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Verification and Validation of Merging Patient-Specific Computational Fluid Dynamics and 4D-Flow MRI1Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI, United States, 2Neurosurgery, Medical College of Wisconsin, Milwaukee, WI, United States, 3University of Wisconsin-Milwaukee, Milwaukee, WI, United States, 4New York Institute of Technology, Long Island, NY, United States, 5Radiology, Medical College of Wisconsin, Milwaukee, WI, United States, 6Research Campus STIMULATE, University of Magdeburg, Magdeburg, Germany
Synopsis
In this work, we present the result of verification and validation of our previously developed method that enabled merging of patient-specific Computational Fluid Dynamics (CFD) and 4D-Flow MRI using Proper Orthogonal Decomposition (POD) to address limitations of both modalities. A constant fluid flow boundary condition was applied on a transparent in vitro aneurysm phantom geometry and the volumetric velocity field was scanned using 4D-Flow MRI, and tomographic Particle Image Velocimetry (tPIV). The latter has much higher spatial resolution and can be used to verify the accuracy of the results of merging CFD and volumetric 4D-Flow MRI. Results show that the POD-based merging algorithm enables reconstruction of fine flow details not seen in 4D-Flow MRI due to limited spatial resolution.
Introduction
4D-Flow MRI and patient-specific Computational Fluid Dynamics (CFD) are two modalities for evaluating hemodynamics in human vascular system. 4D-Flow MRI is an in-vivo imaging technique which directly measures blood flow velocities. It is limited by spatio-temporal resolution and acquisition noise. On the other hand CFD is noise-free and the spatio-temporal resolution is only limited by computer memory and computing power. The accuracy of CFD is affected by flow model assumptions, uncertainties in model parameters, boundary conditions, and the segmented vascular geometry. Previously, we developed a technique for merging patient-specific CFD and volumetric 4D-Flow MRI to simultaneously address the limitations of both modalities [1]. In this work, we present validation and verification of this method using an in-vitro phantom by comparing the results of our algorithm against flow fields obtained from Tomographic Particle Image Velocimetry (tPIV), a technique that has much higher resolution as compared to 4D-Flow MRI.Methods
A time of flight angiography (TOFA) scan of an actual aneurysm was segmented and a smooth luminal surface mesh was created. Rapid prototyping techniques were used to build a transparent phantom from the aneurysm geometry. The transparent phantom was subject to constant flow conditions and was scanned both using a tPIV machine as well as a 7 T MRI machine using a 4D-Flow MRI sequence. Details of scan parameters can be found in [2]. A mixture of distilled water, glycerin, sodium iodide, and sodium thiosulfate ensured Reynolds similarity by matching the kinematic viscosity of human blood with dynamic viscosity of μ=5∙103 Pa-s. Boundary flow conditions were sampled at both the inlet and outlet at several location from the 4D-Flow MRI data. The sample mean and variance of the sampled boundary conditions was computed. Based on this distribution, several steady-state CFD simulations using ANSYS Fluent 14.5 were conducted by sampling boundary conditions in the distribution given by the sample mean and variance. The simulation mesh size was set to 0.124mm resulting in ~427k mesh elements. The resulting flow fields were used to characterize the solution space using Proper Orthogonal Decomposition (POD). Following the method in [1], a process of projecting the 4D-Flow MRI data onto the POD basis followed by upsampling into the high-resolution CFD mesh was conducted by a process of mapping projection coefficients.Results
Fig. 1(a) shows the 2-D section of the aneursym geometry where the 3D velocity magnitude was sampled. Fig. 1(b) shows the processed (corrected for eddy current and other phase offsets) 4D-Flow MRI data. This data has 0.57 mm isotropic resolution. Fig. 1(c) shows the result of the tPIV scan. This data has 0.234 mm isotropic resolution. Fig. 1(c) is the result of CFD simulation using the mean of boundary conditions measured from 4D-Flow MRI data. Finally, Fig. 1(d) shows the result of merging CFD with volumetric 4D-Flow MRI data using our novel POD algorithm. Note that the input to our algorithm is the low resolution and noisy 4D-Flow MRI data from Fig. 1(b) and geometry obtained from segmenting TOFA as shown in Fig. 1(a). Clearly, it can be seen that our algorithm is able to recover fine flow patterns that can be seen in the tomographic PIV images that are clearly not visible in the 4D-Flow MRI data set.Conclusions
We have successfully implemented and tested using in-vitro models a method for super-resolution of 4D-Flow MRI data by merging patient-specific CFD and volumetric 4D-Flow MRI. As can be seen from the results (Fig. 1(c) vs Fig. 1(b)) , pure patient-specific CFD with boundary conditions obtained from 4D-Flow MRI does not yield satisfactory results because of errors in model parameters and uncertainties in measured boundary conditions. Our method is capable of overcoming these limitations. In the near future, we plan to validate the aforementioned algorithm on in vitro models with pulsatile boundary conditions.Acknowledgements
No acknowledgement found.References
[1] Bakhshinejad, A., Baghaie, A., Vali, A., Saloner, D., Rayz, V. L., & D’Souza, R. M. (2017). Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression. Journal of Biomechanics, 58, 162–173. https://doi.org/10.1016/j.jbiomech.2017.05.004
[2] Roloff, C., Stucht, D., Beuing, O., & Berg, P. (2018). Comparison of intracranial aneurysm flow quantification techniques: standard PIV vs stereoscopic PIV vs tomographic PIV vs phase-contrast MRI vs CFD. Journal of neurointerventional surgery, neurintsurg-2018
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