Computational fluid-structure interaction analysis of the end-to-side radio-cephalic arteriovenous fistula.

BACKGROUND AND OBJECTIVE: In the current work, we present a descriptive fluid-structure interaction computational study of the end-to-side radio-cephalic arteriovenous fistula. This allows us to account for the different thicknesses and elastic properties of the radial artery and cephalic vein. METHODS: The core of the work consists in simulating different arteriovenous fistula configurations obtained by virtually varying the anastomosis angle, i.e. the angle between the end of the cephalic vein and the side of the radial artery. Since the aim of the work is to understand the blood dynamics in the very first days after the surgical intervention, the radial artery is considered stiffer and thicker than the cephalic vein. RESULTS: Our results demonstrate that both the diameter of the cephalic vein and the anastomosis angle play a crucial role to obtain a blood dynamics without re-circulation regions that could prevent fistula failure. CONCLUSIONS: When an anastomosis angle close to the perpendicular direction with respect to the radial artery is combined with a large diameter of the cephalic vein, the recirculation regions and the low Wall Shear Stress (WSS) zones are reduced. Conversely, from a structural point of view, a low anastomosis angle with a large diameter of the cephalic vein reduces the mechanical stress acting on the vessel walls.

A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system.

Impaired cardiac function has been described as a frequent complication of COVID-19-related pneumonia. To investigate possible underlying mechanisms, we represented the cardiovascular system by means of a lumped-parameter 0D mathematical model. The model was calibrated using clinical data, recorded in 58 patients hospitalized for COVID-19-related pneumonia, to make it patient-specific and to compute model outputs of clinical interest related to the cardiocirculatory system. We assessed, for each patient with a successful calibration, the statistical reliability of model outputs estimating the uncertainty intervals. Then, we performed a statistical analysis to compare healthy ranges and mean values (over patients) of reliable model outputs to determine which were significantly altered in COVID-19-related pneumonia. Our results showed significant increases in right ventricular systolic pressure, diastolic and mean pulmonary arterial pressure, and capillary wedge pressure. Instead, physical quantities related to the systemic circulation were not significantly altered. Remarkably, statistical analyses made on raw clinical data, without the support of a mathematical model, were unable to detect the effects of COVID-19-related pneumonia in pulmonary circulation, thus suggesting that the use of a calibrated 0D mathematical model to describe the cardiocirculatory system is an effective tool to investigate the impairments of the cardiocirculatory system associated with COVID-19.

Whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations.

Cardiac digital twins provide a physics and physiology informed framework to deliver personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. We use Latent Neural Ordinary Differential Equations (LNODEs) to learn the pressure-volume dynamics of a heart failure patient. Our surrogate model is trained from 400 simulations while accounting for 43 parameters describing cell-to-organ cardiac electromechanics and cardiovascular hemodynamics. LNODEs provide a compact representation of the 3D-0D model in a latent space by means of an Artificial Neural Network that retains only 3 hidden layers with 13 neurons per layer and allows for numerical simulations of cardiac function on a single processor. We employ LNODEs to perform global sensitivity analysis and parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor.

A comprehensive stroke risk assessment by combining atrial computational fluid dynamics simulations and functional patient data.

Stroke, a major global health concern often rooted in cardiac dynamics, demands precise risk evaluation for targeted intervention. Current risk models, like the CHA 2 DS 2 -VASc score, often lack the granularity required for personalized predictions. In this study, we present a nuanced and thorough stroke risk assessment by integrating functional insights from cardiac magnetic resonance (CMR) with patient-specific computational fluid dynamics (CFD) simulations. Our cohort, evenly split between control and stroke groups, comprises eight patients. Utilizing CINE CMR, we compute kinematic features, revealing smaller left atrial volumes for stroke patients. The incorporation of patient-specific atrial displacement into our hemodynamic simulations unveils the influence of atrial compliance on the flow fields, emphasizing the importance of LA motion in CFD simulations and challenging the conventional rigid wall assumption in hemodynamics models. Standardizing hemodynamic features with functional metrics enhances the differentiation between stroke and control cases. While standalone assessments provide limited clarity, the synergistic fusion of CMR-derived functional data and patient-informed CFD simulations offers a personalized and mechanistic understanding, distinctly segregating stroke from control cases. Specifically, our investigation reveals a crucial clinical insight: normalizing hemodynamic features based on ejection fraction fails to differentiate between stroke and control patients. Differently, when normalized with stroke volume, a clear and clinically significant distinction emerges and this holds true for both the left atrium and its appendage, providing valuable implications for precise stroke risk assessment in clinical settings. This work introduces a novel framework for seamlessly integrating hemodynamic and functional metrics, laying the groundwork for improved predictive models, and highlighting the significance of motion-informed, personalized risk assessments.

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.

A comprehensive stroke risk assessment by combining atrial computational fluid dynamics simulations and functional patient data.

Stroke, a major global health concern often rooted in cardiac dynamics, demands precise risk evaluation for targeted intervention. Current risk models, like the CHA2DS2-VASc score, often lack the granularity required for personalized predictions. In this study, we present a nuanced and thorough stroke risk assessment by integrating functional insights from cardiac magnetic resonance (CMR) with patient-specific computational fluid dynamics (CFD) simulations. Our cohort, evenly split between control and stroke groups, comprises eight patients. Utilizing CINE CMR, we compute kinematic features, revealing smaller left atrial volumes for stroke patients. The incorporation of patient-specific atrial displacement into our hemodynamic simulations unveils the influence of atrial compliance on the flow fields, emphasizing the importance of LA motion in CFD simulations and challenging the conventional rigid wall assumption in hemodynamics models. Standardizing hemodynamic features with functional metrics enhances the differentiation between stroke and control cases. While standalone assessments provide limited clarity, the synergistic fusion of CMR-derived functional data and patient-informed CFD simulations offers a personalized and mechanistic understanding, distinctly segregating stroke from control cases. Specifically, our investigation reveals a crucial clinical insight: normalizing hemodynamic features based on ejection fraction fails to differentiate between stroke and control patients. Differently, when normalized with stroke volume, a clear and clinically significant distinction emerges and this holds true for both the left atrium and its appendage, providing valuable implications for precise stroke risk assessment in clinical settings. This work introduces a novel framework for seamlessly integrating hemodynamic and functional metrics, laying the groundwork for improved predictive models, and highlighting the significance of motion-informed, personalized risk assessments.

Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation.

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio-temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high-performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning-based operator approximation, which we refer to as Deep-HyROMnet technique. Our strategy combines a projection-based POD-Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper-reduction techniques employed in reduced-order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient-specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter-dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection-based ROMs, in terms of orders of magnitude of computational speed-up, and to return accurate pressure-volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

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.

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.

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.

A detailed mathematical model of the human atrial cardiomyocyte: integration of electrophysiology and cardiomechanics.

Mechano-electric regulations (MER) play an important role in the maintenance of cardiac performance. Mechano-calcium and mechano-electric feedback (MCF and MEF) pathways adjust the cardiomyocyte contractile force according to mechanical perturbations and affects electro-mechanical coupling. MER integrates all these regulations in one unit resulting in a complex phenomenon. Computational modelling is a useful tool to accelerate the mechanistic understanding of complex experimental phenomena. We have developed a novel model that integrates the MER loop for human atrial cardiomyocytes with proper consideration of feedforward and feedback pathways. The model couples a modified version of the action potential (AP) Koivumäki model with the contraction model by Quarteroni group. The model simulates iso-sarcometric and isometric twitches and the feedback effects on AP and Ca2+ -handling. The model showed a biphasic response of Ca2+ transient (CaT) peak to increasing pacing rates and highlights the possible mechanisms involved. The model has shown a shift of the threshold for AP and CaT alternans from 4.6 to 4 Hz under post-operative atrial fibrillation, induced by depressed SERCA activity. The alternans incidence was dependent on a chain of mechanisms including RyRs availability time, MCF coupling, CaMKII phosphorylation, and the stretch levels. As a result, the model predicted a 10% slowdown of conduction velocity for a 20% stretch, suggesting a role of stretch in creation of substrate formation for atrial fibrillation. Overall, we conclude that the developed model provides a physiological CaT followed by a physiological twitch. This model can open pathways for the future studies of human atrial electromechanics. KEY POINTS: With the availability of human atrial cellular data, interest in atrial-specific model integration has been enhanced. We have developed a detailed mathematical model of human atrial cardiomyocytes including the mechano-electric regulatory loop. The model has gone through calibration and evaluation phases against a wide collection of available human in-vitro data. The usefulness of the model for analysing clinical problems has been preliminaryly tested by simulating the increased incidence of Ca2+ transient and action potential alternans at high rates in post-operative atrial fibrillation condition. The model determines the possible role of mechano-electric feedback in alternans incidence, which can increase vulnerability to atrial arrhythmias by varying stretch levels. We found that our physiologically accurate description of Ca2+ handling can reproduce many experimental phenomena and can help to gain insights into the underlying pathophysiological mechanisms.

Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: An application to the Italian scenario.

In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a given time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Compared to other recent works, our model incorporates all stages of the COVID-19 disease, including death or recovery, without accounting for additional specific compartments that would increase computational complexity and that are not relevant for our purposes. Moreover, we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns. Indeed, in each considered scenario, our optimization framework guarantees noticeable improvements in terms of reducing deceased, infected or hospitalized individuals with respect to the baseline vaccination policy.

Uncertainty Quantification for Fisher-Kolmogorov Equation on Graphs with Application to Patient-Specific Alzheimer Disease.

The Fisher-Kolmogorov equation is a diffusion-reaction PDE that is used to model the accumulation of prionic proteins, which are responsible for many different neurological disorders. Likely, the most important and studied misfolded protein in literature is the Amyloid-$\beta$, responsible for the onset of Alzheimer disease. Starting from medical images we construct a reduced-order model based on a graph brain connectome. The reaction coefficient of the proteins is modelled as a stochastic random field, taking into account all the many different underlying physical processes, which can hardly be measured. Its probability distribution is inferred by means of the Monte Carlo Markov Chain method applied to clinical data. The resulting model is patient-specific and can be employed for predicting the disease's future development. Forward uncertainty quantification techniques (Monte Carlo and sparse grid stochastic collocation) are applied with the aim of quantifying the impact of the variability of the reaction coefficient on the progression of protein accumulation within the next 20 years.

lifex-fiber: an open tool for myofibers generation in cardiac computational models.

BACKGROUND: Modeling the whole cardiac function involves the solution of several complex multi-physics and multi-scale models that are highly computationally demanding, which call for simpler yet accurate, high-performance computational tools. Despite the efforts made by several research groups, no software for whole-heart fully-coupled cardiac simulations in the scientific community has reached full maturity yet. RESULTS: In this work we present [Formula: see text]-fiber, an innovative tool for the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, which are the essential building blocks for modeling the electrophysiological, mechanical and electromechanical cardiac function, from single-chamber to whole-heart simulations. [Formula: see text]-fiber is the first publicly released module for cardiac simulations based on [Formula: see text], an open-source, high-performance Finite Element solver for multi-physics, multi-scale and multi-domain problems developed in the framework of the iHEART project, which aims at making in silico experiments easily reproducible and accessible to a wide community of users, including those with a background in medicine or bio-engineering. CONCLUSIONS: The tool presented in this document is intended to provide the scientific community with a computational tool that incorporates general state of the art models and solvers for simulating the cardiac function within a high-performance framework that exposes a user- and developer-friendly interface. This report comes with an extensive technical and mathematical documentation to welcome new users to the core structure of [Formula: see text]-fiber and to provide them with a possible approach to include the generated cardiac fibers into more sophisticated computational pipelines. In the near future, more modules will be successively published either as pre-compiled binaries for x86-64 Linux systems or as open source software.

An Image-Based Computational Fluid Dynamics Study of Mitral Regurgitation in Presence of Prolapse.

PURPOSE: In this work we performed an imaged-based computational study of the systolic fluid dynamics in presence of mitral valve regurgitation (MVR). In particular, we compared healthy and different regurgitant scenarios with the aim of quantifying different hemodynamic quantities. METHODS: We performed computational fluid dynamic (CFD) simulations in the left ventricle, left atrium and aortic root, with a resistive immersed method, a turbulence model, and with imposed systolic wall motion reconstructed from Cine-MRI images, which allowed us to segment also the mitral valve. For the regurgitant scenarios we considered an increase of the heart rate and a dilation of the left ventricle. RESULTS: Our results highlighted that MVR gave rise to regurgitant jets through the mitral orifice impinging against the atrial walls and scratching against the mitral valve leading to high values of wall shear stresses (WSSs) with respect to the healthy case. CONCLUSION: CFD with prescribed wall motion and immersed mitral valve revealed to be an effective tool to quantitatively describe hemodynamics in case of MVR and to compare different regurgitant scenarios. Our findings highlighted in particular the presence of transition to turbulence in the atrium and allowed us to quantify some important cardiac indices such as cardiac output and WSS.

Fluid-structure interaction analysis of transcatheter aortic valve implantation.

Transcatheter aortic valve implantation (TAVI) is a minimally invasive intervention for the treatment of severe aortic valve stenosis. The main cause of failure is the structural deterioration of the implanted prosthetic leaflets, possibly inducing a valvular re-stenosis 5-10 years after the implantation. Based solely on pre-implantation data, the aim of this work is to identify fluid-dynamics and structural indices that may predict the possible valvular deterioration, in order to assist the clinicians in the decision-making phase and in the intervention design. Patient-specific, pre-implantation geometries of the aortic root, the ascending aorta, and the native valvular calcifications were reconstructed from computed tomography images. The stent of the prosthesis was modeled as a hollow cylinder and virtually implanted in the reconstructed domain. The fluid-structure interaction between the blood flow, the stent, and the residual native tissue surrounding the prosthesis was simulated by a computational solver with suitable boundary conditions. Hemodynamical and structural indicators were analyzed for five different patients that underwent TAVI - three with prosthetic valve degeneration and two without degeneration - and the comparison of the results showed a correlation between the leaflets' structural degeneration and the wall shear stress distribution on the proximal aortic wall. This investigation represents a first step towards computational predictive analysis of TAVI degeneration, based on pre-implantation data and without requiring additional peri-operative or follow-up information. Indeed, being able to identify patients more likely to experience degeneration after TAVI may help to schedule a patient-specific timing of follow-up.

Fast and robust parameter estimation with uncertainty quantification for the cardiac function.

BACKGROUND AND OBJECTIVES: Parameter estimation and uncertainty quantification are crucial in computational cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Many model parameters regarding cardiac electromechanics and cardiovascular hemodynamics need to be robustly fitted by starting from a few, possibly non-invasive, noisy observations. Moreover, short execution times and a small amount of computational resources are required for the effective clinical translation. METHODS: In the framework of Bayesian statistics, we combine Maximum a Posteriori estimation and Hamiltonian Monte Carlo to find an approximation of model parameters and their posterior distributions. Fast simulations and minimal memory requirements are achieved by using an accurate and geometry-specific Artificial Neural Network surrogate model for the cardiac function, matrix-free methods, automatic differentiation and automatic vectorization. Furthermore, we account for the surrogate modeling error and measurement error. RESULTS: We perform three different in silico test cases, ranging from the ventricular function to the entire cardiocirculatory system, involving whole-heart mechanics, arterial and venous hemodynamics. By employing a single central processing unit on a standard laptop, we attain highly accurate estimations for all model parameters in short computational times. Furthermore, we obtain posterior distributions that contain the true values inside the 90% credibility regions. CONCLUSIONS: Many model parameters regarding the entire cardiovascular system can be fastly and robustly identified with minimal hardware requirements. This can be achieved when a small amount of non-invasive data is available and when high levels of signal-to-noise ratio are present in the quantities of interest. With these features, our approach meets the requirements for clinical exploitation, while being compliant with Green Computing practices.

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

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.