Search

We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid and fluid species, interacting on the basis of mass balance and momentum conservation, we decide to adopt a solution strategy of the discrete problem based on iterative splitting schemes. As the model is similar (but not equivalent to) the Biot poromechanics problem, we follow the abundant literature for solvers of the latter equations, developing two approaches that resemble the well known undrained and fixed-stress splits for the Biot model. A thorough convergence analysis of the proposed schemes is performed. In particular, the undrained-like split is developed and analyzed in the framework of generalized gradient flows, whereas the fixed-stress-like split is understood as block-diagonal L 2 -type stabilization and analyzed by means of a relative stability analysis. In addition, the application of Anderson acceleration is suggested, improving the robustness of the split schemes. Finally, we test these methods on different benchmark tests, and we also compare their performance with respect to a monolithic approach. Together with the theoretical analysis, the numerical examples provide guidelines to appropriately choose what split scheme shall be used to address realistic applications of the soft material poromechanics model.

The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is proposed with the aim of reproducing the past history of the epidemic in Italy, surfaced in late February and still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are daily made available from the Italian Civil Protection. The new model is then applied to the analysis of the Italian epidemic with emphasis on the second outbreak emerged in Fall 2020. In particular, we show that the epidemiological model SUIHTER can be suitably used in a predictive manner to perform scenario analysis at national level., Comment: 25 pages

In order to simulate the cardiac function for a patient‐specific geometry, the generation of the computational mesh is crucially important. In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images. These surfaces need ad‐hoc processing to be suitable for a volumetric mesh generation. In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process. In particular, we focus on different aspects of a cardiac mesh generation pipeline: (1) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs; (2) generation of accurate boundary tags; (3) definition of mesh‐size functions dependent on relevant geometric quantities; (4) processing and connecting together several volumetric meshes. The new algorithms—implemented in the open‐source software vmtk—can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled. Thanks to these features, the proposed tools can significantly speed‐up the mesh generation process for a large range of cardiac applications, from single‐chamber single‐physics simulations to multi‐chambers multi‐physics simulations. We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines., We propose a set of algorithms and tools aiming to facilitate and speed‐up the mesh generation process for cardiac geometries.The main novelties regard the polygonal surface processing, the boundary tags definition, the mesh‐size definition, and the volumetric mesh processing.The new algorithms can be combined with each other to create personalized application‐specific pipelines.We demonstrate the robustness and the flexibility of the proposed tools through various examples on different kinds of cardiac geometries.

We developed a novel patient-specific computational model for the numerical simulation of ventricular electromechanics in patients with ischemic cardiomyopathy (ICM). This model reproduces the activity both in sinus rhythm (SR) and in ventricular tachycardia (VT). The presence of scars, grey zones and non-remodeled regions of the myocardium is accounted for by the introduction of a spatially heterogeneous coefficient in the 3D electromechanics model. This 3D electromechanics model is firstly coupled with a 2-element Windkessel afterload model to fit the pressure-volume (PV) loop of a patient-specific left ventricle (LV) with ICM in SR. Then, we employ the coupling with a 0D closed-loop circulation model to analyze a VT circuit over multiple heartbeats on the same LV. We highlight similarities and differences on the solutions obtained by the electrophysiology model and those of the electromechanics model, while considering different scenarios for the circulatory system. We observe that very different parametrizations of the circulation model induce the same hemodynamical considerations for the patient at hand. Specifically, we classify this VT as unstable. We conclude by stressing the importance of combining electrophysiological, mechanical and hemodynamical models to provide relevant clinical indicators in how arrhythmias evolve and can potentially lead to sudden cardiac death.

Since myocardial fibers drive the electric signal propagation throughout the myocardium, accurately modeling their arrangement is essential for simulating heart electrophysiology (EP). Rule-Based-Methods (RBMs) represent a commonly used strategy to include cardiac fibers in computational models. A particular class of such methods is known as Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) since they rely on the solution of Laplace problems. In this work we provide a unified framework, based on LDRBMs, for generating full heart muscle fibers. First, we review existing ventricular LDRBMs providing a communal mathematical description and introducing also some modeling improvements with respect to the existing literature. We then carry out a systematic comparison of LDRBMs based on meaningful biomarkers produced by numerical EP simulations. Next we propose, for the first time, a LDRBM to be used for generating atrial fibers. The new method, tested both on idealized and realistic atrial models, can be applied to any arbitrary geometries. Finally, we present numerical results obtained in a realistic whole heart where fibers are included for all the four chambers using the discussed LDRBMs. (C) 2020 Elsevier B.V. All rights reserved.

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.

We construct an idealized computational model of the left human heart for the study of the blood flow dynamics in the left atrium and ventricle. We solve the Navier-Stokes equations in the ALE formulation and we prescribe the left heart wall displacement based on physiological data; moreover, we consider the presence of both the mitral and aortic valves through the resistive method. We simulate the left heart hemodynamics by means of the finite element method and we consider the variational multiscale large eddy simulation (LES) formulation to account for the transitional and nearly turbulent regimes of the blood flow in physiological conditions. The main contribution of this paper is the characterization of the blood flow in an idealized configuration of the left heart aiming at reproducing function in normal conditions. Our assessment is based on the analysis of instantaneous and phase averaged velocity fields, blood pressure, and other clinically meaningful fluid dynamics indicators. Finally, we show that our idealized computational model can be suitably used to study and critically discuss pathological scenarios like that of a regurgitant mitral valve.

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.

In this paper we present a mathematical and numerical model for human cardiac perfusion which accounts for the different length scales of the vessels in the coronary tree. Epicardial vessels are represented with fully three-dimensional (3D) fluid-dynamics, whereas intramural vessels are modeled as a multi-compartment porous medium. The coupling of these models takes place through interface conditions based on the continuity of mass and momentum. Instead, is neglected in this first preliminary model the myocardium deformation. To estimate the physical parameters of the multi-compartment model, a virtual intramural vascular network is generated using a novel algorithm which works in non-convex domains. Modeling epicardial vessels with a 3D model and intramural ones with a porous medium approach makes it possible to apply the proposed strategy to patient-specific heart geometries reconstructed from clinical imaging data. We also address the derivation of numerical solvers for the coupled problem. In particular, we propose a splitting algorithm for the monolithic problem, with the corresponding convergence analysis performed in a simplified linearized case, and a suitable preconditioner for the multi-compartment porous sub-model. Finally, we test the computational framework in a realistic human heart, obtaining results that fall in the physiological range for both pressures and local myocardial flows. (C) 2020 Elsevier Inc. All rights reserved.

In the framework of cardiac electrophysiology for the human heart, we apply multipatch NURBS-based Isogeometric Analysis for the space discretization of the Monodomain model. Isogeometric Analysis (IGA) is a technique for the solution of Partial Differential Equations (PDEs) that facilitates encapsulating the exact representation of the computational geometry by using basis functions with high-order continuity. IGA features very small numerical dissipation and dispersion when compared to other methods for the solution of PDEs. The use of multiple patches allows to overcome the conventional limitations of single patch IGA, thanks to the gained flexibility in the design of the computational domain, especially when its representation is quite involved as in bioengineering applications. We propose two algorithms for the preprocessing of CAD models of complex surface and volumetric NURBS geometries with cavities, such as atria and ventricles: our purpose is to obtain geometrically and parametrically conforming NURBS multipatch models starting from CAD models. We employ those algorithms for the construction of an IGA realistic representation of a human heart. We apply IGA for the discretization of the Monodomain equation, which describes the evolution of the cardiac action potential in space and time at the tissue level. This PDE is coupled with suitable microscopic models to define the behavior at cellular scale: the Courtemanche-Ramirez-Nattel model for the atrial simulation, and the Luo-Rudy model for the ventricular one. Numerical simulations on realistic human atria and ventricle geometries are carried out, obtaining accurate and smooth excitation fronts by combining IGA with the multipatch approach for the geometrical representation of the computational domains, either surfaces for the atria or solids for the ventricles. (C) 2021 The Authors. Published by Elsevier B.V.

Emerging studies address how COVID-19 infection can impact the human cardiovascular system. This relates particularly to the development of myocardial injury, acute coronary syndrome, myocarditis, arrhythmia, and heart failure. Prospective treatment approach is advised for these patients. To study the interplay between local changes (reduced contractility), global variables (peripheral resistances, heart rate) and the cardiac function, we considered a lumped parameters computational model of the cardiovascular system and a three-dimensional multiphysics model of cardiac electromechanics. Our mathematical model allows to simulate the systemic and pulmonary circulations, the four cardiac valves and the four heart chambers, through equations describing the underlying physical processes. By the assessment of conventionally relevant parameters of cardiac function obtained through our numerical simulations, we propose a computational model to effectively reveal the interactions between the cardiac and pulmonary functions in virtual subjects with normal and impaired cardiac function at baseline affected by mild or severe COVID-19.

In this paper we describe a mathematical and numerical approach that combines physics-based simulated ground motion caused by earthquakes with fragility functions to model the structural damages induced to buildings. To simulate earthquake ground motion we use the discontinuous Galerkin spectral element method to solve a three-dimensional differential model at regional scale describing the propagation of seismic waves through the earth layers up to the surface. Selected intensity measures, retrieved from the synthetic time histories, are then employed as input for a vulnerability model based on fragility functions, in order to predict building damage scenarios at urban scale. The main features and effectiveness of the proposed numerical approach are tested on the Beijing metropolitan area.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.

In this paper, we present a mathematical model able to simulate the cardiac function. We first describe the basic physical principles behind the mathematical equations, then we illustrate a few examples of application to problems of clinical relevance.

We propose four novel mathematical models, describing the microscopic mechanisms of force generation in the cardiac muscle tissue, which are suitable for multiscale numerical simulations of cardiac electromechanics. Such models are based on a biophysically accurate representation of the regulatory and contractile proteins in the sarcomeres. Our models, unlike most of the sarcomere dynamics models that are available in the literature and that feature a comparable richness of detail, do not require the time-consuming Monte Carlo method for their numerical approximation. Conversely, the models that we propose only require the solution of a system of PDEs and/or ODEs (the most reduced of the four only involving 20 ODEs), thus entailing a significant computational efficiency. By focusing on the two models that feature the best trade-off between detail of description and identifiability of parameters, we propose a pipeline to calibrate such parameters starting from experimental measurements available in literature. Thanks to this pipeline, we calibrate these models for room-temperature rat and for body-temperature human cells. We show, by means of numerical simulations, that the proposed models correctly predict the main features of force generation, including the steady-state force-calcium and force-length relationships, the length-dependent prolongation of twitches and increase of peak force, the force-velocity relationship. Moreover, they correctly reproduce the Frank-Starling effect, when employed in multiscale 3D numerical simulation of cardiac electromechanics., Comment: The codes implementing the proposed models are available in an open-source repository at https://github.com/FrancescoRegazzoni/cardiac-activation. The datasets accompanying the article are available at https://doi.org/10.5281/zenodo.3992553

BackgroundThe effect of COVID-19 on the cardiac function and on the vascular system increases the morbidity and mortality of infected subjects with cardiovascular diseases.ObjectivesTo provide preliminary results on cardiac global outcomes (such as cardiac output, ventricular pressures) obtained by means of computational models in plausible scenarios characterized by COVID-19.MethodsWe considered a lumped parameters computational model of the cardiovascular system, which models, from the mechanical point of view, the systemic and pulmonary circulations, the four cardiac valves and the four heart chambers, through mathematical equations of the underlying physical processes. To study the effect of COVID-19, we varied the heart rate, the contractility and the pulmonary resistances in suitable ranges.ResultsOur computations on individuals with both otherwise normal and impaired cardiac functions revealed that COVID-19 worsen cardiac function, as shown by a decrease of some cardiac biomarkers values such as cardiac output and ejection fraction. In the case of existing impaired cardiac function, the presence of COVID-19 lead to values outside the normal ranges.ConclusionsComputational models revealed to be an effective tool to study the effect of COVID-19 on the cardiovascular system. Such effect could be significant for patients with impaired cardiac function. This is especially useful to perform a sensitivity analysis of the hemodynamics for different conditions.CONDENSED ABSTRACTEmerging studies address how COVID-19 infection might impact the cardiovascular system. This relates particularly to the development of myocardial injury, acute coronary syndrome, myocarditis, arrhythmia, and heart failure. Prospective treatment approach is advised for these patients. By the assessment of conventional important biomarkers obtained with new sources as a 0-dimentional computational model, we propose a new study protocol as an effective method to evaluate short-term prognosis. The clinical protocol proposed will help to rapidly identify which patients require intensive monitoring, diagnostic strategy and most adequate therapy.

Systolic Anterior Motion (SAM) of the mitral valve – often associated with Hypertrophic Obstructive Cardiomyopathy (HOCM) – is a cardiac pathology in which a functional subaortic stenosis is induced during systole by the mitral leaflets partially obstructing the outflow tract of the left ventricle. Its assessment by diagnostic tests is often difficult, possibly underestimating its severity and thus increasing the risk of heart failure. In this paper, we propose a new computational pipeline, based on cardiac cine Magnetic Resonance Imaging (cine-MRI) data, for the assessment of SAM. The pipeline encompasses image processing of the left ventricle and the mitral valve, and numerical investigation of cardiac hemodynamics by means of Computational Fluid Dynamics (CFD) in a moving domain with image-based prescribed displacement. Patient-specific geometry and motion of the left ventricle are considered in view of an Arbitrary Lagrangian–Eulerian approach for CFD, while the reconstructed mitral valve is immersed in the computational domain by means of a resistive method. We assess clinically relevant flow and pressure indicators in a parametric study for different degrees of SAM severity, in order to provide a better quantitative evaluation of the pathological condition. Moreover, we provide specific indications for its possible surgical treatment, i.e. septal myectomy.

Atrial fibrillation (AF) is responsible for 15–18 % of all strokes. In AF patients, the left atrial appendage (LAA) represents the main thrombogenic spot, being the site of 90% of intracardiac thrombus formation. Therefore, the occlusion of the LAA (LAAO) is a novel strategy for cardioembolic stroke prophylaxis. The aim of this study was the simulation of the fluid dynamics effects of the LAAO in AF patients, by applying two different devices (Amulet™ and Watchman™), in order to predict patient-specific hemodynamic changes due to LAAO and to detect the most effective devices in reducing stroke risk as well.

We have learnt that a mathematical model of a physical (or real) problem requires a good knowledge of the problem itself. Often – almost always – this knowledge must be shared with the experts on the problem, be these engineers, biologists, economists, physicists or physicians.

Given the function f(x) = −x2 + 4x + 1, construct fmp over the interval [1, 4] using a partition made of M = 6 subintervals of the same length. Plot f and fmp on the same plane.

The various aspects of the real world, their interaction and their dynamics can very often be described by mathematical formulas, functions and equations, in other words by mathematical models.

It is the 22nd of May and we decide to look up born on 22 May on Google. In the blink of an eye, 0.35 seconds to be precise, we get back around 624,000 hits. We click on the first link Google proposes (22 May – Wikipedia) and discover that on this very day in 1859 Sir Arthur Conan Doyle was born in Edinburgh, Scotland (see Fig. 4.1).

This work concerns the mathematical and numerical modeling of the heart. The aim is to enhance the understanding of the cardiac function in both physiological and pathological conditions. Along this road, a challenge arises from the multi-scale and multi-physics nature of the mathematical problem at hand. In this paper, we propose an electromechanical model that, in bi-ventricle geometries, combines the monodomain equation, the Bueno-Orovio minimal ionic model, and the Holzapfel-Ogden strain energy function for the passive myocardial tissue modelling together with the active strain approach combined with a model for the transmurally heterogeneous thickening of the myocardium. Since the distribution of the electric signal is dependent on the fibres orientation of the ventricles, we use a Laplace-Dirichlet Rule-Based algorithm to determine the myocardial fibres and sheets configuration in the whole bi-ventricle. In this paper, we study the influence of different fibre directions and incompressibility constraint and penalization on the compressibility of the material (bulk modulus) on the pressure-volume relation simulating a full heart beat. The coupled electromechanical problem is addressed by means of a fully segregated scheme. The numerical discretization is based on the Finite Element Method for the spatial discretization and on Backward Differentiation Formulas for the time discretization. The arising non-linear algebraic system coming from application of the implicit scheme is solved through the Newton method. Numerical simulations are carried out in a patient-specific bi-ventricle geometry to highlight the most relevant results of both electrophysiology and mechanics and to compare them with physiological data and measurements. We show how various fibre configurations and bulk modulus modify relevant clinical quantities such as stroke volume, ejection fraction and ventricle contractility.

The cardiovascular system allows the nutrients essential to life to reach all the cells in our body (it is estimated there are more than 37 thousand billion cells!). The fundamental engine of the system is our heart, an organ of extraordinary complexity and efficiency. The heart pumps the blood into the aorta and from there, through successive ramifications, in the bigger and smaller arteries, then in the arterioles and finally in the capillaries. And it is exactly inside the capillary beds that the nutrients are delivered to the cells and the toxic substances – the residues of the cellular reactions – are removed. The waste CO2, for instance, is transported back through the venous system and is eventually released into the pulmonary alveoli where the respiration expels it.

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

When a numerical model generates an algorithm, the latter must be implemented in a program by means of a programming language. Among the many languages available we shall focus on Octave, because on one hand it is a simple language, and on the other it is particularly efficient for scientific computing.

Background: Hemodynamics has been known to play a major role in the development of intimal hyperplasia leading to arteriovenous fistula failure. The goal of our study is to investigate the influence of different angles of side-to-end radiocephalic anastomosis on the hemodynamic parameters that promote intimal dysfunction and therefore intimal hyperplasia., Methods: Realistic three-dimensional meshes were reconstructed using ultrasound measurements from distal side-to-end radiocephalic fistulas. The velocity at the proximal and distal radial inflows and at specific locations along the anastomosis and cephalic vein was measured through duplex ultrasound performed by a single examiner. A computational parametric study, virtually changing the inner angle of anastomosis, was performed. For this purpose, we used advanced computational models that include suitable tools to capture the pulsatile and turbulent nature of the blood flow found in arteriovenous fistulas. The results were analyzed in terms of velocity fields, wall shear stress distribution, and oscillatory shear index., Results: Results show that the regions with high oscillatory shear index, which are more prone to the development of hyperplasia, are greater and progressively shift toward the anastomosis area and the proximal vein segment with the decrease of the inner angle of anastomosis. These results are specific to distal radiocephalic fistulas because they are subject to proximal and distal radial inflow., Conclusions: The results of this study show that inner anastomosis angles approaching 60-70 degrees seem to yield the best hemodynamic conditions for maturation and long-term patency of distal radiocephalic fistulas. Inner angles greater than 90 degrees, representing the smooth loop technique, did not show a clear hemodynamic advantage.

In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisson problem, which we select as a benchmark Partial Differential Equation. Our focus is on their convergence properties, the algebraic structure and the spectral properties of the corresponding discrete arrays (mass and stiffness matrices). We review the available theoretical results for these methods and verify them numerically by performing an error analysis on the solution of the Poisson problem. Where theory is lacking, we use numerical investigation of the results to draw conjectures on the behaviour of the corresponding theoretical laws in terms of the design parameters, such as the (mesh) element size, the local polynomial degree, the smoothness of the NURBS basis functions, the space dimension, and the total number of degrees of freedom involved in the computations.

We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE) methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground motion induced by large earthquakes. DGSE methods combine the exibility of discontinuous Galerkin meth-ods to patch together, through a domain decomposition paradigm, Spectral Element blocks where high-order polynomials are used for the space discretization. This approach allows local adaptivity on discretization parameters, thus improving the quality of the solution without affecting the compu-tational costs. The theoretical properties of the semidiscrete formulation are also revised, including well-posedness, stability and error estimates. A discussion on the dissipation, dispersion and stability properties of the fully-discrete (in space and time) formulation is also presented. Here space dis-cretization is obtained based on employing the leap-frog time marching scheme. The capabilities of the present approach are demonstrated through a set of computations of realistic earthquake scenar-ios obtained using the code SPEED (http://speed.mox.polimi.it), an open-source code specifically designed for the numerical modeling of large-scale seismic events jointly developed at Politecnico di Milano by The Laboratory for Modeling and Scientific Computing MOX and by the Department of Civil and Environmental Engineering.