Robust and fast stochastic 4D flow vector-field signature technique for quantifying composite flow dynamics from 4D flow MRI: Application to left atrial flow in atrial fibrillation

4D flow MRI is an emerging imaging modality that maps voxel-wise blood flow information as velocity vector fields that is acquired in 7-dimensional image volumes (3 spatial dimensions + 3 velocity directions + time). Blood flow in the cardiovascular system is often complex and composite involving multiple flow dynamics and patterns (e.g., vortex flow, jets, stagnating flow) that occur and interact simultaneously. The spectrum of such complex flow dynamics is embedded in the velocity vector field dynamics derived from 4D Flow MRI. However, current flow metrics cannot fully measure high-dimensional vector-field data and embedded complex composite flow data. Instead, these methods need to break down the vector-field data into secondary scalar fields of individual flow components using fluid dynamics operators. These methods are gradient-based and sensitive to data uncertainties, and only focus on individual flow components of the overall composite flow, therefore potentially underestimating the severity of overall flow changes associated with cardiovascular diseases. To address these limitations, in MICCAI 2021, we introduced a novel comprehensive stochastic 4D Flow vector-field signature technique that works directly on the entire spatiotemporal velocity vector field. This technique uses efficient stochastic gradient-free interrogation of multi-million flow vector-pairs per patient to derive the patient's unique flow profile of the complex composite flow alterations and in real-time processing. The signature technique's probabilistic gradient-free formulation should allow for highly robust quantification despite inherent errors in 4D flow MRI acquisitions. Here, we extend the application of the 4D flow vector-field signature technique to the left atrium to analyze complex composite flow changes in patients with atrial fibrillation. In 128 subjects, we performed extensive sensitivity testing and determined that the vector-field signature technique is highly robust to typical sources of data uncertainties in 4D flow MRI: degradation in spatiotemporal resolution, added Gaussian noise, and segmentation errors. We demonstrate the excellent generalizability of the stochastic convergence from the aorta to the left atrium and between different 4D Flow MRI acquisition protocols. We compare the robustness of our technique to existing advanced flow quantification metrics of kinetic energy, vorticity, and energy loss demonstrating a superior performance of up-to 14-fold. Our results show the potential diagnostic and clinical utility of our signature technique in identifying distinctly altered composite flow signatures in atrial fibrillation patients independent of existing flow metrics.