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Research Papers

Methodology for Computational Fluid Dynamic Validation for Medical Use: Application to Intracranial Aneurysm

[+] Author and Article Information
Nikhil Paliwal, Robert J. Damiano, Nicole A. Varble

Department of Mechanical and Aerospace Engineering,
University at Buffalo,
Buffalo, NY 14260;
Toshiba Stroke and Vascular Research Center,
University at Buffalo,
Buffalo, NY 14203

Vincent M. Tutino

Toshiba Stroke and Vascular Research Center,
University at Buffalo,
Buffalo, NY 14203;
Department of Biomedical Engineering,
University at Buffalo,
Buffalo, NY 14260

Zhongwang Dou

Department of Mechanical and Aerospace Engineering,
University at Buffalo,
Buffalo, NY 14260

Adnan H. Siddiqui

Toshiba Stroke and Vascular Research Center,
University at Buffalo,
Buffalo, NY 14260;
Department of Neurosurgery,
University at Buffalo,
Buffalo, NY 14226

Hui Meng

Department of Mechanical and Aerospace Engineering,
University at Buffalo,
324 Jarvis Hall,
Buffalo, NY 14260;
Toshiba Stroke and Vascular Research Center,
University at Buffalo,
Buffalo, NY 14203;
Department of Biomedical Engineering,
University at Buffalo,
Buffalo, NY 14260;
Department of Neurosurgery,
University at Buffalo,
Buffalo, NY 14226
e-mail: huimeng@buffalo.edu

1Corresponding author.

Manuscript received January 20, 2017; final manuscript received August 28, 2017; published online September 28, 2017. Assoc. Editor: Alison Marsden.

J Biomech Eng 139(12), 121004 (Sep 28, 2017) (10 pages) Paper No: BIO-17-1030; doi: 10.1115/1.4037792 History: Received January 20, 2017; Revised August 28, 2017

Computational fluid dynamics (CFD) is a promising tool to aid in clinical diagnoses of cardiovascular diseases. However, it uses assumptions that simplify the complexities of the real cardiovascular flow. Due to high-stakes in the clinical setting, it is critical to calculate the effect of these assumptions in the CFD simulation results. However, existing CFD validation approaches do not quantify error in the simulation results due to the CFD solver’s modeling assumptions. Instead, they directly compare CFD simulation results against validation data. Thus, to quantify the accuracy of a CFD solver, we developed a validation methodology that calculates the CFD model error (arising from modeling assumptions). Our methodology identifies independent error sources in CFD and validation experiments, and calculates the model error by parsing out other sources of error inherent in simulation and experiments. To demonstrate the method, we simulated the flow field of a patient-specific intracranial aneurysm (IA) in the commercial CFD software star-ccm+. Particle image velocimetry (PIV) provided validation datasets for the flow field on two orthogonal planes. The average model error in the star-ccm+ solver was 5.63 ± 5.49% along the intersecting validation line of the orthogonal planes. Furthermore, we demonstrated that our validation method is superior to existing validation approaches by applying three representative existing validation techniques to our CFD and experimental dataset, and comparing the validation results. Our validation methodology offers a streamlined workflow to extract the “true” accuracy of a CFD solver.

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Figures

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Fig. 1

Overview of the validation concept with sources of error in round-edged rectangular boxes. δmodel (shaded box, error due to modeling assumptions) represents the true accuracy of the simulation model. (a) Generalized sources of errors in a computational model and experimental measurements. (b) Sources of errors considered while calculating δmodel based on our example CFD simulation and PIV experiments on the IA model.

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Fig. 2

The patient-specific IA model used for validation of star-ccm+ CFD solver: (a) 3D angiographic image of the IA, (b) surface geometry reconstructed from the angiographic image, (c) clear silicone aneurysm phantom fabricated for PIV experiment, and (d) reconstructed surface geometry from reimaging the silicone phantom

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Fig. 3

PIV setup and orthogonal planes in the IA model for PIV data acquisition: (a) schematic diagram of the PIV experimental setup and (b) IA geometry with orthogonal sagittal and transverse planes used for PIV flow measurements. The dotted line of intersection of the planes was used as the domain of validation (validation line) for the star-ccm+ CFD solver.

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Fig. 4

Velocity magnitude (v¯mag, left) and validation error percentage (E¯, right) monitored for different solver parameters in star-ccm+. (a) Grid convergence analysis. (b) Temporal resolution analysis. (c) Solver discretization accuracy analysis (spatial: first, second, and third; temporal: first (unfilled) and second (hatched)). The optimal solver parameters are indicated by an arrow in the v¯mag plots (left) for grid sensitivity and temporal resolution analysis, and by the shaded gray rectangle in the solver discretization analysis. The corresponding minimum E¯ for the optimum parameters are also indicated in the plots on the right.

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Fig. 5

Result of the validation analysis on star-ccm+ CFD solver along the validation line. (a) Equations used to quantify the model error (δmodel). (b) Spatial numerical uncertainty (unum,s) percentage normalized by the average experimental velocity magnitude (v¯mag,piv) for each combination of mesh pairs in the sequence from the grid convergence analysis in Fig. 4(a). (c) Pointwise plot of δmodel along the validation line, hollow circles are the validation error (E) values, and error bars are the validation uncertainty (uval) at each point. (d) The average values of the validation error (E¯) and the uncertainties (u¯num,u¯inputandu¯D) along the validation line, resulting in the overall average model error (δ¯model).

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Fig. 6

Results of application of different validation approaches to the CFD results and experimental measurements. (a)–(c) Previous validation techniques and (d) proposed validation methodology. (a) Qualitative comparison showing velocity magnitude contours with in-plane velocity vectors of constant length plotted on top (in black) to illustrate the flowdirection in the sagittal plane in CFD and PIV. (b) Pointwise velocity magnitudes from star-ccm+ simulation (CFD, hollow circles) and experimental measurement (PIV, shaded squares) plotted along the validation line normalized from 0 to 1. (c) Average ASI and MSI calculated over the validation line. (d) Pointwise mode error (δmodel) plotted along the validation line showing the error and uncertainty in star-ccm+ simulation results.

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Fig. 7

Visualization of 3D flow dynamics using velocity streamlines and volume rendering of velocity magnitude showing the complex 3D flow in the IA model (arrow: flow direction). A strong flow jet impinges on the aneurysm wall, resulting in high velocity and gradients in the region 0.8 ≤x≤ 0.1, marked as the IZ.

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