Sensitivity of patient-specific numerical simulation of cerebal aneurysm hemodynamics to inflow boundary conditions

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Object

Due to the difficulty of obtaining patient-specific velocity measurements during imaging, many assumptions have to be made while imposing inflow boundary conditions in numerical simulations conducted using patient-specific, imaging-based cerebral aneurysm models. These assumptions can introduce errors, resulting in lack of agreement between the computed flow fields and the true blood flow in the patient. The purpose of this study is to evaluate the effect of the assumptions made while imposing inflow boundary conditions on aneurysmal hemodynamics.

Methods

A patient-based anterior communicating artery aneurysm model was selected for this study. The effects of various inflow parameters on numerical simulations conducted using this model were then investigated by varying these parameters over ranges reported in the literature. Specifically, we investigated the effects of heart and blood flow rates as well as the distribution of flow rates in the A1 segments of the anterior cerebral artery.

The simulations revealed that the shear stress distributions on the aneurysm surface were largely unaffected by changes in heart rate except at locations where the shear stress magnitudes were small. On the other hand, the shear stress distributions were found to be sensitive to the ratio of the flow rates in the feeding arteries as well as to variations in the blood flow rate.

Conclusions

Measurement of the blood flow rate as well as the distribution of the flow rates in the patient's feeding arteries may be needed for numerical simulations to accurately reproduce the intraaneurysmal hemodynamics in a specific aneurysm in the clinical setting.

Abbreviations used in this paper: ACA = anterior cerebral artery; ACoA = anterior communicating artery; bpm = beats per minute; CT = computed tomography; MR = magnetic resonance; STL = stereolithography; TCD = transcranial Doppler.

Article Information

Address reprint requests to: Prem Venugopal, Ph.D., Novo Nor-disk Delivery Technologies, 3920 Point Eden Way, Hayward, California 94545. email: prem.venugopal@gmail.com.

© AANS, except where prohibited by US copyright law.

Headings

Figures

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    Schematic diagram illustrating the steps in the simulation pipeline.

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    Surface-rendered CT angiography images showing the region around the aneurysm. A: Image obtained on November 15, 2001, at the time of initial diagnosis. B: Image obtained on September 4, 2003, showing growth in the dome region of the aneurysm.

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    Surface model of the ACoA aneurysm and the parent arteries after segmentation, smoothing, and closing of holes.

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    Waveform used to modulate the inlet velocity profile in the simulations. The x-axis values represent the ratio of time, t, to the time period of the waveform, T; the y-axis values represent the ratio of the maximum to the minimum flow rate in the artery.

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    Computational predictions generated using a patient-specific ACoA aneurysm model. Left: Distribution of mean pressure on the aneurysm surface. Re = 340–675, Wo = 1.92, Ql/Qr = 1.87. Pressure values are given in N/m2. Right: Streamline pattern at maximum flow rate indicating the impingement location. The rectangle denotes the region where the “seeds” used to generate the streamline pattern were located.

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    Computational predictions showing shear stress distribution on the aneurysm surface. Re = 340–675, Wo = 1.92, Ql/Qr = 1.87. Left: Time-averaged mean, Right: Fluctuations about the time-averaged mean, . Shear stress is given in N/m2.

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    Graphs showing shear stress distributions for Simulations 1 (solid lines) and 2 (broken lines) along contour lines formed by coronal sections passing through a model of the ACoA aneurysm. In Simulation 1 the inflow Reynolds number range is 340–675, whereas in Simulation 2 it is 100–198. In A and B, y = −1.290620; in C and D, y = −1.145670; in E and F, y = −1.062840. The x axis represents s, the distance along the contour line in cm. Shear stress is given in N/m2.

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    Computational prediction showing showing the ratio of the mean shear stress obtained in Simulation 1 to that obtained in Simulation 2. In Simulation 1 the inflow Reynolds number range was 340–675; in Simulation 2 it was 100–198.

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    Computational predictions showing distribution of mean pressure on the aneurysm surface for different flow rate ratios in the A1 segments. A: Ql/Qr = 1.87. B: Ql/Qr = 4.10. C: Ql/Qr = 10.24. The inflow Reynolds and Womersley numbers were kept the same in all three simulations. Pressure is given in N/m2.

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    Computational predictions showing the distribution of mean shear stress on the aneurysm surface for different flow rate ratios in the A1 segments. A: Ql/Qr = 1.87. B: Ql/Qr = 4.10. C: Ql/Qr = 10.24. The inflow Reynolds and Womersley numbers were maintained the same in all three cases. Shear stress is given in N/m2.

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    Computational predictions showing the distribution of fluctuating shear stress on the aneurysm surface for different flow rate ratios in the A1 segments. A: Ql/Qr = 1.87. B: Ql/Qr = 4.10. C: Ql/Qr = 10.24. The inflow Reynolds and Womersley numbers were the same in all three cases. Shear stress is given in N/m2.

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    Computational predictions showing the relative change in shear stress (absolute value) from Simulation 1 to Simulation 3. In Simulation 1 the flow rate ratio in the A1 segments (Ql/Qr) was 1.87, and in Simulation 3 it was 4.10. Left: Relative change in . Right: Relative change in .

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    Computational predictions showing the relative change in shear stress (absolute value) from Simulation 3 to Simulation 4. In Simulation 3 the flow rate ratio in the A1 segments (Ql /Qr) was 4.10, and in Simulation 4 it was 10.24. Left: Relative change in . Right: Relative change in .

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    Graphs showing the shear stress distributions for Simulations 1 (solid line) and 5 (broken line) along contour lines formed by coronal sections passing through a model of the ACoA aneurysm. In Simulation 1 an inflow Womersley number of 1.92 was used; in Simulation 5 an inflow Womersley number of 2.71 was used. In A and B, y = −1.290620; in C and D, y = −1.145670; in E and F, y = −1.062840. The x axis represents s, the distance along the contour line in cm. Shear stress is given in N/m2.

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    Scatter plots showing the shear stress values for the low Womersley number simulation on the x axis and the relative change in shear stress from the low Womersley number to the high Womersley number simulation on the y axis. Upper: Mean shear stress. Lower: Fluctuations about the time-averaged mean. Shear stress is given in N/m2.

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