Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

Biomechanics and Modeling in Mechanobiology

Volumn 13, Issue 5, 2014, Pages 1137-1154

  Qureshi, M Umar ^a,b   Vaughan, Gareth D A ^b   Sainsbury, Christopher ^c   Johnson, Martin ^d   Peskin, Charles S ^e   Olufsen, Mette S ^f   Hill, N A ^b  

^a INTERNATIONAL ISLAMIC UNIVERSITY   (Pakistan)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

^c UNIVERSITY OF GLASGOW   (United Kingdom)

^d GOLDEN JUBILEE NATIONAL HOSPITAL   (United Kingdom)

^e NEW YORK UNIVERSITY   (United States)

^f NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Multiscale mathematical model; Pulmonary circulation; Pulmonary hypertension; Resistance arteries; Structured tree

Indexed keywords

BLOOD; BLOOD PRESSURE; BLOOD VESSELS; DIAGNOSIS; DISEASES; FORESTRY; HEMODYNAMICS; NEWTONIAN LIQUIDS; NONLINEAR EQUATIONS; TREES (MATHEMATICS);

ARTERIAL PRESSURES; BLOOD FLOW; COMPUTATIONAL MODELLING; MULTISCALE MATHEMATICAL MODEL; PULMONARY CIRCULATION; PULMONARY HYPERTENSION; RESISTANCE ARTERY; STRUCTURED TREE; THREE GENERATIONS; VENOUS PRESSURE;

MAGNETIC RESONANCE IMAGING;

BLOOD PRESSURE; HUMAN; LUNG CIRCULATION; MATHEMATICAL COMPUTING; PATHOPHYSIOLOGY; PHYSIOLOGY; PULMONARY ARTERY; PULMONARY HYPERTENSION; PULMONARY VEIN;

BLOOD PRESSURE; HUMANS; HYPERTENSION, PULMONARY; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PULMONARY ARTERY; PULMONARY CIRCULATION; PULMONARY VEINS;

EID: 84920249464     PISSN: 16177959     EISSN: 16177940     Source Type: Journal    
DOI: 10.1007/s10237-014-0563-y     Document Type: Article

References (74)

1. Alastruey J, Parker KH, Peiro J, Byrd SM, Sherwin SJ (2007) Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J Biomech 40:1794–1805
2. Alastruey J, (2011) Numerical assessment of time-domain methods for estimation of local arterial pulse wave speed. J Biomech 44:885–891
3. Attinger EO (1963) Pressure transmission in pulmonary arteries related to frequency and geometry. Circ Res 12(6):623–641
4. Azer K, Peskin CS (2007) A one-dimensional model of blood flow in arteries with friction and convection based on the womersley velocity profile. Cardiovasc Eng 7(2):51–73
5. Barnes PJ, Liu SF (1995) Regulation of pulmonary vascular tone. Pharmacol Rev 47:87–131
6. Barst RJ, McGoon M, Torbicki A, Sitbon O, Krowka MJ, Olschewski H, Gaine S (2004) Diagnosis and differential assessment of pulmonary arterial hypertension. J Am Coll Cardiol 43:40S–47S
7. Bovendeerd PH, Borsje P, Arts T, van de Vosse FN (2006) Dependence of intramyocardial pressure and coronary flow on ventricular loading and contractility: a model study. Ann Biomed Eng 34:1833–1845
8. Burton AC (1972) Physiology and biophysics of the circulation. Year Book Medical Publishers, Chicago, IL, pp 86–94
9. Castelain V, Herve P, Lecarpentier Y, Duroux P, Simonneau G, Chemla D (2001) Pulmonary artery pulse pressure and wave reflection in chronic pulmonary thromboembolism and primary pulmonary hypertension. J Am Coll Cardiol 7:1085–1092
10. Clipp RB, Steele BN (2009) Impedance boundary conditions for the pulmonary vasculature including the effects of geometry, compliance, and respiration. IEEE Trans Biomed Eng 56:862–870
11. Clipp RB, Steele BN (2012) An evaluation of dynamic outlet boundary conditions in a 1D fluid dynamics model. Math Biosci Eng 9:61–74
12. Cousins W, Gremaud PA (2012) Boundary conditions for hemodynamics: The structured tree revisited. J Comp Phys 231:6086–6096
13. Cousins W, Gremaud PA, Tartakovsky DM (2013) A new physiological boundary condition for hemodynamics. SIAM J Appl Math 3(73):1203–1233
14. Dartevelle P, Fadell E, Mussot S, Chapelier A, Hervel P, de Perrot M, Cerrinal J, Laduriel FL, Lehouerou D, Humbert M, Sitbon O, Simonneau G (2004) Chronic thromboembolic pulmonary hypertension. Eur Respir J 23:637–648
15. Evans RL, Pelley JW, Quenemoen L (1960) Some simple geometric and mechanical characteristics of mammalian blood vessels. Am J Physiol 199:1150–1152
16. Figueroa CA, Vignon-Clementel IE, Jansen KE, Hughes T, Taylor CA (2006) A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput Methods Appl Mech Eng 195:5685–5706
17. Fonseca GH, Souza R, Salemi VM, Jardim CV, Gualandro SF (2012) Pulmonary hypertension diagnosed by right heart catheterization in sickle cell disease. Eur Respir J 39(1):112–8
18. Formaggia L, Lamponi D, Tuveri M, Veneziani A (2006) Numerical modelling of 1D networks coupled with a lumped parameters description of the heart. Comput Methods Biomech Biomed Eng 9:273–288
19. Fullana J, Zaleski S (2009) A branched one-dimensional model of vessel networks. J Fluid Mech 621:183–204
20. Fung YC (1996) Biomechanics: circulation, 2nd edn. Springer, New York
21. Gao Y, Raj UJ (2005) Role of veins in regulation of pulmonary circulation. Am J Physiol Lung Cell Mol Physiol 288:L213–L226
22. Greenfield JC, Douglas MG (1963) Relation between pressure and diameter in main pulmonary artery of man. J Appl Physiol 18:557–559
23. Hachulla E, Gressin V, Guillevin L et al (2005) Early detection of pulmonary arterial hypertension in systemic sclerosis: a French nationwide prospective multicenter study. Arthritis Rheum 52:3792–3800
24. Hall JE (2011) Guyton and Hall textbook of medical physiology, 12th edn. Saunders Elsevier, Philadelphia
25. Herve P, Musset D, Simonneau G, Wagner W Jr, Duroux P (1989) Almitrine decreases the distensibility of the large pulmonary arteries in man. Chest 96:572–577
26. Hollander EH, Wang JJ, Dobson GM, Parker KH, Tyberg JV (2001) Negative wave reflections in pulmonary arteries. Am J Physiol Heart Circ Physiol 281:H895–902
27. Huang W, Yen RT, McLaurine M, Bledsoe G (1996) Morphometry of the human pulmonary vasculature. J Appl Physiol 81:2123–2133
28. Huo Y, Kassab GS (2007) A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree. Am J Physiol Heart Circ Physiol 292:H2623–H2633
29. Kato R, Lickfett L, Meininger G, Dickfeld T, Wu R, Juang G, Angkeow P, LaCorte J, Bluemke D, Berger R, Halperin HR, Calkins H (2003) Pulmonary vein anatomy in patients undergoing catheter ablation of atrial fibrillation. Lessons learned by use of magnetic resonance imaging. Circulation 107:2004–2010
30. Kawahira Y, Kishimoto H, Kawata H, Ikawa S, Ueda H, Nakajima T, Kayatani F, Inamura N, Nakada T (1997) Diameters of the pulmonary arteries and veins as an indicator of bilateral and unilateral pulmonary blood flow in patients with congenital heart disease. J Card Surg 12:253–260
31. Kim YH, Marom EM, Herndon JE, McAdams HP (2005) Pulmonary vein diameter, cross-sectional area, and shape: CT analysis. Radiology 235:43–50
32. Krenz GS, Dawson CA (2003) Flow and pressure distributions in vascular networks consisting of distensible vessels. Am J Physiol 284:H2192–H2203
33. Lankhaar JW, Westerhof N, Faes TJC, Marques KMJ, Marcus JT, Post-mus PE, Vonk-Noordegraaf A (2006) Quantification of right ventricular afterload in patients with and without pulmonary hypertension. Am J Physiol Heart Circ Physiol 291:H1731–H1737
34. Levy BI, Ambrosio G, Pries AR, Struijker-Boudier HA (2001) Microcirculation in hypertension: a new target for treatment? Circulation 104(6):735–740
35. Li CW, Cheng HD (1993) A nonlinear fluid model for pulmonary blood circulation. J Biomech 26:653–664
36. Machado RF, Gladwin MT (2010) Pulmonary hypertension in hemolytic disorders: pulmonary vascular disease: the global perspective. Chest 137:30S–38S
37. Matthys KS, Alastruey J, Peiro J, Khir AW, Segers P, Verdonck PR, Parker KH, Sherwin SJ (2007) Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements. J Biomech 40:3476–3486
38. Milnor WR (1989) Hemodynamics, 2nd edn. Williams and Wilkins, Baltimore
39. Mukerjee D, George D, St Coleiro B et al (2003) Prevalence and outcome in systemic sclerosis associated pulmonary arterial hypertension: application of a registry approach. Ann Rheum Dis 62:1088–1093
40. Müller LO, Toro EF (2014) A global multi-scale mathematical model for the human circulation with emphasis on the venous system. Int J Num Methods Bio Med Eng. doi:10.1002/cnm.2622
41. Nichols WW, O’Rourke MF (1998) MacDonald’s blood flow in arteries: theoretical, experimental and clinical principles, 4th edn. Edward Arnold, Philadelphia
42. Olufsen MS (1998) Modeling the arterial system with reference to an anesthesia simulator. PhD Thesis, Department of Mathematics, Roskilde University, Denmark
43. Olufsen MS (1999) Structured tree outflow condition for blood flow in larger systemic arteries. Am J Physiol Heart Circ Physiol 276:H257–H268
44. Olufsen MS, Peskin CS, Kim WY, Pedersen EM, Nadim A (2000) Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann Biomed Eng 28:1281–1299
45. Olufsen MS, Hill NA, Vaughan GDA, Sainsbury C, Johnson M (2012) Rarefaction and blood pressure in systemic and pulmonary arteries. J Fluid Mech 705:280–305
46. Patel DJ, Schilder DP, Mallos AJ (1960) Mechanical properties and dimensions of major pulmonary arteries. J Appl Physiol 15:92–106
47. Patel DJ, De Freitas FM, Mallos AJ (1962) Mechanical function of the main pulmonary artery. J Appl Physiol 17:205–208
48. Peacock AJ, Rubin LJ (2004) Pulmonary circulation: diseases and their treatment, 2nd edn. Hodder Arnold Publication, London
49. Peacock AJ, Murphy NF, McMurray JJV et al (2007) An epidemiological study of pulmonary arterial hypertension. Eur Respir J 30:104–109
50. Peskin E (1961) Transient and steady-state analysis of electric networks. Van Nostrand Company, Princeton, NJ, pp 304–378
51. Pollanen MS (1992) Dimensional optimization at different levels at the arterial hierarchy. J Theor Biol 159:267–270
52. Pries AR, Secomb TW, Gaehtgens P (1995) Design principles of vascular beds. Circ Res 77:1017–1023
53. Reeves JT, Linehan JH, Stenmark KR (2005) Distensibility of the normal human lung circulation during exercise. Am J Physiol Lung Cell Mol Physiol 288:L419–L425
54. Reymond P, Merenda F, Perren F, Rüfenacht D, Stergiopulos N (2009) Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol 297:H208–H222
55. Sherwin SJ, Franke V, Perio J, Parker K (2003) One-dimensional modelling of a vascular network in space-time variables. J Eng Math 47:217–250
56. Simonneau G, Galle N, Rubin LJ, Langleben D, Seeger W, Domenighetti G, Gibbs S, Lebrec D, Speich R, Beghetti M, Rich S, Fishman A (2004) Clinical classification of pulmonary hypertension. J Am Coll Cardiol 43:5–12
57. Singhal S, Henderson R, Horsfield K, Harding K, Cumming G (1973) Morphometry of the human pulmonary arterial tree. Circ Res 33:190–197
58. Sitbon O, Lascoux-Combe C, Delfraissy JF et al (2008) Prevalence of HIV-related pulmonary arterial hypertension in the current antiretroviral therapy era. Am J Respir Crit Care Med 177:108–111
59. Steele BN, Olufsen MS, Taylor CA (2007) Fractal network model for simulating abdominal and lower extremity blood flow during resting and exercise conditions. Comput Methods Biomech Biomed Eng 10:39–51
60. Suwa N, Niwa T, Fukasawa H, Sasaki Y (1963) Estimation of intravascular blood pressure gradients by mathematical analysis of arterial casts. Tohoku J Exp Med 79:168–198
61. Taylor CA, Draney MT, Ku JP, Parker D, Steele BN et al (1999) Predictive medicine: computational techniques in therapeutic decision-making. Comput Aided Surg 4:231–247
62. Thurlbeck WM, Churg AM (1995) Pathology of the lungs, 2nd edn. Thieme Medical Publishers, New York
63. Tuder RM, Yun JH, Bhunia A, Fijalkowska I (2007) Hypoxia and chronic lung disease. J Mol Med 85:1317–1324
64. Uylings HBM (1977) Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bull Math Biol 39:509–520
65. Valdez-Jasso D, Haider MA, Campbell AL, Bia D, Zocalo Y, Armentano RL, Olufsen MS (2009) Modeling viscoelastic wall properties of ovine arteries. In: Proceedings of ASME 2009, summer bioengineering conference SBC2009-205640
66. Vaughan GDA (2010) Pulse propagation in the pulmonary and systemic arteries. PhD Thesis, Faculty of Information and Mathematical Sciences, University of Glasgow, UK
67. Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 195:3776–3796
68. van de Vosse FN, Stergiopulos N (2011) Pulse wave propagation in the arterial tree. Annu Rev Fluid Mech 43:467–499
69. Weibel ER (2009) What makes a good lung? The morphometric basis of lung function. Swiss Med Wkly 139:375–386
70. Xiao N, Humphrey JD, Figueroa CA (2013) Multi-scale computational model of three-dimensional hemodynamics within a deformable full-body arterial network. J Comput Phys 244:22–40
71. Yen RT, Rong Z, Zhang B (1990) Elasticity of pulmonary blood vessels in human lungs. In: Farrell Epstein MA, Ligas JR (eds) Respiratory biomechanics: engineering analysis of structure and function. Springer, New York, pp 109–116
72. Yen RT, Sobin SS (1988) Elasticity of arterioles and venules in postmortem human lungs. J Appl Physiol 64(2):611–619
73. Zhuang FY, Fung YC, Yen RT (1983) Analysis of blood flow in cats lung with detailed anatomical and elasticity data. J Appl Physiol 55(4):1341–1348
74. Zhuang FY, Fung YC, Yen RT (1983) Analysis of blood flow in cats lung with detailed anatomical and elasticity data. J Appl Physiol 55(4):1341–1348