Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression

Abstract

Time resolved phase-contrast magnetic resonance imaging 4D-PCMR (also called 4D Flow MRI) data while capable of non-invasively measuring blood velocities, can be affected by acquisition noise, flow artifacts, and resolution limits. In this paper, we present a novel method for merging 4D Flow MRI with computational fluid dynamics (CFD) to address these limitations and to reconstruct de-noised, divergence-free high-resolution flow-fields. Proper orthogonal decomposition (POD) is used to construct the orthonormal basis of the local sampling of the space of all possible solutions to the flow equations both at the low-resolution level of the 4D Flow MRI grid and the high-level resolution of the CFD mesh. Low-resolution, de-noised flow is obtained by projecting in-vivo 4D Flow MRI data onto the low-resolution basis vectors. Ridge regression is then used to reconstruct high-resolution de-noised divergence-free solution. The effects of 4D Flow MRI grid resolution, and noise levels on the resulting velocity fields are further investigated. A numerical phantom of the flow through a cerebral aneurysm was used to compare the results obtained using the POD method with those obtained with the state-of-the-art de-noising methods. At the 4D Flow MRI grid resolution, the POD method was shown to preserve the small flow structures better than the other methods, while eliminating noise. Furthermore, the method was shown to successfully reconstruct details at the CFD mesh resolution not discernible at the 4D Flow MRI grid resolution. This method will improve the accuracy of the clinically relevant flow-derived parameters, such as pressure gradients and wall shear stresses, computed from in-vivo 4D Flow MRI data.

High Spatiotemporal Resolution 4D Flow MRI of Intracranial Aneurysms at 7T in 10 Minutes

“…It can also be used as a means of reducing imperfections in the 4D flow MR imaging measurements and may improve the ability to accurately derive clinically relevant secondary parameters such as WSS and pressure gradients at a much higher level of detail and confidence than was previously possible. 29,30 Because highly accelerated 4D flow MR imaging with high temporal resolution provided reliable quantitative flow values, we encourage using 4D flow MR imaging more often for UIA monitoring and growth prediction in future clinically focused studies. 6,26 The techniques must be investigated in a larger study of patients with UIAs to determine whether the derived WSS is affected by either the calculation method or the temporal resolution or both.…”

4DFlowNet: Super-Resolution 4D Flow MRI Using Deep Learning and Computational Fluid Dynamics

“…While the CFD simulations were informed by real MRI measurements, we did not attempt to model accurate boundary conditions, non-linear viscosity, fluid-structure interactions or transitions to turbulence. Previous CFD studies [7][8][9][10], have been concerned with achieving accurate personalized CFD solutions given 4D flow data. In contrast, we have shown how CFD simulations can be used in a deep learning environment to learn how to reconstruct uncorrupted images from those corrupted by noise and low resolution.…”

“…To obtain improved resolution, several studies have explored the use of computational fluid dynamics (CFD) in combination with 4D flow MRI [7][8][9][10]. CFD simulations are computed by solving the continuity equation and Navier-Stokes equation within the region of interest.…”

Hemodynamic Data Assimilation in a Subject-specific Circle of Willis Geometry

“…Although widely used in many areas of science and engineering, the application of DA in hemodynamics is still in its infancy. Only a handful of studies have considered intracranial aneurysms, using either sequential or variational DA approaches [15][16][17][18][19][20][21]. Variational methods can be computationally expensive due to the adjoint equations, which are about twice as costly to solve as the direct equations, and often require several iterations until convergence.…”