Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks.

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equations, thus demanding extensive computational resources. In contrast, data-driven approaches leverage deep learning algorithms to describe system evolution in low-dimensional spaces. We introduce an architecture, termed Latent Dynamics Network, capable of uncovering low-dimensional intrinsic dynamics in potentially non-Markovian systems. Latent Dynamics Networks automatically discover a low-dimensional manifold while learning the system dynamics, eliminating the need for training an auto-encoder and avoiding operations in the high-dimensional space. They predict the evolution, even in time-extrapolation scenarios, of space-dependent fields without relying on predetermined grids, thus enabling weight-sharing across query-points. Lightweight and easy-to-train, Latent Dynamics Networks demonstrate superior accuracy (normalized error 5 times smaller) in highly-nonlinear problems with significantly fewer trainable parameters (more than 10 times fewer) compared to state-of-the-art methods.

The role of computational methods in cardiovascular medicine: a narrative review.

Background and Objective: Computational models of the cardiovascular system allow for a detailed and quantitative investigation of both physiological and pathological conditions, thanks to their ability to combine clinical-possibly patient-specific-data with physical knowledge of the processes underlying the heart function. These models have been increasingly employed in clinical practice to understand pathological mechanisms and their progression, design medical devices, support clinicians in improving therapies. Hinging upon a long-year experience in cardiovascular modeling, we have recently constructed a computational multi-physics and multi-scale integrated model of the heart for the investigation of its physiological function, the analysis of pathological conditions, and to support clinicians in both diagnosis and treatment planning. This narrative review aims to systematically discuss the role that such model had in addressing specific clinical questions, and how further impact of computational models on clinical practice are envisaged. Methods: We developed computational models of the physical processes encompassed by the heart function (electrophysiology, electrical activation, force generation, mechanics, blood flow dynamics, valve dynamics, myocardial perfusion) and of their inherently strong coupling. To solve the equations of such models, we devised advanced numerical methods, implemented in a flexible and highly efficient software library. We also developed computational procedures for clinical data post-processing-like the reconstruction of the heart geometry and motion from diagnostic images-and for their integration into computational models. Key Content and Findings: Our integrated computational model of the heart function provides non-invasive measures of indicators characterizing the heart function and dysfunctions, and sheds light on its underlying processes and their coupling. Moreover, thanks to the close collaboration with several clinical partners, we addressed specific clinical questions on pathological conditions, such as arrhythmias, ventricular dyssynchrony, hypertrophic cardiomyopathy, degeneration of prosthetic valves, and the way coronavirus disease 2019 (COVID-19) infection may affect the cardiac function. In multiple cases, we were also able to provide quantitative indications for treatment. Conclusions: Computational models provide a quantitative and detailed tool to support clinicians in patient care, which can enhance the assessment of cardiac diseases, the prediction of the development of pathological conditions, and the planning of treatments and follow-up tests.

lifex-ep: a robust and efficient software for cardiac electrophysiology simulations.

BACKGROUND: Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations, capable of accurately replicating both normal and pathological conditions, are still in the process of achieving full maturity within the scientific community. RESULTS: This work introduces [Formula: see text]-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both normal and pathological conditions. [Formula: see text]-ep employs the monodomain equation to model the heart's electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, [Formula: see text]-ep integrates the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within [Formula: see text]-fiber. As an alternative, users can also choose to import myofibers from a file. This paper provides a concise overview of the mathematical models and numerical methods underlying [Formula: see text]-ep, along with comprehensive implementation details and instructions for users. [Formula: see text]-ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of [Formula: see text]-ep through various idealized and realistic simulations conducted in both normal and pathological scenarios. Furthermore, the software offers a user-friendly and flexible interface, simplifying the setup of simulations using self-documenting parameter files. CONCLUSIONS: [Formula: see text]-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface. [Formula: see text]-ep represents a valuable tool for conducting in silico patient-specific simulations.

Universal Solution Manifold Networks (USM-Nets): Non-Intrusive Mesh-Free Surrogate Models for Problems in Variable Domains.

We introduce universal solution manifold network (USM-Net), a novel surrogate model, based on artificial neural networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. We employ a mesh-less architecture, thus overcoming the limitations associated with image segmentation and mesh generation required by traditional discretization methods. Our method encodes geometrical variability through scalar landmarks, such as coordinates of points of interest. In biomedical applications, these landmarks can be inexpensively processed from clinical images. We present proof-of-concept results obtained with a data-driven loss function based on simulation data. Nonetheless, our framework is non-intrusive and modular, as we can modify the loss by considering additional constraints, thus leveraging available physical knowledge. Our approach also accommodates a universal coordinate system, which supports the USM-Net in learning the correspondence between points belonging to different geometries, boosting prediction accuracy on unobserved geometries. Finally, we present two numerical test cases in computational fluid dynamics involving variable Reynolds numbers as well as computational domains of variable shape. The results show that our method allows for inexpensive but accurate approximations of velocity and pressure, avoiding computationally expensive image segmentation, mesh generation, or re-training for every new instance of physical parameters and shape of the domain.

Slow Conduction Corridors and Pivot Sites Characterize the Electrical Remodeling in Atrial Fibrillation.

OBJECTIVES: This study aimed to evaluate the progression of electrophysiological phenomena in a cohort of patients with paroxysmal atrial fibrillation (PAF) and persistent atrial fibrillation (PsAF). BACKGROUND: Electrical remodeling has been conjectured to determine atrial fibrillation (AF) progression. METHODS: High-density electroanatomic maps during sinus rhythm of 20 patients with AF (10 PAF, 10 PsAF) were compared with 5 healthy control subjects (subjects undergoing ablation of a left-sided accessory pathway). A computational postprocessing of electroanatomic maps was performed to identify specific electrophysiological phenomena: slow conductions corridors, defined as discrete areas of conduction velocity <50 cm/s, and pivot points, defined as sites showing high wave-front curvature documented by a curl module >2.5 1/s. RESULTS: A progressive decrease of mean conduction velocity was recorded across the groups (111.6 ± 55.5 cm/s control subjects, 97.1 ± 56.3 cm/s PAF, and 84.7 ± 55.7 cm/s PsAF). The number and density of slow conduction corridors increase in parallel with the progression of AF (8.6 ± 2.2 control subjects, 13.3 ± 3.2 PAF, and 20.5 ± 4.5 PsAF). In PsAF the atrial substrate is characterized by a higher curvature of wave-front propagation (0.86 ± 0.71 1/s PsAF vs 0.74 ± 0.63 1/s PAF; P = 0.003) and higher number of pivot points (25.1 ± 13.8 PsAF vs 9.5 ± 6.7 PAF; P < 0.0001). Slow conductions: corridors were mostly associated with pivot sites tending to cluster around pulmonary veins antra. CONCLUSIONS: The electrical remodeling hinges mainly on corridors of slow conduction and higher curvature of wave-front propagation. Pivot points associated to SC corridors may be the major determinants for functional localized re-entrant circuits creating the substrate for maintenance of AF.

The role of mechano-electric feedbacks and hemodynamic coupling in scar-related ventricular tachycardia.

Mechano-electric feedbacks (MEFs), which model how mechanical stimuli are transduced into electrical signals, have received sparse investigation by considering electromechanical simulations in simplified scenarios. In this paper, we study the effects of different MEFs modeling choices for myocardial deformation and nonselective stretch-activated channels (SACs) in the monodomain equation. We perform numerical simulations during ventricular tachycardia (VT) by employing a biophysically detailed and anatomically accurate 3D electromechanical model for the left ventricle (LV) coupled with a 0D closed-loop model of the cardiocirculatory system. We model the electromechanical substrate responsible for scar-related VT with a distribution of infarct and peri-infarct zones. Our mathematical framework takes into account the hemodynamic effects of VT due to myocardial impairment and allows for the classification of their hemodynamic nature, which can be either stable or unstable. By combining electrophysiological, mechanical and hemodynamic models, we observe that all MEFs may alter the propagation of the transmembrane potential. In particular, we notice that the presence of myocardial deformation in the monodomain equation may change the VT basis cycle length and the conduction velocity but do not affect the hemodynamic nature of the VT. Finally, nonselective SACs may affect VT stability, by possibly turning a hemodynamically stable VT into a hemodynamically unstable one.

Electrogram fractionation during sinus rhythm occurs in normal voltage atrial tissue in patients with atrial fibrillation.

INTRODUCTION: Electrogram (EGM) fractionation is often associated with diseased atrial tissue; however, mechanisms for fractionation occurring above an established threshold of 0.5 mV have never been characterized. We sought to investigate during sinus rhythm (SR) the mechanisms underlying bipolar EGM fractionation with high-density mapping in patients with atrial fibrillation (AF). METHODS: Forty-five patients undergoing AF ablation (73% paroxysmal, 27% persistent) were mapped at high density (18562 ± 2551 points) during SR (Rhythmia). Only bipolar EGMs with voltages above 0.5 mV were considered for analysis. When fractionation (> 40 ms and >4 deflections) was detected, we classified the mechanisms as slow conduction, wave-front collision, or a pivot point. The relationship between EGM duration and amplitude, and tissue anisotropy and slow conduction, was then studied using a computational model. RESULTS: Of the 45 left atria analyzed, 133 sites of EGM fragmentation were identified with voltages above 0.5 mV. The most frequent mechanism (64%) was slow conduction (velocity 0.45 m/s ± 0.2) with mean EGM voltage of 1.1 ± 0.5 mV and duration of 54.9 ± 9.4 ms. Wavefront collision was the second most frequent (19%), characterized by higher voltage (1.6 ± 0.9 mV) and shorter duration (51.3 ± 11.3 ms). Pivot points (9%) were associated with the highest degree of fractionation with 70.7 ± 6.6 ms and 1.8 ± 1 mV. In 10 sites (8%) fractionation was unexplained. The EGM duration was significantly different among the 3 mechanisms (p = .0351). CONCLUSION: In patients with a history of AF, EGM fractionation can occur at amplitudes > 0.5 mV when in SR in areas often considered not to be diseased tissue. The main mechanism of EGM fractionation is slow conduction, followed by wavefront collision and pivot sites.

Characterization of cardiac electrogram signals in atrial arrhythmias.

Despite significant advancements in 3D cardiac mapping systems utilized in daily electrophysiology practices, the characterization of atrial substrate remains crucial for the comprehension of supraventricular arrhythmias. During mapping, intracardiac electrograms (EGM) provide specific information that the cardiac electrophysiologist is required to rapidly interpret during the course of a procedure in order to perform an effective ablation. In this review, EGM characteristics collected during sinus rhythm (SR) in patients with paroxysmal atrial fibrillation (pAF) are analyzed, focusing on amplitude, duration and fractionation. Additionally, EGMs recorded during atrial fibrillation (AF), including complex fractionated atrial EGMs (CFAE), may also provide precious information. A complete understanding of their significance remains lacking, and as such, we aimed to further explore the role of CFAE in strategies for ablation of persistent AF. Considering focal atrial tachycardias (AT), current cardiac mapping systems provide excellent tools that can guide the operator to the site of earliest activation. However, only careful analysis of the EGM, distinguishing low amplitude high frequency signals, can reliably identify the absolute best site for RF. Evaluating macro-reentrant atrial tachycardia circuits, specific EGM signatures correspond to particular electrophysiological phenomena: the careful recognition of these EGM patterns may in fact reveal the best site of ablation. In the near future, mathematical models, integrating patient-specific data, such as cardiac geometry and electrical conduction properties, may further characterize the substrate and predict future (potential) reentrant circuits.

Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning.

We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.

Data integration for the numerical simulation of cardiac electrophysiology.

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing therapies and interventions. In this direction, mathematical and numerical models provide a complementary relevant tool, able not only to reproduce patient-specific clinical indicators but also to predict and explore unseen scenarios. With this goal, clinical data are processed and provided as inputs to the mathematical model, which quantitatively describes the physical processes that occur in the cardiac tissue. In this paper, the process of integration of clinical data and mathematical models is discussed. Some challenges and contributions in the field of cardiac electrophysiology are reported.

Outer loop and isthmus in ventricular tachycardia circuits: Characteristics and implications.

BACKGROUND: The isthmus of ventricular tachycardia (VT) circuits has been extensively characterized. Few data exist regarding the contribution of the outer loop (OL) to the VT circuit. OBJECTIVE: The purpose of this study was to characterize the electrophysiological properties of the OL. METHODS: Complete substrate activation mapping during sinus rhythm (SR) and full activation mapping of the VT circuit with high-density mapping were performed. Maps were analyzed mathematically to reconstruct conduction velocities (CVs) within the circuit. CV >100 cm/s was defined as normal and <50 cm/s as slow. Electrograms along the entire circuit were analyzed for fractionation, duration, and amplitude. RESULTS: Six postmyocardial infarction patients were enrolled. The VT circuit was a figure-of-eight reentrant circuit in 4 patients and a single-loop circuit in 2 patients. The OL exhibited a mean of 1.9 ± 0.9 and 1.6 ± 0.5 corridors of slow conduction (SC) during VT and SR, respectively. SC in the OL were longer and faster than SC in the isthmus during SR. At the OL, SC sites showed local abnormal ventricular activity in 92%, and a bipolar voltage <0.5 mV was identified in 80.7%. Of the double-loop circuits, only 1 patient had fixed lines of block as isthmus boundaries, whereas in 3 patients the circuits were at least partially functional. CONCLUSION: In ischemic reentrant VT circuits, the OL contributes significantly to reentry with multiple corridors of SC. These corridors can result from structural or functional phenomena. Isthmus boundaries may correspond to functional or fixed lines of block.