Cardiovascular health is vital to human well-being, and cardiac magnetic resonance (CMR) imaging is considered the clinical reference standard for diagnosing cardiovascular disease. However, its adoption is hindered by long scan times, complex contrasts, and inconsistent quality. While deep learning methods perform well on specific CMR imaging sequences, they often fail to generalize across modalities and sampling schemes. The lack of benchmarks for high-quality, fast CMR image reconstruction further limits technology comparison and adoption. The CMRxRecon2024 challenge, attracting over 200 teams from 18 countries, addressed these issues with two tasks: generalization to unseen modalities and robustness to diverse undersampling patterns. We introduced the largest public multi-modality CMR raw dataset, an open benchmarking platform, and shared code. Analysis of the best-performing solutions revealed that prompt-based adaptation and enhanced physics-driven consistency enabled strong cross-scenario performance. These findings establish principles for generalizable reconstruction models and advance clinically translatable AI in cardiovascular imaging.

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.

We present a method to automatically segment 4D flow magnetic resonance imaging (MRI) by identifying net flow effects using the standardized difference of means (SDM) velocity. The SDM velocity quantifies the ratio between the net flow and observed flow pulsatility in each voxel. Vessel segmentation is performed using an F-test, identifying voxels with significantly higher SDM velocity values than background voxels. We compare the SDM segmentation algorithm against pseudo-complex difference (PCD) intensity segmentation of 4D flow measurements in in vitro cerebral aneurysm models and 10 in vitro Circle of Willis (CoW) datasets. We also compared the SDM algorithm to convolutional neural network (CNN) segmentation in 5 thoracic vasculature datasets. The in vitro flow phantom geometry is known, while the ground truth geometries for the CoW and thoracic aortas are derived from high-resolution time-of-flight (TOF) magnetic resonance angiography and manual segmentation, respectively. The SDM algorithm demonstrates greater robustness than PCD and CNN approaches and can be applied to 4D flow data from other vascular territories. The SDM to PCD comparison demonstrated an approximate 48% increase in sensitivity in vitro and 70% increase in the CoW, respectively; the SDM and CNN sensitivities were similar. The vessel surface derived from the SDM method was 46% closer to the in vitro surfaces and 72% closer to the in vitro TOF surfaces than the PCD approach. The SDM and CNN approaches both accurately identify vessel surfaces. The SDM algorithm is a repeatable segmentation method, enabling reliable computation of hemodynamic metrics associated with cardiovascular disease.

We present a model to estimate the bias error of 4D flow magnetic resonance imaging (MRI) velocity measurements. The local instantaneous bias error is defined as the difference between the expectation of the voxel's measured velocity and actual velocity at the voxel center. The model accounts for bias error introduced by the intra-voxel velocity distribution and partial volume (PV) effects. We assess the intra-voxel velocity distribution using a 3D Taylor Series expansion. PV effects and numerical errors are considered using a Richardson extrapolation. The model is applied to synthetic Womersley flow and in vitro and in vivo 4D flow MRI measurements in a cerebral aneurysm. The bias error model is valid for measurements with at least 3.75 voxels across the vessel diameter and signal-to-noise ratio greater than 5. All test cases exceeded this diameter to voxel size ratio with diameters, isotropic voxel sizes, and velocity ranging from 3-15mm, 0.5-1mm, and 0-60cm/s, respectively. The model accurately estimates the bias error in voxels not affected by PV effects. In PV voxels, the bias error is an order of magnitude higher, and the accuracy of the bias error estimation in PV voxels ranges from 67.3% to 108% relative to the actual bias error. The bias error estimated for in vivo measurements increased two-fold at systole compared to diastole in partial volume and non-partial volume voxels, suggesting the bias error varies over the cardiac cycle. This bias error model quantifies 4D flow MRI measurement accuracy and can help plan 4D flow MRI scans.

A novel divergence-free constrained phase unwrapping method was proposed and evaluated for 4D flow MRI. The unwrapped phase field was obtained by integrating the phase variations estimated from the wrapped phase data using weighted least-squares. The divergence-free constraint for incompressible blood flow was incorporated to regulate and denoise the resulting phase field. The proposed method was tested on synthetic phase data of left ventricular flow and in vitro 4D flow measurement of Poiseuille flow. The method was additionally applied to in vivo 4D flow measurements in the thoracic aorta from 30 human subjects. The performance of the proposed method was compared to the state-of-the-art 4D single-step Laplacian algorithm. The synthetic phase data were completely unwrapped by the proposed method for all the cases with velocity encoding (venc) as low as 20% of the maximum velocity and signal-to-noise ratio as low as 5. The in vitro Poiseuille flow data were completely unwrapped with a 60% increase in the velocity-to-noise ratio. For the in-vivo aortic datasets with venc ratio less than 0.4, the proposed method significantly improved the success rate by as much as 40% and reduced the velocity error levels by a factor of 10 compared to the state-of-the-art method. The divergence-free constrained method exhibits reliability and robustness on phase unwrapping and shows improved accuracy of velocity and hemodynamic quantities by unwrapping the low-venc 4D flow MRI data.

This work introduces a 4D flow magnetic resonance imaging (MRI) pressure reconstruction method which employs weighted least-squares (WLS) for pressure integration. Pressure gradients are calculated from the velocity fields, and velocity errors are estimated from the velocity divergence for incompressible flow. Pressure gradient errors are estimated by propagating the velocity errors through Navier-Stokes momentum equation. A weight matrix is generated based on the pressure gradient errors, then employed for pressure reconstruction. The pressure reconstruction method was demonstrated and analyzed using synthetic velocity fields as well as Poiseuille flow measured using in vitro 4D flow MRI. Performance of the proposed WLS method was compared to the method of solving the pressure Poisson equation which has been the primary method used in the previous studies. Error analysis indicated that the proposed method is more robust to velocity measurement errors. Improvement on pressure results was found to be more significant for the cases with spatially-varying velocity error level, with reductions in error ranging from 50% to over 200%. Finally, the method was applied to flow in patient-specific cerebral aneurysms. Validation was performed with in vitro flow data collected using Particle Tracking Velocimetry (PTV) and in vivo flow measurement obtained using 4D flow MRI. Pressure calculated by WLS, as opposed to the Poisson equation, was more consistent with the flow structures and showed better agreement between the in vivo and in vitro data. These results suggest the utility of WLS method to obtain reliable pressure field from clinical flow measurement data.

In the last years, illustrative methods have found their way into flow visualization since they communicate difficult information in a comprehensible way. This is of great benefit especially in domains where the audience does not necessarily have flow expertise. One such domain is the medical field where the development of 4D MR imaging (for in-vivo 3D blood flow measurement) lead to an increased demand for easy flow analysis techniques. The goal and the challenge is to transfer the data into simple visualizations supporting the physician with flow interpretation and decision making. In this work, we take one step towards this goal. We present an approach for the illustrative visualization of steady flow features occurring in 4D MRI data of heart and aorta. Like shown in manually created illustrations, we restrict our visualization to the main data characteristics and do not depict every flow detail. The input for our method are flow features extracted from a dataset's complete set of streamlines with the help of line predicates. We create an abstract depiction of these line bundles by selecting a set of bundle representatives reflecting the most important flow aspects. These lines are rendered as three-dimensional arrows that are fused in areas where they represent the same flow. Since vortices are another important flow information for a physician, we identify these regions in the 4D MRI data and display them as unobtrusive, tube-like structures. A hatching texture provides for a visual effect of rotational blood flow. By applying our illustration technique to diverse flow structures of several 4D MRI datasets, we demonstrate that the abstract visualization is useful to gain an easier insight into the data. Feedback of medical experts confirmed the usefulness and revealed limitations of our work. The images are restricted to the essential flow features and, therefore, clearer and less cluttered. Our method has great potential and offers many possible applications, e.g., in comparative visualization and also beyond the medical domain.

Four-dimensional MRI is an in vivo flow imaging modality that is expected to significantly enhance the understanding of cardiovascular diseases. Among other fields, 4D MRI provides valuable data for the research of cardiac blood flow and with that the development, diagnosis, and treatment of various cardiac pathologies. However, to gain insights from larger research studies or to apply 4D MRI in the clinical routine later on, analysis techniques become necessary that allow to robustly identify important flow characteristics without demanding too much time and expert knowledge. Heart muscle contractions and the particular complexity of the flow in the heart imply further challenges when analyzing cardiac blood flow. Working toward the goal of simplifying the analysis of 4D MRI heart data, we present a visual analysis method using line predicates. With line predicates precalculated integral lines are sorted into bundles with similar flow properties, such as velocity, vorticity, or flow paths. The user can combine the line predicates flexibly and by that carve out interesting flow features helping to gain overview. We applied our analysis technique to 4D MRI data of healthy and pathological hearts and present several flow aspects that could not be shown with current methods. Three 4D MRI experts gave feedback and confirmed the additional benefit of our method for their understanding of cardiac blood flow.

4D MRI is an in vivo flow imaging modality which has the potential to significantly enhance diagnostics and therapy of cardiovascular diseases. However, current analysis methods demand too much time and expert knowledge in order to apply 4D MRI in the clinics or larger clinical studies. One missing piece are methods allowing to gain a quick overview of the flow data's main properties. We present a line predicate approach that sorts precalculated integral lines, which capture the complete flow dynamics, into bundles with similar properties. We introduce several streamline and pathline predicates that allow to structure the flow according to various features useful for blood flow analysis, such as, e.g., velocity distribution, vortices, and flow paths. The user can combine these predicates flexibly and by that create flow structures that help to gain overview and carve out special features of the current dataset. We show the usefulness of our approach by means of a detailed discussion of 4D MRI datasets of healthy and pathological aortas.

The evaluation of cardiovascular velocities, their changes through the cardiac cycle and the consequent pressure gradients has the capacity to improve understanding of subject-specific blood flow in relation to adjacent soft tissue movements. Magnetic resonance time-resolved 3D phase contrast velocity acquisitions (4D flow) represent an emerging technology capable of measuring the cyclic changes of large scale, multi-directional, subject-specific blood flow. A subsequent evaluation of pressure differences in enclosed vascular compartments is a further step which is currently not directly available from such data. The focus of this work is to address this deficiency through the development of a novel simulation workflow for the direct computation of relative cardiovascular pressure fields. Input information is provided by enhanced 4D flow data and derived MR domain masking. The underlying methodology shows numerical advantages in terms of robustness, global domain composition, the isolation of local fluid compartments and a treatment of boundary conditions. This approach is demonstrated across a range of validation examples which are compared with analytic solutions. Four subject-specific test cases are subsequently run, showing good agreement with previously published calculations of intra-vascular pressure differences. The computational engine presented in this work contributes to non-invasive access to relative pressure fields, incorporates the effects of both blood flow acceleration and viscous dissipation, and enables enhanced evaluation of cardiovascular blood flow.