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The Advantages of Viscous Dissipation Rate over Simplified Power Loss as a Fontan Hemodynamic Metric

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Abstract

Flow efficiency through the Fontan connection is an important factor related to patient outcomes. It can be quantified using either a simplified power loss or a viscous dissipation rate metric. Though practically equivalent in simplified Fontan circulation models, these metrics are not identical. Investigation is needed to evaluate the advantages and disadvantages of these metrics for their use in in vivo or more physiologically-accurate Fontan modeling. Thus, simplified power loss and viscous dissipation rate are compared theoretically, computationally, and statistically in this study. Theoretical analysis was employed to assess the assumptions made for each metric and its clinical calculability. Computational simulations were then performed to obtain these two metrics. The results showed that apparent simplified power loss was always greater than the viscous dissipation rate for each patient. This discrepancy can be attributed to the assumptions derived in theoretical analysis. Their effects were also deliberately quantified in this study. Furthermore, statistical analysis was conducted to assess the correlation between the two metrics. Viscous dissipation rate and its indexed quantity show significant, strong, linear correlation to simplified power loss and its indexed quantity (p < 0.001, r > 0.99) under certain assumptions. In conclusion, viscous dissipation rate was found to be more advantageous than simplified power loss as a hemodynamic metric because of its lack of limiting assumptions and calculability in the clinic. Moreover, in addition to providing a time-averaged bulk measurement like simplified power loss, viscous dissipation rate has spatial distribution contours and time-resolved values that may provide additional clinical insight. Finally, viscous dissipation rate could maintain the relationship between Fontan connection flow efficiency and patient outcomes found in previous studies. Consequently, future Fontan hemodynamic studies should calculate both simplified power loss and viscous dissipation rate to maintain ties to previous studies, but also provide the most accurate measure of flow efficiency. Additional attention should be paid to the assumptions required for each metric.

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References

  1. Bakhshinejad, A., A. Baghaie, A. Vali, D. Saloner, V. L. Rayz, and R. M. D’Souza. Merging computational fluid dynamics and 4D flow MRI using proper orthogonal decomposition and ridge regression. J. Biomech 2017. https://doi.org/10.1016/j.jbiomech.2017.05.004.

    PubMed  Google Scholar 

  2. Bland, J. M., and D. G. Altman. Measuring agreement in method comparison studies. Stat. Methods Med. Res 8:135–160, 1999.

    Article  CAS  PubMed  Google Scholar 

  3. Chandran, K. B., S. E. Rittgers, and A. P. Yoganathan. Biofluid Mechanics: The Human Circulation. CRC Press, Taylor & Francis Group, 2012, p. 431. https://www.crcpress.com/Biofluid-Mechanics-The-Human-Circulation-Second-Edition/Chandran-Rittgers-Yoganathan/p/book/9781439845165.

  4. 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.

    Article  PubMed  PubMed Central  Google Scholar 

  5. Chopski, S. G., O. M. Rangus, W. B. Moskowitz, and A. L. Throckmorton. Experimental measurements of energy augmentation for mechanical circulatory assistance in a patient-specific fontan model. Artif. Organs 38:791–799, 2014.

    PubMed  Google Scholar 

  6. 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.

    Article  PubMed  PubMed Central  Google Scholar 

  7. Dasi, L. P., K. Pekkan, H. D. Katajima, and A. P. Yoganathan. Functional analysis of Fontan energy dissipation. J. Biomech. 41:2246–2252, 2008.

    Article  PubMed  Google Scholar 

  8. Dubini, G., M. R. de Leval, R. Pietrabissa, F. M. Montevecchi, and R. Fumero. A numerical fluid mechanical study of repaired congenital heart defects. Application to the total cavopulmonary connection. J. Biomech. 29:111–121, 1996.

    Article  CAS  PubMed  Google Scholar 

  9. 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. Thorac. Surg. 68:1384–1390, 1999.

    Article  CAS  PubMed  Google Scholar 

  10. Fung, Y. C. Biomechanics: Circulation. New York: Springer, 1997.

    Book  Google Scholar 

  11. Grigioni, M., G. D. Avenio, C. Del Gaudio, and U. Morbiducci. Critical issues in studies of flow through the Fontan circuit after 10 years of investigation. Cardiol. Young 15:68–73, 2005.

    Article  PubMed  Google Scholar 

  12. Ha, H., G. B. Kim, J. Kweon, S. J. Lee, Y.-H. Kim, D. H. Lee, D. H. Yang, and N. Kim. Hemodynamic measurement using four-dimensional phase-contrast MRI: Quantification of hemodynamic parameters and clinical applications. Korean J. Radiol. 17:445, 2016.

    Article  PubMed  PubMed Central  Google Scholar 

  13. Haggerty, C. M., M. Restrepo, E. Tang, D. A. de Zélicourt, K. S. Sundareswaran, L. Mirabella, J. Bethel, K. K. Whitehead, M. A. Fogel, and A. P. Yoganathan. Fontan hemodynamics from 100 patient-specific cardiac magnetic resonance studies: A computational fluid dynamics analysis. J. Thorac. Cardiovasc. Surg. 148:1481–1489, 2014.

    Article  PubMed  Google Scholar 

  14. Haggerty, C. M., K. K. Whitehead, J. Bethel, M. A. Fogel, and A. P. Yoganathan. Relationship of single ventricle filling and preload to total cavopulmonary connection hemodynamics. Ann. Thorac. Surg. 99:911–917, 2015.

    Article  PubMed  PubMed Central  Google Scholar 

  15. Healy, T. M., C. Lucas, and A. P. Yoganathan. Noninvasive fluid dynamic power loss assessments for total cavopulmonary connections using the viscous dissipation function: A feasibility study. J. Biomech. Eng. 123:317, 2001.

    Article  CAS  PubMed  Google Scholar 

  16. 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.

    Article  PubMed  Google Scholar 

  17. Khiabani, R. H., K. K. Whitehead, D. Han, M. Restrepo, E. Tang, J. Bethel, S. M. Paridon, M. A. Fogel, and A. P. Yoganathan. Exercise capacity in single-ventricle patients after Fontan correlates with haemodynamic energy loss in TCPC. Heart 101:139–143, 2015.

    Article  PubMed  Google Scholar 

  18. Lardo, A. C., S. A. Webber, I. Friehs, P. J. Del Nido, and E. G. Cape. Fluid dynamic comparison of intra-atrial and extracardiac total cavopulmonary connections. J. Thorac. Cardiovasc. Surg. 117:697–704, 1999.

    Article  CAS  PubMed  Google Scholar 

  19. Long, C. C., M.-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. Numer. Method. Biomed. Eng. 28:513–527, 2012.

    Article  CAS  PubMed  Google Scholar 

  20. Low, H. T. T., Y. T. T. Chew, and C. N. N. Lee. Flow studies on atriopulmonary and cavopulmonary connections of the Fontan operations for congenital heart defects. J. Biomed. Eng. 15:303–307, 1993.

    Article  CAS  PubMed  Google Scholar 

  21. Moyle, K., G. Mallinson, and B. Cowan. Volumetric methods for evaluating irreversible energy losses and entropy production with application to bioengineering flows. Int. J. Numer. Methods Fluids 50:1357–1368, 2006.

    Article  Google Scholar 

  22. Munson, B. R., D. F. Young, and T. H. Okiishi. Fundamentals of Fluid Mechanics. New York: Wiley, 2006.

    Google Scholar 

  23. Restrepo, M., M. Luffel, J. Sebring, K. R. Kanter, P. J. Del Nido, A. Veneziani, J. Rossignac, and A. P. Yoganathan. Surgical planning of the total cavopulmonary connection: robustness analysis. Ann. Biomed. Eng. 2014. https://doi.org/10.1007/s10439-014-1149-7.

    PubMed  PubMed Central  Google Scholar 

  24. Restrepo, M., E. Tang, C. M. Haggerty, R. H. Khiabani, L. Mirabella, J. Bethel, A. M. Valente, K. K. Whitehead, D. B. McElhinney, M. A. Fogel, and A. P. Yoganathan. Energetic implications of vessel growth and flow changes over time in fontan patients. Ann. Thorac. Surg. 99:163–170, 2015.

    Article  PubMed  Google Scholar 

  25. Santhanakrishnan, A., K. O. Maher, E. Tang, R. H. Khiabani, J. Johnson, and A. P. Yoganathan. Hemodynamic effects of implanting a unidirectional valve in the inferior vena cava of the Fontan circulation pathway: An in vitro investigation. Am. J. Physiol Heart. Circ. Physiol. 305:H1538–H1547, 2013.

    Article  CAS  PubMed  Google Scholar 

  26. Soerensen, D. D., K. Pekkan, K. S. Sundareswaran, and A. P. Yoganathan. New power loss optimized Fontan connection evaluated by calculation of power loss using high resolution PC-MRI and CFD. Conf. Proc. IEEE Eng. Med. Biol. Soc. 2:1144–1147, 2004.

    CAS  PubMed  Google Scholar 

  27. Tang, E., M. Restrepo, C. M. Haggerty, L. Mirabella, J. Bethel, K. K. Whitehead, M. A. Fogel, and A. P. Yoganathan. Geometric characterization of patient-specific total cavopulmonary connections and its relationship to hemodynamics. JACC Cardiovasc. Imaging 7:215–224, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  28. Tang, E., Z. 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 2017. https://doi.org/10.1136/heartjnl-2016-310855.

    Google Scholar 

  29. Volonghi, P., D. Tresoldi, M. Cadioli, A. M. Usuelli, R. Ponzini, U. Morbiducci, A. Esposito, and G. Rizzo. Automatic extraction of three-dimensional thoracic aorta geometric model from phase contrast MRI for morphometric and hemodynamic characterization. Magn. Reson. Med. 882:873–882, 2016.

    Article  Google Scholar 

  30. Vukicevic, M., T. A. Conover, M. Jaeggli, J. Zhou, G. Pennati, T.-Y. T. Hsia, and R. S. Figliola. Control of respiration-driven retrograde flow in the subdiaphragmatic venous return of the Fontan circulation. ASAIO J. 60:21–23, 2014.

    Article  Google Scholar 

  31. Wang, C., K. Pekkan, D. de Zélicourt, M. Horner, A. Parihar, A. Kulkarni, and A. P. Yoganathan. Progress in the CFD modeling of flow instabilities in anatomical total cavopulmonary connections. Ann. Biomed. Eng. 35:1840–1856, 2007.

    Article  PubMed  Google Scholar 

  32. 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.

    Article  PubMed  Google Scholar 

  33. 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.

    Article  PubMed  PubMed Central  Google Scholar 

  34. Whitehead, K. K., K. Pekkan, H. D. Kitajima, S. M. Paridon, A. P. Yoganathan, and M. A. Fogel. Nonlinear power loss during exercise in single-ventricle patients after the Fontan: Insights from computational fluid dynamics. Circulation 116:I-165–I-171, 2000.

    Google Scholar 

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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. Additionally, the authors would like to acknowledge Luyu Zhang from Emory University for assistance in statistical analysis.

Conflict of interest

The authors report no conflicts of interest.

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Authors and Affiliations

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

    Zhenglun Alan Wei, Phillip M. Trusty, Wenjun Wu, Shelly Singh-Gryzbon & Ajit Yoganathan

  2. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael Tree

  3. Institute of Computational Science and Cardiovascular Disease, Nanjing Medical University, Nanjing, China

    Zhenglun Alan Wei

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  1. Zhenglun Alan Wei
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  2. Michael Tree
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Correspondence to Ajit Yoganathan.

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Associate Editor Peter E. McHugh oversaw the review of this article.

Appendix

Appendix

See Table 2.

Table 2 Details for Table 1: time-averaged viscous dissipation rate, power loss, and analyses of assumptions 2,3, and 5.
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Wei, Z.A., Tree, M., Trusty, P.M. et al. The Advantages of Viscous Dissipation Rate over Simplified Power Loss as a Fontan Hemodynamic Metric. Ann Biomed Eng 46, 404–416 (2018). https://doi.org/10.1007/s10439-017-1950-1

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  • DOI: https://doi.org/10.1007/s10439-017-1950-1

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