A 4D flow MRI evaluation of the impact of shear-dependent fluid viscosity on in vitro Fontan circulation flow

Abstract

The Fontan procedure for univentricular heart defects creates a nonphysiologic circulation where systemic venous blood drains directly into the pulmonary arteries, leading to multiorgan dysfunction secondary to chronic low-shear nonpulsatile pulmonary blood flow and central venous hypertension. Although blood viscosity increases exponentially in this low-shear environment, the role of shear-dependent ("non-Newtonian") blood viscosity in this pathophysiology is unclear. We studied three-dimensional (3D)-printed Fontan models in an in vitro flow loop with a Philips 3-T magnetic resonance imaging (MRI) scanner. A 4D flow phase-contrast sequence was used to acquire a time-varying 3D velocity field for each experimental condition. On the basis of blood viscosity of a cohort of patients who had undergone the Fontan procedure, it was decided to use 0.04% xanthan gum as a non-Newtonian blood analog; 45% glycerol was used as a Newtonian control fluid. MRI data were analyzed using GTFlow and MATLAB software. The primary outcome, power loss, was significantly higher with the Newtonian fluid [14.8 (13.3, 16.4) vs. 8.1 (6.4, 9.8)%, medians with 95% confidence interval, P < 0.0001]. The Newtonian fluid also demonstrated marginally higher right pulmonary artery flow, marginally lower shear stress, and a trend toward higher caval flow mixing. Outcomes were modulated by Fontan model complexity, cardiac output, and caval flow ratio. Vortexes, helical flow, and stagnant flow were more prevalent with the non-Newtonian fluid. Our data demonstrate that shear-dependent viscosity significantly alters qualitative flow patterns, power loss, pulmonary flow distribution, shear stress, and caval flow mixing in synthetic models of the Fontan circulation. Potential clinical implications include effects on exercise capacity, ventilation-perfusion matching, risk of pulmonary arteriovenous malformations, and risk of thromboembolism.NEW & NOTEWORTHY Although blood viscosity increases exponentially in low-shear environments, the role of shear-dependent ("non-Newtonian") blood viscosity in the pathophysiology of the low-shear Fontan circulation is unclear. We demonstrate that shear-dependent viscosity significantly alters qualitative flow patterns, power loss, pulmonary flow distribution, shear stress, and caval flow mixing in synthetic models of the Fontan circulation. Potential clinical implications include effects on exercise capacity, ventilation-perfusion matching, risk of pulmonary arteriovenous malformations, and risk of thromboembolism.

Keywords: Fontan procedure; cardiac magnetic resonance imaging; fluid dynamics; rheology; single ventricle.

Fig. 1.

Relationship between viscosity, shear rate, and shear stress for a Newtonian fluid vs. a shear-thinning non-Newtonian fluid with the same asymptotic viscosity. Blood viscosity increases exponentially at shear rates <100 s⁻¹ and is essentially constant (Newtonian) at shear rates above 100–200 s⁻¹ (6). Shaded boxes indicate typical ranges of mean shear stress and shear rate in veins and arteries (8, 27, 31).

Fig. 2.

Viscosity characteristics of the experimental (xanthan gum) and control (glycerol) fluids. Herschel-Bulkley and Casson fluid models were used to interpolate between data points for xanthan gum. Standard deviation bars are shown for the Fontan cohort.

Fig. 3.

Three-dimensional printed models of the total cavopulmonary connection. The superior vena cava [SVC, right superior vena cava (RSVC), and left superior vena cava (LSVC)], inferior vena cava (IVC), azygous vein (Azy), and hepatic veins (Hep) are inlets. The right and left pulmonary arteries (RPA and LPA, respectively) are outlets.

Fig. 4.

Schematic of circulatory flow loop. MRI, magnetic resonance imaging; TCPC, total cavopulmonary connection.

Fig. 5.

Flow patterns in the simplified symmetric total cavopulmonary connection model (simple model). Flow is illustrated by pathlines, lines that dye or particles injected into the velocity field would follow over time. Red pathlines originate from the inferior vena cava. Blue pathlines originate from the superior vena cava. Arrows indicate inferior vena cava pathlines crossing midline to the right pulmonary artery. Flow patterns of the Newtonian and non-Newtonian fluid are not significantly different under any of the experimental conditions. IVC, inferior vena cava; SVC, superior vena cava.

Fig. 6.

Flow patterns in the total cavopulmonary connection model of a typical patient who had undergone the Fontan procedure (typical model). Flow is illustrated by pathlines, lines that dye or particles injected into the velocity field would follow over time. Red pathlines originate from the inferior vena cava. Blue pathlines originate from the superior vena cava. Overall flow patterns are similar between the two fluids under all conditions; however, insets highlight differences in the inferior vena cava flow patterns between the two solutions. Arrows indicate helical secondary flow seen only with the non-Newtonian fluid in the left pulmonary artery. IVC, inferior vena cava; LPA, left pulmonary artery; RPA, right pulmonary artery; SVC, superior vena cava.

Fig. 7.

Flow patterns in the total cavopulmonary connection model of a patient with heterotaxy syndrome who had undergone the Fontan procedure (complex model). Flow is illustrated by pathlines, lines that dye or particles injected into the velocity field would follow over time. Red pathlines originate from the hepatic veins. Green pathlines originate from the azygous vein. Aqua pathlines originate from the right superior vena cava. Blue pathlines originate from the left superior vena cava. Under all experimental conditions, helical secondary flows are seen with the non-Newtonian fluid but not with the Newtonian fluid. Vortexes are also present in the mid-pulmonary artery segment in both low-cardiac output conditions with the non-Newtonian fluid but not with the Newtonian fluid. Azy, azygous vein; H, helical flow; Hep, conduit from hepatic veins; IVC, inferior vena cava; LPA, left pulmonary artery; LSVC, left superior vena cava; RPA, right pulmonary artery; RSVC, right superior vena cava; SVC, superior vena cava; V, vortex.

Fig. 8.

Comparison of power loss between the Newtonian and non-Newtonian fluids. A: percent power loss. B: indexed power loss. Here, n = 50 samples for each experimental condition. Data are shown as medians with interquartile range (whiskers extend to 1.5 times interquartile range). Statistical analysis was by Mood’s median test followed by Bonferroni multiple comparison test.

Fig. 9.

Comparison of right pulmonary artery (RPA) flow between the Newtonian and non-Newtonian fluids. A: percent RPA flow. B: indexed RPA flow. Here, n = 50 samples for each experimental condition. Data are shown as medians with interquartile range (whiskers extend to 1.5 times interquartile range). Statistical analysis was by Mood’s median test followed by Bonferroni multiple comparison test. NS, nonsignificant P value (>0.05).

Fig. 10.

Comparison of caval flow mixing between the Newtonian and non-Newtonian fluids. Here, n = 5 samples for each experimental condition. Data are shown as medians with interquartile range (whiskers extend to 1.5 times interquartile range). Statistical analysis was by Mood’s median test. The Bonferroni method did not yield a converging solution for this analysis. Therefore, as an alternative means of correcting for multiple comparisons, we adjusted the threshold for significance by the number of experimental conditions (i.e., P values < 0.05/12 = 0.0042 were considered significant for this analysis). NS, nonsignificant P value.