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Research Papers

Considerations for Numerical Modeling of the Pulmonary Circulation—A Review With a Focus on Pulmonary Hypertension

[+] Author and Article Information
V. O. Kheyfets

Department of Biomedical Engineering,
The University of Texas at San Antonio,
AET 1.360, One UTSA Circle,
San Antonio, TX 78249

W. O'Dell

Department of Radiation Oncology,
University of Florida,
Shands Cancer Center,
P.O. Box 100385,
2033 Mowry Road,
Gainesville, FL 32610

T. Smith

Western Allegheny Health System,
Allegheny General Hospital,
Gerald McGinnis Cardiovascular Institute,
320 East North Avenue,
Pittsburgh, PA 15212

J. J. Reilly

Department of Medicine,
The University of Pittsburgh,
1218 Scaife Hall,
3550 Terrace Street,
Pittsburgh, PA 15261

E. A. Finol

Department of Biomedical Engineering,
The University of Texas at San Antonio,
AET 1.360, One UTSA Circle,
San Antonio, TX 78249
e-mail: ender.finol@utsa.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received December 6, 2012; final manuscript received March 25, 2013; accepted manuscript posted April 4, 2013; published online May 9, 2013. Assoc. Editor: Dalin Tang.

J Biomech Eng 135(6), 061011 (May 09, 2013) (15 pages) Paper No: BIO-12-1598; doi: 10.1115/1.4024141 History: Received December 06, 2012; Revised March 25, 2013; Accepted April 04, 2013

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.

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References

Su, Z., Hunter, K. S., and Shandas, R., 2012, “Impact of Pulmonary Vascular Stiffness and Vasodilator Treatment in Pediatric Pulmonary Hypertension: 21 Patient-Specific Fluid-Structure Interaction Studies,” Comput. Meth. Prog. Biomed., 108(2), pp. 617–628. [CrossRef]
De Leval, M. R., 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]
Taylor, C. A., and Steinman, D. A., 2010, “Image-Based Modeling of Blood Flow and Vessel Wall Dynamics: Applications, Methods and Future Directions,” Sixth International Bio-Fluid Mechanics Symposium and Workshop, March 28–30, 2008 Pasadena, CA, (Ann. Biomed. Eng., 38(3), pp. 1188–1203). [CrossRef] [PubMed]
Taylor, C. A., and Figueroa, C. A., 2009, “Patient-Specific Modeling of Cardiovascular Mechanics,” Ann. Rev. Biomed. Eng., 11, pp. 109–134. [CrossRef]
Hunter, K. S., Feinstein, J. A., Ivy, D. D., and Shandas, R., 2010, “Computational Simulation of the Pulmonary Arteries and Its Role in the Study of Pediatric Pulmonary Hypertension,” Prog. Pediatr. Cardiol., 30(1–2), pp. 63–69. [CrossRef] [PubMed]
Khamdaeng, T., Luo, J., Vappou, J., Terdtoon, P., and Konofagou, E. E., 2012, “Arterial Stiffness Identification of the Human Carotid Artery Using the Stress-Strain Relationship In Vivo,” Ultrasonics, 52(3), pp. 402–411. [CrossRef] [PubMed]
Resnick, N., Yahav, H., Shay-Salit, A., Shushy, M., Schubert, S., Zilberman, L. C., and Wofovitz, E., 2003, “Fluid Shear Stress and the Vascular Endothelium: For Better and for Worse,” Prog. Biophys. Mol. Biol., 81(3), pp. 177–199. [CrossRef] [PubMed]
Ando, J., and Yamamoto, K., 2011, “Effects of Shear Stress and Stretch on Endothelial Function,” Antioxid. Redox. Signal., 15(5), pp. 1389–1403. [CrossRef] [PubMed]
Depaola, N., Gimbrone, M. A.Jr., Davies, P. F., and Dewey, C. F., Jr., 1992, “Vascular Endothelium Responds to Fluid Shear Stress Gradients,” Arterioscler. Thromb., 12(11), pp. 1254–1257. [CrossRef] [PubMed]
Kakisis, J. D., Liapis, C. D., and Sumpio, B. E., 2004, “Effects of Cyclic Strain on Vascular Cells,” Endothelium, 11(1), pp. 17–28. [CrossRef] [PubMed]
Toda, M., Yamamoto, K., Shimizu, N., Obi, S., Kumagaya, S., Igarashi, T., Kamiya, A., and Ando, J., 2008, “Differential Gene Responses in Endothelial Cells Exposed to a Combination of Shear Stress and Cyclic Stretch,” J. Biotechnol., 133(2), pp. 239–244. [CrossRef] [PubMed]
Haga, M., Chen, A., Gortler, D., Dardik, A., and Sumpio, B. E., 2003, “Shear Stress and Cyclic Strain May Suppress Apoptosis in Endothelial Cells by Different Pathways,” Endothelium, 10(3), pp. 149–157. [CrossRef] [PubMed]
Rabinovitch, M., 2008, “Molecular Pathogenesis of Pulmonary Arterial Hypertension,” J. Clin. Invest., 118(7), pp. 2372–2379. [CrossRef] [PubMed]
Tian, L., Lammers, S. R., Kao, P. H., Albietz, J. A., Stenmark, K. R., Qi, H. J., Shandas, R., and Hunter, K. S., 2012, “Impact of Residual Stretch and Remodeling on Collagen Engagement in Healthy and Pulmonary Hypertensive Calf Pulmonary Arteries at Physiological Pressures,” Ann. Biomed. Eng., 40(7), pp. 1419–1433. [CrossRef] [PubMed]
Humphrey, J. D., 2008, “Mechanisms of Arterial Remodeling in Hypertension: Coupled Roles of Wall Shear and Intramural Stress,” Hypertension, 52(2), pp. 195–200. [CrossRef] [PubMed]
Wang, Z., and Chesler, N. C., 2011, “Pulmonary Vascular Wall Stiffness: An Important Contributor to the Increased Right Ventricular Afterload With Pulmonary Hypertension,” Pulm. Circ., 1(2), pp. 212–223. [CrossRef] [PubMed]
Fourie, P. R., Coetzee, A. R., and Bolliger, C. T., 1992, “Pulmonary Artery Compliance: Its Role in Right Ventricular-Arterial Coupling,” Cardiovasc. Res., 26(9), pp. 839–844. [CrossRef] [PubMed]
Scott-Drechsel, D., Su, Z., Hunter, K., Li, M., Shandas, R., and Tan, W., 2012, “A New Flow Co-Culture System for Studying Mechanobiology Effects of Pulse Flow Waves,” Cytotechnology, 64(6), pp. 649–666. [CrossRef] [PubMed]
Huang, W., Yen, R. T., Mclaurine, M., and Bledsoe, G., 1996, “Morphometry of the Human Pulmonary Vasculature,” J. Appl. Physiol., 81(5), pp. 2123–2133. [PubMed]
Huang, W., Zhou, Q., Gao, J., and Yen, R. T., 2011, “A Continuum Model for Pressure-Flow Relationship in Human Pulmonary Circulation,” Mol. Cell Biomech., 8(2), pp. 105–122. [CrossRef] [PubMed]
Nauser, T. D., and Stites, S. W., 2001, “Diagnosis and Treatment of Pulmonary Hypertension,” Am. Fam. Physician, 63(9), pp. 1789–1798. [PubMed]
Hatano, S., and Strasser, T., 1975, Primary Pulmonary Hypertension: Report on a WHO Meeting, Geneva, 15–17 October 1973, World Health Organization, Geneva.
Ap, F., 2001, “Clinical Classification of Pulmonary Hypertension,” Clin. Chest Med., 22(3), pp. 385–391. [CrossRef] [PubMed]
Simonneau, G., Robbins, I. M., Beghetti, M., Channick, R. N., Delcroix, M., Denton, C. P., Elliott, C. G., Gaine, S. P., Gladwin, M. T., Jing, Z. C., Krowka, M. J., Langleben, D., Nakanishi, N., and Souza, R., 2009, “Updated Clinical Classification of Pulmonary Hypertension,” J. Am. Coll. Cardiol., 54(1 Suppl), pp. S43–S54. [CrossRef] [PubMed]
Badesch, D. B., Champion, H. C., Sanchez, M. A., Hoeper, M. M., Loyd, J. E., Manes, A., Mcgoon, M., Naeije, R., Olschewski, H., Oudiz, R. J., and Torbicki, A., 2009, “Diagnosis and Assessment of Pulmonary Arterial Hypertension,” J. Am. Coll. Cardiol., 54(1 Suppl), pp. S55–S66. [CrossRef] [PubMed]
Mclaughlin, V. V., Archer, S. L., Badesch, D. B., Barst, R. J., Farber, H. W., Lindner, J. R., Mathier, M. A., Mcgoon, M. D., Park, M. H., Rosenson, R. S., Rubin, L. J., Tapson, V. F., Varga, J., 2009, “ACCF/AHA 2009 Expert Consensus Document on Pulmonary Hypertension: A Report of the American College of Cardiology Foundation Task Force on Expert Consensus Documents and the American Heart Association Developed in Collaboration with the American College of Chest Physicians; American Thoracic Society, Inc.; and the Pulmonary Hypertension Association,” J. Am. Coll. Cardiol., 53(17), pp. 1573–1619. [CrossRef] [PubMed]
Rubin, L. J., 2002, “Therapy of Pulmonary Hypertension: The Evolution From Vasodilators to Antiproliferative Agents,” Am. J. Respir. Crit. Care Med., 166(10), pp. 1308–1309. [CrossRef] [PubMed]
Sitbon, O., Humbert, M., Jais, X., Ioos, V., Hamid, A. M., Provencher, S., Garcia, G., Parent, F., Herve, P., and Simonneau, G., 2005, “Long-Term Response to Calcium Channel Blockers in Idiopathic Pulmonary Arterial Hypertension,” Circulation, 111(23), pp. 3105–3111. [CrossRef] [PubMed]
Mclaughlin, V. V., 2002, “Survival in Primary Pulmonary Hypertension: The Impact of Epoprostenol Therapy,” Circulation, 106(12), pp. 1477–1482. [CrossRef] [PubMed]
Galie, N., Ghofrani, H. A., Torbicki, A., Barst, R. J., Rubin, L. J., Badesch, D., Fleming, T., Parpia, T., Burgess, G., Branzi, A., Grimminger, F., Kurzyna, M., and Simonneau, G., 2005, “Sildenafil Use in Pulmonary Arterial Hypertension Study Sildenafil Citrate Therapy for Pulmonary Arterial Hypertension,” N. Engl. J. Med., 353(20), pp. 2148–2157. [CrossRef] [PubMed]
Agarwal, R., and Gomberg-Maitland, M., 2011, “Current Therapeutics and Practical Management Strategies for Pulmonary Arterial Hypertension,” Am. Heart J., 162(2), pp. 201–213. [CrossRef] [PubMed]
Clapp, L. H., Finney, P., Turcato, S., Tran, S., Rubin, L. J., and Tinker, A., 2002, “Differential Effects of Stable Prostacyclin Analogs on Smooth Muscle Proliferation and Cyclic Amp Generation in Human Pulmonary Artery,” Am. J. Respir. Cell Mol. Biol., 26(2), pp. 194–201. [CrossRef] [PubMed]
Hoendermis, E. S., 2011, “Pulmonary Arterial Hypertension: An Update,” Neth. Heart J., 19(12), pp. 514–522. [CrossRef] [PubMed]
Benza, R. L., Miller, D. P., Gomberg-Maitland, M., Frantz, R. P., Foreman, A. J., Coffey, C. S., Frost, A., Barst, R. J., Badesch, D. B., Elliott, C. G., Liou, T. G., and Mcgoon, M. D., 2010, “Predicting Survival in Pulmonary Arterial Hypertension: Insights From the Registry to Evaluate Early and Long-Term Pulmonary Arterial Hypertension Disease Management (Reveal),” Circulation, 122(2), pp. 164–172. [CrossRef] [PubMed]
Lee, W. T., Ling, Y., Pepke-Zeba, J., Peacock, A. J., and Johnson, M. K., 2012, “Predicting Survival in Pulmonary Arterial Hypertension in the UK,” Eur Respir J., 40(3), pp. 604–611. [CrossRef] [PubMed]
Agarwal, R., and Gomberg-Maitland, M., 2012, “Prognostication in Pulmonary Arterial Hypertension,” Heart Fail. Clin., 8(3), pp. 373–383. [CrossRef] [PubMed]
Galie, N., Palazzini, M., and Manes, A., 2010, “Pulmonary Arterial Hypertension: From the Kingdom of the Near-Dead to Multiple Clinical Trial Meta-Analyses,” Eur. Heart J., 31(17), pp. 2080–2086. [CrossRef] [PubMed]
O'Callaghan, D. S., and Humbert, M., 2012, “A Critical Analysis of Survival in Pulmonary Arterial Hypertension,” Eur. Respir. Rev., 21(125), pp. 218–222. [CrossRef] [PubMed]
Mcgoon, M., Gutterman, D., Steen, V., Barst, R., Mccrory, D. C., Fortin, T. A., and Loyd, J. E., 2004, “Screening, Early Detection, and Diagnosis of Pulmonary Arterial Hypertension ACCP Evidence-Based Clinical Practice Guidelines,” Chest, 126, pp. 14S–34S. [CrossRef] [PubMed]
Tang, B. T., Fonte, T. A., Chan, F. P., Tsao, P. S., Feinstein, J. A., and Taylor, C. A., 2011, “Three-Dimensional Hemodynamics in the Human Pulmonary Arteries Under Resting and Exercise Conditions,” Ann. Biomed. Eng., 39(1), pp. 347–358. [CrossRef] [PubMed]
Rich, S., D'alonzo, G. E., Dantzker, D. R., and Levy, P. S., 1985, “Magnitude and Implications of Spontaneous Hemodynamic Variability in Primary Pulmonary Hypertension,” Am. J. Cardiol., 55(1), pp. 159–163. [CrossRef] [PubMed]
Mcgoon, M. D., and Kane, G. C., 2009, “Pulmonary Hypertension—Diagnosis and Management,” Mayo Clin. Proc., 84(2), pp. 191–207. [CrossRef] [PubMed]
Dalen, J. E., and Bone, R. C., 1996, “Is It Time to Pull the Pulmonary Artery Catheter?,” JAMA, 276(11), pp. 916–918. [CrossRef] [PubMed]
Yock, P. G., and Popp, R. L., 1984, “Noninvasive Estimation of Right Ventricular Systolic Pressure by Doppler Ultrasound in Patients With Tricuspid Regurgitation,” Circulation, 70(4), pp. 657–662. [CrossRef] [PubMed]
Fakhri, A. A., Hughes-Doichev, R. A., Biederman, R. W., and Murali, S., 2012, “Imaging in the Evaluation of Pulmonary Artery Hemodynamics and Right Ventricular Structure and Function,” Heart Fail. Clin., 8(3), pp. 353–372. [CrossRef] [PubMed]
Rudski, L. G., Lai, W. W., Afilalo, J., Hua, L., Handschumacher, M. D., Chandrasekaran, K., Solomon, S. D., Louie, E. K., and Schiller, N. B., 2010, “Guidelines for the Echocardiographic Assessment of the Right Heart in Adults: A Report from the American Society of Echocardiography Endorsed by the European Association of Echocardiography, a Registered Branch of the European Society of Cardiology, and the Canadian Society of Echocardiography,” J. Am. Soc. Echocardiogr., 23(7), pp. 685–713. [CrossRef] [PubMed]
Fisher, M. R., Forfia, P. R., Chamera, E., Housten-Harris, T., Champion, H. C., Girgis, R. E., Corretti, M. C., and Hassoun, P. M., 2009, “Accuracy of Doppler Echocardiography in the Hemodynamic Assessment of Pulmonary Hypertension,” Am. J. Respir. Crit. Care Med., 179(7), pp. 615–621. [CrossRef] [PubMed]
Roberts, J. D., and Forfia, P. R., 2011, “Diagnosis and Assessment of Pulmonary Vascular Disease by Doppler Echocardiography,” Pulm. Circ., 1(2), pp. 160–181. [CrossRef] [PubMed]
López-Candales, A., Rajagopalan, N., Saxena, N., Gulyasy, B., Edelman, K., and Bazaz, R., 2006, “Right Ventricular Systolic Function Is Not the Sole Determinant of Tricuspid Annular Motion.,” Am. J. Cardiol., 98(7), pp. 973–977. [CrossRef] [PubMed]
Kjaergaard, J., Iversen, K. K., Akkan, D., Møller, J. E., Køber, L. V., Torp-Pedersen, C., and Hassager, C., 2009, “Predictors of Right Ventricular Function as Measured by Tricuspid Annular Plane Systolic Excursion in Heart Failure,” Cardiovasc. Ultra., 7(51), pp.
Formaggia, L., Lamponi, D., and Quarteroni, A., 2003, “One-Dimensional Models for Blood Flow in Arteries,” J. Eng. Math., 47(3), pp. 251–276. [CrossRef]
Olufsen, M. S., Peskin, C. S., Kim, W. Y., Pedersen, E. M., Nadim, A., and Larsen, J., 2000, “Numerical Simulation and Experimental Validation of Blood Flow in Arteries With Structured-Tree Outflow Conditions,” Ann. Biomed. Eng., 28(11), pp. 1281–1299. [CrossRef] [PubMed]
Olufsen, M. S., and Nadim, A., 2004, “On Deriving Lumped Models for Blood Flow and Pressure in the Systemic Arteries,” Math. Biosci. Eng., 1(1), pp. 61–80. [CrossRef] [PubMed]
Olufsen, M. S., 2000, “A One-Dimensional Fluid Dynamic Model of the Systemic Arteries,” Stud. Health Technol. Info., 71, pp. 79–98. [CrossRef]
Johnson, D. A., Rose, W. C., Edwards, J. W., Naik, U. P., and Beris, A. N., 2011, “Application of 1D Blood Flow Models of the Human Arterial Network to Differential Pressure Predictions,” J. Biomech., 44(5), pp. 869–876. [CrossRef] [PubMed]
Olufsen, M. S., 1999, “Structured Tree Outflow Condition for Blood Flow in Larger Systemic Arteries,” Am. J. Physiol., 276(1), pp. H257–H268. [PubMed]
Vignon-Clementel, I. E., Marsden, A. L., and Feinstein, J. A., 2010, “A Primer on Computational Simulation in Congenital Heart Disease for the Clinician,” Prog. Ped. Cardiol., 30(1–2), pp. 3–13. [CrossRef]
Box, F. M., Van Der Geest, R. J., Rutten, M. C., and Reiber, J. H., 2005, “The Influence of Flow, Vessel Diameter, and Non-Newtonian Blood Viscosity on the Wall Shear Stress in a Carotid Bifurcation Model for Unsteady Flow,” Invest. Radiol., 40(5), pp. 277–294. [CrossRef] [PubMed]
Xiang, J., Tremmel, M., Kolega, J., Levy, E. I., Natarajan, S. K., and Meng, H., 2011, “Newtonian Viscosity Model Could Overestimate Wall Shear Stress in Intracranial Aneurysm Domes and Underestimate Rupture Risk,” J. Neurointerv. Surg., 4(5), pp. 351–357. [CrossRef] [PubMed]
Tawhai, M., Clark, A., Donovan, G., and Burrowes, K., 2011, “Computational Modeling of Airway and Pulmonary Vascular Structure and Function: Development of a Lung Physiome,” Crit. Rev. Biomed. Eng., 39(4), pp. 319–336. [CrossRef] [PubMed]
Boyd, J., Buick, J. M., and Green, S., 2007, “Analysis of the Casson and Carreau–Yasuda Non-Newtonian Blood Models in Steady and Oscillatory Flows Using the Lattice Boltzmann Method,” Phys. Fluid., 19(9), pp. 093103. [CrossRef]
Abraham, F., Behr, M., and Heinkenschloss, M., 2005, “Shape Optimization in Steady Blood Flow: A Numerical Study of Non-Newtonian Effects,” Comput. Meth. Biomech. Biomed. Eng., 8(2), pp. 127–137. [CrossRef]
Merrill, E. W., 1969, “Rheology of Blood,” Physiol. Rev., 49(4), pp. 863–888. Available at: http://web.mit.edu/andrew3/Public/Papers/1969/Merrill/1969_PhYSIOLOCIICAL%20REVIEWEs_Rheology%20of%20Blood_Merrill.pdf [PubMed]
O'Dell, W. G., 2012, “Automatic Segmentation of Tumor-Laden Lung Volumes From the LIDC Database,” SPIE, 8315(1), p. 831531. [CrossRef]
Buelow, T., Wiemker, R., Blaffert, T., Lorenz, C., and Renisch, S., 2005, “Automatic Extraction of the Pulmonary Artery Tree From Multi-Slice CT Data,” Medical Imaging 2005: Physiology, Function, and Structure from Medical Images, Proceedings of the SPIE, pp. 730–740.
Shikata, H., Mclennan, G., Hoffman, E. A., and Sonka, M., 2009, “Segmentation of Pulmonary Vascular Trees From Thoracic 3D CT Images,” J. Biomed. Imag., 2009, pp. 1–11. [CrossRef]
Kaftan, J. N., Kiraly, A. P., Bakai, A., Das, M., Novak, C. L., and Aach, T., 2008, “Fuzzy Pulmonary Vessel Segmentation in Contrast Enhanced CT Data,” Medical Imaging 2008: Image Processing; Proceedings of the SPIE, 6914, p. 69141Q.
Van Dongen, E., and Van Ginneken, B., 2010, “Automatic Segmentation of Pulmonary Vasculature in Thoracic CT Scans With Local Thresholding and Airway Wall Removal,” 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 668–671.
Ebrahimdoost, Y., Qanadli, S. D., Nikravanshalmani, A., Ellis, T. J., Shojaee, Z. F., and Dehmeshki, J., 2011, “Automatic Segmentation of Pulmonary Artery (PA) in 3D Pulmonary CTA Images,” 17th International Conference on Digital Signal Processing (DSP), pp. 1–5.
Burrowes, K. S., Hunter, P. J., and Tawhai, M. H., 2005, “Anatomically Based Finite Element Models of the Human Pulmonary Arterial and Venous Trees Including Supernumerary Vessels,” J. Appl. Physiol., 99(2), pp. 731–738. [CrossRef]
Horsfield, K., 1978, “Morphometry of the Small Pulmonary Arteries in Man,” Circ. Res., 42(5), pp. 593–597. [CrossRef]
Tu, J., Yeoh, G. H., and Liu, C., 2008, Computational Fluid Dynamics—a Practical Approach, Elsevier Inc., Burlington, MA.
Spiegel, M., 2011, “Patient-Specific Cerebral Vessel Segmentation With Application in Hemodynamic Simulation,” Ph.D. Thesis, Universität Erlangen Nürnberg, Erlangen, Germany.
Prakash, S., and Ethier, C. R., 2001, “Requirements for Mesh Resolution in 3D Computational Hemodynamics,” ASME J. Biomech. Eng., 123(2), pp. 134–144. [CrossRef]
Bove, E. L., De Leval, M. R., Migliavacca, F., Guadagni, G., and Dubini, G., 2003, “Computational Fluid Dynamics in the Evaluation of Hemodynamic Performance of Cavopulmonary Connections After the Norwood Procedure for Hypoplastic Left Heart Syndrome,” J. Thorac. Cardiovasc. Surg., 126(4), pp. 1040–1047. [CrossRef]
Antiga, L., Ene-Iordache, B., and Remuzzi, A., 2003, “Computational Geometry for Patient-Specific Reconstruction and Meshing of Blood Vessels From MR and CT Angiography,” IEEE Trans. Med. Imag., 22(5), pp. 674–684. [CrossRef]
Steinman, D. A., Hoi, Y., Fahy, P., Morris, L., Walsh, M. T., Aristokleous, N., Anayiotos, A., Papaharilaou, Y., Arzani, A., Shadden, S., Berg, P., Janiga, G., Bols, J., Segers, P., Bressloff, N. W., Cibis, M., Gijsen, F. H., Cito, S., Pallarés, J., Browne, L. D., Costelloe, J. A., Lynch, A. G., Degroote, J., Vierendeels, J., Fu, W., Qiao, A., Hodis, S., Kallmes, D. F., Kalsi, H., Long, Q., Kheyfets, V. O., Finol, E. A., Kono, K., Malek, A. M., Lauric, A., Menon, P. G., Pekkan, K., Moghadam, M. E., Marsden, A. L., Oshima, M., Katagiri, K., Peiffer, V., Mohamied, Y., Sherwin, S. J., Schaller, J., Goubergrits, L., Usera, G., Mendina, M., Valen-Sendstad, K., Habets, D. F., Xiang, J., Meng, H., Yu, Y., Karniadakis, G. E., Shaffer, N., and Loth, F., 2013, “Variability of CFD Solutions for Pressure and Flow in a Giant Aneurysm: The SBC2012 CFD Challenge,” ASME J. Biomech. Eng., 135(2), p. 021016. [CrossRef]
Nielsen, P. M. F., and Wittek, A., 2012, Computational Biomechanics for Medicine: Deformation and Flow, Springer, New York.
Boutsianis, E., Gupta, S., Boomsma, K., and Poulikakos, D., 2008, “Boundary Conditions by Schwarz-Christoffel Mapping in Anatomically Accurate Hemodynamics,” Ann. Biomed. Eng., 36(12), pp. 2068–2084. [CrossRef]
Ponzini, R., Lemma, M., Morbiducci, U., Montevecchi, F. M., and Redaelli, A., 2008, “Doppler Derived Quantitative Flow Estimate in Coronary Artery Bypass Graft: A Computational Multiscale Model for the Evaluation of the Current Clinical Procedure,” Med. Eng. Phys., 30(7), pp. 809–816. [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]
Antiga, L., Piccinelli, M., Botti, L., Ene-Iordache, B., Remuzzi, A., and Steinman, D. A., 2008, “An Image-Based Modeling Framework for Patient-Specific Computational Hemodynamics,” Med. Biol. Eng. Comput., 46(11), pp. 1097–1112. [CrossRef]
Kauczor, H. U., Ley-Zaporozhan, J., and Ley, S., 2009, “Imaging of Pulmonary Pathologies: Focus on Magnetic Resonance Imaging,” Proc. Am. Thorac. Soc., 6(5), pp. 458–463. [CrossRef]
Zamir, M., 2000, The Physics of Pulsatile Flow, Springer-Verlag, New York.
Womersley, J. R., 1955, “Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries When the Pressure Gradient Is Known,” J. Physiol., 127(3), pp. 553–563.
Morgan, V. L., Roselli, R. J., and Lorenz, C. H., 1998, “Normal Three-Dimensional Pulmonary Artery Flow Determined by Phase Contrast Magnetic Resonance Imaging,” Ann. Biomed. Eng., 26(4), pp. 557–566. [CrossRef]
Miyasaka, K., and Takata, M., 1993, “Flow Velocity Profile of the Pulmonary Artery Measured by the Continuous Cardiac Output Monitoring Catheter,” Can. J. Anaesth., 40(2), pp. 183–187. [CrossRef]
Clipp, R. B., and Steele, B. N., 2009, “Impedance Boundary Conditions for the Pulmonary Vasculature Including the Effects of Geometry, Compliance, and Respiration,” IEEE Trans. Biomed. Eng., 56(3), pp. 862–870. [CrossRef]
Grinberg, L., and Karniadakis, G. E., 2008, “Outflow Boundary Conditions for Arterial Networks With Multiple Outlets,” Ann. Biomed. Eng., 36(9), pp. 1496–1514. [CrossRef]
Morbiducci, U., Gallo, D., Massai, D., Consolo, F., Ponzini, R., Antiga, L., Bignardi, C., Deriu, M. A., and Redaelli, A., 2010, “Outflow Conditions for Image-Based Hemodynamic Models of the Carotid Bifurcation: Implications for Indicators of Abnormal Flow,” ASME J. Biomech. Eng., 132(9), p. 091005. [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. Meth. Appl. Mech. Eng., 195, pp. 3776–3796. [CrossRef]
Botnar, R., Rappitsch, G., Scheidegger, M. B., Liepsch, D., Perktold, K., and Boesiger, P., 2000, “Hemodynamics in the Carotid Artery Bifurcation: A Comparison Between Numerical Simulations and In Vitro MRI Measurements,” J. Biomech., 33(2), pp. 137–144. [CrossRef]
Ansys, 2011, ANSYS® Academic Research, Release 14.0, Help System, Coupled Field Analysis Guide, ANSYS, Inc, Canonsburg, PA.
Horsfield, K., and Woldenberg, M. J., 1989, “Diameters and Cross-Sectional Areas of Branches in the Human Pulmonary Arterial Tree,” Anat Rec, 223(3), pp. 245–251. [CrossRef]
Orlando, W., Shandas, R., and Degroff, C., 2006, “Efficiency Differences in Computational Simulations of the Total Cavo-Pulmonary Circulation With and Without Compliant Vessel Walls,” Comput Methods Programs Biomed, 81(3), pp. 220–227. [CrossRef]
Hunter, K. S., Lanning, C. J., Chen, S. Y., Zhang, Y., Garg, R., Ivy, D. D., and Shandas, R., 2006, “Simulations of Congenital Septal Defect Closure and Reactivity Testing in Patient-Specific Models of the Pediatric Pulmonary Vasculature: A 3D Numerical Study With Fluid-Structure Interaction,” ASME, J. Biomech. Eng., 128(4), pp. 564–572. [CrossRef]
Kung, E., and Taylor, C., 2011, “Development of a Physical Windkessel Module to Re-Create In Vivo Vascular Flow Impedance for In Vitro Experiments,” Cardiovasc. Eng. Tech., 2(1), pp. 2–14. [CrossRef]
Westerhof, N., Lankhaar, J.-W., and Westerhof, B., 2009, “The Arterial Windkessel,” Med. Bio. Eng. Comput., 47(2), pp. 131–141. [CrossRef]
Vignon-Clementel, I. E., Figueroa, C. A., Jansen, K. E., and Taylor, C. A., 2010, “Outflow Boundary Conditions for 3D Simulations of Non-Periodic Blood Flow and Pressure Fields in Deformable Arteries,” Comput. Meth. Biomech. Biomed. Eng., 13(5), pp. 625–640. [CrossRef]
Pahlevan, N. M., Amlani, F., Hossein Gorji, M., Hussain, F., and Gharib, M., 2011, “A Physiologically Relevant, Simple Outflow Boundary Model for Truncated Vasculature,” Ann. Biomed. Eng., 39(5), pp. 1470–1481. [CrossRef]
Formaggia, L., Lamponi, D., Tuveri, M., and Veneziani, A., 2006, “Numerical Modeling of 1D Arterial Networks Coupled With a Lumped Parameters Description of the Heart,” Comput. Meth. Biomech. Biomed. Eng., 9(5), pp. 273–288. [CrossRef]
Van Den Bos, G. C., Westerhof, N., and Randall, O. S., 1982, “Pulse Wave Reflection: Can It Explain the Differences Between Systemic and Pulmonary Pressure and Flow Waves? A Study in Dogs,” Circ. Res., 51(4), pp. 479–485. [CrossRef]
Steele, B. N., Olufsen, M. S., and Taylor, C. A., 2007, “Fractal Network Model for Simulating Abdominal and Lower Extremity Blood Flow During Resting and Exercise Conditions,” Comput. Meth. Biomech. Biomed. Eng., 10(1), pp. 39–51. [CrossRef]
Spilker, R. L., Feinstein, J. A., Parker, D. W., Reddy, V. M., and Taylor, C. A., 2007, “Morphometry-Based Impedance Boundary Conditions for Patient-Specific Modeling of Blood Flow in Pulmonary Arteries,” Ann. Biomed. Eng., 35(4), pp. 546–559. [CrossRef]
Bazilevs, Y., Hsu, M. C., Benson, D. J., Sankaran, S., and Marsden, A. L., 2009, “Computational Fluid–Structure Interaction: Methods and Application to a Total Cavopulmonary Connection,” Comput. Mech., 45(1), pp. 77–89. [CrossRef]
Figueroa, C. A., Vignon-Clementel, I. E., Jansen, K. E., Hughes, T. J. R., and Taylor, C. A., 2006, “A Coupled Momentum Method for Modeling Blood Flow in Three-Dimensional Deformable Arteries,” Comput. Meth. Appl. Mech. Eng., 195(41–43), pp. 5685–5706. [CrossRef]
Zhou, J., and Fung, Y. C., 1997, “The Degree of Nonlinearity and Anisotropy of Blood Vessel Elasticity,” Proc. Natl. Acad. Sci. USA, 94(26), pp. 14255–14260. [CrossRef]
Kim, J., and Baek, S., 2011, “Circumferential Variations of Mechanical Behavior of the Porcine Thoracic Aorta During the Inflation Test,” J. Biomech., 44(10), pp. 1941–1947. [CrossRef]
Sacks, M. S., 2000, “Biaxial Mechanical Evaluation of Planar Biological Materials,” J. Elast., 61(1–3), pp. 199–246. [CrossRef]
Sacks, M. S., and Sun, W., 2003, “Multiaxial Mechanical Behavior of Biological Materials,” Ann. Rev. Biomed. Eng., 5, pp. 251–284. [CrossRef]
Lammers, S. R., Kao, P. H., Qi, H. J., Hunter, K., Lanning, C., Albietz, J., Hofmeister, S., Mecham, R., Stenmark, K. R., and Shandas, R., 2008, “Changes in the Structure-Function Relationship of Elastin and Its Impact on the Proximal Pulmonary Arterial Mechanics of Hypertensive Calves,” Am. J. Physiol. Heart. Circ. Physiol., 295(4), pp. H1451–H1459. [CrossRef] [PubMed]
Sacks, M. S., 2003, “Incorporation of Experimentally-Derived Fiber Orientation Into a Structural Constitutive Model for Planar Collagenous Tissues,” ASME J. Biomech. Eng., 125(2), pp. 280–287. [CrossRef]
Genovese, K., Lee, Y. U., and Humphrey, J. D., 2011, “Novel Optical System for In Vitro Quantification of Full Surface Strain Fields in Small Arteries: II. Correction for Refraction and Illustrative Results,” Comput. Meth. Biomech. Biomed. Eng., 14(3), pp. 227–237. [CrossRef]
Genovese, K., Lee, Y. U., and Humphrey, J. D., 2011, “Novel Optical System for In Vitro Quantification of Full Surface Strain Fields in Small Arteries: I. Theory and Design,” Comput. Meth. Biomech. Biomed. Eng., 14(3), pp. 213–225. [CrossRef]
Kao, P. H., Lammers, S. R., Tian, L., Hunter, K., Stenmark, K. R., Shandas, R., and Qi, H. J., 2011, “A Microstructurally Driven Model for Pulmonary Artery Tissue,” ASME J. Biomech. Eng., 133(5), p. 051002. [CrossRef]
Quaini, A., Canic, S., Glowinski, R., Igo, S., Hartley, C. J., Zoghbi, W., and Little, S., 2012, “Validation of a 3D Computational Fluid–Structure Interaction Model Simulating Flow Through an Elastic Aperture,” J. Biomech., 45(2), pp. 310–318. [CrossRef] [PubMed]
Zhu, Y., and Granick, S., 2002, “Limits of the Hydrodynamic No-Slip Boundary Condition,” Phys. Rev. Lett., 88(10), p. 106102. [CrossRef] [PubMed]
Bukač, M., Čanić, S., Glowinski, R., Tambača, J., and Quaini, A., 2013, “Fluid–Structure Interaction in Blood Flow Capturing Non-Zero Longitudinal Structure Displacement,” J. Comput. Phys., 235, pp. 515–541. [CrossRef]
Formaggia, L., Gerbeau, J. F., Nobile, F., and Quarteroni, A., 2001, “On the Coupling of 3D and 1D Navier–Stokes Equations for Flow Problems in Compliant Vessels,” Comput. Meth. Appl. Mech. Eng., 191(6–7), pp. 561–582. [CrossRef]
Zarins, C. K., Zatina, M. A., Giddens, D. P., Ku, D. N., and Glagov, S., 1987, “Shear Stress Regulation of Artery Lumen Diameter in Experimental Atherogenesis,” J. Vasc. Surg., 5(3), pp. 413–420. [CrossRef] [PubMed]
Kleinstreuer, C., 2006, Biofluid Dynamics—Principles and Selected Applications, CRC Press; Taylor and Francis Group, LLC, Boca Raton, FL.
Miyamoto, S., Nagaya, N., Satoh, T., Kyotani, S., Sakamaki, F., Fujita, M., Nakanishi, N., and Miyatake, K., 2000, “Clinical Correlates and Prognostic Significance of Six-Minute Walk Test in Patients With Primary Pulmonary Hypertension. Comparison With Cardiopulmonary Exercise Testing,” Am. J. Respir. Crit. Care Med., 161(2), pp. 487–492. [CrossRef] [PubMed]
Sotelo, J. A., Bachler, P., Chabert, S., Hurtado, D., Irarrazaval, P., Tejos, C., and Uribe, S., 2012, “Normal Values of Wall Shear Stress in the Pulmonary Artery From 4D Flow Data,” J. Cardiovasc. Magn. Reson., 14(1 Suppl), p. W66. [CrossRef]
Chien, S., 2008, “Effects of Disturbed Flow on Endothelial Cells,” Ann. Biomed. Eng., 36(4), pp. 554–562. [CrossRef] [PubMed]
Hunter, K. S., Lee, P. F., Lanning, C. J., Ivy, D. D., Kirby, K. S., Claussen, L. R., Chan, K. C., and Shandas, R., 2008, “Pulmonary Vascular Input Impedance Is a Combined Measure of Pulmonary Vascular Resistance and Stiffness and Predicts Clinical Outcomes Better Than Pulmonary Vascular Resistance Alone in Pediatric Patients With Pulmonary Hypertension,” Am. Heart J., 155(1), pp. 166–174. [CrossRef] [PubMed]
Christophe, J. J., Ishikawa, T., Imai, Y., Takase, K., Thiriet, M., and Yamaguchi, T., 2012, “Hemodynamics in the Pulmonary Artery of a Patient With Pneumothorax,” Med. Eng. Phys., 34(6), pp. 725–732. [CrossRef] [PubMed]
De Leval, M. R., 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 Cavo-Pulmonary Connections,” J. Thorac. Cardiovasc. Surg., 111(3), pp. 502–513. [CrossRef] [PubMed]
Rodes-Cabau, J., Domingo, E., Roman, A., Majo, J., Lara, B., Padilla, F., Anivarro, I., Angel, J., Tardif, J. C., and Soler-Soler, J., 2003, “Intravascular Ultrasound of the Elastic Pulmonary Arteries: A New Approach for the Evaluation of Primary Pulmonary Hypertension,” Heart, 89(3), pp. 311–315. [CrossRef] [PubMed]
Henk, C. B., Schlechta, B., Grampp, S., Gomischek, G., Klepetko, W., and Mostbeck, G. H., 1998, “Pulmonary and Aortic Blood Flow Measurements in Normal Subjects and Patients After Single Lung Transplantation at 0.5 T Using Velocity Encoded Cine MRI,” Chest, 114(3), pp. 771–779. [CrossRef] [PubMed]

Figures

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Fig. 1

Outline of disease progression in chronic pulmonary hypertension. The white boxes refer to effects on the pulmonary arterial vasculature (vessel wall thickness, vessel wall stiffness, arterial pressure). The orange box refers to effects on the right ventricle. Note: EC = endothelial cells; SMC = smooth muscle cells; RV = right ventricle; Q = flow; σz = longitudinal stress; σθ = circumferential stress; τw = wall shear stress; eNO = endothelial nitric oxide; ET-1 = endothelin-1.

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Fig. 2

Procedure for conducting patient-specific computational modeling of pulmonary vasculature. (a) Starting with a thoracic CT scan of the patient, (b) a 3D solid model of the pulmonary vasculature is reconstructed. (c) The model outlets are truncated normal to the centerline and fixed to outlet extensions measuring 10 times the outlet diameter in length. (d) A volume mesh is applied to the entire solid model, which is imported into a numerical CFD/FSI simulation. Note: CFD = computational fluid dynamics; FSI = fluid-structure interaction.

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Fig. 3

Resulting arterial trees, reconstructed using different automated and manual techniques from in vivo human volumetric CT scans. Different degrees of fine structure reconstruction are due, in part, to differences in image resolution: [65]-Buelow (voxel dimensions not given); [66] Shikata (0.6 × 0.6 × 1.3 mm); [67] Kaftan (0.6 × 0.6 × 0.6 mm); [68] Dongen (submillimeter, isotropic, but not specified); [69] Ebrahimdoost (0.66 × 0.66 × 1.0 mm); [70] Burrowes (0.68 × 0.68 × 1.4 mm).

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Fig. 4

Vasculature generated by manual segmentation using Mimics. Magnification: example segmentation fault requiring manual intervention. Circled parts show branches that could not be fully segmented due to inadequate image resolution.

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Fig. 5

Wall shear stress distribution of patient-specific pulmonary vasculature, at two levels of segmentation (A and B). The hemodynamics are dependent on the number of tree generations that are segmented and the inlet-to-outlet cross-sectional area ratio. Both simulations are carried out with a zero traction outflow boundary condition. The segmentation with a greater total outlet cross-sectional area (B) develops lower pressure at the inlet and lower velocities in the terminal vessels (not indicated in figure).

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Fig. 6

(a) Region of analysis for the mesh independence convergence study. (b) Mesh independence convergence data for pulmonary vasculature obtained with a commercial solver, Fluent (ANSYS), using steady state inlet plug flow with zero traction outflow boundary conditions. The graph depicts the residual error in the estimated wall shear stress (WSS) as a function of the number of elements in the mesh used for calculation.

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Fig. 7

(a) Inlet waveforms measured for pulmonary vasculature: solid—Henk et al. [129]; dashed—Swan–Ganz balloon tip catheter measurements of normal subject, taken at University of Pittsburgh Medical Center; (b) inlet of typical segmented pulmonary artery and Schwarz–Christoffel (SC) mapping procedure: A unit circle is superimposed onto the inlet. Any point within the domain can be represented as a complex number: R∧ = x+iy, in which the modulus corresponds to the distance from the center of gravity (CG).

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Fig. 8

Outflow boundary conditions applied to pulmonary vascular models. (a) The pure resistance model consists of a single resistor causing a linear relationship between the outlet pressure and flow. (b) The Windkessel models extend the pure resistance model with a compliance term but do not capture fully the complex flow patterns through compliant vascular networks. (c) The structured tree model is a hypothetical reconstruction of the compliant vascular tree distal to each truncated outlet. The pressure-flow relationship at each outlet is calculated by computing the tree impedance. (d) The fluid-structure interaction (FSI) boundary condition is a useful add-on to any FSI simulation, which encompasses all the sophistication of the compliant structured tree.

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Fig. 9

(a) Wall shear stress (WSS) distribution calculated from Tang et al. [40]. (b) Magnification showing nonphysiological stress concentrations arising from uncompensated errors in segmentation using our model, which did not assume cylindrical vessels in the distal arteries but with similar inflow and outflow boundary conditions as used by Tang et al.

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