Collaborative Research: Enhanced 4D-Flow MRI through Deep Data Assimilation for Hemodynamic Analysis of Cardiovascular Flows

Forces resulting from blood flow interaction with walls of blood vessels have major impact on the initiation and progression of vascular diseases such as aneurysms, atherosclerosis, and vasospasms. Consequently, detailed and accurate blood flow analysis could be key to prognosis and treatment of such diseases. There are two popular modalities that are currently used to study 3D blood flow. The first is based on computational fluid dynamic (CFD) simulations. The second is through direct non-invasive imaging using techniques such as phase contrast magnetic resonance imaging (a.k.a 4D-Flow MRI). CFD requires accurate vascular geometry, model parameters, and estimates of boundary flow and initial conditions. These are time consuming and very difficult, if not impossible to estimate. Furthermore, the fidelity of CFD is limited by model assumptions. On the other hand, 4D-Flow MRI directly measures in-vivo volumetric blood flow velocities, but has low spatio-temporal resolution and the scans are contaminated by noise and image artifacts. The proposed project overcomes the limitations of both CFD and 4D-Flow MRI through a novel technique called deep data-assimilation. Here deep neural nets are used to model the blood flow. The training process imposes data fidelity with 4D-Flow MRI and simultaneously ensures that the physics of fluid flow and magnetic resonance are satisfied. The neural nets are then used to generate accurate dense spatio-temporal flow fields and flow dependent parameters such as wall shear stresses, vorticity etc. The ability to enhance 4D-Flow MRI will enable clinical researchers to investigate the impact of hemodynamics on the initiation and progression of vascular diseases. This will lead to novel physics-based flow image analysis tools for disease management that will significantly reduce cost and optimize treatment plans. The goal of the proposed project is to enable accurate and reliable hemodynamic analysis of cardio-vascular flows from time resolved three dimensional phase contrast magnetic resonance imaging (4D-Flow MRI). The proposed approach uses physics informed deep learning wherein time-varying flow (velocity and pressure) and field (magnetic moment) variables are modeled as deep neural nets. The training process fits 4D-Flow MRI data and also imposes blood flow physics (Navier-Stokes equation) and MRI acquisition physics (Bloch equations) as constraints. Creative design of loss functions in the learning process will achieve super-resolution, attenuate noise, and eliminate various image artifacts. Automatic differentiation will facilitate truncation error-free computation of velocity-dependent higher order hemodynamic parameters. Carefully designed in-vitro experiments will be used to validate and optimize the method. The proposed hybrid experimental and deep learning approach will create a new paradigm in cardiovascular flow research wherein the governing equations will be directly applied to low quality imaging data using deep learning to raise the reliability and accuracy to the level needed for scientific discovery. The project will provide opportunities to train graduate students in the latest deep-learning based techniques in engineering, engage undergraduate students in research through numerous programs at UW-Milwaukee and Northern Arizona University, and outreach to high school students belonging to marginalized communities through summer programs at UW-Milwaukee. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.