^{1,a)}, Kevin Johnson

^{1}, Kristian Valen-Sendstad

^{2}, Kent-Andre Mardal

^{3}, Oliver Wieben

^{4}and Charles Strother

^{5}

### Abstract

**Purpose**

: Our purpose was to compare quantitatively velocity fields in and around experimental canine aneurysms as measured using an accelerated 4D PC-MR angiography (MRA) method and calculated based on animal-specific CFD simulations.

**Methods**

: Two animals with a surgically created bifurcation aneurysm were imaged using an accelerated 4D PC-MRA method. Meshes were created based on the geometries obtained from the PC-MRA and simulations using “subject-specific” pulsatile velocity waveforms and geometries were then solved using a commercial CFD solver. Qualitative visual assessments and quantitative comparisons of the time-resolved velocity fields obtained from the PC-MRA measurements and the CFD simulations were performed using a defined similarity metric combining both angular and magnitude differences of vector fields.

**Results**

: PC-MRA and image-basedCFD not only yielded visually consistent representations of 3D streamlines in and around both aneurysms, but also showed good agreement with regard to the spatialvelocity distributions. The estimated similarity between time-resolved velocity fields from both techniques was reasonably high (mean value >0.60; one being the highest and zero being the lowest). Relative differences in inflow and outflow zones among selected planes were also reasonable (on the order of 10%–20%). The correlation between CFD-calculated and PC-MRA-measured time-averaged wall shear stresses was low (0.22 and 0.31, p < 0.001).

**Conclusions:**

In two experimental canine aneurysms, PC-MRA and image-basedCFD showed favorable agreement in intra-aneurismal velocity fields. Combining these two complementary techniques likely will further improve the ability to characterize and interpret the complex flow that occurs in human intracranial aneurysms.

We are grateful to our colleague Mr. Dan Consigny, B.S., from the Radiology Department at the University of Wisconsin’s School of Medicine of Public Health and Mr. Kevin Royalty, M.S., from Siemens Healthcare (USA) Inc. for their help with animal studies. This project is funded, in part, by a NIH Grant No. (2R01HL072260-05A1) and a Wallace H. Coulter Foundation phase one grant awarded to the University of Wisconsin, and a Center of Excellence Grant from the Norwegian Research Council awarded to the Simula Research Laboratory.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. Creation of canine experimental aneurysms

II.B. Description and calibration of the accelerated PC-VIPR MRA technique

II.C. Description of “animal-specific” CFD simulations

II.D. Off-line visualization and data analysis

II.D.1. Comparison between PC-MRA measured and CFD-simulated velocity fields

II.D.2. Generation of 3D streamlines

II.D.3. Comparison of wall shear stress obtained from the PC-MRA measured and CFD-simulated velocity fields

II.D.4. Statistical analysis

III. RESULTS AND INTERPRETATION

III.A. Similarity of velocityvector fields

III.B. Visualization of 3D streamlines

III.C. Comparisons of WSS

III.D. Accuracy of WSS estimation versus image resolution and noise

IV. DISCUSSION

V. CONCLUSION

### Key Topics

- Flow simulations
- 74.0
- Velocity measurement
- 34.0
- Haemodynamics
- 32.0
- Flow visualization
- 16.0
- Spatial resolution
- 15.0

## Figures

Segmented and meshed geometries of the two aneurysms from PC-VIPR MRA registered with adjacent soft tissue: (a) Aneurysm A and (b) aneurysm B.

Segmented and meshed geometries of the two aneurysms from PC-VIPR MRA registered with adjacent soft tissue: (a) Aneurysm A and (b) aneurysm B.

Comparison of 3D velocity vector fields at diastole [three components Vx, Vy, and Vz and the velocity amplitude V] obtained from subject-specific CFD simulations and PC-VIPR MRA measurements for (a) a transverse plane and (b) a longitudinal plane in aneurysm A. In both plots, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively. Color bars corresponding to three plots of each column are shown at the end of each column. The unit used for velocity is m/s for all plots in (a) and (b).

Comparison of 3D velocity vector fields at diastole [three components Vx, Vy, and Vz and the velocity amplitude V] obtained from subject-specific CFD simulations and PC-VIPR MRA measurements for (a) a transverse plane and (b) a longitudinal plane in aneurysm A. In both plots, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively. Color bars corresponding to three plots of each column are shown at the end of each column. The unit used for velocity is m/s for all plots in (a) and (b).

The estimated similarity values [see Eq. (A1)], absolute magnitude and angular differences between three pairs of velocity fields [MRA vs. CFD_{1}, MRA vs. CFD_{2}, and CFD_{1} vs. CFD_{2}] for (a) the transverse and (b) the longitudinal planes in aneurysm A illustrated in Figs. 2(a) and 2(b), respectively. The velocity data correspond to a phase at the diastole. Arrows on 3D velocity vector plots [top plots of both (a) and (b)] indicate a border region between the velocity jet and the low-velocity recirculation zone. In this figure, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively. Manually-delineated contours on both (a) and (b) indicate regions within the aneurysm dome. Mag (m/s), Ang (degree) and Sim [0-1] denote the absolute magnitude and angular differences, and the similarity metric between two velocity vectors, respectively. The arrows in the similarity plots (left lower three columns) point to low similarity values, where arrows in the absolute magnitude (right lower three columns) and angular (middle lower three columns) difference plots point to large discrepancies in both magnitude and direction of two sets of comparing vectors.

The estimated similarity values [see Eq. (A1)], absolute magnitude and angular differences between three pairs of velocity fields [MRA vs. CFD_{1}, MRA vs. CFD_{2}, and CFD_{1} vs. CFD_{2}] for (a) the transverse and (b) the longitudinal planes in aneurysm A illustrated in Figs. 2(a) and 2(b), respectively. The velocity data correspond to a phase at the diastole. Arrows on 3D velocity vector plots [top plots of both (a) and (b)] indicate a border region between the velocity jet and the low-velocity recirculation zone. In this figure, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively. Manually-delineated contours on both (a) and (b) indicate regions within the aneurysm dome. Mag (m/s), Ang (degree) and Sim [0-1] denote the absolute magnitude and angular differences, and the similarity metric between two velocity vectors, respectively. The arrows in the similarity plots (left lower three columns) point to low similarity values, where arrows in the absolute magnitude (right lower three columns) and angular (middle lower three columns) difference plots point to large discrepancies in both magnitude and direction of two sets of comparing vectors.

Comparison of 3D velocity vector fields at the peak systole (three components Vx, Vy and Vz and the velocity amplitude V) obtained from subject-specific CFD simulations and PC-VIPR MRA measurements for (a) a transverse plane and (b) a longitudinal plane in aneurysm A. In both plots, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively. Color bars corresponding to three plots of each column are shown at the end of each column. The unit used for velocity is m/s for all plots in (a) and (b). The arrow in (b) points to possible MRA measurement errors.

Comparison of 3D velocity vector fields at the peak systole (three components Vx, Vy and Vz and the velocity amplitude V) obtained from subject-specific CFD simulations and PC-VIPR MRA measurements for (a) a transverse plane and (b) a longitudinal plane in aneurysm A. In both plots, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively. Color bars corresponding to three plots of each column are shown at the end of each column. The unit used for velocity is m/s for all plots in (a) and (b). The arrow in (b) points to possible MRA measurement errors.

The estimated similarity values [see Eq. (A1)], absolute magnitude and angular differences between three pairs of velocity fields [MRA vs. CFD_{1}, MRA vs. CFD_{2}, and CFD_{1} vs. CFD_{2}] for (a) the transverse and (b) the longitudinal planes in aneurysm A illustrated in Figs. 2(a) and 2(b), respectively. The velocity data correspond to the peak systole. In this figure, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively. Mag (m/s), Ang (degree) and Sim [0-1] denote the absolute magnitude and angular differences, and the similarity metric between two velocity vectors, respectively. The arrow in the similarity plots (left lower three columns) points to low similarity values, where arrows in the absolute magnitude (right lower three columns) and angular (middle lower three columns) difference plots point to large discrepancies in both magnitude and direction of two sets of comparing vectors.

The estimated similarity values [see Eq. (A1)], absolute magnitude and angular differences between three pairs of velocity fields [MRA vs. CFD_{1}, MRA vs. CFD_{2}, and CFD_{1} vs. CFD_{2}] for (a) the transverse and (b) the longitudinal planes in aneurysm A illustrated in Figs. 2(a) and 2(b), respectively. The velocity data correspond to the peak systole. In this figure, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively. Mag (m/s), Ang (degree) and Sim [0-1] denote the absolute magnitude and angular differences, and the similarity metric between two velocity vectors, respectively. The arrow in the similarity plots (left lower three columns) points to low similarity values, where arrows in the absolute magnitude (right lower three columns) and angular (middle lower three columns) difference plots point to large discrepancies in both magnitude and direction of two sets of comparing vectors.

Plots of streamlines (i.e., lines of tangent to instantaneous velocity vectors) of CFD simulated and PC-MRA measured velocity vectors at diastole for (a) Aneurysms A and (b) B, respectively. Streamlines were color encoded using velocity amplitude (0–0.8 m/s). In this figure, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively.

Plots of streamlines (i.e., lines of tangent to instantaneous velocity vectors) of CFD simulated and PC-MRA measured velocity vectors at diastole for (a) Aneurysms A and (b) B, respectively. Streamlines were color encoded using velocity amplitude (0–0.8 m/s). In this figure, CFD_{1} and CFD_{2} denote non-Newtonian and Newtonian CFD simulations, respectively.

Side-by-side comparisons for TA-WSS values derived from PC-MRA-estimated and CFD. Arrows points to the likely locations where the inflow jets impinge the walls.

Side-by-side comparisons for TA-WSS values derived from PC-MRA-estimated and CFD. Arrows points to the likely locations where the inflow jets impinge the walls.

Selected images of the estimated WSS under noise-free for three different voxel sizes (5, 250 and 750 μm) and their estimated correlation values.

Selected images of the estimated WSS under noise-free for three different voxel sizes (5, 250 and 750 μm) and their estimated correlation values.

A plot of the estimated correlation values with respect to different simulated voxel sizes and measurement noise. Ten realizations were used to obtain each data point displayed in this plot.

A plot of the estimated correlation values with respect to different simulated voxel sizes and measurement noise. Ten realizations were used to obtain each data point displayed in this plot.

Estimated correlation values for simulated velocity data with voxel sizes of 0.525 mm and 0.620 mm that are comparable to MRA-measured velocity data in Aneurysms A and B, respectively. Each data point was obtained by ten realizations and error bars stand for one standard deviation. Two black stars denote two data points for the correlation values corresponding to these TA-WSS estimates shown in Figs. 7(a) and 7(b).

Estimated correlation values for simulated velocity data with voxel sizes of 0.525 mm and 0.620 mm that are comparable to MRA-measured velocity data in Aneurysms A and B, respectively. Each data point was obtained by ten realizations and error bars stand for one standard deviation. Two black stars denote two data points for the correlation values corresponding to these TA-WSS estimates shown in Figs. 7(a) and 7(b).

Illustrations of the calculation of WSS.

Illustrations of the calculation of WSS.

## Tables

Basic geometrical and flow parameters of Aneurysms A and B. The aspect ratio is defined as the ratio between the aneurysm height and the neck width.

Basic geometrical and flow parameters of Aneurysms A and B. The aspect ratio is defined as the ratio between the aneurysm height and the neck width.

Estimated absolute magnitude and angular differences, and similarity values with two aneurysm sacs for three pairs of velocity vector fields: MRA versus non-Newtonian CFD simulations (CFD_{1}), MRA versus Newtonian CFD simulations (CFD_{2}) and CFD_{1} versus CFD_{2}. The mean values (±one standard deviation) were estimated within the manually-segmented aneurysm domes [see Figs. 3(a) and 3(b)].

Estimated absolute magnitude and angular differences, and similarity values with two aneurysm sacs for three pairs of velocity vector fields: MRA versus non-Newtonian CFD simulations (CFD_{1}), MRA versus Newtonian CFD simulations (CFD_{2}) and CFD_{1} versus CFD_{2}. The mean values (±one standard deviation) were estimated within the manually-segmented aneurysm domes [see Figs. 3(a) and 3(b)].

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