2008), 11212,501–11221,502. Google Scholar
A. Fishman, N. Cherniack, J. Widdicombe, A. P. Society, Handbook of Physiology : A Critical, Comprehensive Presentation of Physiological Knowledge and Concepts. The respiratory system. Control of breathing, / volume editors, Neil S. Cherniack, John G. Widdicombe / executive editor, Stephen R. Geiger, American Physiological Society, 1986.
Formaggia, L., Gerbeau, J. F., Nobile, F., Quarteroni, A.. On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Computer Methods in Applied Mechanics and Engineering, 191 (2001), 561–582. CrossRefGoogle Scholar
G. C. Goodwin, R. L. Payne. Dynamic System Identification, Experimental Design and Data Analysis. vol. 136 of Mathematics in Science and Engineering, Academic Press, New York, 1977.
Goswami, N., Lackner, H., Papousek, I., Montani, J. P., Jezova, D. D., Hinghofer-Szalkay, H.. Does mental arithmetic before head up tilt have an effect on the orthostatic cardiovascular and hormonal responses. Acta Astronautica, 68 (2011), 1589–1594. CrossRefGoogle Scholar
Gu, D. M., Eisenstat, S. C.. Efficient algorithms for computing a strong rank-revealing QR factorization. SIAM J. Sci. Comput., 17 (1996), 848–869. CrossRefGoogle Scholar
A. C. Guyton, Textbook of Medical Physiology, W. B. Saunders Company, Philadelphia, Pa, 8 ed., 1991.
A. C. Guyton, J. E. Hall, Guyton Hall Textbook of Medical Physiology, Saunders/Elsevier, Philadelphia, Pa, 11 ed., 2005.
M. Habib. Control of the Human Cardiovascular-Respiratory System under a Time-Varying Ergonometric Workload. PhD thesis, University of Graz, Graz (Austria), May 2011.
Heldt, T., Shim, E. B., Kamm, R. D., Mark, R. G.. Computational modeling of cardiovascular response to orthostatic stress. J. Appl. Physiol., 92 (2002), 1239–1254. CrossRefGoogle ScholarPubMed
F. C. Hoppensteadt, C. S. Peskin. Mathematics in Medicine and the Life Sciences. vol. 10 of Texts in Applied Mathematics, Springer Verlag, New York, NY, 1992.
F. Kappel, J. J. Batzel. Survey of research in modeling the human respiratory and cardiovascular systems. Research Directions in Distributed Parameter Systems, R. C. Smith and M. A. Demetriou, eds., vol. 27 of Frontiers in Applied Mathematics, SIAM, Philadelphia, Pa, 2003, ch. 8, 187–218.
Kappel, F., Fink, M., Batzel, J.. Aspects of control of the cardiovascular-respiratory system during orthostatic stress induced by lower body negative pressure. Math. Biosciences, 206 (2007), 273–308. CrossRefGoogle ScholarPubMed
Kappel, F., Lafer, S., Peer, R. O.. A model for the cardiovascular system under an ergometric workload. Surv. Math. Ind., 7 (1997), 239–250. Google Scholar
Kappel, F., Peer, R. O.. A mathematical model for fundamental regulation processes in the cardiovascular system. J. Math. Biol., 31 (1993), 611–631. CrossRefGoogle ScholarPubMed
J. Keener, J. Sneyd, Mathematical Physiology, Vol II : Systems Physiology, vol. 8 of Interdisciplinary Applied Mathematics, Springer Verlag, New York, 2nd ed., 2008.
T. Kenner. Physiology of circulation. Cardiology, 1st ed., S. D. Volta, E. Braunwald, A. B. D. Luna, V. Jezek, M. L. Brochier, S. A. Mortensen, F. Dienstl, P. A. Poole-Wilson, eds., Clinical Medicine, New York, 1999, McGraw-Hill, 15–25.
R. C. P. Kerckhoffs, ed.. Patient-Specific Modeling of the Cardiovascular System, Technology-Driven Personalized Medicine, Springer-Verlag, New York, 2010.
A. S. Kholodov, S. S. Simakov, A. V. Evdokimov, Y. A. Kholodov.Matter transport simulations using 2D model of peripheral circulation coupled with the model of large vessels. Proc. II Int. Conf. On Comput. Bioeng., September 14-16, Lisbon, H. Rodrigues, M. Cerrolaza, M. Doblaré, J. Ambrósio, and M. Viceconti, eds., vol. 1, Lisbon, 2005, IST Press, 479–490.
R. E. Klabunde. Cardiovascular Physiology Concepts. Lippincott Williams & Wilkins, Baltimore, Md, 2005.
Kuijper, P., Torres, H. G., Lammers, J.-W., Sixma, J., Koenderman, L., Zwaginga, J.. Platelet and fibrin deposition at the damaged vessel wall : Cooperative substrates for neutrophil adhesion under flow conditions. Blood, 89 (1997), 166–175. Google ScholarPubMed
J. R. Levick. An Introduction to Cardiovascular Physiology. Oxford Univ. Press, New York, 4th ed., 2003.
S. L. Mabry, L. F. Bic, K. M. Baldwin. CVSys : a coordination framework for dynamic and fully distributed cardiovascular modeling and simulation. Biomedical Sensing and Imaging Technologies, R. A. Lieberman and T. Vo-Dinh, eds., vol. 3253 of Proc. SPIE, 1998, 208–218.
Mittal, R., Iaccarino, G.. Immersed boundary methods. Annual Rev. Fluid Mech., 37 (2005), 239–261. CrossRefGoogle Scholar
Mutsaers, M. E. C., Bachar, M., Batzel, J. J., Kappel, F., Volkwein, S.. Receding horizon controller for the baroreceptor loop in a model for the cardiovascular system. Cardiovascular Engineering : An international Journal, 8 (2008), 14–22. CrossRefGoogle Scholar
S. Muzdeka, E. Barbieri. Control theory inspired considerations of the mathematical models of defibrillation. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, IEEE Conderence Publications, 2005, 7416–7421.
S. Neumann. Modeling Acute Hemorrhage in the Human Cardiovascular System. PhD thesis, University of Pennsylvania, Pensylvania, 1996.
P. Novak, V. Novak, J. Spies, V. Gordon, T. Lagerlund, G. Petty. Evaluation of cerebral autoregulation in orthostatic hypotension and POTS. Clin. Auton. Res., 7 (1997), p. 238.
Novak, V., Novak, P., Spies, J. M., Low, P. A.. Autoregulation of cerebral blood flow in orthostatic hypotension. Stroke, 29 (1998), 104–111. CrossRefGoogle ScholarPubMed
M. S. Olufsen. Modeling flow and pressure in systemic arteries. Applied Mathematical Models in Human Physiology, J. T. Ottesen, M. Olufsen, and J. K. Larsen, eds., SIAM Monographs on Mathematical Modeling and Computation, SIAM, Philadelphia, Pa, 2004, ch. 5, 91–136.
Olufsen, M. S., Nadim, A., Lipsitz, L. A.. Dynamics of cerebral blood flow regulation explained using a lumped parameter model. Am. J. Physiol., 282 (2002), R611–R622. Google ScholarPubMed
Olufsen, M. S., Ottesen, J. T., Tran, H. T.. Modeling cerebral blood flow control during posture change from sitting to standing. J. Cardiov. Eng., 4 (2004), 47–58. CrossRefGoogle Scholar
Olufsen, M. S., Ottesen, J. T., Tran, H. T., Ellwein, L. M., Lipsitz, L. A., Novak, V.. Blood pressure and blood flow variation during postural change from sitting to standing : Model development and validation. J. Appl. Physiol., 99 (2005), 1523–1537. CrossRefGoogle ScholarPubMed
Ottesen, J. T.. Modelling the baroreflex-feedback mechanism with time-delay. J. Math. Biol., 36 (1997), 41–63. CrossRefGoogle ScholarPubMed
J. T. Ottesen, M. Danielsen, eds., Mathematical Modelling in Medicine, vol. 71 of Studies in Health Technology and Informatics, IOS Press, Amsterdam, 2000.
J. T. Ottesen, M. S. Olufsen, J. K. Larsen, eds., Applied Mathematical Models in Human Physiology, Monographs on Mathematical Modeling and Computation, SIAM, Philadelphia, 2004.
Passerini, T., de Luca, M., Formaggia, L., Quarteroni, A., Veneziani, A.. A 3D/1D geometrical multiscale model of cerebral vasculature. Journal of Engineering Mathematics, 64 (2009), 319 – 330. CrossRefGoogle Scholar
A. Pázman. Foundations of Optimum Experimental Design, Mathematics and Its Applications. D. Reidel Publ. Comp., Dordrecht, 1986.
Perktold, K., Hofer, M., Rappitsch, G., Loew, M., Kuban, B. D., Friedman, M. H.. Validated computation of physiologic flow in a realistic coronary artery branch. J. Biomech., 31 (1998), 217–228. CrossRefGoogle Scholar
Perktold, K., Rappitsch, G.. Mathematical modeling of arterial blood flow and correlation to atherosclerosis. Technol. Health Care, 3 (1995), 139 – 151. Google ScholarPubMed
C. S. Peskin. Flow Patterns around Heart Valves. PhD thesis, Albert Einstein College of Medicine, New York, 1972.
Peskin, C. S., McQueen, D. M.. Modeling prosthetic heart valves for numerical analysis of blood flow in the heart. J. Comput. Phys., 37 (1980), 113–132. CrossRefGoogle Scholar
C. S. Peskin, D. M. McQueen. Cardiac fluid dynamics. High-performance Computing in Biomedical Research, T. C. Pilkington et al., ed., CRC Press, Boca Raton, 1993.
Peskin, C. S., McQueen, D. M.. Mechanical equilibrium determines the fractal fiber architecture of aortic heart valve leaflets. Am. J. Physiol., 266 (1994), H319–H328. Google ScholarPubMed
C. S. Peskin, D. M. McQueen.Fluid dynamics of the heart and its valves, in Case Studies in Mathematical Modeling – Ecology, Physiology, and Cell Biology, H. G. Othmer, F. R. Adler, M. A. Lewis, J. C. Dallon, eds., Prentice Hall, Englewood Cliffs, New Jersey, 1996, ch. 14, 309–337.
Peskin, C. S., Printz, B. F.. Improved volume conservation in the computation of flows with immersed boundaries. J. Comput. Phys., 105 (1993), 33–46. CrossRefGoogle Scholar
Pope, S. R., Ellwein, L. M., Zapata, C. L., Novak, V., Kelley, C. T., Olufsen, M. S.. Estimation and identification of parameters in a lumped cerebrovascular model. Mathematical Biosciences and Engineering, 6 (2009), 93–115. CrossRefGoogle Scholar
Prosi, M., Zunino, P., Perktold, K., Quarteroni, A.. Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls : A new methodology for the model set up with applications to the study of disturbed lumenal flow. Journal of Biomechanics, 38 (2005), 903–917. CrossRefGoogle ScholarPubMed
F. Pukelsheim. Optimal Design of Experiments. JohnWiley & Sons, New York, NY, 1993.
Quarteroni, A., Veneziani, A., Zunino, P.. Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls. SIAM Journal on Numerical Analysis, 39 (2001), 1488 – 511. CrossRefGoogle Scholar
L. B. Rowell. Human Cardiovascular Control. Oxford University Press, New York, 1993.
G. A. F. Seber, C. J. Wild, Nonlinear Regression.Wiley Series in Probability and Mathematical Statistics. J. Wiley, New York, 1989.
W. Smith, B., G. Chase, J., M. Shaw, G., I. Nokes, R.. Experimentally verified minimal cardiovascular system model for rapid diagnostic assistance, Control Engineering Practice, 13 (2005), 1183–1193. CrossRefGoogle Scholar
J. Smith, J. Kampine.Circulatory Physiology. Williams, Wilkins, Baltimore, 1990.
W.-B. Tay, Y.-H. Tseng, L.-Y. Lin, W.-Y. Tseng. Towards patient-specific cardiovascular modeling system using the immersed boundary technique. BioMedical Engineering OnLine, 10 (2011).
W. D. Timmons.Cardiovascular models and control. “The Biomedical Engineering Handbook” (Chapter 160), J. D. Branzino, ed., Boca Raton, 2000, CRC Press LLC.
Trayanova, N., Plank, G., Rodríguez, B.. What have we learned from mathematical models of defibrillation and postshock arrhythmogenesis ? Application of bidomain simulations. Heart Rhythm, 3 (2006), 1232–1235. CrossRefGoogle ScholarPubMed
R. F. Tuma, W. N. Duràn, K. Ley, eds.. Microcirculation. Elsevier, Amsterdam, 2 ed., 2008.
D. Ucinski, A. Atkinson. Experimental design for time-dependent models with correlated observations. Studies in Nonlinear Dynamics and Econometrics, 8 (2004).
Ursino, M.. Interaction between carotid baroregulation and the pulsating heart : A mathematical model. Am. J. Physiol., 275 (1998), H1733–H1747. Google Scholar
Ursino, M.. A mathematical model of the carotid baroregulation in pulsating conditions. IEEE Trans. Biomed. Eng., 46 (1999), 382–392. CrossRefGoogle ScholarPubMed
Ursino, M., Fiorenzi, A., Belardinelli, E.. The role of pressure pulsatility in the carotid baroreflex control : A computer simulation study. Comput. Biol. Med., 26 (1996), 297–314. CrossRefGoogle ScholarPubMed
Ursino, M., Innocenti, M.. Mathematical investigation of some physiological factors involved in hemodialysis hypotension. Artif. Organs, 21 (1997), 891–902. CrossRefGoogle ScholarPubMed
Ursino, M., Innocenti, M.. Modeling arterial hypotension during hemodialysis. Artif. Organs, 21 (1997), 873–890. CrossRefGoogle Scholar
Vadakkumpadan, F., Rantner, L. J., Tice, B., Boyle, P., Prassl, A. J., Vigmond, E., Plank, G., Trayanova, N.. Image-based models of cardiac structure with applications in arrhythmia and defibrillation studies. J Electrocardiol, 42 (2009), 157.e1–157.10. CrossRefGoogle ScholarPubMed
N. Westerhof, N. Stergiopulos. Models of the arterial tree. Mathematical Modelling in Medicine, J. T. Ottesen, M. Danielsen, eds., vol. 71 of Studies in Health Technology and Informatics, Amsterdam, The Netherlands, 2000, IOS Press, 65–78.
N. Westerhof, N. Stergiopulos, M. I. M. Noble. Snapshots of Hemodynamics. vol. 18 of Basic Science for the Cardiologist, Kluwer Academic Publishers, Dordrecht, 2005.