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Mechanical Support for Heart Failure pp 429–447Cite as

Hemodynamic Modelling and Simulations for Mechanical Circulatory Support

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Abstract

This chapter illustrates the concept of circulatory models for the investigation of mechanical circulatory support (MCS) devices. MCS devices require an extensive validation and testing for their approval in the clinics, a process that includes the assessment of their efficacy and safety while interacting with the human body.

The chapter provides an overview of the basic principles on which cardiovascular simulators for MCS devices are founded. A description of Zero-D models is provided along with an outline on how to implement some physiological components and phenomena for specific applications. The chapter also offers an overview on physical and hybrid simulators and on different techniques for their implementation. Several simulator configurations are discussed, suitable to study the performance of different MCSs (e.g., LVAD, BVAD, ECMO) and to assess their effect on patient’s hemodynamics.

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Abbreviations

BVAD/LVAD/RVAD:

Biventricular/left ventricular/right ventricular assist device

CFD:

Computational fluid dynamics

ECMO:

Extracorporeal membrane oxygenator

HCS:

Hybrid cardiovascular simulator

HI:

Hybrid interface

IABP:

Intra-aortic balloon pump

LPM:

Lumped parameters model

MCL:

Mock circulatory loop

MCS:

Mechanical circulatory support

Pap:

Pulmonary arterial pressure

Pas:

Arterial systemic pressure

Pla:

Left atrial pressure

Plv:

Left ventricular pressure

Pra:

Right atrial pressure

TAH:

Total artificial heart

References

  1. Guyton AC, Jones CE, Coleman TG. Circulatory physiology: cardiac output and its regulation. Philadelphia: W.B. Saunders Company; 1973.

    Google Scholar 

  2. Sagawa K, Maughan L, Suga H, Sunagawa K. Cardiac contraction and the pressure-volume relationship. New York: Oxford University Press; 1988.

    Google Scholar 

  3. Yi Wu, Allaire P, Tao G; Olsen D. Modeling, estimation and control of cardiovascular systems with a left ventricular assist device. EEE Trans Cont Systems Technol 2007;15(4).

    Google Scholar 

  4. Ferrari G, Darowski M, Kozarski M. Physical models and components. In: Darowski M, Ferrari G, editors. Comprehensive models of cardiovascular and respiratory systems: their mechanical support and interactions. New York: Nova Science Publishers; 2010.

    Google Scholar 

  5. Korakianitis T, Shi Y. A concentrated parameter model for the human cardiovascular system including heart valve dynamics and atrioventricular interaction. Med Eng Phys. 2006;28(7):613–28.

    PubMed  Google Scholar 

  6. Kim YS, Kim EH, Kim HG, Shim EB, Song KS, Lim KM. Mathematical analysis of the effects of valvular regurgitation on the pumping efficacy of continuous and pulsatile left ventricular assist devices. Integr Med Res. 2016 Mar;5(1):22–9.

    PubMed  PubMed Central  Google Scholar 

  7. Szabó G, Soans D, Graf AJ, Beller C, Waite L, Hagl S. New computer model of mitral valve hemodynamics during ventricular filling. Eur J Cardiothorac Surg. 2004;26(2):239–47.

    PubMed  Google Scholar 

  8. Westerof N, Elzinga G, Sipkema P. An artificial arterial system for pumping hearts. J Appl Physiol. 1971;31(5):776–81.

    Google Scholar 

  9. Stergiopolus N, Berend E, Westerhof N. Total arterial inertance as the fourth element of the Winkessel model. AJP-Heart. 1999;276(1):H81–8.

    Google Scholar 

  10. Frank O.. Die Grundform des arteriellen Pulses. Z Biol. 1899;37:483:526.

    Google Scholar 

  11. Burkhoff D, Alexander J Jr, Schipke J. Assessment of Windkessel as a model of aortic input impedance. Am J Phys. 1988;255(4 Pt 2):H742–53.

    CAS  Google Scholar 

  12. Heldt T, Shim EB. Kamm RD and. Mark RG. Computational modeling of cardiovascular response to orthostatic stress. J Appl Physiol. 2002;92:1239–54.

    PubMed  Google Scholar 

  13. Ursino M. Interaction between carotid baroregulation and the pulsating heart: a mathematical model. Am J Physiol Heart Circ Physiol. 1998;275:1733–47.

    Google Scholar 

  14. Ferrari G, Kozarski M, Zieliński K, Fresiello L, Di Molfetta A, Górczyńska K, Pałko KJ, Darowski M. A modular computational circulatory model applicable to VAD testing and training. J Artif Organs. 2012;15(1):32–43.

    PubMed  Google Scholar 

  15. Olufsen MS, Ottesen JT, Tran HT. Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation. J Appl Physio. 2005;99:1523–37.

    Google Scholar 

  16. Blanco PJ, Trenhago PR, Fernandes L, Gand Feijóo RA. On the integration of the baroreflex control mechanism in a heterogeneous model of the cardiovascular system. Int J Numer MethBiomed Engin. 2012;28:412–33.

    CAS  Google Scholar 

  17. Fresiello L, Khir AW, Di Molfetta A, Kozarski M, Ferrari G. Effects of intra-aortic balloon pump timing on baroreflex activities in a closed-loop cardiovascular hybrid model. Artif Organs. 2013;37(3):237–47.

    PubMed  Google Scholar 

  18. Lim KM, Kim IS, Choi SW, Min BG, Won YS, Kim HY, Shim EB. Computational analysis of the effect of the type of LVAD flow on coronary perfusion and ventricular afterload. J Physiol Sci. 2009;59(4):307–16.

    PubMed  Google Scholar 

  19. McDowall LM and Dampney R.A.L. Calculation of threshold and saturation points of sigmoidal baroreflex function curves. Am J Physiol Heart Circ Physiol 2006;291:H2003–H2007.

    Google Scholar 

  20. Ursino M, Fiorenzi A, Belardinelli E. The role of pressure pulsatility in the carotid baroreflex control: a computer simulation study. Comput Biol Med. 1996;26(4):297–314.

    CAS  PubMed  Google Scholar 

  21. Batzel JJ, Trany HT. Stability of the human respiratory control system. Part I: analysis of a two-dimensional delay state-space model. J Math Biol. 2000;41(1):45–79.

    CAS  PubMed  Google Scholar 

  22. Batzel JJ, Trany HT. Stability of the human respiratory control system. Part II: analysis of a two-dimensional delay state-space model. J Math Biol. 2000;41(1):80–102.

    CAS  PubMed  Google Scholar 

  23. Van Meurs W. Modeling and simulation in biomedical engineering: applications in cardiorespiratory physiology. New York: McGraw-Hill Professional; 2011.

    Google Scholar 

  24. Fresiello L, Rademakers F, Claus P, Ferrari G, Di Molfetta A, Meyns B. Exercise physiology with a left ventricular assist device: analysis of heart-pump interaction with a computational simulator. PLoS One. 2017;12(7).

    Google Scholar 

  25. Graefe R, Henseler A, Körfer R, Meyns B, Fresiello L. Influence of left ventricular assist device pressure-flow characteristic on exercise physiology: assessment with a verified numerical model. Int J Artif Organs. 2019;42(9):490–9.

    PubMed  Google Scholar 

  26. Cheng L, Ivanova O, Fan HH, Khoo MC. An integrative model of respiratory and cardiovascular control in sleep-disordered breathing. Respir Physiol Neurobiol. 2010;174(1–2):4–28.

    PubMed  PubMed Central  Google Scholar 

  27. Broomé M, Maksuti E, Bjällmark A, Frenckner B, Janerot-Sjöberg B. Closed-loop real-time simulation model of hemodynamics and oxygen transport in the cardiovascular system. Biomed Eng Online. 2013;12:69.

    PubMed  PubMed Central  Google Scholar 

  28. Golczewski T, Darowski M. Virtual respiratory system in investigation of CPAP influence on optimal breathing frequency in obstructive lungs disease. Nonlinear Biomed Phys. 2007;1:6.

    PubMed  PubMed Central  Google Scholar 

  29. Ben-Tal A. Simplified models for gas exchange in the human lungs. J Theor Biol. 2006;238(2):474–95.

    PubMed  Google Scholar 

  30. Cross TJ, Sabapathy S, Beck KC, Morris NR, Johnson BD. The resistive and elastic work of breathing during exercise in patients with chronic heart failure. Eur Respir J. 2012;39(6):1449–57.

    PubMed  Google Scholar 

  31. Albanese A, Cheng L, Ursino M, Chbat NW. An integrated mathematical model of the human cardiopulmonary system: model development. Am J Physiol Heart Circ Physiol. 2016;310(7):H899–921.

    PubMed  Google Scholar 

  32. Nunn JF. Control of breathing. In: Nunn JF, editor. Applied respiratory physiology with special reference to. Anaesthesia, London: Butterworth & Co Publishers Ltd Press; 1969.

    Google Scholar 

  33. Cormack RS, Cunningham DJ, Gee JB. The effect of carbon dioxide on the respiratory response to want of oxygen in man. Q J Exp Physiol Cogn Med Sci. 1957;42(3):303–19.

    CAS  PubMed  Google Scholar 

  34. Batzel JJ, Kappel F, Schneditz D, Hien TT. Cardiovascular and respiratory systems, modeling, analysis and control. Philadelphia: Society for Industrial and Applied Mathematics; 2006.

    Google Scholar 

  35. Ben-Tal A. Computational models for the study of heart-lung interactions in mammals. Wiley Interdiscip Rev Syst Biol Med. 2012;4(2):163–70.

    PubMed  Google Scholar 

  36. Spencer JL, Firouztale E, Mellins RB. Computational expressions for blood oxygen and carbon dioxide concentrations. Ann Biomed Eng. 1979;7(1):59–66.

    CAS  PubMed  Google Scholar 

  37. Golczewski T. Gas exchange in a virtual respiratory system--simulation of ventilation without lung movement. Int J Artif Organs. 2007;30(12):1047–56.

    CAS  PubMed  Google Scholar 

  38. Lanzarone E, Liani P, Baselli G, Costantino ML. Model of arterial tree and peripheral control for the study of physiological and assisted circulation. Med Eng Phys. 2007;29(5):542–55.

    CAS  PubMed  Google Scholar 

  39. Magosso E, Ursino M. Cardiovascular response to dynamic aerobic exercise: a mathematical model. Med Biol Eng Comput. 2002;40(6):660–74.

    CAS  PubMed  Google Scholar 

  40. Fresiello L, Meyns B, Di Molfetta A, Ferrari G. A model of the cardiorespiratory response to aerobic exercise in healthy and heart failure conditions. Front Physiol. 2016;7:189.

    PubMed  PubMed Central  Google Scholar 

  41. Ursino M, Di Giammarco P. A mathematical model of the relationship between cerebral blood volume and intracranial pressure changes: the generation of plateau waves. Ann Biomed Eng. 1991;19(1):15–42.

    CAS  PubMed  Google Scholar 

  42. Pietrabissa R, Mantero S, Marotta T, Menicanti L. A lumped parameter model to evaluate the fluid dynamics of different coronary bypasses. Med Eng Phys. 1996;18(6):477–84.

    CAS  PubMed  Google Scholar 

  43. Di Molfetta A, Ferrari G, Iacobelli R, Filippelli S, Amodeo A. Concurrent use of continuous and pulsatile flow ventricular assist device on a Fontan patient: a simulation study. Artif Organs. 2017;41(1):32–9.

    PubMed  Google Scholar 

  44. Throckmorton AL, Carr JP, Tahir SA, Tate R, Downs EA, Bhavsar SS, Wu Y, Grizzard JD, Moskowitz WB. Mechanical cavopulmonary assistance of a patient-specific Fontan physiology: numerical simulations, lumped parameter modeling, and suction experiments. Artif Organs. 2011;35(11):1036–47.

    PubMed  Google Scholar 

  45. Fresiello L, Ferrari G, Di Molfetta A, Zieliński K, Tzallas A, Jacobs S, Darowski M, Kozarski M, Meyns B, Katertsidis NS, Karvounis EC, Tsipouras MG, Trivella MG. A cardiovascular simulator tailored for training and clinical uses. J Biomed Inform. 2015;57:100–12.

    CAS  PubMed  Google Scholar 

  46. Yih-Choung Y, Simaan M, Boston R, Miller PJ, Antaki JF. Estimation of blood pump parameters for cardiovascular system identification. New Mexico: Proceedings of the American Control Conference Albuquerque; 1997.

    Google Scholar 

  47. Ferrari G, De Lazzari C, Mimmo R, Tosti G, Ambrosi D. A modular numerical model of the cardiovascular system for studying and training in the field of cardiovascular physiopathology. J Biomed Eng. 1992;14(2):91–107.

    CAS  PubMed  Google Scholar 

  48. Moscato F, Danieli GA, Schima H. Dynamic modeling and identification of an axial flow ventricular assist device. Int J Artif Organs. 2009 Jun;32(6):336–43.

    PubMed  Google Scholar 

  49. Choi A, Boston JR, Thomas S, Antaki JF. Modeling and identification of an axial flow blood pump. Alburquerque, New Mexico: Proceeding of the Americal Control Conference; 1997.

    Google Scholar 

  50. Kitamura T, Matsushima Y, Tokuyama T, Kono S, Nishimura K, Komeda M, Yanai M, Kijima T, Nojiri C. Physical model-based indirect measurements of blood pressure and flow using a centrifugal pump. Artif Organs. 2000;24(8):589–93.

    CAS  PubMed  Google Scholar 

  51. Verkerke GJ, Mihaylov D, Geertsema AA, Lubbers J, Rakhorst G. Numerical simulation of the pulsating catheter pump: a left ventricular assist device. Artif Organs. 1999;23(10):924–31.

    CAS  PubMed  Google Scholar 

  52. Chen S, Antaki JF, Simaan MA, Robert Boston JR. Physiological control of left ventricular assist devices based on gradient of flow. Portland, OR, USA: American Control Conference; 2005.

    Google Scholar 

  53. Giridharan GA, Skliar M. Physiological control of blood pumps using intrinsic pump parameters: a computer simulation study. Artif Organs. 2006;30:301–7.

    PubMed  Google Scholar 

  54. Cox LG, Loerakker S, Rutten MC, de Mol BA, van de Vosse FN. A mathematical model to evaluate control strategies for mechanical circulatory support. Artif Organs. 2009;33(8):593–603.

    PubMed  Google Scholar 

  55. Harvey. The Cardiopulmonary Patient Simulator [Internet]. [cited 2020 July 13]. Available from: https://www.laerdal.com/us/item/HARVEY.

  56. HPS Anesthesia Human Patient Simulator [Internet]. [cited 2020 July 13]. Available from: https://caehealthcare.com/patient-simulation/hps/.

  57. European Union Directive 2010/63/EU [Internet]. [cited 2020 July 13]. Available from: https://eur-lex.europa.eu/eli/dir/2010/63/oj.

  58. Kolff WJ. Mock circulation to test pumps designed for permanent replacement of damaged hearts. Cleve Clin Q. 1959;26:223–6.

    CAS  PubMed  Google Scholar 

  59. Donovan FM. Design of a hydraulic analog of the circulatory system for evaluating artificial hearts. Biomater Med Devices Artif Organs. 1975;3(4):439–49.

    PubMed  Google Scholar 

  60. Swanson WM, Clark RE. A simple cardiovascular system simulator: design and performance. J Bioeng. 1977;1(2):135–45.

    CAS  PubMed  Google Scholar 

  61. Rosenberg G, Phillips WM, Landis DL, Pierce WS. Design and evaluation of the Pennsylvania State University mock circulatory system. ASAIO J. 1981;4(2):41–9.

    Google Scholar 

  62. Knierbein B, Reul H, Eilers R, Lange M, Kaufmann R, Rau G. Compact mock loops of the systemic and pulmonary circulation for blood pump testing. Int J Artif Organs. 1992;15(1):40–8.

    CAS  PubMed  Google Scholar 

  63. Ferrari G, De Lazzari C, Mimmo R, Ambrosi D, Tosti G. Mock circulatory system for in vitro reproduction of the left ventricle, the arterial tree and their interaction with a left ventricular assist device. J Med Eng Technol. 1994;18(3):87–95.

    CAS  PubMed  Google Scholar 

  64. Kolyva C, Biglino G, Pepper JR, Khir AW. A mock circulatory system with physiological distribution of terminal resistance and compliance: application for testing the intra-aortic balloon pump. Artif Organs. 2012;36(3):E62–70.

    CAS  PubMed  Google Scholar 

  65. Timms DL, Gregory SD, Greatrex NA, Pearcy MJ, Fraser JF, Steinseifer U. A compact mock circulation loop for the in vitro testing of cardiovascular devices. Artif Organs. 2011;35(4):384–91.

    PubMed  Google Scholar 

  66. Vukicevic M, Conover T, Jaeggli M, Zhou J, Pennati G, Hsia T-Y, et al. Control of respiration-driven retrograde flow in the subdiaphragmatic venous return of the Fontan circulation. ASAIO J. 2014;60(4):391–9.

    PubMed  PubMed Central  Google Scholar 

  67. Li Y, Parker KH, Khir AW. Using wave intensity analysis to determine local reflection coefficient in flexible tubes. J Biomech. 2016;49(13):2709–17.

    PubMed  Google Scholar 

  68. Ng BC, Smith PA, Nestler F, Timms D, Cohn WE, Lim E. Application of adaptive Starling-like controller to Total artificial heart using dual rotary blood pumps. Ann Biomed Eng. 2017;45(3):567–79.

    PubMed  Google Scholar 

  69. Stevens MC, Gregory SD, Nestler F, Thomson B, Choudhary J, Garlick B, et al. In vitro and in vivo characterization of three different modes of pump operation when using a left ventricular assist device as a right ventricular assist device. Artif Organs. 2014;38(11):931–9.

    PubMed  Google Scholar 

  70. Pillon M, Duffour H, Jufer M. In vitro experiments: Circulatory assist device interaction with a virtual cardiovascular system. 1992 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 1992:740–1.

    Google Scholar 

  71. ANSYS Discovery Live: Real-Time Simulation Revolution [Internet]. [cited 2020 July 13]. Available from: https://www.ansys.com/about-ansys/advantage-magazine/volume-xi-issue-3-2017/ansys-discovery-live-real-time-simulation-revolution.

  72. Zielinski K, Darowski M, Kozarski M, Ferrari G. The need for hybrid modeling in analysis of cardiovascular and respiratory support. Int J Artif Organs. 2016;39(6):265–71.

    PubMed  Google Scholar 

  73. Baloa LA, Boston JR, Antaki JF. Elastance-based control of a mock circulatory system. Ann Biomed Eng. 2001;29(3):244–51.

    CAS  PubMed  Google Scholar 

  74. Colacino FM, Moscato F, Piedimonte F, Danieli G, Nicosia S, Arabia M. A modified elastance model to control mock ventricles in real-time: numerical and experimental validation. ASAIO J. 2008;54(6):563–73.

    PubMed  Google Scholar 

  75. Gwak KW, Paden BE, Antaki JF, Ahn IS. Experimental verification of the feasibility of the cardiovascular impedance simulator. IEEE Trans Biomed Eng. 2010;57(5):1176–83.

    PubMed  Google Scholar 

  76. Ferrari G, De Lazzari C, Kozarski M, et al. A hybrid mock circulatory system: testing a prototype under physiologic and pathological conditions. ASAIO J. 2002;48(5):487–94.

    PubMed  Google Scholar 

  77. Cuenca-Navalon E, Finocchiaro T, Laumen M, Fritschi A, Schmitz-Rode T, Steinseifer U. Design and evaluation of a hybrid mock circulatory loop for total artificial heart testing. Int J Artif Organs. 2014;37(1):71–80.

    PubMed  Google Scholar 

  78. Misgeld BJE, Rüschen D, Schwandtner S, Heinke S, Walter M, Leonhardt S. Robust decentralised control of a hydrodynamic human circulatory system simulator. Biomedical Signal Processing and Control. 2015;20:35–44.

    Google Scholar 

  79. Nestler F, Bradley AP, Wilson SJ, Timms DL, Frazier OH, Cohn WE. A hybrid mock circulation loop for a total artificial heart. Artif Organs. 2014;38(9):775–82.

    PubMed  Google Scholar 

  80. Ochsner G, Amacher R, Amstutz A, Plass A, Schmid Daners M, Tevaearai H, et al. A novel interface for hybrid mock circulations to evaluate ventricular assist devices. IEEE Trans Biomed Eng. 2013;60(2):507–16.

    PubMed  Google Scholar 

  81. SensorART EU Project. [Internet]. [cited 2020 July 13]. Available from: http://www.sensorart.eu/.

  82. Fresiello L, Zieliński K, Jacobs S, Di Molfetta A, Pałko KJ, Bernini F, et al. Reproduction of continuous flow left ventricular assist device experimental data by means of a hybrid cardiovascular model with baroreflex control. Artif Organs. 2014;38(6):456–68.

    PubMed  Google Scholar 

  83. Darowski M, Kozarski M, Ferrari G, Zieliński K, Górczyńska K, Szczepanowski A, et al. A new hybrid (hydro-numerical) model of the circulatory system. Bull Pol Ac Tech. 2013;61(4):993–1003.

    Google Scholar 

  84. Tortora G, Fontana R, Fresiello L, Molfetta AD, Silvestri M, Vatteroni M, et al. Experimental integration of Autoregulation Unit for left ventricular assist devices in a cardiovascular hybrid simulator. 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 2014:282–5.

    Google Scholar 

  85. Ferrari G, Di Molfetta A, Zieliński K, Fresiello L, Górczyńska K, Pałko KJ, et al. Control of a pediatric pulsatile ventricular assist device: a hybrid cardiovascular model study. Artif Organs. 2017;41(12):1099–108.

    PubMed  Google Scholar 

  86. Di Molfetta A, Filippelli S, Ferrari G, Secinaro A, Zielinski K, Amodeo A. Berlin heart EXCOR ventricular assist device: multilayer membrane rupture in a pediatric patient. Ann Thorac Surg. 2016;102(2):e129–30.

    PubMed  Google Scholar 

  87. Di Molfetta A, Zieliński K, Ferrari G, Kozarski M, Okrzeja P, Iacobelli R, Filipelli S, Perri G, Darowski M, Massetti M, Jarvik R, Amodeo A. Is the new infant Jarvik 2015 suitable for patients<8 kg? In vitro study using a hybrid simulator. Artif Organs. 2019;43(1):E1–8.

    PubMed  Google Scholar 

  88. Kozarski M, Ferrari G, Zieliński K, Górczyńska K, Di Molfetta A, Palko KJ, Fresiello L, Darowski M. Biventricular heart assistance: preliminary tests on the hybrid (hydro-numerical) circulatory model. Int J Artif Organs. 2010;33(7):450.

    Google Scholar 

  89. Kozarski M, Suwalski P, Zieliński K, Górczyńska K, Szafron B, Pałko KJ, et al. A hybrid (hydro-numerical) circulatory model: investigations of mechanical aortic valves and a numerical valve model. Bull Pol Ac: Tech. 2015;63(3):605–12.

    Google Scholar 

  90. Zieliński K, Okrzeja P, Stecka A, Kozarski M, Darowski M. A hybrid cardio-pulmonary simulation platform—an application for extracorporeal assist devices. In: Lhotska L, Sukupova L, Lacković I, Ibbott GS, editors. World Congress on Medical Physics and Biomedical Engineering 2018. Singapore: Springer; 2019. p. 703–6. (IFMBE Proceedings).

    Google Scholar 

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Authors and Affiliations

  1. Department of Cardiovascular Sciences, Cardiac Surgery, Katholieke Universiteit Leuven, Leuven, Belgium

    Libera Fresiello PhD

  2. Institute of Clinical Physiology, National Research Council, Pisa, Italy

    Libera Fresiello PhD

  3. Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland

    Krzysztof Zieliński PhD

Authors
  1. Libera Fresiello PhD
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  2. Krzysztof Zieliński PhD
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Correspondence to Libera Fresiello PhD .

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Editors and Affiliations

  1. Lerner Research Institute, Cleveland Clinic, Cleveland Clinic Lerner College of Medicine of Case Western Reserve University Cleveland Clinic, Cleveland, OH, USA

    Jamshid H. Karimov

  2. Lerner Research Institute, Cleveland Clinic, Cleveland Clinic Lerner College of Medicine of Case Western Reserve University Cleveland Clinic, Cleveland, OH, USA

    Kiyotaka Fukamachi

  3. Kaufman Center for Heart Failure Heart, Thoracic, and Vascular Institute, Cleveland Clinic Lerner College of Medicine of Case Western Reserve University Cleveland Clinic, Cleveland, OH, USA

    Randall C. Starling

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Fresiello, L., Zieliński, K. (2020). Hemodynamic Modelling and Simulations for Mechanical Circulatory Support. In: Karimov, J., Fukamachi, K., Starling, R. (eds) Mechanical Support for Heart Failure . Springer, Cham. https://doi.org/10.1007/978-3-030-47809-4_26

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