Hernán Mella

Physics-Informed Neural Networks (PINNs) show significant potential for solving inverse problems, especially when observations are limited and sparse, provided that the relevant physical equations are known. We use PINNs to estimate smooth velocity and pressure fields from synthetic 4D flow Magnetic Resonance Imaging (MRI) data. We analyze five non-Newtonian dynamic 3D blood flow cases within a realistic aortic model, covering a range of hematocrit values from anemic to polycythemic conditions. To enhance state estimation results, we consider various design and training techniques for PINNs, including adaptive loss balancing, curriculum training, and a realistic measurement operator. Regarding blood rheology, the PINN approach accurately estimates viscosity globally and locally under peak systolic conditions. It also provides a clear pattern recognition for diastolic stages. Regarding mass conservation, PINN estimations effectively reproduce the bifurcation of flow through the different branches of the aorta, demonstrate an excellent representation of the non-slip conditions at the walls, and accurately estimate pressure drops with relative errors below the 5% in the whole pressure field. We test our pressure drop estimations against the state of the art Virtual Work Energy Relative Pressure (vWERP) estimator, and we observe how our results outperform vWERP in terms of both accuracy and time resolution. Additionally, we find that the best results are achieved by computing the velocity field using the PINN, which is then integrated into the vWERP framework, leading to time super-sampled and high-order approximations, with a clinically admissible accuracy.

Water‐fat separation MRI techniques use frequency differences between water and fat encoded in the phase of the MR signal. Similarly, phase‐contrast MRI (2D PC‐MRI) uses phase differences to estimate blood flow velocity. This study proposes to enhance efficiency by acquiring both images in a single scan, resulting in co‐registered images of water‐fat species and velocity. This work introduces a method that combines phase‐contrast with T2*‐IDEAL to acquire water‐fat components and velocity images in a single MR acquisition. We developed a phase‐contrast multi‐echo (PCME‐MRI) acquisition to obtain IDEAL MR images with velocity encoding. Our T2*‐IDEAL method estimates velocity and separates water‐fat components by considering three chemical species: fat concentration and two water components with velocity information. The proposed PC T2*‐IDEAL method was validated with a numerical phantom and 2D MR axial images of the neck in 14 healthy volunteers, measuring blood flow in the carotid arteries and water‐fat components around the region of interest. In volunteers, the median and range MAE when comparing PC T2*‐IDEAL and standard T2*‐IDEAL fat fraction was 0.06 0.02. The median and range of velocity for PC T2*‐IDEAL were 8.44 and [6.23, 10.6] mL, compared to 7.16 and [4.79, 8.78] mL obtained by 2D PC‐MRI. Numerical phantom simulations demonstrated similar results in water‐fat components and velocity information compared to standard T2*‐IDEAL and 2D PC‐MRI methods. Volunteer images showed accurate estimations of water‐fat components and differences in velocity information using PC T2*‐IDEAL in comparison with standard 2D PC‐MRI.

4D Flow Magnetic Resonance Imaging (MRI) is the state‐of‐the‐art technique to comprehensively measure the complex spatio‐temporal and multidirectional patterns of blood flow. However, it is subject to artifacts such as noise and aliasing, which due to the 3D and dynamic structure is difficult to detect in clinical practice. In this work, a new mathematical and computational model to determine the quality of 4D Flow MRI is presented. The model is derived by assuming the true velocity satisfies the incompressible Navier–Stokes equations and that can be decomposed by the measurements plus an extra field . Therefore, a non‐linear problem with as unknown arises, which serves as a measure of data quality. A stabilized finite element formulation tailored to this problem is proposed and analyzed. Then, extensive numerical examples—using synthetic 4D Flow MRI data as well as real measurements on experimental phantom and subjects—illustrate the ability to use for assessing the quality of 4D Flow MRI measurements over space and time.

Purpose: Three‐dimensional (3D) quantification of circulation using a Finite Elements methodology.Methods: We validate our 3D method using an in‐silico arch model, for different mesh resolutions, image resolution and noise levels, and we compared this with a currently used 2D method. Finally, we evaluated the application of our methodology in 4D Flow MRI data of ascending aorta of six healthy volunteers, and six bicuspid aortic valve (BAV) patients, three with right and three with left handed flow, at peak systole. The in‐vivo data was compared using a Mann‐Whitney U‐test between volunteers and patients (right and left handed flow).Results: The robustness of our method throughout different image resolutions and noise levels showed subestimation of circulation less than 45 cm²/s in comparison with the 55cm²/s generated by the current 2D method. The circulation (mean ± SD) of the healthy volunteer group was 13.83 ± 28.78 cm²/s, in BAV patients with right‐handed flow 724.37 ± 317.53 cm²/s, and BAV patients with left‐handed flow −480.99 ± 387.29 cm²/s. There were significant differences between healthy volunteers and BAV patients groups (P‐value < .01), and also between BAV patients with a right‐handed or left‐handed helical flow and healthy volunteers (P‐value < .01).Conclusion: We propose a novel 3D formulation to estimate the circulation in the thoracic aorta, which can be used to assess the differences between normal and diseased hemodynamic from 4D‐Flow MRI data. This method also can correctly differentiate between the visually seen right‐ and left‐handed helical flow, which suggests that this approach may have high clinical sensitivity, but requires confirmation in longitudinal studies with a large cohort.

Purpose: To develop an Off‐Resonance Insensitive Orthogonal CSPAMM sequence (ORI‐O‐CSPAMM) for the acquisition of CSPAMM and MICSR grids in half of the acquisition time.Methods: Phantom and mid‐level left ventricle short‐axis tagged images were acquired using CSPAMM, ORI‐CSPAMM, O‐CSPAMM, and the proposed ORI‐O‐CPAMM sequences to interrogate and compare its behavior under off‐resonance effects produced by vegetable oil and subcutaneous and epicardial fat. The images were compared in terms of signal and the capacity to obtain complex difference and MICSR images.Results: Like ORI‐CSPAMM, the proposed ORI‐O‐CSPAMM sequence removed almost completely the off‐resonance artifacts produced during the tagging preparation. Tagging grids without DC components were obtained with ORI‐O‐CSPAMM using complex difference and MICSR from only two complementary images, which reduced the scan time to a half compared to CSPAMM and ORI‐CSPAMM. The removal of off‐resonance effects and the capacity to obtain MICSR images are advantages of ORI‐O‐CSPAMM over the O‐CSPAMM sequence.Conclusion: We developed a novel and fast tagging sequence designed to remove off‐resonance effects during the tagging preparation, and to obtain complex difference and MICSR grids in half of the scan time compared to CSPAMM and ORI‐CSPAMM sequences, which could allow its application to clinical protocols.

We proposed a novel method called HARP-I, which enhances the estimation of motion from tagged Magnetic Resonance Imaging (MRI). The harmonic phase of the images is unwrapped and treated as noisy measurements of reference coordinates on a deformed domain, obtaining motion with high accuracy using Radial Basis Functions interpolations. Results were compared against Shortest Path HARP Refinement (SP-HR) and Sine-wave Modeling (SinMod), two harmonic image-based techniques for motion estimation from tagged images. HARP-I showed a favorable similarity with both methods under noise-free conditions, whereas a more robust performance was found in the presence of noise. Cardiac strain was better estimated using HARP-I at almost any motion level, giving strain maps with less artifacts. Additionally, HARP-I showed better temporal consistency as a new method was developed to fix phase jumps between frames. In conclusion, HARP-I showed to be a robust method for the estimation of motion and strain under ideal and non-ideal conditions.