Skip to main content
SpringerLink
Log in

Non-Newtonian Effects on Patient-Specific Modeling of Fontan Hemodynamics

  • Original Article
  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

The Fontan procedure is a common palliative surgery for congenital single ventricle patients. In silico and in vitro patient-specific modeling approaches are widely utilized to investigate potential improvements of Fontan hemodynamics that are related to long-term complications. However, there is a lack of consensus regarding the use of non-Newtonian rheology, warranting a systematic investigation. This study conducted in silico patient-specific modeling for twelve Fontan patients, using a Newtonian and a non-Newtonian model for each patient. Differences were quantified by examining clinically relevant metrics: indexed power loss (iPL), indexed viscous dissipation rate (iVDR), hepatic flow distribution (HFD), and regions of low wall shear stress (AWSS). Four sets of “non-Newtonian importance factors” were calculated to explore their effectiveness in identifying the non-Newtonian effect. No statistical differences were observed in iPL, iVDR, and HFD between the two models at the population-level, but large inter-patient variations exist. Significant differences were detected regarding AWSS, and its correlations with non-Newtonian importance factors were discussed. Additionally, simulations using the non-Newtonian model were computationally faster than those using the Newtonian model. These findings distinguish good importance factors for identifying non-Newtonian rheology and encourage the use of a non-Newtonian model to assess Fontan hemodynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  1. Anand, M., J. Kwack, and A. Masud. A new generalized Oldroyd-B model for blood flow in complex geometries. Int. J. Eng. Sci. 72:78–88, 2013.

    Google Scholar 

  2. Arzani, A. Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries? J. R. Soc. Interface 15:20180486, 2018.

    PubMed  PubMed Central  Google Scholar 

  3. Avitabile, C. M., D. J. Goldberg, M. B. Leonard, Z. A. Wei, E. Tang, S. M. Paridon, A. P. Yoganathan, M. A. Fogel, and K. K. Whitehead. Leg lean mass correlates with exercise systemic output in young Fontan patients. Heart 104:680–684, 2018.

    CAS  PubMed  Google Scholar 

  4. Aycock, K. I., R. L. Campbell, F. C. Lynch, K. B. Manning, and B. A. Craven. The importance of hemorheology and patient anatomy on the hemodynamics in the inferior vena cava. Ann. Biomed. Eng. 44:3568–3582, 2016.

    PubMed  Google Scholar 

  5. Ballyk, P. D., D. A. Steinman, and C. R. Ethier. Simulation of non-Newtonian blood flow in an end-to-side anastomosis. Biorheology 31:565–586, 1994.

    CAS  PubMed  Google Scholar 

  6. Bernabeu, M. O., R. W. Nash, D. Groen, H. B. Carver, J. Hetherington, T. Kruger, and P. V. Coveney. Impact of blood rheology on wall shear stress in a model of the middle cerebral artery. Interface Focus 3:20120094, 2013.

    PubMed  PubMed Central  Google Scholar 

  7. Bossers, S. S. M., M. Cibis, F. J. Gijsen, M. Schokking, J. L. M. Strengers, R. F. Verhaart, A. Moelker, J. J. Wentzel, and W. A. Helbing. Computational fluid dynamics in Fontan patients to evaluate power loss during simulated exercise. Heart 100:696–701, 2014.

    PubMed  Google Scholar 

  8. Caballero, A. D., and S. Lain. Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta. Comput. Methods Biomech. Biomed. Eng. 18:1200–1216, 2015.

    CAS  Google Scholar 

  9. Castro, M. A., M. C. Ahumada Olivares, C. M. Putman, and J. R. Cebral. Unsteady wall shear stress analysis from image-based computational fluid dynamic aneurysm models under Newtonian and Casson rheological models. Med. Biol. Eng. Comput. 52:827–839, 2014.

    PubMed  Google Scholar 

  10. Cheng, A. L., N. M. Pahlevan, D. G. Rinderknecht, J. C. Wood, and M. Gharib. Experimental investigation of the effect of non-Newtonian behavior of blood flow in the Fontan circulation. Eur. J. Mech. B 68:184–192, 2018.

    Google Scholar 

  11. Cheng, A. L., C. M. Takao, R. B. Wenby, H. J. Meiselman, J. C. Wood, and J. A. Detterich. Elevated low-shear blood viscosity is associated with decreased pulmonary blood flow in children with univentricular heart defects. Pediatr. Cardiol. 37:789–801, 2016.

    PubMed  PubMed Central  Google Scholar 

  12. Chitra, K., T. Sundararajan, S. Vengadesan, and P. Nithiarasu. Non-Newtonian blood flow study in a model cavopulmonary vascular system. Int. J. Numer. Meth. Fluids 66:269–283, 2011.

    Google Scholar 

  13. Cibis, M., K. Jarvis, M. Markl, M. Rose, C. Rigsby, A. J. Barker, and J. J. Wentzel. The effect of resolution on viscous dissipation measured with 4D flow MRI in patients with Fontan circulation: Evaluation using computational fluid dynamics. J. Biomech. 48:2984–2989, 2015.

    PubMed  PubMed Central  Google Scholar 

  14. Corsini, C., C. Baker, A. Baretta, G. Biglino, A. M. Hlavacek, T.-Y. Hsia, E. Kung, A. Marsden, F. Migliavacca, I. Vignon-Clementel, and G. Pennati. Integration of clinical data collected at different times for virtual surgery in single ventricle patients: a case study. Ann. Biomed. Eng. 43:1310–1320, 2014.

    PubMed  Google Scholar 

  15. DeGroff, C. G. Modeling the Fontan circulation: where we are and where we need to go. Pediatr. Cardiol. 29:3–12, 2008.

    CAS  PubMed  Google Scholar 

  16. Doost, S. N., L. Zhong, B. Su, and Y. S. Morsi. The numerical analysis of non-Newtonian blood flow in human patient-specific left ventricle. Comput. Methods Prog. Biomed. 127:232–247, 2015.

    Google Scholar 

  17. Ensley, A. E., P. Lynch, G. P. Chatzimavroudis, C. Lucas, S. Sharma, and A. P. Yoganathan. Toward designing the optimal total cavopulmonary connection: an in vitro study. Ann. Thoracic Surg. 68:1384–1390, 1999.

    CAS  Google Scholar 

  18. Fedorov, A., R. Beichel, J. Kalpathy-Cramer, J. Finet, J. C. Fillion-Robin, S. Pujol, C. Bauer, D. Jennings, F. Fennessy, M. Sonka, J. Buatti, S. Aylward, J. V. Miller, S. Pieper, and R. Kikinis. 3D Slicer as an image computing platform for the Quantitative Imaging Network. Magn. Reson. Imaging 30:1323–1341, 2012.

    PubMed  PubMed Central  Google Scholar 

  19. Good, B. C., S. Deutsch, and K. B. Manning. Hemodynamics in a pediatric ascending aorta using a viscoelastic pediatric blood model. Ann. Biomed. Eng. 44:1019–1035, 2016.

    PubMed  Google Scholar 

  20. Heiberg, E., J. Sjögren, M. Ugander, M. Carlsson, H. Engblom, and H. Arheden. Design and validation of segment - freely available software for cardiovascular image analysis. BMC Med Imaging 10:1, 2010.

    PubMed  PubMed Central  Google Scholar 

  21. Johnston, B. M., P. R. Johnston, S. Corney, and D. Kilpatrick. Non-Newtonian blood flow in human right coronary arteries: steady state simulations. J. Biomech. 37:709–720, 2004.

    PubMed  Google Scholar 

  22. Liu, X., Y. Fan, X. Y. Xu, and X. Deng. Nitric oxide transport in an axisymmetric stenosis. J. R. Soc. Interface 9:2468–2478, 2012.

    CAS  PubMed  PubMed Central  Google Scholar 

  23. Long, C. C., M. Hsu, Y. Bazilevs, J. A. Feinstein, and A. L. Marsden. Fluid–structure interaction simulations of the Fontan procedure using variable wall properties. Int. J. Num. Methods in Biomed. Eng. 28:513–527, 2012.

    CAS  Google Scholar 

  24. Malek, A. M., S. L. Alper, and S. Izumo. Hemodynamic shear stress and its role in atherosclerosis. JAMA 282:2035–2042, 1999.

    CAS  PubMed  Google Scholar 

  25. Marino, B. S., M. Fogel, L. M.-R. Mercer-Rosa, Z. A. W. Wei, P. M. Trusty, M. Tree, E. Tang, M. Restrepo, K. K. Whitehead, S. M. Paridon, and A. Yoganathan. Poor Fontan geometry, hemodynamics, and computational fluid dynamics are associated with worse quality of life. Circulation 25:A18082–A18082, 2017.

    Google Scholar 

  26. Marrero, V. L., J. A. Tichy, O. Sahni, and K. E. Jansen. Numerical study of purely viscous non-Newtonian flow in an abdominal aortic aneurysm. J. Biomech. Eng. 136:101001, 2014.

    PubMed  Google Scholar 

  27. Pennati, G., C. Corsini, D. Cosentino, T. Y. Hsia, V. Luisi, G. Dubini, and F. Migliacca. Boundary conditions of patient-specific fluid dynamics modelling of cavopulmonary connections: possible adaptation of pulmonary resistances results in a critical issue for a virtual surgical planning. Interface Focus 1:297–307, 2009.

    Google Scholar 

  28. Pike, N. A., L. A. Vricella, J. A. Feinstein, M. D. Black, and B. A. Reitz. Regression of severe pulmonary arteriovenous malformations after Fontan revision and “hepatic factor” rerouting. Ann. Thorac. Surg. 78:697–699, 2004.

    PubMed  Google Scholar 

  29. Rijnberg, F. M., M. G. Hazekamp, J. J. Wentzel, P. J. H. de Koning, J. J. M. Westenberg, M. R. M. Jongbloed, N. A. Blom, and A. A. W. Roest. Energetics of blood flow in cardiovascular disease: concept and clinical implications of adverse energetics in patients with a Fontan circulation. Circulation 137:2393–2407, 2018.

    PubMed  Google Scholar 

  30. Robertson, A. M., A. Sequeira, and R. G. Owens. Rheological models for blood. In: Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System, edited by L. Formaggia, A. Quarteroni, and A. Veneziani. Milano: Springer Milan, 2009, pp. 211–241.

    Google Scholar 

  31. Ryu, K., T. M. Healy, A. E. Ensley, S. Sharma, C. Lucas, and A. P. Yoganathan. Importance of accurate geometry in the study of the total cavopulmonary connection: computational simulations and in vitro experiments. Ann. Biomed. Eng. 29:844–853, 2001.

    CAS  PubMed  Google Scholar 

  32. Tang, T. L. E. Effect of Geometry, Respiration and Vessel Deformability on Fontan Hemodynamics: A Numerical Investigation. Atlanta: Georgia Institute of Technology, 2015.

    Google Scholar 

  33. Tang, E., Z. A. Wei, P. M. Trusty, K. K. Whitehead, L. Mirabella, A. Veneziani, M. A. Fogel, and A. P. Yoganathan. The effect of respiration-driven flow waveforms on hemodynamic metrics used in Fontan surgical planning. J. Biomech. 82:87–95, 2019.

    PubMed  Google Scholar 

  34. Tang, E., Z. A. Wei, K. K. Whitehead, R. H. Khiabani, M. Restrepo, L. Mirabella, J. Bethel, S. M. Paridon, B. S. Marino, M. A. Fogel, and A. P. Yoganathan. Effect of Fontan geometry on exercise haemodynamics and its potential implications. Heart 103:1806–1812, 2017.

    PubMed  Google Scholar 

  35. Throckmorton, A. L., S. Lopez-Isaza, and W. Moskowitz. Dual-pump support in the inferior and superior vena cavae of a patient-specific fontan physiology. Artif. Organs 37:513–522, 2013.

    PubMed  Google Scholar 

  36. Tree, M., Z. A. Wei, P. M. Trusty, V. Raghav, M. Fogel, K. Maher, and A. Yoganathan. Using a novel in vitro Fontan model and condition-specific real-time MRI data to examine hemodynamic effects of respiration and exercise. Ann. Biomed. Eng. 46:135–147, 2018.

    PubMed  Google Scholar 

  37. Trusty, P. M., T. C. Slesnick, Z. A. Wei, J. Rossignac, K. R. Kanter, M. A. Fogel, and A. P. Yoganathan. Fontan surgical planning: previous accomplishments, current challenges, and future directions. J. Cardiovasc. Transl. Res. 11:133–144, 2018.

    PubMed  PubMed Central  Google Scholar 

  38. Trusty, P. M., Z. Wei, J. Rychik, A. Graham, P. A. Russo, L. F. Surrey, D. J. Goldberg, A. P. Yoganathan, and M. A. Fogel. Cardiac magnetic resonance derived metrics are predictive of liver fibrosis in fontan patients. Ann. Thorac. Surg. 2019. https://doi.org/10.1016/j.athoracsur.2019.09.070.

    Article  PubMed  Google Scholar 

  39. Trusty, P. M., Z. Wei, J. Rychik, P. A. Russo, L. F. Surrey, D. J. Goldberg, M. A. Fogel, and A. P. Yoganathan. Impact of hemodynamics and fluid energetics on liver fibrosis after Fontan operation. J. Thorac. Cardiovasc. Surg. 156:267–275, 2018.

    PubMed  Google Scholar 

  40. Trusty, P. M., Z. A. Wei, T. C. Slesnick, K. R. Kanter, T. L. Spray, M. A. Fogel, and A. P. Yoganathan. The first cohort of prospective Fontan surgical planning patients with follow-up data: How accurate is surgical planning? J. Thorac. Cardiovasc. Surg. 157:1146–1155, 2019.

    PubMed  Google Scholar 

  41. Trusty, P. M., Z. Wei, M. Tree, K. R. Kanter, M. A. Fogel, A. P. Yoganathan, and T. C. Slesnick. Local hemodynamic differences between commercially available Y-grafts and traditional fontan baffles under simulated exercise conditions: implications for exercise tolerance. Cardiovasc. Eng. Technol. 8:390–399, 2017.

    PubMed  Google Scholar 

  42. Wei, Z. A., C. Huddleston, P. M. Trusty, S. Singh-Gryzbon, M. A. Fogel, A. Veneziani, and A. P. Yoganathan. Analysis of inlet velocity profiles in numerical assessment of Fontan hemodynamics. Ann Biomed Eng 47:2258, 2019.

    PubMed  Google Scholar 

  43. Wei, Z. A., S. J. Sonntag, M. Toma, S. Singh-Gryzbon, and W. Sun. Computational fluid dynamics assessment associated with transcatheter heart valve prostheses: a position paper of the ISO Working Group. Cardiovasc Eng Technol 9:289–299, 2018.

    PubMed  PubMed Central  Google Scholar 

  44. Wei, Z. A., M. Tree, P. M. Trusty, W. Wu, S. Singh-Gryzbon, and A. Yoganathan. The advantages of viscous dissipation rate over simplified power loss as a Fontan hemodynamic metric. Ann. Biomed. Eng. 46:404–416, 2018.

    PubMed  Google Scholar 

  45. Wei, Z. A., P. M. Trusty, M. Tree, C. M. Haggerty, E. Tang, M. Fogel, and A. P. Yoganathan. Can time-averaged flow boundary conditions be used to meet the clinical timeline for Fontan surgical planning? J. Biomech. 50:172–179, 2017.

    PubMed  Google Scholar 

  46. Wei, Z. A., P. M. Trusty, Y. Zhang, E. Tang, K. K. Whitehead, M. A. Fogel, and A. P. Yoganathan. Impact of free-breathing phase-contrast MRI on decision-making in Fontan surgical planning. J. Cardiovasc. Transl. Res. 15:1−8, 2019.

    CAS  Google Scholar 

  47. Wei, Z., K. K. Whitehead, R. H. Khiabani, M. Tree, E. Tang, S. M. Paridon, M. A. Fogel, and A. P. Yoganathan. Respiratory effects on Fontan circulation during rest and exercise using real-time cardiac magnetic resonance imaging. Ann. Thorac. Surg. 101:1818–1825, 2016.

    PubMed  PubMed Central  Google Scholar 

  48. Yang, W., F. P. Chan, V. M. Reddy, A. L. Marsden, and J. A. Feinstein. Flow simulations and validation for the first cohort of patients undergoing the Y-graft Fontan procedure. J. Thorac. Cardiovasc. Surg. 149:247–255, 2015.

    PubMed  Google Scholar 

  49. Yeleswarapu, K. K., M. V. Kameneva, K. R. Rajagopal, and J. F. Antaki. The flow of blood in tubes: theory and experiment. Mech. Res. Commun. 25:257–262, 1998.

    Google Scholar 

Download references

Acknowledgments

This study was supported by the National Heart, Lung, and Blood Institute Grants HL67622 and HL098252. The authors acknowledge the use of ANSYS software which was provided through an Academic Partnership between ANSYS, Inc. and the Cardiovascular Fluid Mechanics Lab at the Georgia Institute of Technology.

Author information

Authors and Affiliations

  1. Wallace H. Coulter School of Biomedical Engineering, Georgia Institute of Technology, 313 Ferst Drive NW, Atlanta, GA, 30332, USA

    Zhenglun Wei, Shelly Singh-Gryzbon, Phillip M. Trusty, Yingnan Zhang & Ajit P. Yoganathan

  2. School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA, USA

    Connor Huddleston

  3. Department of Cardiology, Children’s Hospital of Philadelphia, Philadelphia, PA, USA

    Mark A. Fogel

  4. Department of Mathematics and Computer Science, Emory, Atlanta, GA, USA

    Alessandro Veneziani

Authors
  1. Zhenglun Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shelly Singh-Gryzbon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Phillip M. Trusty
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Connor Huddleston
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yingnan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mark A. Fogel
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Alessandro Veneziani
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ajit P. Yoganathan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ajit P. Yoganathan.

Additional information

Associate Editor Lakshmi Prasad Dasi oversaw the review of this article.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Shelly Singh-Gryzbon and Connor Huddleston—not the current affiliation of the authors. All their work involved in this manuscript was performed when the authors were employees of the Georgia Institute of Technology.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, Z., Singh-Gryzbon, S., Trusty, P.M. et al. Non-Newtonian Effects on Patient-Specific Modeling of Fontan Hemodynamics. Ann Biomed Eng 48, 2204–2217 (2020). https://doi.org/10.1007/s10439-020-02527-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-020-02527-8

Keywords

Search

Navigation