Validation of computational fluid dynamics-based analysis to evaluate hemodynamic significance of access stenosis

INTRODUCTION

Stenoses are the major cause for access dysfunction necessitating repeated interventions and often result in access failure. The stenoses in arteriovenous fistulae (AVFs) can be present days, months or years after their creation. The effect of stenosis on access flow depends on their location within the access circuit (in arterial, juxta-anastomotic, outflow vein or central vein), the percentage of luminal diameter affected and their length. While stenoses closer to the anastomosis tend to be flow limiting, stenoses in the outflow vein result in increased intra-access pressure and pressure-related problems. Based on their hemodynamic significance, stenosis may manifest as varied clinical symptoms and may interfere with dialysis delivery. While not all stenoses interfere with the delivery of dialysis prescription, the current vascular access management guidelines for stenosis recommend angioplasty for stenosis >50% (1). There are no reliable tools that can assess the hemodynamic significance of a specific vascular access stenosis at a given location with a given severity in an individual vascular access circuit.

Duplex Doppler Ultrasound (DDUS) has evolved as an effective tool which can provide structural definition of stenosis in the peripheral veins in the fistula outflow circuit (2). It also provides very reliable information on the functional impact of the stenosis (3). Recently, ultrasound assessment of the AVF has been validated with computational fluid dynamics (CFD) analysis (4, 5). However, hemodynamic evaluation of an AVF using ultrasound is neither routinely practiced nor is available in most interventional suites.

CFD analysis has been used extensively to evaluate blood flow pattern and hemodynamic parameters in AVF and other anatomical and surgically created vascular connections (6-7-8-9). CFD analysis can model blood flow through any anatomical model. We have used CFD to model an AV access circuit with the intention of improving our understanding of hemodynamic implications of stenosis.

In this study, we report our findings on the effect of various ranges of stenosis on hemodynamics of AVF using a CFD model and its reproducibility. We also report the validation of the CFD results using DDUS evaluation of patients with AVF stenosis by comparing the parameters in DDUS and CFD.

MATERIALS AND METHODS

Single stenosis vascular models were designed to have a typical AVF diameter with a stenosis of varying diameter within the middle of the fistula. This model does not address stenoses that may be near the anastomosis or elsewhere. The stenoses models were created in 3D computer-aided drafting program SolidWorks (Dassault Systems SolidWorks Corp, Waltham, MA). The stenosis diameter of the models varied from 1.0 to 3.0 mm in 0.5 mm increments. The length of the stenoses was varied from 5.0 to 60 mm in 5.0 mm increments. The diameter of the model AVF was 7 mm for stenoses of 1.0 to 2.5 mm diameter and 8 mm for the 3.0 mm diameter stenosis. The diameter and lengths of the stenoses reflect the range of stenoses observed clinically.

CFD analyses of the stenoses models were performed in FloWorks (which is a part of the SolidWorks) using the geometric models created in SolidWorks. A mesh inside the models was first created which contained 16,470 complete cells and 6,888 partial cells. The CFD solution converged to a six order of magnitude reduction in residuals in 69 iterations using the FloWorks solver. In the calculation, blood was treated as a non-Newtonian Fluid described by a power-law model with consistency coefficient of 0.012171 PA, and maximum dynamic viscosity of 0.012171 Pa, minimum dynamic viscosity of 0.003038269 Pa and a power-law index of 0.7991 (defined in SolidWorks).

In the analysis, the outlet pressure of the fistula was set at 10 mmHg to reflect a typical central venous pressure. The mean inlet pressure was varied from 50 to 160 mmHg to model the flows over a wide range of potential systemic pressures (encountered during dialysis treatment). A mean pressure was used for the analysis without pulsatile effects. Over the range of inlet pressures, the flow rates through the stenoses of varying diameter and lengths were calculated. The CFD analysis also provides details of velocity, pressure and shear stress variations resulting from the stenosis. The results have been organized into tables for each stenosis diameter with flow rates calculated for given inlet pressures and stenosis lengths.

Considering all of the stenoses diameters, lengths and inlet pressures, computations of all the cases would have resulted in over 1,000 CFD analyses. To reduce the number of calculations, the CFD analyses were performed for each stenosis diameter for lengths of 5, 30, 45 and 60 mm with mean inlet pressures of 50, 70, 100, 130 and 160 mmHg. The increase in flow rate due to increase in the inlet pressure was found to be linear; therefore, the flow rates for the intermediate inlet pressures could be obtained by simple interpolation. The flow rates for the remainder of the stenosis lengths were calculated as a best fit logarithmic equation using Excel (Microsoft, Redmond, WA).

It was expected that the diameter of the AVF would not significantly impact the measured flow rate but the stenosis would be the dominant constituent influencing the flow rates. Thus, the results presented in this paper should be applicable to any diameter of AVF for a particular stenosis diameter and length and the corresponding blood pressure. To investigate the effect of a different size AVF on the flow rate, CFD sensitivity analyses of 1 mm diameter and 30 mm long stenosis within an AVF of 4 to 9 mm diameter in 1 mm increments were performed. The inlet pressure ranged from 50 to 160 mmHg and the outlet pressure was fixed at 10 mmHg.

The results of the CFD analyses were validated by comparisons with patient-specific data. Eight patients with AVFs with single outflow vein stenosis were evaluated by ultrasound. The fistula stenosis was imaged and the dimensions were obtained from the ultrasound images which included the stenosis diameter, stenosis length and the fistula diameter. Fistula flow was determined by DDUS evaluation of the brachial artery. No anastomotic or juxta-anastomotic stenoses were included. For the eight patients, geometric models of their stenoses were created in SolidWorks and the CFD analyses were conducted using patient-specific blood pressure measurements for the inlet pressure obtained at the time of ultrasound with estimated fistula outlet pressure of 10 mmHg. The resulting calculated flow rates from the CFD analyses were compared to the flow rates measured by the ultrasound using the coefficient of determination.

To confirm the results obtained with SolidWorks, the CFD results were also computed using Fluent (ANSYS, Canonsburg, PA). The flow field simulation results obtained using these two different systems were compared to assess their reproducibility.

RESULTS

The axisymmetric geometric model created in SolidWorks for the flow field analysis is shown in Figure 1. CFD calculations derived from using both SolidWorks and Fluent for a stenosis of diameter 2 mm and length 30 mm for various mean inlet pressures are shown in Figure 2. The results show excellent agreement between the results from SolidWorks and Fluent. Figure 3 shows the velocity and shear stress plots in three typical stenosis models. The calculated blood flow rates for a fistula with a mean inlet blood pressure of 100 mmHg with stenosis length of 5, 30 or 60 mm for a range of stenosis diameters are shown in Figure 4.

Fig. 1 - Fig. 2 -Fig. 3 -Fig. 4 -

For each stenosis diameter, the flow rates were calculated for several stenosis lengths for a range of blood pressures; the flow rates for other cases were computed by interpolation using a best fitting logarithmic equation. The R² values (Pearson) for these equations ranged from 0.9952 to 1 demonstrating excellent correlation. Table I provides the flow rates for a 2 mm stenosis of various lengths at a given mean pressure. A more detailed table with flow rates at different pressures and differing lengths may be found online (Table 1s).

TABLE I -

Axisymmetric model of arteriovenous fistula stenosis. A) Wireframe model. B) Isometric half-view of the model.

Comparison of computational fluid dynamics results from FloWorks (red line) and Fluent (blue line) for a stenosis of diameter 2 mm and length 30 mm.

Shear stress distribution in the model of Figure 1 using computation. A) The scale for shear stress distribution. B) Shear stress distribution in a 1.5 mm diameter, 2 cm length stenosis with 90 mmHg mean arterial pressure. C) Shear stress distribution in 2.0 mm diameter, 2 cm length stenosis with 90 mmHg mean arterial pressure. D) Shear stress distribution in a 2.5 mm diameter, 2 cm length stenosis with 90 mmHg mean arterial pressure.

Variation in calculated flow rate in a fistula with a mean inlet blood pressure of 100 mmHg with stenosis diameter for stenosis lengths of 5, 30 or 60 mm.

CALCULATED FLOW RATE IN ARTERIAL VENOUS FISTULA STENOSIS FOR GIVEN MEAN ARTERIAL PRESSURE AND STENOSIS LENGTH FOR FISTULA STENOSIS DIAMETERS OF A) 1.5 MM, B) 2.0 MM, C) 2.5 MM, AND D) 3.0 MM

A. 1.5 mm diameter stenosis
	Stenosis Length (mm)
Mean Inlet Pressure (mmHg)	5	10	15	20	25	30	35	40	45	50	55	60
50	301	259	234	217	203	192	183	175	167	161	155	150
60	340	294	267	248	233	221	211	202	194	187	181	175
70	378	329	300	279	263	250	239	229	221	213	206	200
80	411	358	327	305	288	274	262	252	243	235	228	221
90	443	387	354	331	313	298	286	275	265	257	249	242
100	475	416	382	357	338	322	309	298	288	279	271	263
110	504	442	406	380	360	344	330	318	307	298	289	282
120	532	467	430	403	382	365	350	338	327	317	308	300
130	561	493	454	426	404	386	371	358	346	336	327	318
140	588	517	476	447	424	406	390	376	364	354	344	335
150	615	542	499	468	444	425	409	395	382	371	361	352
160	642	566	521	489	465	445	428	413	400	388	378	368
B. 2.0 mm diameter stenosis
50	626	543	495	460	434	412	394	378	364	351	340	329
60	720	625	570	530	500	475	454	436	420	405	392	380
70	814	707	645	600	566	538	514	494	476	459	445	431
80	896	779	710	661	624	593	567	544	524	506	490	475
90	978	850	775	722	681	647	619	594	573	553	536	519
100	1060	922	841	783	739	702	671	645	621	600	581	564
110	1134	986	899	838	790	751	718	689	664	642	621	603
120	1207	1050	957	892	841	800	765	734	708	684	662	642
130	1281	1114	1016	946	893	849	811	779	751	725	702	681
140	1344	1170	1068	996	939	894	855	821	792	765	741	719
150	1407	1226	1120	1045	986	939	898	863	833	805	780	757
160	1471	1282	1172	1094	1033	984	942	905	873	845	819	795
C. 2.5 mm diameter stenosis
50	1027	904	831	780	741	708	681	657	636	617	600	585
60	1183	1039	955	895	849	811	779	751	727	705	685	667
70	1340	1175	1078	1010	957	914	877	845	817	792	769	749
80	1445	1270	1168	1096	1040	994	955	921	892	865	841	819
90	1550	1366	1258	1182	1122	1074	1033	997	966	938	913	890
100	1655	1461	1348	1267	1205	1154	1111	1073	1041	1011	984	960
110	1778	1568	1446	1359	1292	1237	1190	1150	1114	1083	1054	1028
120	1900	1676	1544	1451	1379	1320	1270	1227	1188	1154	1123	1095
130	2023	1783	1643	1543	1466	1403	1349	1303	1262	1226	1193	1163
140	2103	1858	1714	1613	1534	1469	1415	1368	1326	1289	1255	1224
150	2182	1932	1786	1682	1602	1536	1481	1432	1390	1352	1318	1286
160	2262	2007	1858	1752	1670	1603	1546	1497	1454	1415	1380	1348
D. 3.0 mm diameter stenosis
50	1605	1409	1295	1213	1150	1098	1055	1017	984	954	927	902
60	1859	1628	1492	1396	1321	1260	1209	1164	1125	1090	1058	1029
70	2113	1846	1690	1579	1493	1422	1363	1312	1266	1226	1189	1155
80	2253	1980	1820	1706	1618	1546	1486	1433	1386	1345	1307	1273
90	2394	2114	1950	1834	1744	1670	1608	1554	1507	1464	1426	1391
100	2534	2248	2081	1962	1870	1794	1731	1676	1627	1584	1544	1508
110	2687	2388	2212	2088	1992	1913	1846	1788	1738	1692	1651	1613
120	2841	2527	2344	2214	2113	2031	1961	1901	1848	1800	1757	1718
130	2994	2667	2476	2340	2235	2149	2077	2014	1958	1909	1864	1823
140	3156	2809	2607	2463	2351	2260	2182	2116	2057	2004	1956	1913
150	3319	2952	2737	2585	2466	2370	2288	2217	2155	2099	2049	2003
160	3482	3094	2868	2707	2582	2480	2394	2319	2253	2194	2141	2093

These tables represent the flow rates in a 7 mm fistula conduit. The variation of fistula diameter over the range of 4 to 9 mm for a stenosis diameter of 1 mm had a 9.6±0.4% difference in flow rate between 4 and 7 mm fistula and a 10.7±0.5% difference in flow rate between 7 and 9 mm conduit. This indicates that while the flow rate does increase for larger conduits, data for the 7 mm conduits can serve as a reasonable approximation. A decrease of 10% results in the flow rate for a 4 mm conduit for a given stenosis and an increase of 10% results in the flow rate for a 9 mm conduit for the same stenosis.

The correlation of the calculated and measured flow rates for the patient-specific stenosis used for validation of the CFD model is shown in Figure 5. The average difference between the two flow rates was 17.2±11.9% (range 1.3-30.1%).

Fig. 5 -

DISCUSSION

AVF stenosis may be identified by clinical exam or fistulography. Neither of these can provide an estimate of its hemodynamic significance. Current access management guidelines recommend dilation of stenosis >50% of the vessel luminal diameter during fistulography with hemodynamic changes. It is well known that dilation of stenosis results in aggressive recurrence (10). While ultrasound could provide a good delineation of the peripheral stenosis and its functional implication with Doppler flow measurement (3), it is currently not the standard for patient care in most places. Moreover, ultrasound is not accurate in evaluation of central veins. Availability of a tool to provide the hemodynamic impact of a stenosis in an access circuit, based on its severity and location, detected during fistulography would help determine the need for intervention.

Volume flow and pressure differential measurements are not routinely done for AVF stenoses as they are done for coronary stenoses with fractional flow reserve measurements (11). Thus, during fistulography the physicians are left to their own judgment.

We have developed and implemented a reproducible CFD model that can quantify the hemodynamic impact of a stenosis on the volume flow of an AVF based on its anatomical appearance. We have validated the CFD model using the ultrasound flow measurements in AVF patients having stenosis; the stenosis in the CFD model has a matched anatomic appearance. Using this CFD model we intend to generate reference tables that provide the hemodynamic significance of stenosis based on its location and anatomical appearance. The CFD data can possibly be used to determine the need for intervention on a stenosis using ultrasound or interventional data.

This clinically validated model sheds insight into several less understood aspects of vascular access hemodynamics. A 1.5 mm stenosis of 5 mm length in a vascular access circuit under physiologic extremes of mean blood pressures (50-160 mmHg) is capable of delivering a fistula flow rate between 301 and 642 mL/min, suggesting a hemodynamically significant stenosis (Tab. I). A stenosis of 2.5 mm that is 5 mm in length would deliver between 1,027 and 2,262 mL/min of flow under the same extremes of physiologic mean pressures. As the length of the stenosis increases it tends to become hemodynamically significant. Similarly a stenotic diameter of 3 mm up to a length of 6 cm is still capable of supporting a flow between 902 and 2,093 mL/min under the same extremes of mean physiologic pressures.

The CFD data for flow rates are well correlated with the ultrasound data obtained by analysis of eight patient-specific stenoses with less than 20% average variation. While the variation is well within the acceptable range for CFD modeling, there are some shortcomings of our current model. This model takes into consideration a single stenosis model in a closed vascular access circuit with defined anatomic any physiologic parameters that are applicable for a broad range of access circuits. It does not take into account any tributaries that may divert the flow that may exist distal to the stenosis. It also does not take into account the effect of collaterals distal to the stenosis that may divert the flow to the contralateral veins. Collaterals that work as natural conduits to decompress a high-pressure system have an impact on the flow based on their location in relation to the stenosis. For this reason, moving the location of stenosis closer to the anastomosis versus placing it 30-40 cm away from the anastomosis, in this model, makes some but not much of an impact, while in clinical scenario a juxta-anastomotic stenosis has a significant flow-limiting potential compared to an outflow vein stenosis. We did notice a tighter correlation with US measurements and CFD-generated flows in stenosis without distal collaterals. As this is a single stenosis model one could look at the stenosis as the anastomotic diameter. The model clearly suggests that under physiologic extremes of mean pressures, a diameter of 2.5 mm is ample to provide flows over 1,000 mL/min. These findings probably have implication on the understanding of access maturation, variation in flow rates seen in patients with larger anastomosis and vascular steal.

This CFD analysis of a single stenosis model provides valuable insight on the hemodynamic significance of stenoses and can be a springboard for more detailed analysis of stenoses. Future studies may incorporate pulsatile flow and the impact of tributaries and collaterals to further refine the model.

CONCLUSION

AVF stenoses are a common clinical problem that often warrants interventions. Analysis of a single stenosis model of an AVF using CFD provided expected flow rates that showed fairly good clinical correlation. With improved CFD modeling, our hope is to develop a tool that would allow clinicians to predict the hemodynamic impact of stenosis based on its location and anatomic configuration.

Validation of computational fluid dynamics predicted flow rate against ultrasound-measured brachial artery flow rate in eight patients with arteriovenous fistula stenoses.

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