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References

All citations used throughout this documentation. Hyperlinks point to DOI or publisher where available. Click any in-text citation (e.g. [Valen-Sendstad 2018]) to jump here; use the browser back-button to return.

Cardiovascular CFD — methods and validation

  1. Alastruey J, Parker KH, Peiró J, Byrd SM, Sherwin SJ. Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J. Biomech. 2007;40:1794–1805. DOI
  2. ASME. Assessing credibility of computational modeling through verification and validation: application to medical devices (V&V 40). New York: American Society of Mechanical Engineers; 2018.
  3. Bakhshinejad A, et al. 4D Flow MRI estimation of boundary conditions. Ann. Biomed. Eng. 2020;48:2950–2964.
  4. Campbell IC, et al. The effect of inlet and outlet boundary conditions in image-based CFD modeling. Biomed. Eng. Online 2018;17:66. DOI
  5. Dong S, et al. A robust and accurate outflow boundary condition. J. Comput. Phys. 2014;261:83–105. PDF
  6. Du T, et al. Barriers to patient-specific computational fluid dynamics in clinical cardiovascular medicine. Front. Cardiovasc. Med. 2025.
  7. Esmaily-Moghadam M, et al. A comparison of outlet boundary treatments for prevention of backflow divergence. Int. J. Numer. Methods Biomed. Eng. 2011;27:1151–1168.
  8. Goubergrits L, et al. MRI-based CFD for diagnosis and treatment prediction in aortic coarctation. Eur. J. Cardiothorac. Surg. 2019;55:633–640.
  9. Jasak H. Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London; 1996.
  10. Ku DN. Pulsatile flow in a circular tube. Annu. Rev. Fluid Mech. 1997;29:399–434.
  11. LaDisa JF, et al. Computational simulations for aortic coarctation. J. Appl. Physiol. 2011;111:16–34.
  12. Madhavan S, Kemmerling EMC. The effect of inlet velocity profile on WSS. J. Biomech. 2018;71:1–10.
  13. Morbiducci U, et al. Inflow boundary conditions for image-based CFD. J. Biomech. 2013;46:102–109.
  14. Morris PD, et al. Computational fluid dynamics modelling in cardiovascular medicine. Heart 2016;102(1):18–28.
  15. Nørgaard BL, et al. Diagnostic performance of noninvasive fractional flow reserve derived from coronary computed tomography angiography. J. Am. Coll. Cardiol. 2014;63(12):1145–1155.
  16. Olufsen MS, et al. Structured tree outflow condition for blood flow in larger systemic arteries. Am. J. Physiol. Heart Circ. Physiol. 1999;276:H257–H268.
  17. Pfaller MR, et al. Calibration of patient-specific boundary conditions. Front. Bioeng. Biotechnol. 2023;11:1178483.
  18. Pirola S, et al. 4D Flow MRI-based computational analysis. Front. Cardiovasc. Med. 2021;8:806565.
  19. Ponzini R, et al. Exact solution to the inverse Womersley problem for pulsatile flows. J. Biomech. 2012;45:2646–2651. PDF
  20. Reymond P, et al. Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 2009;297:H208–H222.
  21. Rispoli VC, et al. Computational fluid dynamics simulations using 4D Flow MRI. J. Biomech. Eng. 2015;137:091002.
  22. Steinman DA. Image-based computational fluid dynamics modeling in realistic arterial geometries. Ann. Biomed. Eng. 2002;30:483–497.
  23. Steinman DA, et al. Variability of computational fluid dynamics solutions for pressure and flow in a giant aneurysm: the ASME 2012 Summer Bioengineering Conference CFD Challenge. J. Biomech. Eng. 2013;135(2):021016.
  24. Stergiopulos N, et al. Total arterial inertance as the fourth element of the Windkessel model. Am. J. Physiol. Heart Circ. Physiol. 1999;276:H81–H88.
  25. Taylor CA, Figueroa CA. Patient-specific modeling of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 2009;11:109–134. DOI
  26. Valen-Sendstad K, Steinman DA. Mind the gap: impact of computational fluid dynamics solution strategy on prediction of intracranial aneurysm hemodynamics and rupture status. AJNR Am. J. Neuroradiol. 2014;35(3):536–543. DOI
  27. Valen-Sendstad K, et al. Real-world variability in the prediction of intracranial aneurysm wall shear stress. Cardiovasc. Eng. Technol. 2018;9:544–556.
  28. Vignon-Clementel IE, et al. Outflow boundary conditions for three-dimensional finite element modelling. Comput. Methods Appl. Mech. Eng. 2006;195:3776–3796. PDF
  29. Wang J, et al. Patient-specific aortic CFD with user-specified Windkessel flow split for coarctation. In preparation 2025.
  30. Westerhof N, Lankhaar J-W, Westerhof BE. The arterial Windkessel. Med. Biol. Eng. Comput. 2009;47:131–141.
  31. Womersley JR. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 1955;127:553–563.
  32. Young DF, Tsai FY. Flow characteristics in models of arterial stenoses — I. Steady flow. J. Biomech. 1973;6:395–410.
  33. Yuhn C, et al. Uncertainty quantification in a patient-specific one-dimensional arterial network. Int. J. Numer. Methods Biomed. Eng. 2022;38:e3639.

Hemodynamics and clinical thresholds

  1. Malek AM, Alper SL, Izumo S. Hemodynamic shear stress and its role in atherosclerosis. JAMA 1999;282(21):2035–2042. DOI
  2. Glagov S, Zarins C, Giddens DP, Ku DN. Hemodynamics and atherosclerosis: insights and perspectives gained from studies of human arteries. Arch. Pathol. Lab. Med. 1988;112(10):1018–1031.
  3. Meng H, Tutino VM, Xiang J, Siddiqui A. High WSS or low WSS? Complex interactions of hemodynamics with intracranial aneurysm initiation, growth, and rupture. AJNR Am. J. Neuroradiol. 2014;35(5):849–857. DOI
  4. Ku DN, Giddens DP, Zarins CK, Glagov S. Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque location and low oscillating shear stress. Arteriosclerosis 1985;5(3):293–302. DOI
  5. He X, Ku DN. Pulsatile flow in the human left coronary artery bifurcation: average conditions. J. Biomech. Eng. 1996;118(1):74–82. DOI
  6. Himburg HA, Grzybowski DM, Hazel AL, LaMack JA, Li XM, Friedman MH. Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability. Am. J. Physiol. Heart Circ. Physiol. 2004;286(5):H1916–H1922. DOI
  7. Les AS, Shadden SC, Figueroa CA, et al. Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using MRI and computational fluid dynamics. Ann. Biomed. Eng. 2010;38:1288–1313. DOI
  8. Dolan JM, Kolega J, Meng H. High wall shear stress and spatial gradients in vascular pathology: a review. Ann. Biomed. Eng. 2013;41:1411–1427. DOI

OpenFOAM and numerics

  1. OpenFOAM Foundation. OpenFOAM User Guide, version 12. 2024. openfoam.org
  2. Friess C, Manceau R, Gatski TB. Toward an equivalence criterion for hybrid RANS/LES methods. Comput. Fluids 2015;122:233–246.
  3. Crank J, Nicolson P. A practical method for numerical evaluation of partial differential equations of the heat-conduction type. Math. Proc. Camb. Philos. Soc. 1947;43:50–67.
  4. Roache PJ. Verification of codes and calculations. AIAA J. 1998;36(5):696–702.
  5. Roache PJ. Perspective: a method for uniform reporting of grid refinement studies. J. Fluids Eng. 1994;116(3):405–413.
  6. Issa RI. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 1986;62(1):40–65.
  7. Ferziger JH, Perić M. Computational Methods for Fluid Dynamics. 3rd ed. Springer; 2002.
  8. Versteeg HK, Malalasekera W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. 2nd ed. Pearson; 2007.

Turbulence modelling and LES

  1. Pope SB. Turbulent Flows. Cambridge University Press; 2000.
  2. Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994;32(8):1598–1605. DOI
  3. Nicoud F, Ducros F. Subgrid-scale stress modelling based on the square of the velocity gradient tensor (WALE). Flow Turbul. Combust. 1999;62(3):183–200. DOI
  4. Montecchia M, Brethouwer G, Wallin S, Johansson AV, Knacke T. Improving LES with OpenFOAM by minimising numerical dissipation and use of explicit algebraic SGS stress model. J. Turbul. 2019;20(11–12):697–722.
  5. Davidson L. Fluid mechanics, turbulent flow and turbulence modelling. Chalmers University of Technology. PDF
  6. Cheng Z, et al. Characteristics of transition to turbulence in a healthy thoracic aorta using large eddy simulation. Sci. Rep. 2025.
  7. Steinman DA, Migliavacca F. Editorial: special issue on verification, validation, and uncertainty quantification of cardiovascular models. Cardiovasc. Eng. Technol. 2018;9:511–514.

Clinical guidelines and physiology

  1. Erbel R, Aboyans V, Boileau C, et al. 2014 ESC Guidelines on the diagnosis and treatment of aortic diseases. Eur. Heart J. 2014;35(41):2873–2926. DOI
  2. Baumgartner H, De Backer J, Babu-Narayan SV, et al. 2020 ESC Guidelines for the management of adult congenital heart disease. Eur. Heart J. 2020;42(6):563–645.
  3. Murray CD. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. USA 1926;12(3):207–214.
  4. Pirola S, Cheng Z, Jarral OA, et al. On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics. J. Biomech. 2017;60:15–21.

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