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Myocardial-vessel interaction: role of LV pressure and myocardial contractility

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Abstract

Coronary heart disease is one of the most important health problems in Western society. The principal mechanism in this problem is the failure of sufficient blood supply to reach the heart muscle for cardiac metabolic needs and hence failure of the heart as a pump. Despite the magnitude of this health problem, the system of blood supply to the heart (the coronary circulation) remains poorly understood. The reason for this is that clinical work has largely focused on the diseased vessels (e.g., atherosclerosis) rather than on the dynamics of the coronary blood flow system as a whole. The latter requires a bioengineering understanding of both the highly complex system and associated mechanical determinants. Despite progress in this area, many issues remain unresolved. Advancements in high-performance computers make it possible now to attempt anatomically based computational (distributive) models rather than the “lumped” models used in the past, where the anatomical details of the coronary vascular system were ignored. Computer simulation and modeling are an important tool in this work because experimental avenues to the problem are highly limited, particularly in the circulation of the deeper layer of the heart which is not amenable to direct visualization. The mechanism of the effect of the cyclic contraction on coronary blood flow remains unresolved. This review will consider the major cardiac mechanical interactions with coronary blood flow including previous models, current hypotheses, and future directions. Experimental validation of present and future mechanical interaction models will be emphasized as well as the utility of the models to explain the mechanical propensity of the subendocardium to ischemia.

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References

  1. Algranati D, Kassab GS, Lanir Y (2010) Mechanisms of coronary vessel/myocardial interaction. Am J Physiol Heart Circ Physiol 298(3):H861–H873

    Article  PubMed  CAS  Google Scholar 

  2. Algranati D, Kassab GS, Lanir Y (2011) Why is the Subendocardium more vulnerable to ischemia? A new paradigm. Am J Physiol Heart Circ Physiol 300(3):H1090–H1100

    Article  PubMed  CAS  Google Scholar 

  3. Allaart CP, Westerhof N (1996) Effect of length and contraction on coronary perfusion in isolated perfused papillary muscle of rat heart. Am J Physiol 271:H447–H454

    PubMed  CAS  Google Scholar 

  4. Anrep GV, Cruickshank EWH, Downing AC, Sabba Rau A (1927) The coronary circulation in relation to the cardiac cycle. Heart 14:111–133

    Google Scholar 

  5. Arts T, Kruger RTI, Van Gerven W, Lambregts JAC, Reneman RS (1979) Propagation velocity and reflection of pressure waves in the canine coronary artery. Am J Physiol 237:H469–H474

    PubMed  CAS  Google Scholar 

  6. Ashikawa K, Kanatsuka H, Suzuki T, Takishima T (1986) Phasic blood flow velocity pattern in epimyocardial microvessels in the beating canine left ventricle. Circ Res 59(6):704–711

    Article  PubMed  CAS  Google Scholar 

  7. Bassingthwaighte JB, Beard DA, Li Z, Yipintsoi T (1998) Is the fractal nature of intraogan spatial flow distributions based on vascular network growth of local metabolic needs?. Birkhauser, Boston, pp 241–259

    Google Scholar 

  8. Beyar R, Manor D, Zinemans D, Sideman S (1993) Concepts and controversies in modeling the coronary circulation. Springer, New York, pp 135–149

    Google Scholar 

  9. Brugada J, Brugada P, Boersma L, Mont L, Kirchhof C, Wellens HJ, Allessie MA (1991) On the mechanisms of ventricular tachycardia acceleration during programmed electrical stimulation. Circulation 83:1621–1629

    Article  PubMed  CAS  Google Scholar 

  10. Bruinsma P, Arts T, Spaan JAE (1998) Model of the coronary circulation based on pressure dependence of coronary resistance and compliance. Basic Res Cardiol 83:510–524

    Article  Google Scholar 

  11. Chadwick RS, Tedgul A, Michel IB, Ohayon I, Levy BI (1990) Phasic regional myocardial inflow and outflow: comparison of theory and experiments. Am J Physiol 258:H1687–H1698

    PubMed  CAS  Google Scholar 

  12. Chillian WM (1991) Microvascular pressure and resistance in the left ventricular subepicardium and subendocardium. Circ Res 69:561–570

    Article  Google Scholar 

  13. Chillian WM, Layne SM, Klausner EC, Eastham CL, Marcus ML (1989) Redistribution of coronary microvascular resistance produced by dipyridamole. Am J Physiol 256(25):H383–H390

    Google Scholar 

  14. Cookson AN, Lee J, Michler C, Chabiniok R, Hyde E, Nordsletten DA, Sinclair M, Siebes M, Smith NP (2012) A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics. J Biomech 45(5):850–855

    Article  PubMed  CAS  Google Scholar 

  15. Doucette JW, Goto M, Flynn AE, Husseini WK Jr, Hoffman JI (1993) Effects of cardiac contraction and cavity pressure on myocardial blood flow. Am I Physiol 265:H1342–H1352

    CAS  Google Scholar 

  16. Downey JM, Kirk ES (1975) Inhibition of coronary blood flow by a vascular waterfall mechanism. Circ Res 36:753–760

    Article  PubMed  CAS  Google Scholar 

  17. Fibich G, Lanir Y, Liron N (1993) Mathematical model of blood flow in a coronary capillary. J Am Physiol 265:H1829–H1840

    CAS  Google Scholar 

  18. Fokkema DS, VanTeeffelen JW, Dekker S, Vergroesen I, Reitsma JB, Spaan JA (2005) Diastolic time fraction as a determinant of subendocardial perfusion. Am J Physiol Heart Circ Physiol 288(5):H2450–H2456

    Article  PubMed  CAS  Google Scholar 

  19. Fox KM, Ferrari R (2011) Heart rate: a forgotten link in coronary artery disease? Nat Rev Cardiol 8(7):369–379

    Article  PubMed  Google Scholar 

  20. Giezeman MJ, VanBavel E, Grimbergen CA, Spaan JA (1994) Compliance of isolated porcine coronary small arteries and coronary pressure-flow relations. Am J Physiol 267(3 Pt 2): H1190–1198

    PubMed  CAS  Google Scholar 

  21. Gregg DE, Green HD (1940) Registration and interpretation of normal phasic inflow into a left coronary artery by an improved differential manometric method. Am J Physiol 130:114–125

    Google Scholar 

  22. Guccione JM, Kassab GS, Ratcliffe MB (eds), (2010) Computational cardiovascular mechanics: Modeling and applications in heart failure. XVI, 436 p. 186 illus., 8 in color, Hardcover ISBN: 978-1-4419-0729-5. Springer, New York

  23. Hamza L, Dang Q, Lu X, Mian A, Molloi S, Kassab GS (2003) The effect of passive myocardium on the compliance of the coronary arteries. Am J Physiol 285(2):H653–H660

    CAS  Google Scholar 

  24. Heineman FW, Grayson J (1985) Transmural distribution of intramyocardial pressure measured by micropipette technique. Am J Physiol 249(6 Pt 2):H1216–H1223

    PubMed  CAS  Google Scholar 

  25. Hiramatsu O, Goto M, Yada T, Kimura A, Tachibana H, Ogasawara Y, Tsujioka K, Kajiya F (1994) Diameters of subendocardial arterioles and venules during prolonged diastole in canine left ventricles. Circ Res 75(2):393–397

    Article  PubMed  CAS  Google Scholar 

  26. Hiramatsu O, Goto M, Yada T, Kimura A, Chiba Y, Tachibana H, Ogasawara Y, Tsujioka K, Kajiya F (1998) In vivo observations of the intramural arterioles and venules in beating canine hearts. J Physiol 509(Pt 2):619–628

    Article  PubMed  CAS  Google Scholar 

  27. Hoffman JI, Spaan JA (1990) Pressure-flow relations in coronary circulation. Physiol Rev 70(2):331–390

    PubMed  CAS  Google Scholar 

  28. Hoffman JIE, Baer RW, Hanley FL, Messina LM (1985) Regulation of transmural myocardial blood flow. Trans ASME 107:2–9

    CAS  Google Scholar 

  29. Hunter PJ, Smaill BH (1988) The analysis of cardiac function: a continuum approach. Prog Biophys molec Biol 52:101–164

    Article  CAS  Google Scholar 

  30. Hurst JW, Logue RB (1970) The heart, arteries, and veins. McGraw-Hill, New York, p 77

    Google Scholar 

  31. Huygh JM, Oomens CW, Van Campen DH, Heethaar RM (1989) Low Reynolds number steady state flow through a branching network of rigid vessels: I. A mixture theory. Biorheology 26:55–71

    Google Scholar 

  32. Huygh JM, Oomens CW, Van Campen DH (1989) Low Reynolds number steady state flow through a branching network of rigid vessels: II. Finite element mixture model. Biorheology 26:73–84

    Google Scholar 

  33. Huygh JM, Arts T, van Campen DH, Reneman RS (1992) Porous medium finite element model of the beating left ventricle. Am J Physiol 262(4 Pt 2):H1256–H1267

    Google Scholar 

  34. Jacobs J, Algranati D, Lanir Y (2008) Lumped flow modeling in dynamically loaded coronary vessels. J Biomech Eng 130:054504

    Article  PubMed  CAS  Google Scholar 

  35. Judd RM, Redberg DA, Mates RE (1991) Diastolic coronary resistance and capacitance are independent of duration of diastole. Am J Physiol 260:H943–H952

    PubMed  CAS  Google Scholar 

  36. Kaimovitz B, Lanir Y, Kassab GS (2005) Large-scale reconstruction of the porcine coronary arterial vasculature based on detailed anatomical data. Ann Biomed Eng 33(11):1517–1535

    Article  PubMed  Google Scholar 

  37. Kaimovitz B, Lanir Y, Kassab GS (2010) A full 3-D reconstruction of the entire porcine coronary vasculature. Am J Physiol Heart Circ Physiol 299(4):H1064–H1076

    Article  PubMed  CAS  Google Scholar 

  38. Kajiya F, Matsuoka S, Gasawara Y, Hiramatsu O, Kanazawa S, Wada Y, Tadaoka S, Tsu-Jioka K, Fujiwara T, Zamir M (1993) Velocity profiles and phasic flow patterns in the non-stenotic human left anterior descending coronary artery during cardiac surgery. Cardiovasc Res 27:845–850

    Article  PubMed  CAS  Google Scholar 

  39. Kajiya F, Yada T, Hiramatsu O, Ogasawara Y, Inai Y, Kajiya M (2008) Coronary microcirculation in the beating heart. Med Biol Eng Comput 46(5):411–419

    Article  PubMed  Google Scholar 

  40. Kanatsuka H, Lamping KG, Eastham CL, Marcus ML, Dellsperger KC (1991) Coronary microvascular resistance in hypertensive cats. Circ Res 68:726–733

    Article  PubMed  CAS  Google Scholar 

  41. Kassab GS (2000) The coronary vasculature and its reconstruction. Ann Biomed Eng 28:903–915

    Article  PubMed  CAS  Google Scholar 

  42. Kassab GS, Fung YC (1994) Topology and dimensions of the pig coronary capillary network. Am J Physiol 267:H319–H325 (Heart Circ PhysioL 36)

    PubMed  CAS  Google Scholar 

  43. Kassab GS, Molloi S (2001) Cross-sectional area and volume compliance of the porcine left coronary arteries. Am J Physiol 281:H623–H628

    CAS  Google Scholar 

  44. Kassab GS, Rider CA, Tang NJ, Fung YC (1993) Morphometry of pig coronary arterial trees. Am J Physiol 265:H350–H365 (Heart Circ. Physiol. 34)

    PubMed  CAS  Google Scholar 

  45. Kassab GS, Lin D, Fung YC (1994) Morphometry of the pig coronary venous system. Am J Physiol 267:H2100–H2113 (Heart Circ. Physiol. 36)

    PubMed  CAS  Google Scholar 

  46. Kassab GS, Pallencaoe E, Fung YC (1997) The longitudinal position matrix of the pig coronary artery and its hemodynamic implications. Am J Physiol 273:H2832–H2842 (Heart Circ. Physiol. 42)

    PubMed  CAS  Google Scholar 

  47. Kassab GS, Le KN, Fung YC (1999) A hemodynamic analysis of coronary capillary blood flow based on anatomic and distensibility data. Am J Physiol 277:H2158–H2166 (Heart Circ. Physiol. 46)

    PubMed  CAS  Google Scholar 

  48. Klassen GA, Armour JA, Garner JB (1987) Coronary circulatory pressure gradients. Can J Physiol Pharmacol 65:520–531

    Article  PubMed  CAS  Google Scholar 

  49. Kouwenhoven E, Vergroesen I, Han Y, Spaan J (1992) Retrograde coronary flow is limited by time-varying elastance. Am J Physiol 263:H484–H490

    PubMed  CAS  Google Scholar 

  50. Kouwenhoven E, Vergroesen I, Han Y, Spaan JA (1992) Retrograde coronary flow is limited by time-varying elastance. Am J Physiol 263:H484–H490

    PubMed  CAS  Google Scholar 

  51. Krams R, Sipkema P, Zegers J, Westerhof N (1989) Contractility is the main determinant of coronary systolic flow impediment. Am J Physiol 257:H1936–H1944

    PubMed  CAS  Google Scholar 

  52. Krams R, Sipkema P, Wsterhof N (1989) Varying elastance concept may explain coronary systolic flow impediment. Am J Physiol 257:H1471–H1479

    PubMed  CAS  Google Scholar 

  53. Kresh JY, Fox M, Brockman SK, Noordergraaf A (1990) Model-based analysis of transmural vessel impedance and myocardial circulation dynamics. Am J Physiol 258:H262–H276

    PubMed  CAS  Google Scholar 

  54. Kuo L, Chilian WM, Davis MJ (1990) Coronary arteriolar myogenic response is independent of endothelium. Circ Res 66(3):860–866

    Article  PubMed  CAS  Google Scholar 

  55. Lanir Y, Nevo E (1993) The Orientation of an intramyocardial vessel affects its mechanical loading by the surrounding myocardium. J Biomech Eng 115:327–328

    Article  PubMed  CAS  Google Scholar 

  56. Lee J, Chambers DE, Akizuki S, Downey JM (1984) The role of vascular capacitance in coronary arteries. Circ Res 55:751–762

    Article  PubMed  CAS  Google Scholar 

  57. Lu X, Pandit A, Kassab GS (2004) The incremental elastic moduli of coronary artery: a two layer model. Am J Physiol 287(4):H1663–H1669 (Heart Circ Physiol)

    CAS  Google Scholar 

  58. Mates RE (1993) The coronary circulation. J Biomed Eng 115:558–561

    CAS  Google Scholar 

  59. Mihailescu LS, Abel FL (1994) Intramyocardial pressure gradients in working and nonworking isolated cat hearts. Am J Physiol 266(3 Pt 2):H1233–H1241

    PubMed  CAS  Google Scholar 

  60. Mulligan LJ, Escobedo D, Freeman GL (1993) Mechanical determinants of coronary blood flow during dynamic alterations in myocardial contractility. Am J Physiol 265:H1112–H1118

    PubMed  CAS  Google Scholar 

  61. Nash MP (1998) Mechanics and Material Properties of an Anatomically Accurate Mathematical Model of the Heart. PhD thesis, University of Auckland, Auckland, New Zealand

  62. Nevo E, Lanir Y (1989) Dynamic, structural model of the left ventricle under finite deformation.ASME Trans. J Biomechanical Eng 111:342–349

    Article  CAS  Google Scholar 

  63. Nevo E, Lanir Y (1989) Parameter estimation of left ventricle performance. Computers in Cardiology Proceedings 251–254

  64. Nielsen PMF, Le Grice IJ, Smaill BH, Hunter PJ (1991) Mathematical model of geometry and fibrous structure of the heart. Am J Physiol 260:H1365–H1378 (Heart Circ. Physiol. 29)

    PubMed  CAS  Google Scholar 

  65. Pandit A, Lu X, Wang C, Kassab GS (2005) Biaxial elastic material properties of porcine coronary media and adventitia. Am J Physiol Heart Circ Physiol 288:H2581–H2587

    Article  PubMed  CAS  Google Scholar 

  66. Permutt S, Riley RL (1963) Hemodynamics of collapsible vessels with tone: the vascular waterfal. J Appl Phys 18:924–932

    CAS  Google Scholar 

  67. Porter WT (1898) The influence of heart beat on the flow of blood through the walls of the heart. Am J Physiol 1:145–169

    Google Scholar 

  68. Pries AR, Secomb TW, Gessner T, Sperandio MB, Gross JF, Gaehtgens P (1994) Resistance to blood flow in microvessels in vivo. Circ Res 75:904–915

    Article  PubMed  CAS  Google Scholar 

  69. Rabbany SY, Kresh JY, Noordergraaf A (1989) Intramyocardial pressure: interaction of myocardial fluid pressure and fiber stress. Am J Physiol 257:H357–H364

    PubMed  CAS  Google Scholar 

  70. Rabbany SY, Funai JT, Noordergraaf A (1994) Pressure generation in a contracting myocyte. Heart Vessels 9:169–174

    Article  PubMed  CAS  Google Scholar 

  71. Rajagopalan S, Dube S, Canty JM (1995) Regulation of coronary diameter by myogenic mechanisms in arterial microvessels greater than 100 microns in diameter. Am J Physiol 268:H788–H793

    PubMed  CAS  Google Scholar 

  72. Ratcliffe M, Guccione J, Kassab GS (2010) “Introduction to Computational Cardiovascular Mechanics”. In: Guccione JM, Kassab GS, Ratcliffe MB (eds) Computational cardiovascular mechanics: modeling and applications in heart failure. Springer, New York, pp xi–xxv

    Google Scholar 

  73. Rodriguez EK, Hunter WC, Royce MJ, Leppo MK, Douglas AS, Weisman HF (1992) A method to reconstruct myocardial sarcomere lengths and orientations at transmural sites in beating canine hearts. Am J Physiol 263:H293–H306

    PubMed  CAS  Google Scholar 

  74. Sabiston DC, Gregg DE (1957) Effect of cardiac contraction on coronary blood flow. Circulation 15:14–20

    Article  PubMed  Google Scholar 

  75. Smith NP, Kassab GS (2001) Analysis of coronary blood flow interaction with myocardial mechanics based on anatomical models. Phil Trans R Soc Lond A 359:1251–1263

    Article  Google Scholar 

  76. Smith NP, Pullan AI, Hunter PI (2000) The generation of an anatomically accurate geometric coronary model. Ann Biomed Eng 28((I)):14–25

    Article  PubMed  CAS  Google Scholar 

  77. Smith N, de Vecchi A, McCormick M, Nordsletten D, Camara O, Frangi AF, Delingette H, Sermesant M, Relan J, Ayache N, Krueger MW, Schulze WH, Hose R, Valverde I, Beerbaum P, Staicu C, Siebes M, Spaan J, Hunter P, Weese J, Lehmann H, Chapelle D, Rezavi R (2011) euHeart: personalized and integrated cardiac care using patient-specific cardiovascular modelling. Interface Focus 1(3):349–364

    Article  PubMed  Google Scholar 

  78. Spaan JAE (1991) Coronary blood flow: mechanics, distribution, and control. Kluwer Academic, Boston

    Book  Google Scholar 

  79. Spaan JAE (1995) Mechanical determinants of myocardial perfusion. Basic Res Cardiol 90:89–102

    Article  PubMed  CAS  Google Scholar 

  80. Spaan JAE, Breuls NPW, Laird JD (1981) Diastolic—systolic coronary flow differences are caused by intramyocardial pump action in the anesthetised dog. Circ Res 49:584–593

    Article  PubMed  CAS  Google Scholar 

  81. Spaan JA, Cornelissen AJ, Chan C, Dankelman J, Yin FC (2000) Dynamics of flow, resistance, and intramural vascular volume in canine coronary circulation. Am J Physiol Heart Circ Physiol 278(2):H383–H403

    PubMed  CAS  Google Scholar 

  82. Spaan JA, ter Wee R, van Teeffelen JW, Streekstra G, Siebes M, Kolyva C, Vink H, Fokkema DS, VanBavel E (2005) Visualisation of intramural coronary vasculature by an imaging cryomicrotome suggests compartmentalisation of myocardial perfusion areas. Med Biol Eng Comput 43:431–435

    Article  PubMed  CAS  Google Scholar 

  83. Spaan JA, Piek JJ, Hoffman JI, Siebes M (2006) Physiological basis of clinically used coronary hemodynamic indices. Circulation 113(3):446–455

    Article  PubMed  Google Scholar 

  84. Suga H, Sagawa K, Shoukas A (1973) Load independance of the instantaneous pressure-volume ratio of the canine left ventricle and the effects of epinephrine and heart rate on the ratio. Circ Res 32:314–322

    Article  PubMed  CAS  Google Scholar 

  85. Tillmanns H, Steinhausen M, Leinberger H, Thederan H, Kubler W (1981) Pressure measurements in the terminal vascular bed of the epimyocardium of rats and cats. Circ Res 49:1202–1211

    Article  PubMed  CAS  Google Scholar 

  86. Toyota E, Ogasawar Y, Hiramatsu O, Tachibana H, Kajiya F, Yamamori S, Chilian WM (2005) Dynamics of flow velocities in endocardial and epicardial coronary arterioles. Am J Physiol Heart Circ Physiol 288:H1598–H1603

    Article  PubMed  CAS  Google Scholar 

  87. van de Hoef TP, Nolte F, Rolandi MC, Piek JJ, van den Wijngaard JP, Spaan JA, Siebes M (2012) Coronary pressure-flow relations as basis for the understanding of coronary physiology. J Mol Cell Cardiol 52(4):786–793

    Article  PubMed  Google Scholar 

  88. VanBavel E, Spaan JA (1992) Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity. Circ Res 71(5):1200–1212

    Article  PubMed  CAS  Google Scholar 

  89. Vankan WJ, Huygh JM, Slaaf DW, Van Donkelaar CC, Drost MR, Janssen JD, Huson A (1997) Finite-element simulation of blood perfusion in muscle tissue during compression and sustained contraction. Am J Physiol 273(3 Pt 2):H1587–H1594

    PubMed  CAS  Google Scholar 

  90. VanTeeffelen JW, Merkus D, Bos LJ, Vergroesen I, Spaan JA (1998) Impairment of contraction increases sensitivity of epicardial lymph pressure for left ventricular pressure. Am J Physiol 274:H187–H192

    PubMed  CAS  Google Scholar 

  91. Vetter F, McCulloch A (1998) Three-dimensional analysis of regional cardiac function: a model of the rabbit ventricular anatomy. Prog Biophys Mol Biol 69:157–185

    Article  PubMed  CAS  Google Scholar 

  92. Wang C, Garcia M, Lu X, Lanir Y, Kassab GS (2006) A three-dimensional model of mechanical properties of coronary artery: a two layer model. Am J Physiol 291(3):H1200–H1209

    Article  CAS  Google Scholar 

  93. Waters SL, Alastruey J, Beard DA, Bovendeerd PH, Davies PF, Jayaraman G, Jensen OE, Lee J, Parker KH, Popel AS, Secomb TW, Siebes M, Sherwin SJ, Shipley RJ, Smith NP, van de Vosse FN (2011) Theoretical models for coronary vascular biomechanics: progress & challenges. Prog Biophys Mol Biol 104(1–3):49–76

    Article  PubMed  Google Scholar 

  94. Wischgoll T, Meyer J, Kaimovitz B, Lanir Y, Kassab GS (2007) A novel method for visualization of entire coronary arterial tree. Ann Biomed Eng 35(5):694–710

    Article  PubMed  Google Scholar 

  95. Yada T, Hiramatsu O, Kimura A, Goto M, Ogasawara Y, Tsujioka K, Yamamori S, Ohno K, Hosaka H, Kajiya F (1993) In vivo observation of subendocardial microvessels of the beating porcine heart using a needle-probe videomicroscope with a CCD camera. Circ Res 72(5):939–946

    Article  PubMed  CAS  Google Scholar 

  96. Yada T, Hirasmatsu O, Goto M, Ogasawara Y, Kimura A, Yamamoto T, Tsujioka K, Kajiya F (1994) Effects of nitroglycerin on diameter and pulsation amplitude of subendocardial arterioles in beating porcine heart. Am J Physiol 267((5 Pt. 2)):H1719–H1725

    PubMed  CAS  Google Scholar 

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Kassab, G.S., Algranati, D. & Lanir, Y. Myocardial-vessel interaction: role of LV pressure and myocardial contractility. Med Biol Eng Comput 51, 729–739 (2013). https://doi.org/10.1007/s11517-013-1072-3

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