Review Article

Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support

[+] Author and Article Information
Alison L. Marsden, Mahdi Esmaily-Moghadam

Department of Mechanical
and Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093

Manuscript received August 19, 2014; final manuscript received February 19, 2015; published online April 8, 2015. Assoc. Editor: Gianluca Iaccarino.

Appl. Mech. Rev 67(3), 030804 (May 01, 2015) (11 pages) Paper No: AMR-14-1063; doi: 10.1115/1.4029909 History: Received August 19, 2014; Revised February 19, 2015; Online April 08, 2015

Patient-specific cardiovascular simulations can provide clinicians with predictive tools, fill current gaps in clinical imaging capabilities, and contribute to the fundamental understanding of disease progression. However, clinically relevant simulations must provide not only local hemodynamics, but also global physiologic response. This necessitates a dynamic coupling between the Navier–Stokes solver and reduced-order models of circulatory physiology, resulting in numerical stability and efficiency challenges. In this review, we discuss approaches to handling the coupled systems that arise from cardiovascular simulations, including recent algorithms that enable efficient large-scale simulations of the vascular system. We maintain particular focus on multiscale modeling algorithms for finite element simulations. Because these algorithms give rise to an ill-conditioned system of equations dominated by the coupled boundaries, we also discuss recent methods for solving the linear system of equations arising from these systems. We then review applications that illustrate the potential impact of these tools for clinical decision support in adult and pediatric cardiology. Finally, we offer an outlook on future directions in the field for both modeling and clinical application.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Marsden, A. L., Bernstein, A. J., Reddy, V. M., Shadden, S., Spilker, R. L., Chan, F. P., Taylor, C. A., and Feinstein, J. A., 2009, “Evaluation of a Novel Y-Shaped Extracardiac Fontan Baffle Using Computational Fluid Dynamics,” J. Thorac. Cardiovasc. Surg., 137(2), pp. 394–403. [CrossRef] [PubMed]
Leval, M. D., Dubini, G., Migliavacca, F., Jalali, H., Camporini, G., Redington, A., and Pietrabissa, R., 1996, “Use of Computational Fluid Dynamics in the Design of Surgical Procedures: Application to the Study of Competitive Flows in Cavopulmonary Connections,” J. Thorac. Cardiovasc. Surg., 111(3), pp. 502–513. [CrossRef] [PubMed]
Bove, E., Migliavacca, F., de Leval, M., Balossino, R., Pennati, G., Lloyd, T., Khambadkone, S., Hsia, T., and Dubini, G., 2008, “Use of Mathematic Modeling to Compare and Predict Hemodynamic Effects of the Modified Blalock–Taussig and Right Ventricle–Pulmonary Artery Shunts for Hypoplastic Left Heart Syndrome,” J. Thorac. Cardiovasc. Surg., 136(2), pp. 312–320. [CrossRef] [PubMed]
Dasi, L., Pekkan, K., Katajima, H., and Yoganathan, A., 2008, “Functional Analysis of Fontan Energy Dissipation,” J. Biomech., 41(10), pp. 2246–2252. [CrossRef] [PubMed]
de Leval, M. R., Kilner, P., Gewillig, M., and Bull, C., 1988, “Total Cavopulmonary Connection: A Logical Alternative to Atriopulmonary Connection for Complex Fontan Operations. Experimental Studies and Early Clinical Experience,” J. Thorac. Cardiovasc. Surg., 96(5), pp. 682–695. [PubMed]
Lagana, K., Dubini, G., Migliavacca, F., Pietrabissa, R., Pennati, G., Veneziani, A., and Quarteroni, A., 2002, “Multiscale Modelling as a Tool to Prescribe Realistic Boundary Conditions for the Study of Surgical Procedures,” Biorheology, 39(3–4), pp. 359–364. [PubMed]
Nakazato, R., Park, H.-B., Berman, D. S., Gransar, H., Koo, B.-K., Erglis, A., Lin, F. Y., Dunning, A. M., Budoff, M. J., Malpeso, J., Leipsic, J., and Min, J. K., 2012, “Fractional Flow Reserved Derived From Computed Tomographic Angiography (FFRCT) for Intermediate Severity Coronary Lesions: Results From the DeFACTO Trial (Determination of Fractional Flow Reserve by Anatomic Computed Tomographic Angiography),” J. Am. Coll. Cardiol., 60(17), p. B6 [CrossRef].
Sankaran, S., Moghadam, M., Kahn, A., Tseng, E., Guccione, J., and Marsden, A., 2012, “Patient-Specific Multiscale Modeling of Blood Flow for Coronary Artery Bypass Graft Surgery,” Ann. Biomed. Eng., 40(10), pp. 2228–2242. [CrossRef] [PubMed]
Sengupta, D., Kahn, A., Burns, J., Sankaran, S., Shadden, S., and Marsden, A., 2012, “Image-Based Modeling of Hemodynamics and Coronary Artery Aneurysms Caused by Kawasaki Disease,” Biomech. Model. Mechanobiol., 11(6), pp. 915–932. [CrossRef] [PubMed]
Les, A., Shadden, S., Figueroa, C., Park, J., Tedesco, M., Herfkens, R., Dalman, R., and Taylor, C., 2010, “Quantification of Hemodynamics in Abdominal Aortic Aneurysms During Rest and Exercise Using Magnetic Resonance Imaging and Computational Fluid Dynamics,” Ann. Biomed. Eng., 38(4), pp. 1288–1313. [CrossRef] [PubMed]
Castro, M. A., Putman, C. M., and Cebral, J. R., 2006, “Computational Fluid Dynamics Modeling of Intracranial Aneurysms: Effects of Parent Artery Segmentation on Intra-Aneurysmal Hemodynamics,” Am. J. Neuroradiol., 27(8), pp. 1703–1709.
LaDisa, J. F., Jr., Olson, L., Guler, I., Hettrick, D., Audi, S., Kersten, J., Warltier, D., and Pagel, P., 2004, “Stent Design Properties and Deployment Ratio Influence Indices of Wall Shear Stress: A 3D Computational Fluid Dynamics Investigation Within a Normal Artery,” J. Appl. Physiol., 97(1), pp. 424–430. [CrossRef] [PubMed]
LaDisa, J. F., Jr., Olson, L., Molthen, R., Hettrick, D., Hardel, M., Pratt, P., Kersten, J., Warltier, D., and Pagel, P., 2005, “Alterations in Wall Shear Stress Predict Sites of Neointimal Hyperplasia After Stent Implantation in Rabbit Iliac Arteries,” Am. J. Physiol. Heart Circ. Physiol., 288(5), pp. H2465–H2475. [CrossRef] [PubMed]
Gundert, T. J., Marsden, A. L., Yang, W., Marks, D. S., and LaDisa, J. F., 2012, “Identification of Hemodynamically Optimal Coronary Stent Designs Based on Vessel Caliber,” IEEE Trans. Biomed. Eng., 59(7), pp. 1992–2002. [CrossRef] [PubMed]
Gundert, T., Marsden, A., Yang, W., and LaDisa, J., 2012, “Optimization of Cardiovascular Stent Design Using Computational Fluid Dynamics,” ASME J. Biomech. Eng., 134(1), p. 011002. [CrossRef]
Long, C., Marsden, A., and Bazilevs, Y., 2013, “Fluid–Structure Interaction Simulation of Pulsatile Ventricular Assist Devices,” Comput. Mech.52(5), pp. 971–981. [CrossRef]
Figueroa, C., Taylor, C., Chiou, A., Yeh, V., and Zarins, C., 2009, “Magnitude and Direction of Pulsatile Displacement Forces Acting on Thoracic Aortic Endografts,” J. Endovasc. Ther., 16(3), pp. 350–358. [CrossRef] [PubMed]
Lonyai, A., Dubin, A. M., Feinstein, J. A., Taylor, C. A., and Shadden, S. C., 2010, “New Insights Into Pacemaker Lead-Induced Venous Occlusion: Simulation-Based Investigation of Alterations in Venous Biomechanics,” Cardiovasc. Eng., 10(2), pp. 84–90. [CrossRef] [PubMed]
Kung, E., Les, A., Figueroa, C., Medina, F., Arcaute, K., Wicker, R., McConnell, M., and Taylor, C., 2011, “In Vitro Validation of Finite Element Analysis of Blood Flow in Deformable Models,” Ann. Biomed. Eng., 39(7), pp. 1947–1960. [CrossRef] [PubMed]
Vukicevic, M., Chiulli, J. A., Conover, T., Pennati, G., Hsia, T. Y., and Figliola, R. S., 2013, “Mock Circulatory System of the Fontan Circulation to Study Respiration Effects on Venous Flow Behavior,” Comput. Methods Appl. Mech. Eng., 59(3), pp. 253–260 [CrossRef].
Gijsen, F. J. H., Allanic, E., Van de Vosse, F. N., and Janssen, J. D., 1999, “The Influence of the Non-Newtonian Properties of Blood on the Flow in Large Arteries: Unsteady Flow in a 90 Deg Curved Tube,” J. Biomech., 32(7), pp. 705–713. [CrossRef] [PubMed]
Haynes, R. H., and Burton, A. C., 1959, “Role of the Non-Newtonian Behavior of Blood in Hemodynamics,” Am. J. Physiol., 197, pp. 943–950. [PubMed]
Karniadakis, G. E., and Sherwin, S. J., 2005, “Spectral/HP Element Methods for Computational Fluid Dynamics,” Numerical Mathematics and Scientific Computation, Oxford Science Publications, New York.
Valen-Sendstad, K., Mardal, K. A., and Mortensen, M., 2011, “Direct Numerical Simulation of Transitional Flow in a Patient-Specific Intracranial Aneurysm,” J. Biomech., 44(16), pp. 2826–2832. [CrossRef] [PubMed]
Schmidt, J. P., Delp, S. L., Sherman, M. A., Taylor, C. A., Pande, V. S., and Altman, R. B., 2008, “The Simbios National Center: Systems Biology in Motion,” Proc. IEEE, 96(8), pp. 1266–1280. [CrossRef]
Yushkevich, P. A., Piven, J., Hazlett, H. C., Smith, R. G., Ho, S., Gee, J. C., and Gerig, G., 2006, “User-Guided 3D Active Contour Segmentation of Anatomical Structures: Significantly Improved Efficiency and Reliability,” NeuroImage, 31(3), pp. 1116–1128. [CrossRef] [PubMed]
Zheng, Y., Barbu, A., Georgescu, B., Scheuering, M., and Comaniciu, D., 2008, “Four-Chamber Heart Modeling and Automatic Segmentation for 3-D Cardiac CT Volumes Using Marginal Space Learning and Steerable Features,” IEEE Trans. Med. Imaging, 27(11), pp. 1668–1681. [CrossRef] [PubMed]
Zheng, Y., Loziczonek, M., Georgescu, B., Zhou, S. K., Vega-Higuera, F., and Comaniciu, D., 2011, “Machine Learning Based Vesselness Measurement for Coronary Artery Segmentation in Cardiac CT Volumes,” Proc. SPIE Med. Imaging, 7962, pp. 79621K-1–79621K-12 [CrossRef].
Mansi, T., Voigt, I., Leonardi, B., Pennec, X., Durrleman, S., Sermesant, M., Delingette, H., Taylor, A., Boudjemline, Y., Pongiglione, G., and Ayache, N., 2011, “A Statistical Model for Quantification and Prediction of Cardiac Remodelling: Application to Tetralogy of Fallot,” IEEE Trans. Med. Imaging, 30(9), pp. 1605–1616. [CrossRef] [PubMed]
Figueroa, C. A., Vignon-Clementel, I. E., Jansen, K. E., Hughes, T. J., and Taylor, C. A., 2006, “A Coupled Momentum Method for Modeling Blood Flow in Three-Dimensional Deformable Arteries,” Comput. Methods Appl. Mech. Eng., 195(41–43), pp. 5685–5706. [CrossRef]
Xiong, G., Figueroa, C., Xiao, N., and Taylor, C., 2011, “Simulation of Blood Flow in Deformable Vessels Using Subject-Specific Geometry and Spatially Varying Wall Properties,” Int. J. Numer. Methods Biomed. Eng., 27(7), pp. 1000–1016. [CrossRef]
Bazilevs, Y., Hsu, M., Sankaran, D. B. S., and Marsden, A., 2009, “Computational Fluid–Structure Interaction: Methods and Application to a Total Cavopulmonary Connection,” Comput. Mech., 45(1), pp. 77–89. [CrossRef]
Bazilevs, Y., Calo, V. M., Hughes, T. J. R., and Zhang, Y., 2008, “Isogeometric Fluid–Structure Interaction: Theory, Algorithms, and Computations,” Comput. Mech., 43(1), pp. 3–37. [CrossRef]
Peskin, C. S., 1977, “Numerical Analysis of Blood Flow in the Heart,” J. Comput. Phys., 25(3), pp. 220–252. [CrossRef]
Bazilevs, Y., Gohean, J., Hughes, T., Moser, R., and Zhang, Y., 2009, “Patient-Specific Isogeometric Fluid–Structure Interaction Analysis of Thoracic Aortic Blood Flow Due to Implantation of the Jarvik 2000 Left Ventricular Assist Device,” Comput. Methods Appl. Mech. Eng., 198(45–46), pp. 3534–3550. [CrossRef]
Bazilevs, Y., Calo, V., Zhang, Y., and Hughes, T. J., 2006, “Isogeometric Fluid–Structure Interaction Analysis With Applications to Arterial Blood Flow,” Comput. Mech., 38(4–5), pp. 310–322. [CrossRef]
Vignon-Clementel, I. E., Figueroa, C. A., Jansen, K. E., and Taylor, C. A., 2006, “Outflow Boundary Conditions for Three-Dimensional Finite Element Modeling of Blood Flow and Pressure in Arteries,” Comput. Methods Appl. Mech. Eng., 195(29–32), pp. 3776–3796. [CrossRef]
Vignon-Clementel, I., Figueroa, C., Jansen, K., and Taylor, C., 2010, “Outflow Boundary Conditions for Three-Dimensional Simulations of Non-Periodic Blood Flow and Pressure Fields in Deformable Arteries,” Comput. Methods Biomech. Biomed. Eng., 13(5), pp. 625–640. [CrossRef]
Formaggia, L., Lamponi, D., and Quarteroni, A., 2003, “One-Dimensional Models for Blood Flow in Arteries,” J. Eng. Math., 47(3–4), pp. 251–276. [CrossRef]
Formaggia, L., Gerbeau, J., Nobile, F., and Quarteroni, A., 2001, “On the Coupling of 3D and 1D Navier–Stokes Equations for Flow Problems in Compliant Vessels,” Comput. Methods Appl. Mech. Eng., 191(6–7), pp. 561–582. [CrossRef]
Balossino, R., Pennati, G., Migliavacca, F., Formaggia, L., Veneziani, A., Tuveri, M., and Dubini, G., 2009, “Computational Models to Predict Stenosis Growth in Carotid Arteries: Which is the Role of Boundary Conditions?,” Comput. Methods Biomech. Biomed. Eng., 12(1), pp. 113–123. [CrossRef]
Kim, H. J., Vignon-Clementel, I. E., Figueroa, C. A., LaDisa, J. F., Jansen, K. E., Feinstein, J. A., and Taylor, C. A., 2009, “On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model,” Ann. Biomed. Eng., 37(11), pp. 2153–2169. [CrossRef] [PubMed]
Kim, H., Vignon-Clementel, I., Coogan, J., Figueroa, C., Jansen, K., and Taylor, C., 2010, “Patient-Specific Modeling of Blood Flow and Pressure in Human Coronary Arteries,” Ann. Biomed. Eng., 38(10), pp. 3195–3209. [CrossRef] [PubMed]
Corsini, C., Cosentino, D., Pennati, G., Dubini, G., Hsia, T., and Migliavacca, F., 2011, “Multiscale Models of the Hybrid Palliation for Hypoplastic Left Heart Syndrome,” J. Biomech., 44(4), pp. 767–770. [CrossRef] [PubMed]
Migliavacca, F., Dubini, G., Bove, E. L., and de Leval, M. R., 2003, “Computational Fluid Dynamics Simulations in Realistic 3-D Geometries of the Total Cavopulmonary Anastomosis: The Influence of the Inferior Caval Anastomosis,” ASME J. Biomech. Eng., 125(6), pp. 805–813. [CrossRef]
Kung, E., Baretta, A., Baker, C., Arbia, G., Biglino, G., Corsini, C., Schievano, S., Vignon-Clementel, I., Dubini, G., Pennati, G., Taylor, A., Dorfman, A., Hlavacek, A. M., Marsden, A. L., Hsia, T. Y., and Migliavacca, F., Modeling Of Congenital Hearts Alliance (MOCHA)+Investigators, 2013, “Predictive Modeling of the Virtual Hemi-Fontan Operation for Second Stage Single Ventricle Palliation: Two Patient-Specific Cases,” J. Biomech., 46(2), pp. 423–429. [CrossRef] [PubMed]
Esmaily-Moghadam, M., Migliavacca, F., Vignon-Clementel, I. E., Hsia, T.-Y., and Marsden, A. L., and Modeling of Congenital Hearts Alliance (MOCHA) Investigators, 2012, “Optimization of Shunt Placement for the Norwood Surgery Using Multi-Domain Modeling,” ASME J. Biomech. Eng., 134(5), p. 051002. [CrossRef]
Urquiza, S., Blanco, P., Venere, M., and Feijoo, R., 2006, “Multidimensional Modelling for the Carotid Artery Blood Flow,” Comput. Methods Appl. Mech. Eng., 195(33–36), pp. 4002–4017. [CrossRef]
Blanco, P., Feijoo, R., and Urquiza, S., 2007, “A Unified Variational Approach for Coupling 3D–1D Models and Its Blood Flow Applications,” Comput. Methods Appl. Mech. Eng., 196(41–44), pp. 4391–4410. [CrossRef]
Moghadam, M. E., Vignon-Clementel, I., Figliola, R., and Marsden, A., 2013, “A Modular Numerical Method for Implicit 0D/3D Coupling in Cardiovascular Finite Element Simulations,” J. Comput. Phys., 244(1), pp. 63–79. [CrossRef]
Ismail, M., Gravemeier, V., Comerford, A., and Wall, W., 2014, “A Stable Approach for Coupling Multidimensional Cardiovascular and Pulmonary Networks Based on a Novel Pressure-Flow Rate or Pressure-Only Neumann Boundary Condition Formulation,” Int. J. Numer. Methods Biomed. Eng., 30(4), pp. 447–469. [CrossRef]
Kuprat, A., Kabilan, S., Carson, J., Corley, R., and Einstein, D., 2013, “A Bidirectional Coupling Procedure Applied to Multiscale Respiratory Modeling,” J. Comput. Phys., 244, pp. 148–167. [CrossRef]
Quarteroni, A., Ragni, S., and Veneziani, A., 2001, “Coupling Between Lumped and Distributed Models for Blood Flow Problems,” Comput. Visualization Sci., 4(2), pp. 111–124. [CrossRef]
Formaggia, L., Gerbeau, J., Nobile, F., and Quarteroni, A., 2002, “Numerical Treatment of Defective Boundary Conditions for the Navier–Stokes Equations,” SIAM J. Numer. Anal., 40(1), pp. 376–401. [CrossRef]
Leiva, J., Blanco, P., and Buscaglia, G., 2010, “Iterative Strong Coupling of Dimensionally-Heterogeneous Models,” Int. J. Numer. Methods Eng., 81(12), pp. 1558–1580 [CrossRef].
Kim, H., Figueroa, C., Hughes, T., Jansen, K., and Taylor, C., 2009, “Augmented Lagrangian Method for Constraining the Shape of Velocity Profiles at Outlet Boundaries for Three-Dimensional Finite Element Simulations of Blood Flow,” Comput. Methods Appl. Mech. Eng., 198(45–46), pp. 3551–3566. [CrossRef]
Moghadam, M. E., Bazilevs, Y., Hsia, T.-Y., Vignon-Clementel, I., and Marsden, A., 2011, “A Comparison of Outlet Boundary Treatments for Prevention of Backflow Divergence With Relevance to Blood Flow Simulations,” Comput. Mech., 48(3), pp. 277–291. [CrossRef]
Oakes, J. M., Marsden, A. L., Grandmont, C., Shadden, S. C., Darquenne, C., and Vignon-Clementel, I. E., 2014, “Airflow and Particle Deposition Simulations in Health and Emphysema: From In Vitro to In Silico Animal Experiments,” Ann. Biomed. Eng., 42(4), pp. 899–914. [CrossRef] [PubMed]
Gravemeier, V., Comerford, A., Yoshihara, L., Ismail, M., and Wall, W. A., 2012, “A Novel Formulation for Neumann Inflow Boundary Conditions in Biomechanics,” Int. J. Numer. Methods Biomed. Eng., 28(5), pp. 560–573. [CrossRef]
Esmaily-Moghadam, M., Bazilevs, Y., and Marsden, A. L., 2013, “A New Preconditioning Technique for Implicitly Coupled Multidomain Simulations With Applications to Hemodynamics,” Comput. Mech., 52(5), pp. 1141–1152. [CrossRef]
Fontan, F., and Baudet, E., 1971, “Surgical Repair of Tricuspid Atresia,” Thorax, 26(3), pp. 240–248. [CrossRef] [PubMed]
Dubini, G., de Leval, M. R., Pietrabissa, R., Montevecchi, F. M., and Fumero, R., 1996, “A Numerical Fluid Mechanical Study of Repaired Congenital Heart Defects: Application to the Total Cavopulmonary Connection,” J. Biomech., 29(1), pp. 111–121. [CrossRef] [PubMed]
Petrossian, E., Reddy, V. M., Collins, K. K., Culbertson, C. B., MacDonald, M. J., Lamberti, J. J., Reinhartz, O., Mainwaring, R. D., Francis, P. D., Malhotra, S. P., Gremmels, D. B., Suleman, S., and Hanley, F. L., 2006, “The Extracardiac Conduit Fontan Operation Using Minimal Approach Extracorporeal Circulation: Early and Midterm Outcomes,” J. Thorac. Cardiovasc. Surg., 132(5), pp. 1054–1063. [CrossRef] [PubMed]
Marsden, A. L., Vignon-Clementel, I. E., Chan, F., Feinstein, J. A., and Taylor, C. A., 2007, “Effects of Exercise and Respiration on Hemodynamic Efficiency in CFD Simulations of the Total Cavopulmonary Connection,” Ann. Biomed. Eng., 35(2), pp. 250–263. [CrossRef] [PubMed]
Whitehead, K. K., Pekkan, K., Kitahima, H. D., Paridon, S. M., Yoganathan, A. P., and Fogel, M. A., 2007, “Nonlinear Power Loss During Exercise in Single-Ventricle Patients After the Fontan: Insights From Computational Fluid Dynamics,” Circulation, 116(11 Suppl.), pp. I-165–I-171. [CrossRef]
DeGroff, C. G., 2008, “Modeling the Fontan Circulation: Where We Are and Where We Need to Go,” Pediatr. Cardiol., 29(1), pp. 3–12. [CrossRef] [PubMed]
Soerensen, D. D., Pekkan, K., de Zelicourt, D., Sharma, S., Kanter, K., Fogel, M., and Yoganathan, A., 2007, “Introduction of a New Optimized Total Cavopulmonary Connection,” Ann. Thorac. Surg., 83(6), pp. 2182–2190. [CrossRef] [PubMed]
Ensley, A. E., Lynch, P., Chatzimavroudis, G. P., Lucas, C., Sharma, S., and Yoganathan, A. P., 1999, “Toward Designing the Optimal Total Cavopulmonary Connection: An In Vitro Study,” Ann. Thorac. Surg., 68(4), pp. 1384–1390. [CrossRef] [PubMed]
Healy, T. M., Lucas, C., and Yoganathan, A. P., 2001, “Noninvasive Fluid Dynamic Power Loss Assessments for Total Cavopulmonary Connections Using the Viscous Dissipation Function: A Feasibility Study,” ASME J. Biomech. Eng., 123(4), pp. 317–324. [CrossRef]
Ryu, K., Healy, T. M., Ensley, A. E., Sharma, S., Lucas, C., and Yoganathan, A. P., 2001, “Importance of Accurate Geometry in the Study of the Total Cavopulmonary Connection: Computational Simulations and In Vitro Experiments,” Ann. Biomed. Eng., 29(10), pp. 844–853. [CrossRef] [PubMed]
Baretta, A., Corsini, C., Yang, W., Vignon-Clementel, I., Marsden, A., Feinstein, J., Hsia, T.-Y., Dubini, G., Migliavacca, F., and Pennati, G., 2011, “Virtual Surgeries in Patients With Congenital Heart Disease: A Multiscale Modelling Test Case,” Philos. R. Soc. Trans. A, 369(1954), pp. 4316–4330. [CrossRef]
Marsden, A. L., 2013, “Simulation Based Planning of Surgical Interventions in Pediatric Cardiology,” Phys. Fluids, (25), p. 101303. [CrossRef]
Pekkan, K., Dasi, L. P., de Zelicourt, D., Sundareswaran, K. S., Fogel, M. A., Kanter, K. R., and Yoganathan, A. P., 2009, “Hemodynamic Performance of Stage-2 Univentricular Reconstruction: Glenn vs. Hemi-Fontan Templates,” Ann. Biomed. Eng., 37(1), pp. 50–63. [CrossRef] [PubMed]
Kung, E. O., Pennati, G., Migliavacca, F., Hsia, T.-Y., Figliola, R., Marsden, A., and Giardini, A., 2014, “A Simulation Protocol for Exercise Physiology in Fontan Patients Using a Closed-Loop Lumped-Parameter Model,” ASME J. Biomech. Eng., 136(8), p. 081007. [CrossRef]
Hsia, T.-Y., Cosentino, D., Corsini, C., Pennati, G., Dubini, G., and Migliavacca, F., 2011, “Use of Mathematical Modeling to Compare and Predict Hemodynamic Effects Between Hybrid and Surgical Norwood Palliations for Hypoplastic Left Heart Syndrome,” Circulation, 124(11 Suppl.), pp. S204 –S210. [CrossRef] [PubMed]
Hoffman, J., and Spann, J. E., 1990, “Pressure-Flow Relations in Coronary Circulation,” Physiol. Rev., 70(2), pp. 331–390. [PubMed]
Kim, H., Vignon-Clementel, I., Figueroa, C., Jansen, K., and Taylor, C., 2010, “Developing Computational Methods for Three-Dimensional Finite Element Simulations of Coronary Blood Flow,” Finite Elem. Anal. Des., 46(6), pp. 514–525. [CrossRef]
Krams, R., Sipkema, P., and Westerhof, N., 1989, “Varying Elastance Concept May Explain Coronary Systolic Flow Impediment,” Am. J. Physiol., 257(5 Pt 2), pp. H1471–H1479. [PubMed]
Torii, R., Keegan, J., Wood, N. B., Dowsey, A. W., Hughes, A. D., Yang, G.-Z., Firmin, D. N., Thom, S. A. M., and Xu, X. Y., 2010, “MR Image-Based Geometric and Hemodynamic Investigation of the Right Coronary Artery With Dynamic Vessel Motion,” Ann. Biomed. Eng., 38(8), pp. 2606–2620. [CrossRef] [PubMed]
Taylor, C. A., Fonte, T., and Min, J., 2013, “Computational Fluid Dynamics Applied to Cardiac CT for Noninvasive Quantification of Fractional Flow Reserve: Scientific Basis,” J. Am. Coll. Cardiol., 61(22), pp. 2233–2241. [CrossRef] [PubMed]
Smith, N. P., 2004, “A Computational Study of the Interaction Between Coronary Blood Flow and Myocardial Mechanics,” Physiol. Meas., 25(4), pp. 863–877. [CrossRef] [PubMed]
Vankan, J., Huyghe, J. M., Janssen, D., Huson, A., Hacking, W. J. G., and Schreiner, W., 1997, “Finite Element Analysis of Blood Flow Through Biological Tissue,” Int. J. Eng. Sci., 35(4), pp. 375–385. [CrossRef]
Cookson, A., Lee, J., Michler, C., Chabiniok, R., Hyde, E., Nordsletten, D., Sinclair, M., Siebes, M., and Smith, N., 2012, “A Novel Porous Mechanical Framework for Modelling the Interaction Between Coronary Perfusion and Myocardial Mechanics,” J. Biomech., 45(5), pp. 850–855. [CrossRef] [PubMed]
Lee, J., and Smith, N. P., 2012, “The Multi-Scale Modeling of Coronary Blood Flow,” Ann. Biomed. Eng., 40(11), pp. 2399–2413. [CrossRef] [PubMed]
Sankaran, S., and Marsden, A., 2010, “The Impact of Uncertainty on Shape Optimization of Idealized Bypass Graft Models in Unsteady Flow,” Phys. Fluids, 22(12), p. 121902. [CrossRef]
Ghanem, R. G., and Spanos, P. D., 1991, Stochastic Finite Elements: A Spectral Approach, Springer Verlag, New York [CrossRef].
Xiu, D., and Hesthaven, J., 2005, “High-Order Collocation Methods for Differential Equations With Random Inputs,” SIAM J. Sci. Comput., 27(3), pp. 1118–1139. [CrossRef]
Babuška, I., Nobile, F., and Tempone, R., 2007, “A Stochastic Collocation Method for Elliptic Partial Differential Equations With Random Input Data,” SIAM J. Numer. Anal., 45(3), pp. 1005–1034. [CrossRef]
Sankaran, S., and Marsden, A., 2011, “A Stochastic Collocation Method for Uncertainty Quantification and Propagation in Cardiovascular Simulations,” ASME J. Biomech. Eng., 133(3), p. 031001. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic of a RCR (Windkessel) circuit for modeling the 0D domain vasculature. The wall distensibility is modeled by including a capacitor, which stores blood as pressure increases. Pressure drop due to viscous dissipation is modeled using two resistors to model the proximal and distal vessels.

Grahic Jump Location
Fig. 2

Comparison between a closed loop and open loop lumped-parameter model. A dirichlet BC is prescribed at the inlet in the open loop configuration, fixing the flow rate to a user-defined value (or waveform in the case of unsteady flow), whereas flow rate dynamically changes depending on the coupled behavior of the 3D and 0D domains in the closed loop configuration. With the closed loop configuration, additional information, for example, cardiac work load or pressure volume loops, can be extracted from the 0D domain.

Grahic Jump Location
Fig. 4

Schematic of a 2D model with backflow at a Neumann boundary. Three velocity profiles (green/solid, blue/dashed, and red/dot-dash) are shown with different levels of flow reversal, but similar net-flow. All three profiles can satisfy conservation of mass, causing the flow to become unstable as it transitions from the green toward the red profile. This issue is resolved by adding an outward traction proportional to the inward velocity.

Grahic Jump Location
Fig. 3

Schematic of time marching in the 3D and 0D domains. The 0D domain sends corrected Pi,n+1 and Qj,n+1 to the 3D domain and receives Qi,n and Pj,n and the corrected Qi,n+1 and Pj,n+1 values from the 3D domain. Simulation is performed iteratively and proceeds to the next time step only when the coupled system is converged. Neumann boundary (iηh) values are colored blue and Dirichlet boundary (jηg) values are colored red.

Grahic Jump Location
Fig. 5

Schematic of flow in a bifurcating vessel with resistance BC at outlets and inflow condition at the inlet. For high resistance values, flow split to the right and left branches highly depends on the BC, rather than the 3D geometry. The domination of outlet BCs in determining the entire flow solution leads to an ill-conditioning problem stemming from a few dominant eigenvalues coming from the boundaries.

Grahic Jump Location
Fig. 6

Comparison of cost and convergence criteria for explicit, implicit, and implicit-with-preconditioner coupling schemes for a cylinder with resistance outflow BC and prescribed inflow BC. Explicit denotes the case in which KBCab is neglected. Implicit denotes the case in which KBCab is included in the formulation, but the preconditioner described in Sec. 4 is not considered. Imp + PC denotes the case in which KBCab is included in the formulation and used to construct the preconditioner in Eq. (16). Significant improvements in both cost and stability are achieved using implicit coupling and preconditioning methods tailored to account for outflow resistance.

Grahic Jump Location
Fig. 9

Example of a closed loop lumped parameter network coupled to a patient-specific model of coronary artery bypass graft surgery (upper) and a simulated WSS field (lower) (contours WSS magnitude min 0, max 15 dynes/cm2)

Grahic Jump Location
Fig. 7

Modeling process for virtual surgery, beginning with model construction from imaging data followed by virtual surgery (a) and the patient-specific stage one models for two patients (b). The example shown compares the Hemi-Fontan and Glenn surgeries in single ventricle palliation, as well as surgical correction of pulmonary stenosis.

Grahic Jump Location
Fig. 8

Examples of open (upper) and closed (lower) loop BC configurations for a patient-specific model of the Y-graft Fontan procedure. Reprinted with permission from Physics of Fluids [72].



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In