Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 6, pp 2093–2112 | Cite as

Cardiovascular mechanics in the early stages of pulmonary hypertension: a computational study

  • Sebastián Acosta
  • Charles Puelz
  • Béatrice Rivière
  • Daniel J. Penny
  • Ken M. Brady
  • Craig G. Rusin
Original Paper


We formulate and study a new mathematical model of pulmonary hypertension. Based on principles of fluid and elastic dynamics, we introduce a model that quantifies the stiffening of pulmonary vasculature (arteries and arterioles) to reproduce the hemodynamics of the pulmonary system, including physiologically consistent dependence between compliance and resistance. This pulmonary model is embedded in a closed-loop network of the major vessels in the body, approximated as one-dimensional elastic tubes, and zero-dimensional models for the heart and other organs. Increasingly severe pulmonary hypertension is modeled in the context of two extreme scenarios: (1) no cardiac compensation and (2) compensation to achieve constant cardiac output. Simulations from the computational model are used to estimate cardiac workload, as well as pressure and flow traces at several locations. We also quantify the sensitivity of several diagnostic indicators to the progression of pulmonary arterial stiffening. Simulation results indicate that pulmonary pulse pressure, pulmonary vascular compliance, pulmonary RC time, luminal distensibility of the pulmonary artery, and pulmonary vascular impedance are much better suited to detect the early stages of pulmonary hypertension than mean pulmonary arterial pressure and pulmonary vascular resistance, which are conventionally employed as diagnostic indicators for this disease.


Pulmonary arterial hypertension Computational hemodynamics Cardiovascular mechanics Blood flow 



C. Puelz was supported by a fellowship from the Keck Center of the Gulf Coast Consortia, on the Training Program in Biomedical Informatics, US National Library of Medicine T15LM007093.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Acosta S, Penny D, Rusin C (2015) An effective model of blood flow in capillary beds. Microvasc Res 100:40–47. doi: 10.1016/j.mvr.2015.04.009 CrossRefGoogle Scholar
  2. Acosta S, Puelz C, Rivière B, Penny D, Rusin C (2015) Numerical method of characteristics for one-dimensional blood flow. J Comput Phys 294:96–109. doi: 10.1016/ CrossRefzbMATHMathSciNetGoogle Scholar
  3. Alastruey J, Moore SM, Parker KH, David T, Peiró J, Sherwin SJ (2008) Reduced modelling of blood flow in the cerebral circulation: coupling 1-D, 0-D and cerebral auto-regulation models. Int J Numer Methods Fluids 56(8):1061–1067. doi: 10.1002/fld CrossRefzbMATHMathSciNetGoogle Scholar
  4. Aronson D, Darawsha W, Atamna A, Kaplan M, Makhoul B, Mutlak D, Lessick J, Carasso S, Reisner S, Agmon Y, Dragu R, Azzam Z (2013) Pulmonary hypertension, right ventricular function, and clinical outcome in acute decompensated heart failure. J Card Fail 19(10):665–671. doi: 10.1016/j.cardfail.2013.08.007 CrossRefGoogle Scholar
  5. Audebert C, Bucur P, Bekheit M, Vibert E, Vignon-Clementel I, Gerbeau JF (2017) Kinetic scheme for arterial and venous blood flow, and application to partial hepatectomy modeling. Comput Methods Appl Mech Eng 314:102–125. doi: 10.1016/j.cma.2016.07.009 CrossRefMathSciNetGoogle Scholar
  6. Badesch D, Champion H, Gomez Sanchez M, Hoeper M, Loyd J, Manes A, McGoon M, Naeije R, Olschewski H, Oudiz R, Torbicki A (2009) Diagnosis and assessment of pulmonary arterial hypertension. J Am Coll Cardiol 54(1):S55–S66. doi: 10.1016/j.jacc.2009.04.011 CrossRefGoogle Scholar
  7. Blanco P, Feijóo R (2013) A dimensionally-heterogeneous closed-loop model for the cardiovascular system and its applications. Med Eng Phys 35(5):652–67. doi: 10.1016/j.medengphy.2012.07.011 CrossRefGoogle Scholar
  8. Bogaard H, Abe K, Noordegmaf A, Voelkel N (2009) The right ventricle under pressure. Cellular and molecular mechanisms of right-heart failure in pulmonary hypertension. Chest 135:794–804. doi: 10.1378/chest.08-0492 CrossRefGoogle Scholar
  9. Čanić S, Kim E (2003) Mathematical analysis of the quasilinear effects in a hyperbolic model blood flow through compliant axi-symmetric vessels. Math Methods Appl Sci 26(14):1161–1186. doi: 10.1002/mma.407 CrossRefzbMATHMathSciNetGoogle Scholar
  10. Champion H, Michelakis E, Hassoun P (2009) Comprehensive invasive and noninvasive approach to the right ventricle-pulmonary circulation unit. Circulation 120(11):992–1007. doi: 10.1161/CIRCULATIONAHA.106.674028 CrossRefGoogle Scholar
  11. Chemla D, Castelain V, Hervé P, Lecarpentier Y, Brimioulle S (2002) Haemodynamic evaluation of pulmonary hypertension. Eur Respir J 20:1314–1331. doi: 10.1183/09031936.02.00068002 CrossRefGoogle Scholar
  12. Dragu R, Rispler S, Habib M, Sholy H, Hammerman H, Galie N, Aronson D (2015) Pulmonary arterial capacitance in patients with heart failure and reactive pulmonary hypertension. Eur J Heart Fail 17(1):74–80. doi: 10.1002/ejhf.192 CrossRefGoogle Scholar
  13. Dyverfeldt P, Bissell M, Barker A, Bolger A, Carlhäll CJ, Ebbers T, Francios C, Frydrychowicz A, Geiger J, Giese D, Hope M, Kilner P, Kozerke S, Myerson S, Neubauer S, Wieben O, Markl M (2015) 4D flow cardiovascular magnetic resonance consensus statement. J Cardiovasc Magn Reson 17:72. doi: 10.1186/s12968-015-0174-5 CrossRefGoogle Scholar
  14. Farber H, Loscalzo J (2004) Pulmonary arterial hypertension. N Engl J Med 351:1655–1665. doi: 10.1056/NEJMra035488 CrossRefGoogle Scholar
  15. Formaggia L, Nobile F, Quarteroni A (2002) A one dimensional model for blood flow: application to vascular prosthesis. In: Math. Model. Numer. Simul. Contin. Mech. Springer, Berlin, pp 137–153. doi: 10.1007/978-3-642-56288-4_10
  16. Formaggia L, Lamponi D, Tuveri M, Veneziani A (2006) Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Comput Methods Biomech Biomed Eng 9(5):273–288. doi: 10.1080/10255840600857767 CrossRefGoogle Scholar
  17. Gaine S, Rubin L (1998) Primary pulmonary hypertension. Lancet 9129:719–725. doi: 10.1016/S0140-6736(98)02111-4 CrossRefGoogle Scholar
  18. Gibbs JSR (2007) Making a diagnosis in PAH. Eur Respir Rev 16(102):8–12. doi: 10.1183/09059180.00010203 CrossRefGoogle Scholar
  19. Hildenbrand FF, Fauchère I, Huber LC, Keusch S, Speich R, Ulrich S (2012) A low resting heart rate at diagnosis predicts favourable long-term outcome in pulmonary arterial and chronic thromboembolic pulmonary hypertension. A prospective observational study. Respir Res 13(1):76. doi: 10.1186/1465-9921-13-76 CrossRefGoogle Scholar
  20. Hill M, Simon M, Valdez-Jasso D, Zhang W, Champion H, Sacks M (2014) Structural and mechanical adaptations of right ventricle free wall myocardium to pressure overload. Ann Biomed Eng 42(12):2451–2465. doi: 10.1007/s10439-014-1096-3 CrossRefGoogle Scholar
  21. Hughes T, Lubliner J (1973) On the one-dimensional theory of blood flow in the larger vessels. Math Biosci 18:161–170. doi: 10.1016/0025-5564(73)90027-8 CrossRefzbMATHGoogle Scholar
  22. Humbert M, Sitbon O, Chaouat A, Bertocchi M, Habib G, Gressin V, Yaïci A, Weitzenblum E, Cordier JF, Chabot F, Dromer C, Pison C, Reynaud-Gaubert M, Haloun A, Laurent M, Hachulla E, Cottin V, Degano B, Jaïs X, Montani D, Souza R, Simonneau G (2010a) Survival in patients with idiopathic, familial, and anorexigen-associated pulmonary arterial hypertension in the modern management era. Circulation 122(2):156–163. doi: 10.1161/CIRCULATIONAHA.109.911818 CrossRefGoogle Scholar
  23. Humbert M, Sitbon O, Yaïci A, Montani D, O’Callaghan D, Jaïs X, Parent F, Savale L, Natali D, Günther S, Chaouat A, Chabot F, Cordier JF, Habib G, Gressin V, Jing ZC, Souza R, Simonneau G (2010b) Survival in incident and prevalent cohorts of patients with pulmonary arterial hypertension. Eur Respir J 36(3):549–555. doi: 10.1183/09031936.00057010 CrossRefGoogle Scholar
  24. Humbert M, Gerry Coghlan J, Khanna D (2012) Early detection and management of pulmonary arterial hypertension. Eur Respir Rev 21(126):306–312. doi: 10.1183/09059180.00005112 CrossRefGoogle Scholar
  25. Hunter K, Gross J, Lanning C, Kirby K, Dyer K, Ivy D, Shandas R (2008) Noninvasive methods for determining pulmonary vascular function in children with pulmonary arterial hypertension: application of a mechanical oscillator model. Congenit Heart Dis 3:106–116CrossRefGoogle Scholar
  26. Hunter K, Lammers S, Shandas R (2011) Pulmonary vascular stiffness: measurement, modeling, and implications in normal and hypertensive pulmonary circulations. Compr Physiol 1(3):1413–1435. doi: 10.1002/cphy.c100005 Google Scholar
  27. Katz A, Lorell B (2000) Regulation of cardiac contraction and relaxation. Circulation 102:69–74. doi: 10.1161/01.CIR.102.suppl_4.IV-69 CrossRefGoogle Scholar
  28. Kheyfets V, O’Dell W, Smith T, Reilly J, Finol E (2013) Considerations for numerical modeling of the pulmonary circulation—a review with a focus on pulmonary hypertension. J Biomech Eng 135(6):061011–061015. doi: 10.1115/1.4024141 CrossRefGoogle Scholar
  29. Komajda M, Lam C (2014) Heart failure with preserved ejection fraction: a clinical dilemma. Eur Heart J 35(16):1022–1032. doi: 10.1093/eurheartj/ehu067 CrossRefGoogle Scholar
  30. Krishnamurthy R, Cheong B, Muthupillai R (2014) Tools for cardiovascular magnetic resonance imaging. Cardiovasc Diagn Ther 4(2):104–125. doi: 10.3978/j.issn.2223-3652.2014.03.06 Google Scholar
  31. Kuehne T, Yilmaz S, Steendijk P, Moore P, Groenink M, Saaed M, Weber O, Higgins C, Ewert P, Fleck E, Nagel E, Schulze-Neick I, Lange P (2004) Magnetic resonance imaging analysis of right ventricular pressure-volume loops. Circulation 110(14):2010–2016. doi: 10.1161/01.CIR.0000143138.02493.DD CrossRefGoogle Scholar
  32. Lankhaar JW, Westerhof N, Faes T, Marques K, Marcus J, Postmus P, Vonk-Noordegraaf A (2006) Quantification of right ventricular afterload in patients with and without pulmonary hypertension. Am J Physiol Heart Circ Physiol 291(4):H1731–7. doi: 10.1152/ajpheart.00336.2006 CrossRefGoogle Scholar
  33. Lankhaar JW, Westerhof N, Faes T, Gan C, Marques K, Boonstra A, van den Berg F, Postmus P, Vonk-Noordegraaf A (2008) Pulmonary vascular resistance and compliance stay inversely related during treatment of pulmonary hypertension. Eur Heart J 29(13):1688–1695. doi: 10.1093/eurheartj/ehn103 CrossRefGoogle Scholar
  34. Lungu A, Wild J, Capener D, Kiely D, Swift A, Hose D (2014) MRI model-based non-invasive differential diagnosis in pulmonary hypertension. J Biomech 47(12):2941–2947. doi: 10.1016/j.jbiomech.2014.07.024 CrossRefGoogle Scholar
  35. Lungu A, Swift A, Capener D, Kiely D, Hose R, Wild J (2016) Diagnosis of pulmonary hypertension from magnetic resonance imaging-based computational models and decision tree analysis. Pulm Circ 6(2):181–190. doi: 10.1086/686020 CrossRefGoogle Scholar
  36. MacKenzie Ross R, Toshner M, Soon E, Naeije R, Pepke-Zaba J (2013) Decreased time constant of the pulmonary circulation in chronic thromboembolic pulmonary hypertension. Am J Physiol Heart Circ Physiol 305:H259–H264. doi: 10.1152/ajpheart.00128.2013 CrossRefGoogle Scholar
  37. Mahapatra S, Nishimura R, Sorajja P, Cha S, McGoon M (2006) Relationship of pulmonary arterial capacitance and mortality in idiopathic pulmonary arterial hypertension. J Am Coll Cardiol 47(4):799–803. doi: 10.1016/j.jacc.2005.09.054 CrossRefGoogle Scholar
  38. Markl M, Schnell S, Barker A (2014) 4D flow imaging: current status to future clinical applications. Curr Cardiol Rep 16:481. doi: 10.1007/s11886-014-0481-8 CrossRefGoogle Scholar
  39. Matthews JC, McLaughlin V (2008) Acute right ventricular failure in the setting of acute pulmonary embolism or chronic pulmonary hypertension: a detailed review of the pathophysiology, diagnosis, and management. Curr Cardiol Rev 4(1):49–59. doi: 10.2174/157340308783565384 CrossRefGoogle Scholar
  40. McGoon M, Kane G (2009) Pulmonary hypertension: diagnosis and management. Mayo Clin Proc 84(2):191–207. doi: 10.1016/S0025-6196(11)60828-8 CrossRefGoogle Scholar
  41. McLaughlin V, McGoon M (2006) Pulmonary arterial hypertension. Circulation 114(13):1417–1431. doi: 10.1161/CIRCULATIONAHA.104.503540 CrossRefGoogle Scholar
  42. Melicher V, Gajdošík V (2008) A numerical solution of a one-dimensional blood flow model-moving grid approach. J Comput Appl Math 215(2):512–520CrossRefzbMATHMathSciNetGoogle Scholar
  43. Mikelic A, Guidoboni G, Canic S (2007) Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem. Netw Heterog Media 2(3):397–423. doi: 10.3934/nhm.2007.2.397 CrossRefzbMATHMathSciNetGoogle Scholar
  44. Moraes D, Colucci W, Givertz M (2000) Secondary pulmonary hypertension in chronic heart failure: the role of the endothelium in pathophysiology and management. Circulation 102:1718–1723. doi: 10.1161/01.CIR.102.14.1718 CrossRefGoogle Scholar
  45. Mynard J (2011) PhD Thesis: Computer modeling and wave intensity analysis of perinatal cardiovascular function and dysfunction. Ph.D. thesis, University of MelbourneGoogle Scholar
  46. Mynard J, Smolich J (2015) One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation. Ann Biomed Eng 43(6):1443–1460. doi: 10.1007/s10439-015-1313-8 CrossRefGoogle Scholar
  47. Naeije R, Huez S (2007) Right ventricular function in pulmonary hypertension: physiological concepts. Eur Heart J Suppl 9:H5–H9. doi: 10.1093/eurheartj/sum023 CrossRefGoogle Scholar
  48. Naeije R, Manes A (2014) The right ventricle in pulmonary arterial hypertension. Eur Respir Rev 23:476–487. doi: 10.1183/09059180.00007414 CrossRefGoogle Scholar
  49. Olufsen M (1999) Structured tree outflow condition for blood flow in larger systemic arteries. Am J Physiol Heart Circ Physiol 276:H257–H268. doi: 10.1017/CBO9781107415324.004 Google Scholar
  50. Olufsen MS, Peskin CS, Kim WY, Pedersen EM, Nadim A, Larsen J (2000) Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann Biomed Eng 28(11):1281–1299CrossRefGoogle Scholar
  51. Provencher S, Chemla D, Hervé P, Sitbon O, Humbert M, Simonneau G (2006) Heart rate responses during the 6-minute walk test in pulmonary arterial hypertension. Eur Respir J 27:114–120. doi: 10.1183/09031936.06.00042705 CrossRefGoogle Scholar
  52. Punnoose L, Burkhoff D, Rich S, Horn E (2012) Right ventricular assist device in end-stage pulmonary arterial hypertension: insights from a computational model of the cardiovascular system. Prog Cardiovasc Dis 55(2):234–243. doi: 10.1016/j.pcad.2012.07.008 CrossRefGoogle Scholar
  53. Pursell E, Vélez-Rendón D, Valdez-Jasso D (2016) Biaxial properties of the left and right pulmonary arteries in a monocrotaline rat animal model of pulmonary arterial hypertension. J Biomech Eng 138(11):111004. doi: 10.1115/1.4034826 CrossRefGoogle Scholar
  54. Quail MA, Knight DS, Steeden JA, Taelman L, Moledina S, Taylor AM, Segers P, Coghlan GJ, Muthurangu V (2015) Noninvasive pulmonary artery wave intensity analysis in pulmonary hypertension. Am J Physiol Heart Circ Physiol 308(12):H1603–H1611CrossRefGoogle Scholar
  55. Qureshi M, Vaughan G, Sainsbury C, Johnson M, Peskin C, Olufsen M, Hill N (2014) Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation. Biomech Model Mechanobiol 13:1137–1154. doi: 10.1007/s10237-014-0563-y CrossRefGoogle Scholar
  56. Rain S, Handoko M, Trip P, Gan T, Westerhof N, Stienen G, Paulus W, Ottenheijm C, Marcus J, Dorfmuller P, Guignabert C, Humbert M, MacDonald P, dos Remedios C, Postmus P, Saripalli C, Hidalgo C, Granzier H, Vonk-Noordegraaf A, van der Velden J, de Man F (2013) Right ventricular diastolic impairment in patients with pulmonary arterial hypertension. Circulation 128(18):2016–25. doi: 10.1161/CIRCULATIONAHA.113.001873 CrossRefGoogle Scholar
  57. Rausch M, Dam A, Göktepe S, Abilez O, Kuhl E (2011) Computational modeling of growth: systemic and pulmonary hypertension in the heart. Biomech Model Mechanobiol 10(6):799–811. doi: 10.1007/s10237-010-0275-x CrossRefGoogle Scholar
  58. Reuben SR (1971) Compliance of the human pulmonary arterial system in disease. Circ Res 29(1):40–50. doi: 10.1161/01.RES.29.1.40 CrossRefGoogle Scholar
  59. Reymond P, Merenda F, Perren F, Rufenacht D, Stergiopulos N (2009) Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol 297:H208–H222. doi: 10.1152/ajpheart.00037.2009 CrossRefGoogle Scholar
  60. Rich J, Rich S (2014) Clinical diagnosis of pulmonary hypertension. Circulation 130(20):1820–1830. doi: 10.1161/CIRCULATIONAHA.114.006971 CrossRefGoogle Scholar
  61. Sanz J, Kariisa M, Dellegrottaglie S, Prat-González S, Garcia M, Fuster V, Rajagopalan S (2009) Evaluation of pulmonary artery stiffness in pulmonary hypertension with cardiac magnetic resonance. JACC Cardiovasc Imaging 2(3):286–295. doi: 10.1016/j.jcmg.2008.08.007 CrossRefGoogle Scholar
  62. Sanz J, García-Alvarez A, Fernández-Friera L, Nair A, Mirelis J, Sawit S, Pinney S, Fuster V (2012) Right ventriculo-arterial coupling in pulmonary hypertension: a magnetic resonance study. Heart 98(3):238–43. doi: 10.1136/heartjnl-2011-300462 CrossRefGoogle Scholar
  63. Saouti N, Westerhof N, Helderman F, Marcus J, Boonstra A, Postmus P, Vonk-Noordegraaf A (2010a) Right ventricular oscillatory power is a constant fraction of total power irrespective of pulmonary artery pressure. Am J Respir Crit Care Med 182(10):1315–20. doi: 10.1164/rccm.200910-1643OC CrossRefGoogle Scholar
  64. Saouti N, Westerhof N, Postmus PE, Vonk-Noordegraaf A (2010b) The arterial load in pulmonary hypertension. Eur Respir Rev 19(117):197–203. doi: 10.1183/09059180.00002210 CrossRefGoogle Scholar
  65. Schuuring M, van Riel A, Vis J, Duffels M, Berger R, Hoendermis E, Van Dijk A, Vliegen H, Mulder B, Bouma B (2013) Resting heart rate is an important determinant of mortality in patients with pulmonary arterial hypertension due to congenital heart disease. J Am Coll Cardiol 61(10):E1271. doi: 10.1016/S0735-1097(13)61271-1 CrossRefGoogle Scholar
  66. Segers P, Stergiopulos N, Westerhof N (2000) Quantification of the contribution of cardiac and arterial remodeling to hypertension. Hypertension 36(5):760–765CrossRefGoogle Scholar
  67. Sherwin S, Formaggia L, Peiro J, Franke V (2003) Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. Int J Numer Methods Fluids 43:673–700CrossRefzbMATHMathSciNetGoogle Scholar
  68. Stankovic Z, Allen B, Garcia J, Jarvis K, Markl M (2014) 4D flow imaging with MRI. Cardiovasc Diagn Ther 4(2):173–192. doi: 10.3978/j.issn.2223-3652.2014.01.02 Google Scholar
  69. Steelet B, Valdez-Jasso D, Haider M (2011) Predicting arterial flow and pressure dynamics using a 1D fluid dynamics model with a viscoelastic wall. SIAM J Appl Math 71(4):1123–1143CrossRefzbMATHMathSciNetGoogle Scholar
  70. Stergiopulos N, Young D, Rogge T (1992) Computer simulation of arterial flow with applications to arterial and aortic stenoses. J Biomech 25(12):1477–1488CrossRefGoogle Scholar
  71. Streeter V, Keitzer W, Bohr D (1963) Pulsatile pressure and flow through distensible vessels. Circ Res 13(1):3–20CrossRefGoogle Scholar
  72. Strocchi M, Contarino C, Zhang Q, Bonmassari R, Toro E (2017) A global mathematical model for the simulation of stenoses and bypass placement in the human arterial system. Appl Math Comput 300:21–39. doi: 10.1016/j.amc.2016.11.028 MathSciNetGoogle Scholar
  73. Tan W, Madhavan K, Hunter K, Park D, Stenmark K (2014) Vascular stiffening in pulmonary hypertension: cause or consequence? Pulm Circ 4(4):560–80. doi: 10.1086/677370 CrossRefGoogle Scholar
  74. Tang B, Pickard S, Chan F, Tsao P, Taylor C, Feinstein J (2012) Wall shear stress is decreased in the pulmonary arteries of patients with pulmonary arterial hypertension: an image-based, computational fluid dynamics study. Pulm Circ 2(4):470–6. doi: 10.4103/2045-8932.105035
  75. Thenappan T, Shah SJ, Rich S, Tian L, Archer SL, Gomberg-Maitland M (2010) Survival in pulmonary arterial hypertension: a reappraisal of the nih risk stratification equation. Eur Respir J 35(5):1079–1087. doi: 10.1183/09031936.00072709 CrossRefGoogle Scholar
  76. Valdez-Jasso D, Haider M, Banks H, Santana D, Germán Y, Armentano R, Olufsen M (2009) Analysis of viscoelastic wall properties in ovine arteries. IEEE Trans Biomed Eng 56(2):210–219. doi: 10.1109/TBME.2008.2003093 CrossRefGoogle Scholar
  77. Valdez-Jasso D, Bia D, Zócalo Y, Armentano R, Haider M, Olufsen M (2011) Linear and nonlinear viscoelastic modeling of aorta and carotid pressure-area dynamics under in vivo and ex vivo conditions. Ann Biomed Eng 39(5):1438–1456. doi: 10.1007/s10439-010-0236-7 CrossRefGoogle Scholar
  78. Voelkel N, Quaife R, Leinwand L, Barst R, McGoon M, Meldrum D, Dupuis J, Long C, Rubin L, Smart F, Suzuki Y, Gladwin M, Denholm E, Gail D (2006) Right ventricular function and failure: report of a National Heart, Lung, and Blood Institute working group on cellular and molecular mechanisms of right heart failure. Circulation 114(17):1883–1891. doi: 10.1161/CIRCULATIONAHA.106.632208 CrossRefGoogle Scholar
  79. Vonk-Noordegraaf A, Haddad F, Chin K, Forfia P, Kawut S, Lumens J, Naeije R, Newman J, Oudiz R, Provencher S, Torbicki A, Voelkel N, Hassoun P (2013) Right heart adaptation to pulmonary arterial hypertension: physiology and pathobiology. J Am Coll Cardiol 62(25):D22–D33. doi: 10.1016/j.jacc.2013.10.027 CrossRefGoogle Scholar
  80. Wang Z, Chesler N (2011) Pulmonary vascular wall stiffness: an important contributor to the increased right ventricular afterload with pulmonary hypertension. Pulm Circ 1(2):212–23. doi: 10.4103/2045-8932.83453 CrossRefGoogle Scholar
  81. Wang Z, Chesler NC (2013) Pulmonary vascular mechanics: important contributors to the increased right ventricular afterload of pulmonary hypertension. Exp Physiol 98(8):1267–1273. doi: 10.1113/expphysiol.2012.069096 CrossRefGoogle Scholar
  82. Wang J, Parker K (2004) Wave propagation in a model of the arterial circulation. J Biomech 37(4):457–70. doi: 10.1016/j.jbiomech.2003.09.007 CrossRefGoogle Scholar
  83. Wang Z, Schreier D, Hacker T, Chesler N (2013) Progressive right ventricular functional and structural changes in a mouse model of pulmonary arterial hypertension. Physiol Rep 1(7):e00184. doi: 10.1002/phy2.184 CrossRefGoogle Scholar
  84. Xiao N, Alastruey J, Figueroa CA (2014) A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models. Int J Numer Methods Biomed Eng 30(2):204–31. doi: 10.1002/cnm.2598 CrossRefMathSciNetGoogle Scholar
  85. Yang W, Feinstein J, Vignon-Clementel I (2016) Adaptive outflow boundary conditions improve post-operative predictions after repair of peripheral pulmonary artery stenosis. Biomech Model Mechanobiol 15(5):1345–1353. doi: 10.1007/s10237-016-0766-5 CrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Pediatrics–CardiologyBaylor College of Medicine and Texas Children’s HospitalHoustonUSA
  2. 2.Department of Computational and Applied MathematicsRice UniversityHoustonUSA
  3. 3.Department of AnesthesiologyBaylor College of Medicine and Texas Children’s HospitalHoustonUSA

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