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

## 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.

## Keywords

Fontan hemodynamics Flow Efficiency Power loss Viscous dissipation## Notes

### 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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