A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

Effect of dispersive electrode position (anterior vs. posterior) in epicardial radiofrequency ablation of ventricular wall: A computer simulation study

An epicardial approach is often used in radiofrequency (RF) catheter ablation to ablate ventricular tachycardia when an endocardial approach fails. Our objective was to analyze the effect of the position of the dispersive patch (DP) on lesion size using computer modeling during epicardial approach. We compared the posterior position (patient's back), commonly used in clinical practice, to the anterior position (patient's chest). The model considered ventricular wall thicknesses between 4 and 8 mm, and electrode insertion depths between .3 and .7 mm. RF pulses were simulated with 20 W of power for 30 s duration. Statistically significant differences (P < .001) were found between both DP positions in terms of baseline impedance, RF current (at 15 s) and thermal lesion size. The anterior position involved lower impedance (130.8 ± 4.7 vs. 146.2 ± 4.9 Ω) and a higher current (401.5 ± 5.6 vs. 377.5 ± 5.1 mA). The anterior position created lesion sizes larger than the posterior position: 8.9 ± 0.4 vs. 8.4 ± 0.4 mm in maximum width, 8.6 ± 0.4 vs. 8.1 ± 0.4 mm in surface width, and 4.5 ± 0.4 vs. 4.3 ± 0.4 mm in depth. Our results suggest that: (1) the redirection of the RF currents due to repositioning the PD has little impact on lesion size and only affects baseline impedance, and (2) the differences in lesion size are only 0.5 mm wider and 0.2 mm deeper for the anterior position, which does not seem to have a clinical impact in the context of VT ablation.

Patient-specific multi-physics simulations of fibrotic changes in left atrial tissue mechanics impact on hemodynamics

Stroke is a leading cause of death and disability worldwide. Atrial myopathy, including fibrosis, is associated with an increased risk of ischemic stroke, but the mechanisms underlying this association are poorly understood. Fibrosis modifies myocardial structure, impairing electrical propagation and tissue biomechanics, and creating stagnant flow regions where clots could form. Fibrosis can be mapped non-invasively using late gadolinium enhancement magnetic resonance imaging (LGE-MRI). However, fibrosis maps are not currently incorporated into stroke risk calculations or computational electro-mechano-fluidic models. We present multi-physics simulations of left atrial (LA) myocardial motion and hemodynamics using patient-specific anatomies and fibrotic maps from LGE-MRI. We modify tissue stiffness and active tension generation in fibrotic regions and investigate how these changes affect LA flow for different fibrotic burdens. We find that fibrotic regions and, to a lesser extent, non-fibrotic regions experience reduced myocardial strain, resulting in decreased LA emptying fraction consistent with clinical observations. Both fibrotic tissue stiffening and hypocontractility independently reduce LA function, but together, these two alterations cause more pronounced effects than either one alone. Fibrosis significantly alters flow patterns throughout the atrial chamber, and particularly, the filling and emptying jets of the left atrial appendage (LAA). The effects of fibrosis in LA flow are largely captured by the concomitant changes in LA emptying fraction except inside the LAA, where a multi-factorial behavior is observed. This work illustrates how high-fidelity, multi-physics models can be used to study thrombogenesis mechanisms in a patient-specific manner, shedding light onto the link between atrial fibrosis and ischemic stroke.

Key points

Left atrial (LA) fibrosis is associated with arrhythmogenesis and increased risk of ischemic stroke; its extent and pattern can be quantified on a patient-specific basis using late gadolinium enhancement magnetic resonance imaging.Current stroke risk prediction tools have limited personalization, and their accuracy could be improvedfib by incorporating patient-specific information like fibrotic maps and hemodynamic patterns.We present the first electro-mechano-fluidic multi-physics computational simulations of LA flow, including fibrosis and anatomies from medical imaging.Mechanical changes in fibrotic tissue impair global LA motion, decreasing LA and left atrial appendage (LAA) emptying fractions, especially in subjects with higher fibrosis burdens.Fibrotic-mediated LA motion impairment alters LA and LAA flow near the endocardium and the whole cavity, ultimately leading to more stagnant blood regions in the LAA.

A Modular Framework for Implicit 3D-0D Coupling in Cardiac Mechanics

In numerical simulations of cardiac mechanics, coupling the heart to a model of the circulatory system is essential for capturing physiological cardiac behavior. A popular and efficient technique is to use an electrical circuit analogy, known as a lumped parameter network or zero-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. Due to the strong physical interaction between the heart and the blood circulation, developing accurate and efficient numerical coupling methods remains an active area of research. In this work, we present a modular framework for implicitly coupling three-dimensional (3D) finite element simulations of cardiac mechanics to 0D models of blood circulation. The framework is modular in that the circulation model can be modified independently of the 3D finite element solver, and vice versa. The numerical scheme builds upon a previous work that combines 3D blood flow models with 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models with 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through multiple examples relevant to the cardiovascular modeling community. Importantly, in an idealized left ventricle example, we show that the coupled model yields physiological pressure-volume loops and naturally recapitulates the isovolumic contraction and relaxation phases of the cardiac cycle without any additional numerical techniques. Furthermore, we provide a new derivation of the scheme inspired by the Approximate Newton Method of Chan (1985), explaining how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Turbulent blood dynamics in the left heart in the presence of mitral regurgitation: a computational study based on multi-series cine-MRI

In this work, we performed a computational image-based study of blood dynamics in the whole left heart, both in a healthy subject and in a patient with mitral valve regurgitation. We elaborated multi-series cine-MRI with the aim of reconstructing the geometry and the corresponding motion of left ventricle, left atrium, mitral and aortic valves, and aortic root of the subjects. This allowed us to prescribe such motion to computational blood dynamics simulations where, for the first time, the whole left heart motion of the subject is considered, allowing us to obtain reliable subject-specific information. The final aim is to investigate and compare between the subjects the occurrence of turbulence and the risk of hemolysis and of thrombi formation. In particular, we modeled blood with the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian framework, with a large eddy simulation model to describe the transition to turbulence and a resistive method to manage the valve dynamics, and we used a finite element discretization implemented in an in-house code for the numerical solution.

Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface method

A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations. These oscillations can strongly affect valve dynamics models driven by the blood flow, making unlikely to recovering physiological dynamics. Hence, prescribed opening and closing times are usually employed, or the isovolumetric phases are neglected altogether. In this article, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., Biomech Model Mechanobiol 2017, 16, 1779-1803) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., Int J Numer Methods Biomed Eng 2020, 36, e3223) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method. Finally, we demonstrate that by the new method the cardiac valves can open and close without prescribing any opening/closing times.

Current progress toward isogeometric modeling of the heart biophysics

In this paper, we review a powerful methodology to solve complex numerical simulations, known as isogeometric analysis, with a focus on applications to the biophysical modeling of the heart. We focus on the hemodynamics, modeling of the valves, cardiac tissue mechanics, and on the simulation of medical devices and treatments. For every topic, we provide an overview of the methods employed to solve the specific numerical issue entailed by the simulation. We try to cover the complete process, starting from the creation of the geometrical model up to the analysis and post-processing, highlighting the advantages and disadvantages of the methodology.

Non-invasive technologies for heart failure, systolic and diastolic dysfunction modeling: a scoping review

The growing global prevalence of heart failure (HF) necessitates innovative methods for early diagnosis and classification of myocardial dysfunction. In recent decades, non-invasive sensor-based technologies have significantly advanced cardiac care. These technologies ease research, aid in early detection, confirm hemodynamic parameters, and support clinical decision-making for assessing myocardial performance. This discussion explores validated enhancements, challenges, and future trends in heart failure and dysfunction modeling, all grounded in the use of non-invasive sensing technologies. This synthesis of methodologies addresses real-world complexities and predicts transformative shifts in cardiac assessment. A comprehensive search was performed across five databases, including PubMed, Web of Science, Scopus, IEEE Xplore, and Google Scholar, to find articles published between 2009 and March 2023. The aim was to identify research projects displaying excellence in quality assessment of their proposed methodologies, achieved through a comparative criteria-based rating approach. The intention was to pinpoint distinctive features that differentiate these projects from others with comparable objectives. The techniques identified for the diagnosis, classification, and characterization of heart failure, systolic and diastolic dysfunction encompass two primary categories. The first involves indirect interaction with the patient, such as ballistocardiogram (BCG), impedance cardiography (ICG), photoplethysmography (PPG), and electrocardiogram (ECG). These methods translate or convey the effects of myocardial activity. The second category comprises non-contact sensing setups like cardiac simulators based on imaging tools, where the manifestations of myocardial performance propagate through a medium. Contemporary non-invasive sensor-based methodologies are primarily tailored for home, remote, and continuous monitoring of myocardial performance. These techniques leverage machine learning approaches, proving encouraging outcomes. Evaluation of algorithms is centered on how clinical endpoints are selected, showing promising progress in assessing these approaches' efficacy.

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.

Pulmonary vein flow split effects in patient-specific simulations of left atrial flow

Disruptions to left atrial (LA) blood flow, such as those caused by atrial fibrillation (AF), can lead to thrombosis in the left atrial appendage (LAA) and an increased risk of systemic embolism. LA hemodynamics are influenced by various factors, including LA anatomy and function, and pulmonary vein (PV) inflow conditions. In particular, the PV flow split can vary significantly among and within patients depending on multiple factors. In this study, we investigated how changes in PV flow split affect LA flow transport, focusing for the first time on blood stasis in the LAA, using a high-fidelity patient-specific computational fluid dynamics (CFD) model. We use an Immersed Boundary Method, simulating the flow in a fixed, uniform Cartesian mesh and imposing the movement of the LA walls with a moving Lagrangian mesh generated from 4D Computerized Tomography images. We analyzed LA anatomies from eight patients with varying atrial function, including three with AF and either a LAA thrombus or a history of Transient Ischemic Attacks (TIAs). Using four different flow splits (60/40% and 55/45% through right and left PVs, even flow rate, and same velocity through each PV), we found that flow patterns are sensitive to PV flow split variations, particularly in planes parallel to the mitral valve. Changes in PV flow split also had a significant impact on blood stasis and could contribute to increased risk for thrombosis inside the LAA, particularly in patients with AF and previous LAA thrombus or a history of TIAs. Our study highlights the importance of considering patient-specific PV flow split variations when assessing LA hemodynamics and identifying patients at increased risk for thrombosis and stroke. This knowledge is relevant to planning clinical procedures such as AF ablation or the implementation of LAA occluders.

A comprehensive mathematical model for cardiac perfusion

The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes-Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework.

Personalized biomechanical insights in atrial fibrillation: opportunities & challenges

INTRODUCTION

Atrial fibrillation (AF) is an increasingly prevalent and significant worldwide health problem. Manifested as an irregular atrial electrophysiological activation, it is associated with many serious health complications. AF affects the biomechanical function of the heart as contraction follows the electrical activation, subsequently leading to reduced blood flow. The underlying mechanisms behind AF are not fully understood, but it is known that AF is highly correlated with the presence of atrial fibrosis, and with a manifold increase in risk of stroke.

AREAS COVERED

In this review, we focus on biomechanical aspects in atrial fibrillation, current and emerging use of clinical images, and personalized computational models. We also discuss how these can be used to provide patient-specific care.

EXPERT OPINION

Understanding the connection betweenatrial fibrillation and atrial remodeling might lead to valuable understanding of stroke and heart failure pathophysiology. Established and emerging imaging modalities can bring us closer to this understanding, especially with continued advancements in processing accuracy, reproducibility, and clinical relevance of the associated technologies. Computational models of cardiac electromechanics can be used to glean additional insights on the roles of AF and remodeling in heart function.

First blood: An efficient, hybrid one- and zero-dimensional, modular hemodynamic solver

Low-dimensional (1D or 0D) models can describe the whole human blood circulation, for example, 1D distributed parameter model for the arterial network and 0D concentrated models for the heart or other organs. This paper presents a combined 1D-0D solver, called first_blood, that solves the governing equations of fluid dynamics to model low-dimensional hemodynamic effects. An extended method of characteristics is applied here to solve the momentum, and mass conservation equations and the viscoelastic wall model equation, mimicking the material properties of arterial walls. The heart and the peripheral lumped models are solved with a general zero-dimensional (0D) nonlinear solver. The model topology can be modular, that is, first_blood can solve any 1D-0D hemodynamic model. To demonstrate the applicability of first_blood, the human arterial system, the heart and the peripherals are modelled using the solver. The simulation time of a heartbeat takes around 2 s, that is, first_blood requires only twice the real-time for the simulation using an average PC, which highlights the computational efficiency. The source code is available on GitHub, that is, it is open source. The model parameters are based on the literature suggestions and on the validation of output data to obtain physiologically relevant results.