Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 1, pp 219–243 | Cite as

Hemodynamic assessment of pulmonary hypertension in mice: a model-based analysis of the disease mechanism

  • M. Umar Qureshi
  • Mitchel J. Colebank
  • L. Mihaela Paun
  • Laura Ellwein Fix
  • Naomi Chesler
  • Mansoor A. Haider
  • Nicholas A. Hill
  • Dirk Husmeier
  • Mette S. OlufsenEmail author
Original Paper


This study uses a one-dimensional fluid dynamics arterial network model to infer changes in hemodynamic quantities associated with pulmonary hypertension in mice. Data for this study include blood flow and pressure measurements from the main pulmonary artery for 7 control mice with normal pulmonary function and 5 mice with hypoxia-induced pulmonary hypertension. Arterial dimensions for a 21-vessel network are extracted from micro-CT images of lungs from a representative control and hypertensive mouse. Each vessel is represented by its length and radius. Fluid dynamic computations are done assuming that the flow is Newtonian, viscous, laminar, and has no swirl. The system of equations is closed by a constitutive equation relating pressure and area, using a linear model derived from stress–strain deformation in the circumferential direction assuming that the arterial walls are thin, and also an empirical nonlinear model. For each dataset, an inflow waveform is extracted from the data, and nominal parameters specifying the outflow boundary conditions are computed from mean values and characteristic timescales extracted from the data. The model is calibrated for each mouse by estimating parameters that minimize the least squares error between measured and computed waveforms. Optimized parameters are compared across the control and the hypertensive groups to characterize vascular remodeling with disease. Results show that pulmonary hypertension is associated with stiffer and less compliant proximal and distal vasculature with augmented wave reflections, and that elastic nonlinearities are insignificant in the hypertensive animal.


Pulmonary hypertension 1D fluid dynamics model Linear and nonlinear wall model Parameter estimation Statistical model selection Wave intensity analysis Impedance analysis 



This study was supported by the National Science Foundation (NSF) awards NSF-DMS # 1615820, NSF-DMS # 1246991 and Engineering and Physical Sciences Research Council (EPSRC) of the UK, grant reference number EP/N014642/1.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material


  1. Acosta S, Puelz C, Rivière B, Penny DJ, Brady KM, Rusin CR (2017) Cardiovascular mechanics in the early stages of pulmonary hypertension: a computational study. Biomech Model Mechanobiol 16:2093–2112CrossRefGoogle Scholar
  2. Alastruey J, Xiao N, Fok H, Schaeffter T, Figueroa CA (2016) On the impact of modelling assumptions in multi-scale, subject-specific models of aortic haemodynamics. J R Soc Interface.
  3. Arnold A, Battista C, Bia D, German YZ, Armentano RL, Tran HT, Olufsen MS (2017) Uncertainty quantification in a patient-specific one-dimensional arterial network model: EnKF-based inflow estimator. ASME J Verif Valid Uncert 2(1):14Google Scholar
  4. Antiga L, Piccinelli M, Botti L, Ene-Iordache B, Remuzzi A, Steinman DA (2008) An image-based modeling framework for patient-specific computational hemodynamics. Med Biol Eng Comput 46:1097–1112.
  5. Aslanidou L, Trachet B, Reymond P, Fraga-silva RA, Segers P, Stergiopulos N (2016) A 1D model of the arterial circulation in mice. ALTEX 33:13–28CrossRefGoogle Scholar
  6. Blanco PJ, Watanabe SM, Dari EA, Passos MARF, Feijo RA (2014) Blood flow distribution in an anatomically detailed arterial network. Biomech Model Mechanobiol 13(6):1303–1330CrossRefGoogle Scholar
  7. Boileau E, Nithiarasu P, Blanco PJ, Mller LO, Fossan FE, Hellevik LR, Donders WP, Huberts W, Willemet M, Alastruey J (2015) A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling. Int J Numer Method Biomed Eng.
  8. Boggs P, Tolle J (2000) Sequential quadratic programming for large-scale nonlinear optimization. J Comput Appl Math 124:123–137MathSciNetCrossRefzbMATHGoogle Scholar
  9. Box GEP, Jenkins GM (1970) Time series analysis: forecasting and control. Holden-Day, San FranciscozbMATHGoogle Scholar
  10. Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  11. Castelain V, Hervé 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 37(4):1085–1092CrossRefGoogle Scholar
  12. Chen WW, Gao HG, Luo XY, Hill NA (2016) Study of cardiovascular function using a coupled left ventricle and systemic circulation model. J Biomech 49(12):2445–2454CrossRefGoogle Scholar
  13. Chnafa C, Brina O, Pereira VM, Steinman DA (2018) Better than nothing: a rational approach for minimizing the impact of outflow strategy on cerebrovascular simulations. AJNR Am J Neuroradiol 39(2):337–343CrossRefGoogle Scholar
  14. Dujardin JP, Stone DN (1981) Characteristic impedance of the proximal aorta determined in the time and frequency domain: a comparison. Med Biol Eng Comput 19:565–568CrossRefGoogle Scholar
  15. Ellwein LM, Marks DS, Migrino RQ, Foley WD, Sherman S, LaDisa JF (2016) Image-based quantification of 3D morphology for bifurcations in the left coronary artery: application to stent design. Catheter Cardiovasc Interv 87:1244–1255CrossRefGoogle Scholar
  16. Eck VG, Sturdy J, Hellevik LR (2017) Effects of arterial wall models and measurement uncertainties on cardiovascular model predictions. J Biomech 50:188–194CrossRefGoogle Scholar
  17. Feldkamp LA, Davis LC, Kress JW (1984) Practical cone-beam algorithm. J Opt Soc Am A 1:612–619CrossRefGoogle Scholar
  18. Formaggia L, Lamponi D, Veneziani A (2006) Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Comput Methods Biomech Biomed Engin 9(5):273–88CrossRefGoogle Scholar
  19. Gan CT, Lankhaar JW, Westerhof N, Marcus JT, Becker A, Twisk JW, Boonstra A, Postmus PE, Vonk-Noordegraaf A (2007) Noninvasively assessed pulmonary artery stiffness predicts mortality in pulmonary arterial hypertension. Chest 132(6):1906–1912CrossRefGoogle Scholar
  20. Guan D, Liang F, Gremaud PA (2016) Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model. J Biomech 49:1583–1592CrossRefGoogle Scholar
  21. Hellmes HK, Haynes FW, Dexter L (1949) Pulmonary capillary pressure in man. J Appl Physiol 2(1):24–29CrossRefGoogle Scholar
  22. Humphrey JD (2008) Mechanisms of arterial remodeling in hypertension: coupled roles of wall shear and intramural stress. Hypertension 52(2):195–200CrossRefGoogle Scholar
  23. Hollander EH, Wang JJ, Dobson GM, Parker KH, Tyberg JV (2001) Negative wave refections in pulmonary arteries. Am J Physiol Heart Circ Physiol 281(2):895–902CrossRefGoogle Scholar
  24. Holzapfel GA, Ogden RW (2010) Constitutive modelling of arteries. Proc R Soc A 466:1551–1597Google Scholar
  25. Hunter KS, Lammers SR, Shandas S (2011) Pulmonary vascular stiffness: measurement, modeling, and implications in normal and hypertensive pulmonary circulations. Comput Physiol 1:1413–1435Google Scholar
  26. Ioannou CV, Stergiopulos N, Katsamouris AN, Startchik I, Kalangos A, Licker MJ, Westerhof N, Morel DR (2003) Hemodynamics induced after acute reduction of proximal thoracic aorta compliance. Eur J Vasc Endovasc Surg 26:195–204CrossRefGoogle Scholar
  27. Karau K, Johnson R, Molthen R, Dhyani A, Haworth S, Hanger C, Roerig D, Dawson C (2011) Microfocal X-ray CT imaging and pulmonary arterial distensibility in excised rat lungs. Am J Physiol Heart Circ Physiol 281:H1447–H1457CrossRefGoogle Scholar
  28. Kheyfets VO, O’Dell W, Smith T, Reilly JJ, Finol EA (2013) Considerations for numerical modeling of the pulmonary circulation-a review with a focus on pulmonary hypertension. J Biomed Eng 135:061011–2Google Scholar
  29. Krenz GS, Dawson CA (2003) Flow and pressure distributions in vascular networks consisting of distensible vessels. Am J Physiol Heart Circ 284(6):H2192–H2203CrossRefGoogle Scholar
  30. Langewouters GJ, Wesseling KH, Goedhard WJ (1985) The pressure dependent dynamic elasticity of 35 thoracic and 16 abdominal human aortas in vitro described by a five component model. J Biomech 18:613–620CrossRefGoogle Scholar
  31. Lee P, Carlson BE, Chesler N, Olufsen MS, Qureshi MU, Smith NP, Sochi T, Beard DA (2016) Heterogeneous mechanics of the mouse pulmonary arterial network. Biomech Model Mechanobiol 15:1245–1261CrossRefGoogle 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 29(4):H1731–173CrossRefGoogle Scholar
  33. Li Y, Parker KH, Khir AW (2016) Using wave intensity analysis to determine local reflection coefficient in flexible tubes. J Biomech 49:2709–2717CrossRefGoogle Scholar
  34. Lungu A, Wild JM, Capener D, Kiely DG, Swift AJ, Hose DR (2014) MRI model-based non-invasive differential diagnosis in pulmonary hypertension. J Biomech 47:2941–2947CrossRefGoogle Scholar
  35. Lumens J, Delhaas T, Kirn B, Arts T (2009) Three-wall segment (TriSeg) model describing mechanics and hemodynamics of ventricular interaction. Ann Biomed Eng 37(11):2234–2255CrossRefGoogle Scholar
  36. McDonald DA, Attinger EO (1965) The characteristics of arterial pulse wave propagation in the dog. Inf Exchange Group No. 3, Sci Mem 7Google Scholar
  37. Meaney JFM, Beddy P (2012) Pulmonary MRA. In: Carr J, Carroll T (eds) Magnetic resonance angiography. Springer, New YorkGoogle Scholar
  38. Mynard J, Penny DJ, Smolich JJ (2008) Wave intensity amplification and attenuation in non-linear flow: implications for the calculation of local reflection coefficients. J Biomech 41:3314–3321CrossRefGoogle Scholar
  39. Mynard JP, Smolich JJ (2015) One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation. Ann Biomed Eng 43:144–1460CrossRefGoogle Scholar
  40. Nichols WW, O’Rourke MF, Vlachopoulos C (2011) MCDonald’s blood flow in arteries: theoretical, experimental and clinical principles, 6th edn. Hodder Arnold, LondonGoogle Scholar
  41. 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 28:1281–1299CrossRefGoogle Scholar
  42. Olufsen MS, Hill NA, Vaughan GD, Sainsbury C, Johnson M (2012) Rarefaction and blood pressure in systemic and pulmonary arteries. J Fluid Mech 705:280–305MathSciNetCrossRefzbMATHGoogle Scholar
  43. Paun LM, Qureshi MU, Colebank M, Hill NA, Olufsen MS, Haider MA, Husmeier D (2018) MCMC methods for inference in a mathematical model of pulmonary circulation. Stat Neerl 1–33:2018MathSciNetGoogle Scholar
  44. Presson RG Jr, Audi SH, Hanger CC, Zenk GM, Sidner RA, Linehan JH, Wagner WW Jr, Dawson CA (1998) Anatomic distribution of pulmonary vascular compliance. J Appl Physiol 84(1):303–310CrossRefGoogle Scholar
  45. Pursell ER, 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. ASME J Biomech Eng 138:111004CrossRefGoogle Scholar
  46. Qureshi MU, Vaughan GD, Sainsbury C, Johnson M, Peskin CS, Olufsen MS, Hill NA (2014) Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation. Biomech Model Mechanobiol 13(5):1137–1154CrossRefGoogle Scholar
  47. Qureshi MU, Hill NA (2015) A computational study of pressure wave reflections in the pulmonary arteries. J Math Biol 71:1525–1549MathSciNetCrossRefzbMATHGoogle Scholar
  48. Qureshi MU, Haider MA, Chesler NC, Olufsen MS (2017) Simulating the effects of hypoxia on pulmonary haemodynamics in mice. Proc CMBE 1:271–274Google Scholar
  49. Qureshi MU, Colebank MJ, Schreier DA, Tabima DM, Haider MA, Chesler NC, Olufsen MS (2018) Characteristic Impedance: frequency or time domain approach? Physiol Meas 39(1):014004. CrossRefGoogle Scholar
  50. Rasmussen CE, Williams CKI (2006) A computational study of pressure wave reflections in the pulmonary arteries. J Math Biol 71:1525–1549MathSciNetGoogle Scholar
  51. 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–H222CrossRefGoogle Scholar
  52. Riches AC, Sharp JG, Thomas DB, Smith SV (1973) Blood volume determination in mouse. J Physiol 228(2):279–284CrossRefGoogle Scholar
  53. Rich JD, Shah SJ, Swamy RS, Kamp A, Rich S (2011) Inaccuracy of Doppler echocardiographic estimates of pulmonary artery pressures in patients with pulmonary hypertension: implications for clinical practice. Chest 139:988–993CrossRefGoogle Scholar
  54. Safaei S, Bradley CP, Suresh V, Mithraratne K, Muller A, Ho H, Ladd D, Hellevik L, Omholt SW, Chase JG, Mller LO, Watanabe SM, Blanco PJ, de Bono B, Hunter PJ (2016) Roadmap for cardiovascular circulation model. J Physiol 594(23):6909–6928CrossRefGoogle Scholar
  55. Schreier DA, Hacker T, Hunder KS, Eickoff J, Liu A, Song G, Chesler NC (2014) Impact of hematocrit on right ventricular afterload during the progression of hypoxic pulmonary hypertension. J Appl Physiol 117(8):833–839CrossRefGoogle Scholar
  56. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464MathSciNetCrossRefzbMATHGoogle Scholar
  57. Segers P, Rietzschel ER, De Buyzere ML, Vermeersch SJ, DeBacquer D, Van Bortel LM, De Backer G, Gillebert TC, Verdonck PR (2007) Noninvasive (input) impedance, pulse wave velocity, and wave reflection in healthy middle-aged men and women. Hypertension 49:1248–1255CrossRefGoogle Scholar
  58. Simonneau G, Gatzoulis MA, Adatia I, Celermajer D, Denton C, Ghofrani A, Sanchez MA, Kumar RK, Landzberg M, Machado RF, Olschewski H, Robbins IM, Souza R (2013) Updated clinical classification of pulmonary hypertension. J Am Coll Cardiol 62:D34–D41CrossRefGoogle Scholar
  59. Stergiopulos N, Meister JJ, Westerhof N (1995) Evaluation of methods for estimation of total arterial compliance. Am J Physiol 268:H1540–1548Google Scholar
  60. Tabima DM, Roldan-Alzate A, Wang Z, Hacker TA, Molthen RC, Chesler NC (2012) Persistent vascular collagen accumulation alters hemodynamic recovery from chronic hypoxia. J Biomech 45:799–804CrossRefGoogle Scholar
  61. 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):470–476CrossRefGoogle Scholar
  62. Tran JS, Schiavazzi DE, Ramachandra AB, Kahnb AM, Marsden AL (2017) Automated tuning for parameter identification and uncertainty quantification in multi-scale coronary simulations. Comput Fluids 142:128–138MathSciNetCrossRefzbMATHGoogle Scholar
  63. Tuder RM, Marecki JC, Richter A, Fijalkowska I, Flores S (2007) Pathology of pulmonary hypertension. Clin Chest Med 28(1):23–27CrossRefGoogle Scholar
  64. Tawhai MH, Clark AR, Burrowes KS (2011) Computational models of the pulmonary circulation: insights and the move towards clinically directed studies. Pulm Circ 1(2):224–238CrossRefGoogle Scholar
  65. Vanderpool RR, Kim AR, Chesler NC (2011) Effects of acute Rho kinase inhibition on chronic hypoxia-induced changes in proximal and distal pulmonary arterial structure and function. J Appl Physiol 110:188–198CrossRefGoogle Scholar
  66. Valdez-Jasso D, Bia D, Zcalo Y, Armentano RL, Haider MA, Olufsen MS (2011) Linear and nonlinear viscoelastic modeling of aorta and carotid pressure-area dynamics under in vivo and ex vivo conditions. Ann Biomed Eng 39:1438–1456CrossRefGoogle Scholar
  67. Valdez-Jasso D (2010) Modeling and identification of vascular biomechanical properties in large arteries. PhD ihesis, North Carolina State University, Raleigh, NCGoogle Scholar
  68. van de Vosse FN, Stergiopulos N (2011) Pulse wave propagation in the arterial tree. Annu Rev Fluid Mech 43:467–499MathSciNetCrossRefzbMATHGoogle Scholar
  69. Watanabe S (2010) Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Machi Learn Res 11:3571–3594MathSciNetzbMATHGoogle Scholar
  70. Watanabe S (2013) A widely applicable bayesian information criterion. J Mach Learn Res 14:867–897MathSciNetzbMATHGoogle Scholar
  71. Wang Z, Chesler NC (2011) Pulmonary vascular wall stiffness: an important contributor to the increased right ventricular afterload with pulmonary hypertension. Pulm Circ 1(2):212–223CrossRefGoogle Scholar
  72. Westerhof N, Sipkema P, Van Den Bos GC, Elzinga G (1972) Forward and backward waves in the arterial system. Cardvasc Res 6:648–656CrossRefGoogle Scholar
  73. Westerhof N, Lankhaar J, Westerhof B (2009) The arterial windkessel. Med Biol Eng Comput 47:131–141CrossRefGoogle Scholar
  74. Williams ND, Wind-Willassen O, Wright AA, Program REU, Mehlsen J, Ottesen JT, Olufsen MS (2014) Patient specific modeling of head-up tilt. Math Med Biol 31:365–392MathSciNetCrossRefzbMATHGoogle Scholar
  75. Willemet M, Alastruey J (2015) Arterial pressure and flow wave analysis using time-domain 1-D hemodynamics. Ann Biomed Eng 43:190–206CrossRefGoogle Scholar
  76. Windberger U, Bartholovitsch A, Plasenzotti R, Korak KJ, Heinze G (2003) Whole blood viscosity, plasma viscosity and erythrocyte aggregation in nine mammalian species: reference values and comparison of data. Exp Physiol 88:431–440CrossRefGoogle Scholar
  77. 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):1345–1353CrossRefGoogle Scholar
  78. Yushkevich PA, Piven J, Hazlett HC, Smith RG, Ho S, Gee JC, Gerig G (2006) User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. Neuroimage 31:1116–1128.

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • M. Umar Qureshi
    • 1
  • Mitchel J. Colebank
    • 1
  • L. Mihaela Paun
    • 2
  • Laura Ellwein Fix
    • 3
  • Naomi Chesler
    • 4
  • Mansoor A. Haider
    • 1
  • Nicholas A. Hill
    • 2
  • Dirk Husmeier
    • 2
  • Mette S. Olufsen
    • 1
    Email author
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
  3. 3.Department of Mathematics and Applied MathematicsVirginia Commonwealth UniversityRichmondUSA
  4. 4.Department of Biomedical EngineeringUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations