Evaluating Newtonian and Non-Newtonian Blood Flow Assumptions in Computational Modeling of Extracardiac Fontan Conduits for Pediatric Single Ventricle Heart Disease

Background: The extracardiac Fontan procedure is a key surgical strategy for children with single ventricle heart disease, redirecting systemic venous return directly to the pulmonary arteries. Optimizing conduit geometry is crucial for minimizing energy loss, balancing hepatic blood flow to both lungs, and reducing central venous pressure. Computational fluid dynamics (CFD) is increasingly used for patient-specific design optimization, yet most simulations assume Newtonian blood flow for simplicity. This neglects the shear-dependent viscosity captured in non-Newtonian models, which may alter predicted hemodynamics. We investigated the impact of Newtonian versus non-Newtonian assumptions on blood flow distribution and average wall shear stress in patients post-Fontan procedure.

Methods: 15 patients (7 male; median age 18 [8–32] years) who had undergone Fontan operations and were referred for cardiovascular magnetic resonance (CMR) to monitor the Fontan pathway, cardiac function, and blood flow circulation were included in this retrospective study. Three-dimensional (3D) magnetic resonance angiography images were used to reconstruct the Fontan pathway (Figure 1a). 2D phase-contrast images were acquired to measure inlet blood flow at the inferior vena cava (IVC) and the superior vena cava (SVC), as well as outlet blood flow at the right and left pulmonary arteries (RPA and LPA). CFD simulations assessed the proportion of IVC and SVC blood flow directed to each lung (Figure 1b), and the average wall shear stress experienced by the cardiac system, using both Newtonian and non-Newtonian assumptions. The estimated blood flow distribution and the average wall shear stress were then compared between the two modeling approaches.

Results: Table 1 presents the comparison of IVC and SVC blood flow distribution to the LPA and RPA from CFD simulations under the two modeling assumptions. A t-test of the results found only significant statistical (p< 0.05) differences between the two models for the right SVC to LPA blood flow. Table 2 presents the comparison of the average wall shear stress calculated using the two different models.

Conclusion: This study demonstrates that the choice of rheological assumption in CFD analysis can substantially impact the average wall shear stress in the cardiac system. It can also have a noticeable effect on the estimated IVC and SVC blood flow distribution to the LPA and RPA. Our results show a statistically significant (p< 0.001) mean difference of about 63% between the average wall shear stress reported by the Newtonian and non-Newtonian models. Additionally, large variations in blood flow distributions exist across the various cases when comparing the Newtonian and non-Newtonian models. These findings support the consideration of non-Newtonian assumptions in CFD-based surgical planning for extracardiac Fontan conduits in single ventricle patients. Future work will compare and validate non-Newtonian CFD results with in vivo measurements obtained from 4D flow CMR.

Comparison of IVC and SVC Blood Flow Distribution to the LPA and RPA from Computational Fluid Dynamics using Newtonian and Non-Newtonian Assumptions

Cases	Newtonian						Non-Newtonian
	LPA (Mass Flow Fraction)			RPA (Mass Flow Fraction)			LPA (Mass Flow Fraction)			RPA (Mass Flow Fraction)
	IVC	SVC-L	SVC-R	IVC	SVC-L	SVC-R	IVC	SVC-L	SVC-R	IVC	SVC-L	SVC-R
1	0.6180	0.2617	0.1203	0.5988	0.1626	0.2386	0.5011	0.4797	0.0192	0.6505	0.0757	0.2738
2	0.5283	0.2359	0.2358	0.9997	0.0001	0.0002	0.6039	0.1981	0.1981	0.9997	0.0002	0.0002
3	0.6767	0.2162	0.1071	0.2841	0.4787	0.2371	0.9861	0.0093	0.0046	0.1381	0.5764	0.2855
4	0.1432	0.5554	0.3014	0.7769	0.0772	0.1458	0.1072	0.5887	0.3040	0.8639	0.0090	0.1271
5	0.6700	0.0811	0.2489	0.5658	0.2712	0.1630	0.4479	0.0948	0.4574	0.6464	0.2222	0.1314
6	0.2954	0.4358	0.2688	0.7924	0.0277	0.1799	0.4050	0.4409	0.1540	0.6748	0.0487	0.2764
7	0.7550	0.1202	0.1248	0.8312	0.0871	0.0817	0.7886	0.1474	0.0640	0.7935	0.0004	0.2061
8	0.9917	0.0003	0.0080	0.4628	0.2760	0.2612	0.9773	0.0003	0.0224	0.5649	0.2338	0.2013
9	0.0390	0.7971	0.1639	0.7942	0.0970	0.1088	0.0224	0.9732	0.0045	0.8053	0.0815	0.1132
10	0.6275	0.1720	0.2005	0.7840	0.1213	0.0947	0.9286	0.0372	0.0341	0.4463	0.2750	0.2787
11	0.9934	0.0062	0.0004	0.4964	0.2497	0.2539	0.9339	0.0655	0.0006	0.6124	0.1810	0.2065
12	0.2792	0.2922	0.4286	0.9192	0.0477	0.0331	0.3259	0.4683	0.2058	0.9437	0.0068	0.0495
13	0.4927	0.1348	0.3725	0.7492	0.1451	0.1057	0.6788	0.2597	0.0615	0.7245	0.1034	0.1721
14	0.5038	0.3134	0.1828	0.8879	0.0315	0.0806	0.7421	0.0847	0.1732	0.7961	0.1162	0.0877
15	0.4953	0.2501	0.2546	0.9577	0.0352	0.0071	0.5741	0.2802	0.1457	0.5047	0.0009	0.4944
Mean	0.541	0.258	0.201	0.727	0.141	0.133	0.602	0.275	0.123	0.678	0.129	0.194
Std	0.273	0.210	0.120	0.203	0.130	0.088	0.304	0.271	0.131	0.215	0.155	0.121
p	0.140	0.624	0.025	0.262	0.534	0.103

Comparison of Average Wall Shear Stress Calculated from Computational Fluid Dynamics using Newtonian and Non-Newtonian Assumptions

Cases	Newtonian	Non-Newtonian	Difference [100*(NN-N)/NN] (%)
	WSSavg (Pa)	WSSavg (Pa)
1	0.335	1.201	72.07
2	0.680	1.816	62.55
3	0.305	0.969	68.56
4	1.000	2.134	53.15
5	1.199	2.720	55.93
6	0.392	1.420	72.38
7	0.378	1.139	66.83
8	0.495	1.471	66.35
9	0.981	2.186	55.14
10	0.616	1.963	68.60
11	0.466	1.532	69.62
12	0.762	1.394	45.32
13	0.137	0.563	75.68
14	0.430	1.492	71.16
15	0.256	0.936	72.61
Mean	0.562	1.529	63.24
Std	0.306	0.559	8.78
p	4.56e-9

a) 3D mesh model of the extracardiac Fontan pathway generated from segmented MR angiography images. Phase-contrast MRI quantified blood flow at the inferior vena cava (IVC), superior vena cava (SVC), right pulmonary artery (RPA), and left pulmonary artery (LPA). b) Computational fluid dynamics (CFD) assessed blood flow distribution for non-Newtonian case.