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An important tool for experimental fluids mechanics research is Particle Image Velocimetry (PIV). Several robust methodologies have been proposed to perform the estimation of velocity field from the images, however, alternative methods are still needed to increase the spatial resolution of the results. This work presents a novel approach for estimating fluid flow fields using neural networks and the optical flow equation to predict displacement vectors between sequential images. The result is a continuous representation of the displacement, that can be evaluated on the full spatial resolution of the image. The methodology was validated on synthetic and experimental images. Accurate results were obtained in terms of the estimation of instantaneous velocity fields, and of the determined time average turbulence quantities and power spectral density. The methodology proposed differs of previous attempts of using machine learning for this task: it does not require any previous training, and could be directly used in any pair of images.

Neural implicit k-space representations (NIK) have shown promising results for dynamic magnetic resonance imaging (MRI) at high temporal resolutions. Yet, reducing acquisition time, and thereby available training data, results in severe performance drops due to overfitting. To address this, we introduce a novel self-supervised k-space loss function $\mathcal{L}_\mathrm{PISCO}$, applicable for regularization of NIK-based reconstructions. The proposed loss function is based on the concept of parallel imaging-inspired self-consistency (PISCO), enforcing a consistent global k-space neighborhood relationship without requiring additional data. Quantitative and qualitative evaluations on static and dynamic MR reconstructions show that integrating PISCO significantly improves NIK representations. Particularly for high acceleration factors (R$\geq$54), NIK with PISCO achieves superior spatio-temporal reconstruction quality compared to state-of-the-art methods. Furthermore, an extensive analysis of the loss assumptions and stability shows PISCO's potential as versatile self-supervised k-space loss function for further applications and architectures. Code is available at: https://github.com/compai-lab/2025-pisco-spieker

The anisotropic structure of the myocardium is a key determinant of the cardiac function. To date, there is no imaging modality to assess in-vivo the cardiac fiber structure. We recently proposed Fibernet, a method for the automatic identification of the anisotropic conduction -- and thus fibers -- in the atria from local electrical recordings. Fibernet uses cardiac activation as recorded during electroanatomical mappings to infer local conduction properties using physics-informed neural networks. In this work, we extend Fibernet to cope with the uncertainty in the estimated fiber field. Specifically, we use an ensemble of neural networks to produce multiple samples, all fitting the observed data, and compute posterior statistics. We also introduce a methodology to select the best fiber orientation members and define the input of the neural networks directly on the atrial surface. With these improvements, we outperform the previous methodology in terms of fiber orientation error in 8 different atrial anatomies. Currently, our approach can estimate the fiber orientation and conduction velocities in under 7 minutes with quantified uncertainty, which opens the door to its application in clinical practice. We hope the proposed methodology will enable further personalization of cardiac digital twins for precision medicine.

Precision cardiology based on cardiac digital twins requires accurate simulations of cardiac arrhythmias. However, detailed models, such as the monodomain model, are computationally costly and have limited applicability in practice. Thus, it desirable to have fast models that can still represent the main physiological features presented during cardiac arrhythmias. The eikonal model is an approximation of the monodomain model that is widely used to describe the arrival times of the electrical wave. However, the standard eikonal model does not generalize to the complex re-entrant dynamics that characterize the cardiac arrhythmias. In this work, we propose an eikonal model that includes the tissue re-excitability, which allows to describe re-entries. The re-excitability properties are inferred from the monodomain model. Our eikonal model also handles the tissue anisotropy and heterogeneity. We compare the eikonal model to the monodomain model in various numerical experiments in the atria and the ventricles. The eikonal model is qualitatively accurate in the simulation of re-entries and can be potentially ran in real-time, opening the door to its clinical applicability., Comment: 18 pages, 11 figures

Recent works have shown that traditional Neural Network (NN) architectures display a marked frequency bias in the learning process. Namely, the NN first learns the low-frequency features before learning the high-frequency ones. In this study, we rigorously develop a partial differential equation (PDE) that unravels the frequency dynamics of the error for a 2-layer NN in the Neural Tangent Kernel regime. Furthermore, using this insight, we explicitly demonstrate how an appropriate choice of distributions for the initialization weights can eliminate or control the frequency bias. We focus our study on the Fourier Features model, an NN where the first layer has sine and cosine activation functions, with frequencies sampled from a prescribed distribution. In this setup, we experimentally validate our theoretical results and compare the NN dynamics to the solution of the PDE using the finite element method. Finally, we empirically show that the same principle extends to multi-layer NNs.

Magnetic resonance imaging (MRI) is fundamental for the assessment of many diseases, due to its excellent tissue contrast characterization. This is based on quantitative techniques, such as T1 , T2 , and T2* mapping. Quantitative MRI requires the acquisition of several contrast-weighed images followed by a fitting to an exponential model or dictionary matching, which results in undesirably long acquisition times. Undersampling reconstruction techniques are commonly employed to speed up the scan, with the drawback of introducing aliasing artifacts. However, most undersampling reconstruction techniques require long computational times or do not exploit redundancies across the different contrast-weighted images. This study introduces a new regularization technique to overcome aliasing artifacts, namely CConnect, which uses an innovative regularization term that leverages several trained convolutional neural networks (CNNs) to connect and exploit information across image contrasts in a latent space. We validate our method using in-vivo T2* mapping of the brain, with retrospective undersampling factors of 4, 5 and 6, demonstrating its effectiveness in improving reconstruction in comparison to state-of-the-art techniques. Comparisons against joint total variation, nuclear low rank and a deep learning (DL) de-aliasing post-processing method, with respect to structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) metrics are presented., Comment: 12 pages, 8 figures

Neural implicit k-space representations have shown promising results for dynamic MRI at high temporal resolutions. Yet, their exclusive training in k-space limits the application of common image regularization methods to improve the final reconstruction. In this work, we introduce the concept of parallel imaging-inspired self-consistency (PISCO), which we incorporate as novel self-supervised k-space regularization enforcing a consistent neighborhood relationship. At no additional data cost, the proposed regularization significantly improves neural implicit k-space reconstructions on simulated data. Abdominal in-vivo reconstructions using PISCO result in enhanced spatio-temporal image quality compared to state-of-the-art methods. Code is available at https://github.com/vjspi/PISCO-NIK., Comment: Under Review

Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or G\"{o}rtler vortices in boundary layers, resulting from the imbalance between the centrifugal forces and the radial pressure gradients, are generated. Curved free shear layer flows, however, have not received sufficient attention, especially in the nonlinear regime. The present work investigates the development of centrifugal instabilities evolving in a curved free shear layer flow in the nonlinear compressible regime. The compressible Navier-Stokes equations are reduced to the nonlinear boundary region equations (BRE) in a high Reynolds number asymptotic framework wherein the streamwise wavelengths of the disturbances are assumed to be much larger than the spanwise and wall-normal counterparts. We study the effect of the freestream Mach number $\boldsymbol{M_\infty}$, the shear layer thickness $\boldsymbol{\delta}$, the amplitude of the incoming disturbance $\boldsymbol{A}$, and the relative velocity difference across the shear layer $\boldsymbol{\Delta V}$ on the development of these centrifugal instabilities., Comment: 17 pages

The classical Hertzian contact model establishes a monotonic correlation between contact force and area. Here, we showed that the interplay between local friction and structural instability can deliberately lead to unconventional contact behavior when a soft elastic shell comes into contact with a flat surface. The deviation from Hertzian contact first arises from bending within the contact area, followed by the second transition induced by buckling, resulting in a notable decrease in the contact area despite increased contact force. Friction delays both transitions and introduces hysteresis during unloading. However, a high amount of friction suppresses both buckling and dissipation. Different contact regimes are discussed in terms of rolling and sliding mechanisms, providing insights for tailoring contact behaviors in soft shells.

The identification of the Purkinje conduction system in the heart is a challenging task, yet essential for a correct definition of cardiac digital twins for precision cardiology. Here, we propose a probabilistic approach for identifying the Purkinje network from non-invasive clinical data such as the standard electrocardiogram (ECG). We use cardiac imaging to build an anatomically accurate model of the ventricles; we algorithmically generate a rule-based Purkinje network tailored to the anatomy; we simulate physiological electrocardiograms with a fast model; we identify the geometrical and electrical parameters of the Purkinje-ECG model with Bayesian optimization and approximate Bayesian computation. The proposed approach is inherently probabilistic and generates a population of plausible Purkinje networks, all fitting the ECG within a given tolerance. In this way, we can estimate the uncertainty of the parameters, thus providing reliable predictions. We test our methodology in physiological and pathological scenarios, showing that we are able to accurately recover the ECG with our model. We propagate the uncertainty in the Purkinje network parameters in a simulation of conduction system pacing therapy. Our methodology is a step forward in creation of digital twins from non-invasive data in precision medicine. An open source implementation can be found at http://github.com/fsahli/purkinje-learning, Comment: 18 pages, 9 figures

Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of these complex materials with high accuracy while satisfying physics-based constraints. However, most of these approaches disregard the uncertainty in the estimates and the spatial heterogeneity of these materials. In this work, we leverage recent advances in generative models to address these issues. We use as building block neural ordinary equations (NODE) that -- by construction -- create polyconvex strain energy functions, a key property of realistic hyperelastic material models. We combine this approach with probabilistic diffusion models to generate new samples of strain energy functions. This technique allows us to sample a vector of Gaussian white noise and translate it to NODE parameters thereby representing plausible strain energy functions. We extend our approach to spatially correlated diffusion resulting in heterogeneous material properties for arbitrary geometries. We extensively test our method with synthetic and experimental data on biological tissues and run finite element simulations with various degrees of spatial heterogeneity. We believe this approach is a major step forward including uncertainty in predictive, data-driven models of hyperelasticity, Comment: 22 pages, 11 figures

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM).

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving inverse problems, especially in cases where no complete information about the system is known and scatter measurements are available. This is especially useful in hemodynamics since the boundary information is often difficult to model, and high-quality blood flow measurements are generally hard to obtain. In this work, we use the PINNs methodology for estimating reduced-order model parameters and the full velocity field from scatter 2D noisy measurements in the ascending aorta. The results show stable and accurate parameter estimations when using the method with simulated data, while the velocity reconstruction shows dependence on the measurement quality and the flow pattern complexity. The method allows for solving clinical-relevant inverse problems in hemodynamics and complex coupled physical systems.

Cardiac cine MRI is the gold standard for cardiac functional assessment, but the inherently slow acquisition process creates the necessity of reconstruction approaches for accelerated undersampled acquisitions. Several regularization approaches that exploit spatial-temporal redundancy have been proposed to reconstruct undersampled cardiac cine MRI. More recently, methods based on supervised deep learning have been also proposed to further accelerate acquisition and reconstruction. However, these techniques rely on usually large dataset for training, which are not always available. In this work, we propose an unsupervised approach based on implicit neural field representations for cardiac cine MRI (so called NF-cMRI). The proposed method was evaluated in in-vivo undersampled golden-angle radial multi-coil acquisitions for undersampling factors of 26x and 52x, achieving good image quality, and comparable spatial and improved temporal depiction than a state-of-the-art reconstruction technique.

Challenges drive the state-of-the-art of automated medical image analysis. The quantity of public training data that they provide can limit the performance of their solutions. Public access to the training methodology for these solutions remains absent. This study implements the Type Three (T3) challenge format, which allows for training solutions on private data and guarantees reusable training methodologies. With T3, challenge organizers train a codebase provided by the participants on sequestered training data. T3 was implemented in the STOIC2021 challenge, with the goal of predicting from a computed tomography (CT) scan whether subjects had a severe COVID-19 infection, defined as intubation or death within one month. STOIC2021 consisted of a Qualification phase, where participants developed challenge solutions using 2000 publicly available CT scans, and a Final phase, where participants submitted their training methodologies with which solutions were trained on CT scans of 9724 subjects. The organizers successfully trained six of the eight Final phase submissions. The submitted codebases for training and running inference were released publicly. The winning solution obtained an area under the receiver operating characteristic curve for discerning between severe and non-severe COVID-19 of 0.815. The Final phase solutions of all finalists improved upon their Qualification phase solutions.HSUXJM-TNZF9CHSUXJM-TNZF9C