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The Journal of Physiological Sciences

, Volume 68, Issue 2, pp 103–111 | Cite as

Lumped parameter model for hemodynamic simulation of congenital heart diseases

  • Shuji ShimizuEmail author
  • Dai Une
  • Toru Kawada
  • Yohsuke Hayama
  • Atsunori Kamiya
  • Toshiaki Shishido
  • Masaru Sugimachi
Review

Abstract

The recent development of computer technology has made it possible to simulate the hemodynamics of congenital heart diseases on a desktop computer. However, multi-scale modeling of the cardiovascular system based on computed tomographic and magnetic resonance images still requires long simulation times. The lumped parameter model is potentially beneficial for real-time bedside simulation of congenital heart diseases. In this review, we introduce the basics of the lumped parameter model (time-varying elastance chamber model combined with modified Windkessel vasculature model) and illustrate its usage in hemodynamic simulation of congenital heart diseases using examples such as hypoplastic left heart syndrome and Fontan circulation. We also discuss the advantages of the lumped parameter model and the problems for clinical use.

Keywords

Lumped parameter model Time-varying elastance Windkessel model Congenital heart diseases Hemodynamic simulation 

Notes

Acknowledgements

A part of this paper was presented at an award presentation at the 94th Annual Meeting of the Physiological Society of Japan, 2017.

Compliance with ethical standards

Funding

This paper has been supported in part by a bounty of Hiroshi and Aya Irisawa Memorial Award for Excellent Papers on Research in Circulation in The Journal of Physiological Sciences.

Conflict of interest

The authors declare that they have no conflicts of interest.

Ethical approval

This paper was written focused on computational simulations. Therefore, there was no ethical approval.

References

  1. 1.
    Baker CE, Corsini C, Cosentino D, Dubini G, Pennati G, Migliavacca F, Hsia TY, Modeling of Congenital Hearts Alliance (MOCHA) Investigators (2013) Effects of pulmonary artery banding and retrograde aortic arch obstruction on the hybrid palliation of hypoplastic left heart syndrome. J Thorac Cardiovasc Surg 146:1341–1348CrossRefGoogle Scholar
  2. 2.
    Riesenkampff E, Rietdorf U, Wolf I, Schnackenburg B, Ewert P, Huebler M, Alexi-Meskishvili V, Anderson RH, Engel N, Meinzer HP, Hetzer R, Berger F, Kuehne T (2009) The practical clinical value of three-dimensional models of complex congenitally malformed hearts. J Thorac Cardiovasc Surg 138:571–580CrossRefGoogle Scholar
  3. 3.
    Corsini C, Baker C, Kung E, Schievano S, Arbia G, Baretta A, Biglino G, Migliavacca F, Dubini G, Pennati G, Marsden A, Vignon-Clementel I, Taylor A, Hsia TY, Dorfman A, Modeling of Congenital Hearts Alliance (MOCHA) Investigators (2014) An integrated approach to patient-specific predictive modeling for single ventricle heart palliation. Comput Methods Biomech Biomed Engin 17:1572–1589CrossRefGoogle Scholar
  4. 4.
    Qian Y, Liu JL, Itatani K, Miyaji K, Umezu M (2010) Computational hemodynamic analysis in congenital heart disease: simulation of the Norwood procedure. Ann Biomed Eng 38:2302–2313CrossRefGoogle Scholar
  5. 5.
    Jalali A, Jones GF, Licht DJ, Nataraj C (2015) Application of mathematical modeling for simulation and analysis of hypoplastic left heart syndrome (HLHS) in pre- and postsurgery conditions. Biomed Res Int 2015:987293CrossRefGoogle Scholar
  6. 6.
    Hay I, Rich J, Ferber P, Burkhoff D, Maurer MS (2005) Role of impaired myocardial relaxation in the production of elevated left ventricular filling pressure. Am J Physiol Heart Circ Physiol 288:H1203–H1208CrossRefGoogle Scholar
  7. 7.
    Suga H, Sagawa K, Shoukas AA (1973) Load independence of the instantaneous pressure–volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio. Circ Res 32:314–322CrossRefGoogle Scholar
  8. 8.
    Shishido T, Hayashi K, Shigemi K, Sato T, Sugimachi M, Sunagawa K (2000) Single-beat estimation of end-systolic elastance using bilinearly approximated time-varying elastance curve. Circulation 102:1983–1989CrossRefGoogle Scholar
  9. 9.
    Santamore WP, Burkhoff D (1991) Hemodynamic consequences of ventricular interaction as assessed by model analysis. Am J Physiol 260:H146–H157PubMedGoogle Scholar
  10. 10.
    Burkhoff D, Alexander J Jr, Schipke J (1988) Assessment of Windkessel as a model of aortic input impedance. Am J Physiol 255:H742–H753PubMedGoogle Scholar
  11. 11.
    Morley D, Litwak K, Ferber P, Spence P, Dowling R, Meyns B, Griffith B, Burkhoff D (2007) Hemodynamic effects of partial ventricular support in chronic heart failure: results of simulation validated with in vivo data. J Thorac Cardiovasc Surg 133:21–28CrossRefGoogle Scholar
  12. 12.
    Westerhof N, Lankhaar JW, Westerhof BE (2009) The arterial Windkessel. Med Biol Eng Comput 47:131–141CrossRefGoogle Scholar
  13. 13.
    Burattini R, Di Salvia PO (2007) Development of systemic arterial mechanical properties from infancy to adulthood interpreted by four-element Windkessel models. J Appl Physiol 103:66–79CrossRefGoogle Scholar
  14. 14.
    Punnoose L, Burkhoff D, Rich S, Horn EM (2012) Right ventricular assist device in end-stage pulmonary arterial hypertension: insights from a computational model of the cardiovascular system. Prog Cardiovasc Dis 55:234–243.e2CrossRefGoogle Scholar
  15. 15.
    Pennati G, Migliavacca F, Dubini G, Pietrabissa R, de Leval MR (1997) A mathematical model of circulation in the presence of the bidirectional cavopulmonary anastomosis in children with a univentricular heart. Med Eng Phys 19:223–234CrossRefGoogle Scholar
  16. 16.
    Recordati G (1999) The contribution of the giraffe to hemodynamic knowledge: a unified physical principle for the circulation. Cardiologia 44:783–789PubMedGoogle Scholar
  17. 17.
    Mroczek T, Małota Z, Wójcik E, Nawrat Z, Skalski J (2011) Norwood with right ventricle-to-pulmonary artery conduit is more effective than Norwood with Blalock–Taussig shunt for hypoplastic left heart syndrome: mathematic modeling of hemodynamics. Eur J Cardiothorac Surg 40:1412–1417PubMedGoogle Scholar
  18. 18.
    Migliavacca F, Pennati G, Dubini G, Fumero R, Pietrabissa R, Urcelay G, Bove EL, Hsia TY, de Leval MR (2001) Modeling of the Norwood circulation: effects of shunt size, vascular resistances, and heart rate. Am J Physiol Heart Circ Physiol 280:H2076–H2086CrossRefGoogle Scholar
  19. 19.
    Jacobs JP, Mayer JE Jr, Mavroudis C, O’Brien SM, Austin EH 3rd, Pasquali SK, Hill KD, Overman DM, St Louis JD, Karamlou T, Pizarro C, Hirsch-Romano JC, McDonald D, Han JM, Becker S, Tchervenkov CI, Lacour-Gayet F, Backer CL, Fraser CD, Tweddell JS, Elliott MJ, Walters H 3rd, Jonas RA, Prager RL, Shahian DM, Jacobs ML (2017) The Society of Thoracic Surgeons congenital heart surgery database: 2017 update on outcomes and quality. Ann Thorac Surg 103:699–709CrossRefGoogle Scholar
  20. 20.
    Sano S, Ishino K, Kawada M, Arai S, Kasahara S, Asai T, Masuda Z, Takeuchi M, Ohtsuki S (2003) Right ventricle–pulmonary artery shunt in first-stage palliation of hypoplastic left heart syndrome. J Thorac Cardiovasc Surg 126:504–509CrossRefGoogle Scholar
  21. 21.
    Shimizu S, Une D, Shishido T, Kamiya A, Kawada T, Sano S, Sugimachi M (2011) Norwood procedure with non-valved right ventricle to pulmonary artery shunt improves ventricular energetics despite the presence of diastolic regurgitation: a theoretical analysis. J Physiol Sci 61:457–465CrossRefGoogle Scholar
  22. 22.
    Young A, Gourlay T, McKee S, Danton MH (2013) Computational modelling to optimize the hybrid configuration for hypoplastic left heart syndrome. Eur J Cardiothorac Surg 44:664–672CrossRefGoogle Scholar
  23. 23.
    Shimizu S, Kawada T, Une D, Shishido T, Kamiya A, Sano S, Sugimachi M (2016) Hybrid stage I palliation for hypoplastic left heart syndrome has no advantage on ventricular energetics: a theoretical analysis. Heart Vessels 31:105–113CrossRefGoogle Scholar
  24. 24.
    Walker SG, Stuth EA (2004) Single-ventricle physiology: perioperative implications. Semin Pediatr Surg 13:188–202CrossRefGoogle Scholar
  25. 25.
    Jaquiss RD, Aziz H (2016) Is four stage management the future of univentricular hearts? Destination therapy in the young. Semin Thorac Cardiovasc Surg Pediatr Card Surg Annu 19:50–54CrossRefGoogle Scholar
  26. 26.
    Di Molfetta A, Amodeo A, Fresiello L, Filippelli S, Pilati M, Iacobelli R, Adorisio R, Colella D, Ferrari G (2016) The use of a numerical model to simulate the cavo-pulmonary assistance in Fontan circulation: a preliminary verification. J Artif Organs 19:105–113CrossRefGoogle Scholar
  27. 27.
    Di Molfetta A, Ferrari G, Iacobelli R, Filippelli S, Amodeo A (2017) Concurrent use of continuous and pulsatile flow ventricular assist device on a Fontan patient: a simulation study. Artif Organs 41:32–39CrossRefGoogle Scholar
  28. 28.
    Shimizu S, Kawada T, Une D, Fukumitsu M, Turner MJ, Kamiya A, Shishido T, Sugimachi M (2016) Partial cavopulmonary assist from the inferior vena cava to the pulmonary artery improves hemodynamics in failing Fontan circulation: a theoretical analysis. J Physiol Sci 66:249–255CrossRefGoogle Scholar
  29. 29.
    Kung E, Pennati G, Migliavacca F, Hsia TY, Figliola R, Marsden A, Giardini A, MOCHA Investigators (2014) A simulation protocol for exercise physiology in Fontan patients using a closed loop lumped-parameter model. J Biomech Eng 136:0810071–08100714PubMedCentralGoogle Scholar
  30. 30.
    Koeken Y, Arts T, Delhaas T (2012) Simulation of the Fontan circulation during rest and exercise. Conf Proc IEEE Eng Med Biol Soc 2012:6673–6676PubMedGoogle Scholar
  31. 31.
    Chowdhury UK, Airan B, Talwar S, Kothari SS, Saxena A, Singh R, Subramaniam GK, Juneja R, Pradeep KK, Sathia S, Venugopal P (2005) One and one-half ventricle repair: results and concerns. Ann Thorac Surg 80:2293–2300CrossRefGoogle Scholar
  32. 32.
    Shimizu S, Shishido T, Une D, Kamiya A, Kawada T, Sano S, Sugimachi M (2010) Right ventricular stiffness constant as a predictor of postoperative hemodynamics in patients with hypoplastic right ventricle: a theoretical analysis. J Physiol Sci 60:205–212CrossRefGoogle Scholar
  33. 33.
    Kilner PJ, Balossino R, Dubini G, Babu-Narayan SV, Taylor AM, Pennati G, Migliavacca F (2009) Pulmonary regurgitation: the effects of varying pulmonary artery compliance, and of increased resistance proximal or distal to the compliance. Int J Cardiol 133:157–166CrossRefGoogle Scholar
  34. 34.
    Broomé M, Maksuti E, Bjällmark A, Frenckner B, Janerot-Sjöberg B (2013) Closed-loop real-time simulation model of hemodynamics and oxygen transport in the cardiovascular system. Biomed Eng Online 12:69CrossRefGoogle Scholar
  35. 35.
    Di Molfetta A, Pilati M, Gagliardi MG, Fresiello L, Amodeo A, Cristofaletti A, Pongiglione G, Ferrari G (2015) Tailoring the hybrid palliation for hypoplastic left heart syndrome: a simulation study using a lumped parameter model. Med Eng Phys 37:898–904CrossRefGoogle Scholar
  36. 36.
    Laser KT, Horst JP, Barth P, Kelter-Klöpping A, Haas NA, Burchert W, Kececioglu D, Körperich H (2014) Knowledge-based reconstruction of right ventricular volumes using real-time three-dimensional echocardiographic as well as cardiac magnetic resonance images: comparison with a cardiac magnetic resonance standard. J Am Soc Echocardiogr 27:1087–1097CrossRefGoogle Scholar
  37. 37.
    Pochet T, Gerard P, Marnette JM, D’Orio V, Marcelle R, Fatemi M, Fossion A, Juchmes J (1992) Identification of three-element Windkessel model: comparison of time and frequency domain techniques. Arch Int Physiol Biochim Biophys 100:295–301PubMedGoogle Scholar
  38. 38.
    Shim Y, Pasipoularides A, Straley CA, Hampton TG, Soto PF, Owen CH, Davis JW, Glower DD (1994) Arterial Windkessel parameter estimation: a new time-domain method. Ann Biomed Eng 22:66–77CrossRefGoogle Scholar
  39. 39.
    Toorop GP, Westerhof N, Elzinga G (1987) Beat-to-beat estimation of peripheral resistance and arterial compliance during pressure transients. Am J Physiol 252:H1275–H1283PubMedGoogle Scholar
  40. 40.
    Essler S, Schroeder MJ, Phaniraj V, Koenig SC, Latham RD, Ewert D (1999) Fast estimation of arterial vascular parameters for transient and steady beats with application to hemodynamic state under variant gravitational conditions. Ann Biomed Eng 27:486–497CrossRefGoogle Scholar
  41. 41.
    Kind T, Faes TJ, Lankhaar JW, Vonk-Noordegraaf A, Verhaegen M (2010) Estimation of three- and four-element Windkessel parameters using subspace model identification. IEEE Trans Biomed Eng 57:1531–1538CrossRefGoogle Scholar
  42. 42.
    Segers P, Rietzschel ER, De Buyzere ML, Stergiopulos N, Westerhof N, Van Bortel LM, Gillebert T, Verdonck PR (2008) Three- and four-element Windkessel models: assessment of their fitting performance in a large cohort of healthy middle-aged individuals. Proc Inst Mech Eng H 222:417–428CrossRefGoogle Scholar
  43. 43.
    Huang H, Yang M, Zang W, Wu S, Pang Y (2011) In vitro identification of four-element Windkessel models based on iterated unscented Kalman filter. IEEE Trans Biomed Eng 58:2672–2680CrossRefGoogle Scholar
  44. 44.
    Schiavazzi DE, Baretta A, Pennati G, Hsia TY, Marsden AL (2017) Patient-specific parameter estimation in single-ventricle lumped circulation models under uncertainty. Int J Numer Method Biomed Eng.  https://doi.org/10.1002/cnm.2799 CrossRefPubMedGoogle Scholar
  45. 45.
    Davos CH, Davlouros PA, Wensel R, Francis D, Davies LC, Kilner PJ, Coats AJ, Piepoli M, Gatzoulis MA (2002) Global impairment of cardiac autonomic nervous activity late after repair of tetralogy of Fallot. Circulation 106:I69–I75CrossRefGoogle Scholar
  46. 46.
    Davos CH, Francis DP, Leenarts MF, Yap SC, Li W, Davlouros PA, Wensel R, Coats AJ, Piepoli M, Sreeram N, Gatzoulis MA (2003) Global impairment of cardiac autonomic nervous activity late after the Fontan operation. Circulation 108:II180–II185CrossRefGoogle Scholar

Copyright information

© The Physiological Society of Japan and Springer Japan KK, part of Springer Nature 2017

Authors and Affiliations

  • Shuji Shimizu
    • 1
    Email author
  • Dai Une
    • 1
  • Toru Kawada
    • 1
  • Yohsuke Hayama
    • 1
  • Atsunori Kamiya
    • 1
  • Toshiaki Shishido
    • 2
  • Masaru Sugimachi
    • 1
  1. 1.Department of Cardiovascular DynamicsNational Cerebral and Cardiovascular CenterSuitaJapan
  2. 2.Department of Research PromotionNational Cerebral and Cardiovascular CenterSuitaJapan

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