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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work dealt with the assessment of a computational tool to estimate the electrical activation in the left ventricle focusing on the latest electrically activated segment (LEAS) in patients with left bundle branch block and possible myocardial fibrosis. We considered the Eikonal-diffusion equation and to recover the electrical activation maps in the myocardium. The model was calibrated by using activation times acquired in the coronary sinus (CS) branches or in the CS solely with an electroanatomic mapping system (EAMS) during cardiac resynchronization therapy (CRT). We applied our computational tool to ten patients founding an excellent accordance with EAMS measures; in particular, the error for LEAS location was less than 4 mm. We also calibrated our model using only information in the CS, still obtaining an excellent agreement with the measured LEAS. The proposed tool was able to accurately reproduce the electrical activation maps and in particular LEAS location in the CS branches, with an almost real-time computational effort, regardless of the presence of myocardial fibrosis, even when information only at CS was used to calibrate the model. This could be useful in the clinical practice since LEAS is often used as a target site for the left lead placement during CRT. Overall picture of the computational pipeline for the estimation of LEAS. [ABSTRACT FROM AUTHOR]

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. 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. 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. 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. • Fluid-structure interaction analysis for different configurations of the arteriovenous fistula. • Mismatch of the arterial and venous Young's moduli and different vessel thicknesses. • Real reconstruction of the shape of the anastomosis region. • The diameter of the cephalic vein drastically influences the hemodynamics. [ABSTRACT FROM AUTHOR]

Purpose: Quantification of myocardial blood flow (MBF) and functional assessment of coronary artery disease (CAD) can be achieved through stress myocardial computed tomography perfusion (stress-CTP). This requires an additional scan after the resting coronary computed tomography angiography (cCTA) and administration of an intravenous stressor. This complex protocol has limited reproducibility and non-negligible side effects for the patient. We aim to mitigate these drawbacks by proposing a computational model able to reproduce MBF maps. Methods: A computational perfusion model was used to reproduce MBF maps. The model parameters were estimated by using information from cCTA and MBF measured from stress-CTP (MBFCTP) maps. The relative error between the computational MBF under stress conditions (MBFCOMP) and MBFCTP was evaluated to assess the accuracy of the proposed computational model. Results: Applying our method to 9 patients (4 control subjects without ischemia vs 5 patients with myocardial ischemia), we found an excellent agreement between the values of MBFCOMP and MBFCTP. In all patients, the relative error was below 8% over all the myocardium, with an average-in-space value below 4%. Conclusion: The results of this pilot work demonstrate the accuracy and reliability of the proposed computational model in reproducing MBF under stress conditions. This consistency test is a preliminary step in the framework of a more ambitious project which is currently under investigation, i.e., the construction of a computational tool able to predict MBF avoiding the stress protocol and potential side effects while reducing radiation exposure. [ABSTRACT FROM AUTHOR]

Atherosclerosis is a systemic disease that leads to accumulation of deposits, known as atherosclerotic plaques, within the walls of the carotids. In particular, three types of plaque can be distinguished: soft, fibrous, and calcific. Most of the computational studies who investigated the interplay between the plaque and the blood flow on patient-specific geometries used nonstandard medical images to directly delineate and segment the plaque and its components. However, these techniques are not so widely available in the clinical practice. In this context, the aim of our work was twofold: (i) to propose a new geometric tool that allowed to reconstruct a plausible plaque in the carotids from standard images and (ii) to perform three-dimensional (3D) fluid-structure interaction (FSI) simulations where we compared some fluid-dynamic and structural quantities among 15 patients characterized by different typologies of plaque. Our results highlighted that both the morphology and the mechanical properties of different plaque components play a crucial role in determining the vulnerability of the plaque. [ABSTRACT FROM AUTHOR]

We consider a loosely-coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface parameter in the Robin condition. In particular, for a model problem we find sufficient conditions for instability and stability of the method. In the latter case, we find a stability condition relating the time discretization parameter, the interface parameter, and the fluid and structure densities. Numerical experiments confirm the theoretical findings and highlight optimal choices of the interface parameter that guarantee accurate solutions. [ABSTRACT FROM AUTHOR]

The arteriovenous fistula (AVF) is the main form of vascular access for hemodialysis patients, but its maintenance is very challenging. Its failure is mainly related to intimal hyperplasia (IH), leading to stenosis. The aim of this work was twofold: (i) to perform a computational study for the comparison of the disturbed blood dynamics in different configurations of AVF and (ii) to assess the amount of transition to turbulence developed by the specific geometric configuration of AVF. For this aim, we reconstructed realistic three-dimensional (3D) geometries of two patients with a side-to-end AVF, performing a parametric study by changing the angle of incidence at the anastomosis. We solved the incompressible Navier-Stokes equations modeling the blood as an incompressible and Newtonian fluid. Large eddy simulations (LES) were considered to capture the transition to turbulence developed at the anastomosis. The values of prescribed boundary conditions are obtained from clinical echo-color Doppler (ECD) measurements. To assess the disturbed flow, we considered hemodynamic quantities such as the velocity field, the pressure distribution, and wall shear stresses (WSS) derived quantities, whereas to quantify the transition to turbulence, we computed the standard deviation of the velocity field among different heartbeats and the turbulent kinetic energy. [ABSTRACT FROM AUTHOR]

We consider an Extended Finite Elements method to handle the case of composite independent unstructured grids that lead to unfitted meshes. In particular, we address the case of two overlapped meshes, a background and a foreground one, where the thickness of the latter is smaller than the elements of the background mesh. This situation may lead to elements split into several portions, thus generating polyhedral elements. We detail the corresponding discrete formulation for the Poisson problem with discontinuous coefficients. We also provide some technical details for the 3D implementation. Finally, we provide some numerical examples with the aim of showing the effectiveness of the proposed formulation. [ABSTRACT FROM AUTHOR]

In this work, we focus on the Optimized Schwarz Method for circular flat interfaces and geometric heterogeneous coupling arising when cylindrical geometries are coupled along the axial direction. In the first case, we provide a convergence analysis for the diffusion-reaction problem and jumping coefficients and we apply the general optimization procedure developed in Gigante and Vergara (Numer. Math.131 (2015) 369–404). In the numerical simulations, we discuss how to choose the range of frequencies in the optimization and the influence of the Finite Element and projection errors on the convergence. In the second case, we consider the coupling between a three-dimensional and a one-dimensional diffusion-reaction problem and we develop a new optimization procedure. The numerical results highlight the suitability of the theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed‐point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium‐Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases. [ABSTRACT FROM AUTHOR]

A numerical procedure that combines an extended finite element formulation and a discontinuous Galerkin technique is presented, with the final aim of providing an effective tool for the simulation of three-dimensional (3D) fluid -structure interaction problems. In this work we consider a thick structure immersed in a fluid . We describe the numerical models and discuss the specific implementation issues arising in three dimensions. Finally, 3D numerical results are provided to show the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider large eddy simulations (LES) for human stenotic carotids in presence of atheromasic plaque, a pathological condition where transitional effects to turbulence may occur, with relevant clinical implications such as plaque rupture. We provide a reference numerical solution obtained at high resolution without any subgrid scale model, to be used to assess the accuracy of LES simulations. In the context we are considering, ie, hemodynamics, we cannot refer to a statistically homogeneous, isotropic, and stationary turbulent regime; hence, the classical Kolmogorov theory cannot be used. For this reason, a mesh size and a time step are deemed fine enough if they allow to capture all the features of the velocity field in the shear layers developed after the bifurcation. To assess these requirements, we consider a simplified model of the evolution of a 2D shear layer, a relevant process in the formation of transitional effects in our case. Then, we compare the results of LES σ model (both static and dynamic) and mixed LES models (where also a similarity contribution is considered). In particular, we consider a realistic scenario of a human carotid, and we use the reference solution as gold standard. The results highlight the accuracy of the LES σ models, especially for the static model. [ABSTRACT FROM AUTHOR]

We study the effects of transition to turbulence in abdominal aortic aneurysms (AAA). The presence of transitional effects in such districts is related to the heart pulsatility and the sudden change of diameter of the vessels, and has been recorded by means of clinical measures as well as of computational studies. Here we propose, for the first time, the use of a large eddy simulation (LES) model to accurately describe transition to turbulence in realistic scenarios of AAA obtained from radiological images. To this aim, we post-process the obtained numerical solutions to assess significant quantities, such as the ensemble-averaged velocity and wall shear stress, the standard deviation of the fluctuating velocity field, and vortical structures educed via the so-called Q-criterion. The results demonstrate the suitability of the considered LES model and show the presence of significant transitional effects around the impingement region during the mid-deceleration phase. [ABSTRACT FROM AUTHOR]

Coronary artery disease is one of the leading causes of death worldwide. The stenotic coronary vessels are generally treated with coronary artery bypass grafts (CABGs), which can be either arterial (internal mammary artery, radial artery) or venous (saphenous vein). However, the different mechanical properties of the graft can influence the outcome of the procedure in terms of risk of restenosis and subsequent graft failure. In this paper, we perform a computational fluid–structure interaction (FSI) analysis of patient-specific multiple CABGs (Y-grafts) with the aim of better understanding the influence of the choice of bypass (arterial vs venous) on the risk of graft failure. Our results show that the use of a venous bypass results in a more disturbed flow field at the anastomosis and in higher stresses in the vessel wall with respect to the arterial one. This could explain the better long-term patency of the arterial bypasses experienced in the clinical practice. [ABSTRACT FROM AUTHOR]

Coronary artery disease, caused by the buildup of atherosclerotic plaques in the coronary vessel wall, is one of the leading causes of death in the world. For high-risk patients, coronary artery bypass graft is the preferred treatment. Despite overall excellent patency rates, bypasses may fail due to restenosis. In this context, the purpose of this work was to perform a parametric computational study of the fluid dynamics in patient-specific geometries with the aim of investigating a possible relationship between coronary stenosis degree and risk of graft failure. Firstly, we propose a strategy to prescribe realistic boundary conditions in the absence of measured data, based on an extension of Murray's law to provide the flow division at bifurcations in case of stenotic vessels and non-Newtonian blood rheology. Then, we carry out numerical simulations in three patients affected by severe coronary stenosis and treated with a graft, in which the stenosis degree is virtually varied in order to compare the resulting fluid dynamics in terms of hemodynamic indices potentially involved in restenosis development. Our findings suggest that low degrees of coronary stenosis produce a more disturbed fluid dynamics in the graft, resulting in hemodynamic conditions that may promote a higher risk of graft failure. [ABSTRACT FROM AUTHOR]

We present a model for the electrophysiology in the heart to handle the electrical propagation through the Purkinje system and in the myocardium, with two-way coupling at the Purkinje–muscle junctions. In both the subproblems the monodomain model is considered, whereas at the junctions a resistor element is included that induces an orthodromic propagation delay from the Purkinje network towards the heart muscle. We prove a sufficient condition for convergence of a fixed-point iterative algorithm to the numerical solution of the coupled problem. Numerical comparison of activation patterns is made with two different combinations of models for the coupled Purkinje network/myocardium system, the eikonal/eikonal and the monodomain/monodomain models. Test cases are investigated for both physiological and pathological activation of a model left ventricle. Finally, we prove the reliability of the monodomain/monodomain coupling on a realistic scenario. Our results underlie the importance of using physiologically realistic Purkinje-trees with propagation solved using the monodomain model for simulating cardiac activation. [ABSTRACT FROM AUTHOR]

The Purkinje network is responsible for the fast and coordinated distribution of the electrical impulse in the ventricle that triggers its contraction. Therefore, it is necessary to model its presence to obtain an accurate patient-specific model of the ventricular electrical activation. In this paper, we present an efficient algorithm for the generation of a patient-specific Purkinje network, driven by measures of the electrical activation acquired on the endocardium. The proposed method provides a correction of an initial network, generated by means of a fractal law, and it is based on the solution of Eikonal problems both in the muscle and in the Purkinje network. We present several numerical results both in an ideal geometry with synthetic data and in a real geometry with patient-specific clinical measures. These results highlight an improvement of the accuracy provided by the patient-specific Purkinje network with respect to the initial one. In particular, a cross-validation test shows an accuracy increase of 19% when only the 3% of the total points are used to generate the network, whereas an increment of 44% is observed when a random noise equal to 20% of the maximum value of the clinical data is added to the measures. [ABSTRACT FROM AUTHOR]

SUMMARY To properly describe the electrical activity of the left ventricle, it is necessary to model the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times related to pathological propagations. In this case, one needs to consider a strongly coupled problem between the network and the muscle, where the feedback from the latter to the former cannot be neglected as in a normal propagation. We apply the proposed strategy to data acquired on three subjects, one of them suffering from muscular conduction problems owing to a scar and the other two with a muscular pre-excitation syndrome (Wolff-Parkinson-White). To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network generated by our strategy with the ones obtained by using a non-patient-specific network. The results show that the mean absolute errors in the activation time is reduced for all the cases, highlighting the importance of including a patient-specific Purkinje network in computational models. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The propagation of the electrical signal in the Purkinje network is the starting point for the activation of the ventricular muscular cells leading to the contraction of the ventricle. In the computational models, describing the electrical activity of the ventricle is therefore important to account for the Purkinje fibers. Until now, the inclusion of such fibers has been obtained either by using surrogates such as space-dependent conduction properties or by generating a network based on an a priori anatomical knowledge. The aim of this work was to propose a new method for the generation of the Purkinje network using clinical measures of the activation times on the endocardium related to a normal electrical propagation, allowing to generate a patient- specific network. The measures were acquired by means of the EnSite NavX system. This system allows to measure for each point of the ventricular endocardium the time at which the activation front, that spreads through the ventricle, has reached the subjacent muscle. We compared the accuracy of the proposed method with the one of other strategies proposed so far in the literature for three subjects with a normal electrical propagation. The results showed that with our method we were able to reduce the absolute errors, intended as the difference between the measured and the computed data, by a factor in the range 9-25 %, with respect to the best of the other strategies. This highlighted the reliability of the proposed method and the importance of including a patient-specific Purkinje network in computational models. [ABSTRACT FROM AUTHOR]

The aim of the present work is to quantitatively assess the three-dimensional distributions of the displacements experienced during the cardiac cycle by the luminal boundary of abdominal aortic aneurysm (AAA) and to correlate them with the local bulk hemodynamics. Ten patients were acquired by means of time resolved computed tomography, and each patient-specific vascular morphology was reconstructed for all available time frames. The AAA lumen boundary motion was tracked, and the lumen boundary displacements (LBD) computed for each time frame. The intra-aneurysm hemodynamic quantities, specifically wall shear stress (WSS), were evaluated with computational fluid dynamics simulations. Co-localization of LBD and WSS distributions was evaluated by means of Pearson correlation coefficient. A clear anisotropic distribution of LBD was evidenced in both space and time; a combination of AAA lumen boundary inward- and outward-directed motions was assessed. A co-localization between largest outward LBD and high WSS was demonstrated supporting the hypothesis of a mechanistic relationship between anisotropic displacement and hemodynamic forces related to the impingement of the blood on the lumen boundary. The presence of anisotropic displacement of the AAA lumen boundary and their link to hemodynamic forces have been assessed, highlighting a new possible role for hemodynamics in the study of AAA progression. [ABSTRACT FROM AUTHOR]

Bicuspid aortic valve (BAV) predisposes to aortic aneurysms with a high prevalence. A first hypothesis for this phenomenon is related to fibrillin deficiency (genetic hypothesis). The present article focused on a complementary, hemodynamic hypothesis stating that it is the peculiar fluid dynamics of blood in the ascending aorta of patients with BAV configurations that leads to aneurysm formation. To corroborate this hypothesis, a parametric study was performed based on numerical simulations of ascending aorta hemodynamics with different configurations of orifice area and valve orientation. The resulting wall shear stress (WSS) distributions and degree of asymmetry of the blood jet were investigated, and surrogate indices introduced. The results showed that WSS was more pronounced in subjects with BAV morphologies, also in the nonstenotic case. In particular, a maximum WSS of 3 Pa was found (vs. 1.5 Pa in subjects with a tricuspid configuration). It is localized at the mid-ascending aorta, the segment more prone to dilate as shown by the index related to maximum WSS (0.869 in BAV vs. 0.322 in tricuspid). Moreover, the asymmetry of the blood flow was found larger for decreasing valve area, the related index at mid-ascending aorta being more than three times higher than that found for tricuspid configuration (0.70 vs. 0.20). Further, WSS and flow asymmetry were higher also at the sinus of Valsalva and sinotubolar junction for a latero-lateral (LL) BAV configuration in keeping with the clinical observation on association between BAV configurations and different aortic aneurysm morphology. These findings may help explain the higher risk of aneurysm formation in BAV patients. The proposed indices will require validation prior to application in clinical settings. [ABSTRACT FROM AUTHOR]

In bicuspid aortic valve (BAV) disease, the role of genetic and hemodynamic factors influencing ascending aortic pathology is controversial. To test the effect of BAV geometry on ascending aortic flow, a finite element analysis was undertaken. A surface model of aortic root and ascending aorta was obtained from magnetic resonance images of patients with BAV and tricuspid aortic valve using segmentation facilities of the image processing code Vascular Modeling Toolkit (developed at the Mario Negri Institute). Analytical models of bicuspid (antero-posterior [AP], type 1 and latero-lateral, type 2 commissures) and tricuspid orifices were mathematically defined and turned into a volumetric mesh of linear tetrahedra for computational fluid dynamics simulations. Numerical simulations were performed with the finite element code LifeV. Flow velocity fields were assessed for four levels: aortic annulus, sinus of Valsalva, sinotubular junction, and ascending aorta. Comparison of finite element analysis of bicuspid and tricuspid aortic valve showed different blood flow velocity pattern. Flow in bicuspid configurations showed asymmetrical distribution of velocity field toward the convexity of mid-ascending aorta returning symmetrical in distal ascending aorta. On the contrary, tricuspid flow was symmetrical in each aortic segment. Comparing type 1 BAV with type 2 BAV, more pronounced recirculation zones were noticed in the latter. Finally, we found that in both BAV configurations, maximum wall shear stress is highly localized at the convex portion of the mid-ascending aorta level. Comparison between models showed asymmetrical and higher flow velocity in bicuspid models, in particular in the AP configuration. Asymmetry was more pronounced at the aortic level known to be more exposed to aneurysm formation in bicuspid patients. This supports the hypothesis that hemodynamic factors may contribute to ascending aortic pathology in this subset of patients. [ABSTRACT FROM AUTHOR]

A common clinical practice during single-point Doppler analysis is to measure the centerline maximum velocity and to recover the time-averaged flow rate by exploiting an assumption on the shape of velocity profile (a priori formula), either a parabolic or a flat one. In a previous study, we proposed a new formula valid for the peak instant linking the maximum velocity and the flow rate by including a well-established dimensionless fluid-dynamics parameter (the Womersley number), in order to account for the hemodynamics conditions (Womersley number-based formula). Several in silico tests confirmed the reliability of the new formula. Nevertheless, an in vivo confirmation is missing limiting the clinical applicability of the formula. An experimental in vivo protocol using cine phase-contrast MRI (2-D PCMRI) technique has been designed and applied to ten healthy young volunteers in three different arterial districts: the abdominal aorta, the common carotid artery, and the brachial artery. Each PCMRI dataset has been used twice: 1) to compute the value of the blood flow rate used as a gold standard and 2) to estimate the flow rate by measuring directly the maximum velocity and the diameter (i.e., emulating the intravascular Doppler data acquisition) and by applying to these data the a priori and the Womersley number-based formulae. All the in vivo results have confirmed that the Womersley number-based formula provides better estimates of the flow rate at the peak instant with respect to the a priori formula. More precisely, mean performances of the Womersley number-based formula are about three times better than the a priori results in the abdominal aorta, five times better in the common carotid artery, and two times better in the brachial artery. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we continue in investigating the approach we have proposed in a paper recently published, for a reliable estimate of (peak systolic) blood flow rate from velocity Doppler measurements. Basic features of this approach together with some in silico test cases were discussed in that work. Here, we provide more insights of this approach by performing a sensitivity analysis of the formulas relating blood flow rate to velocity. In particular we analyze how our estimates are affected by perturbation or errors in measurements in comparison with a standard method for catheter based estimates based on the assumption of a parabolic velocity profile. A first glance to in vivo clinical applications is given as well. [Copyright &y& Elsevier]

In this study, we focus on a specific application, the modeling and simulation of drug release from cardiovascular drug eluting stents. In particular, we analyze the drug release dynamics from the stent coating, where the drug is initially stored, to the surrounding arterial wall. The main challenge consists of accounting for multiple space scales. To this purpose, we derive suitable boundary conditions accounting for the smaller scales on the macroscopic model. This approach, applied to drug delivery, significantly cuts down the computational cost of the numerical simulations and allows us to consider a realistic problem setting. [ABSTRACT FROM AUTHOR]

Abstract: We consider the incompressible Navier–Stokes problem with flow rate boundary conditions. This problem has been investigated in [J. Heywood, R. Rannacher, S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier–Stokes equations, Int. J. Numer. Methods Fluids 22 (1996) 325–352; L. Formaggia, J. F. Gerbeau, F. Nobile, A. Quarteroni, Numerical treatment of defective boundary conditions for the Navier–Stokes equation, SIAM J. Numer. Anal. 40(1) (2002) 376–401; A. Veneziani, C. Vergara, Flow rate defective boundary conditions in haemodynamics simulations, Int. J. Numer. Methods Fluids 47 (2005) 803–816]. In the latter two papers, a feasible numerical formulation of this problem, based on a Lagrange multiplier approach has been investigated. This approach has the drawback of high computational costs. In this paper, we propose an approximate formulation of this problem, yielding a strong reduction of the computational costs. The error analysis shows that the error introduced by this approximate formulation is confined in a small region of the boundary. This is confirmed by the numerical simulations. [Copyright &y& Elsevier]

Abstract: Physically useful measures in current clinical practice refer often to the blood flow rate, that is related to the mean velocity. However, the direct measurement of the latter is currently not possible using a Doppler velocimetry technique. Therefore, the usual approach to calculate the flow rate with this technique consists in measuring the maximum velocity and in estimating the mean velocity, making the hypothesis of parabolic profile that in realistic situations results in strongly inaccurate estimates. In this paper, we propose a different way for estimating the flow rate regarded as a function of maximum velocity and Womersley number. This relation is obtained by fixing a parametrised representation and by evaluating the parameters by means of a least-square approach working on the numerical results of CFD simulations (about 200). Numerical simulations are carried out by prescribing the flow rate, not the velocity profile. In this way, no bias is implicitly induced in prescribing boundary conditions. Validation tests based on numerical simulations show that the proposed relation improves the flow rate estimation. (E-mail: ponzini@cilea.it) [Copyright &y& Elsevier]

We present a new model of human cardiac electromechanics for the left ventricle where electrophysiology is described by a Reaction–Eikonal model and which enables an off-line resolution of the reaction model, thus entailing a big saving of computational time. Subcellular dynamics is coupled with a model of tissue mechanics, which is in turn coupled with a Windkessel model for blood circulation. Our numerical results show that the proposed model is able to provide a physiological response to changes in certain variables (end-diastolic volume, total peripheral resistance, contractility). We also show that our model is able to reproduce with high accuracy and with a considerably lower computational time the results that we would obtain if the monodomain model should be used in place of the Eikonal model. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including inverse hemodynamics, domain parametrization technique and Navier-Stokes equations.

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. [ABSTRACT FROM AUTHOR]

In this work we consider the optimized Schwarz method designed for computational domains that feature spherical or almost spherical interfaces. In the first part, we consider the diffusion-reaction problem. We provide a convergence analysis of the generalized Schwarz method and, following [G. Gigante and C. Vergara, Numer. Math., 131 (2015), pp. 369{404], we discuss an optimization procedure for constant interface parameters leading to a Robin{Robin scheme. Finally, we present some numerical results both in spherical and in ellipsoidal domains. In the second part of the work, we address the uid-structure interaction problem. Again, we provide a convergence analysis and discuss optimized choices of constant interface parameters. Finally, we present three- dimensional numerical results inspired by hemodynamic applications, to validate the proposed choices in the presence of large added mass effect. In particular, we consider numerical experiments both in an ideal spherical domain and in a realistic abdominal aortic aneurysm. [ABSTRACT FROM AUTHOR]

We consider the two-dimensional numerical approximation of the fluid-structure interaction problem over unfitted fluid and structure meshes. In particular, we consider a method where the fluid mesh (on the background) is fixed, apart from the interface with the moving immersed structure, where general polygonal elements of arbitrary shape and changing in time are generated. The new idea of this work is to handle the discretization on such polygons by using the Discontinuous Galerkin method on polyhedral grids (PolyDG), which has been recently developed for different differential equations and here adapted for the first time to a heterogeneous problem. We prove a stability result of the proposed semi-discrete formulation and discuss how to deal with the partial or total covering of a fluid mesh element due to the structure movement. We finally present some numerical results with the aim of showing the effectiveness of the proposed method. • We present a new method based on the Discontinuous Galerkin method for polygonal elements for the interaction of a fluid with an immersed structure. • High order approximations are easily obtained by considering a modal basis functions directly in the physical frame configuration. • We provide a stability analysis of the discretized-in-space formulation. • We present several numerical results with the aim of assessing the validity of the proposed method. • These results show the ability of the method even with very small dimension of mesh elements and very anisotropic elements. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: Industrial wastewaters with a high content of nitrogen are a relevant environmental problem. Currently, treatments to remove nitrogen are not efficient, so is necessary to develop alternative methods. The objective of this study is to investigate a consortium of microalgae — nitrifying, that due to the symbiosis between them could be an interesting alternative. Results: In this study, it was possible to obtain a consortium of nitrifying bacteria (NB) and microalgae (MA) capable of operating with low requirements of dissolved oxygen, using aerobic sludge from wastewater treatment plants. During the operation, this consortium presents removal percentages above 98% of ammonia, even at concentrations of DO of 0.5 mg O2 L-1. It is estimated that the removal was caused both by the action of nitrifying bacteria and microalgae. It was determined that approximately 60% of the ammonia feed was oxidized to nitrate by nitrifying bacteria, while the algae assimilated 40% of the nitrogen feed at steady state. A methodology for measuring the specific activities of nitrifying bacteria and microalgae by comparing the rates in the variation inorganic nitrogen compounds was established with satisfactory results. An average specific activity of 0.05 and 0.02 g NH4 + gVSS-1 d-1 for nitrifying bacteria and microalgae was determined, respectively. Conclusions: The consortium it can be obtained in a single continuous operation, and has a high capacity for nitrogen removal with low oxygen content. The consortium could prove to be a more economical method compared to traditional. [ABSTRACT FROM AUTHOR]

The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a multicompartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasi-incompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential. To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic circulation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with precomputed cardiac displacements, obtained form other models or medical imaging data. We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon, which is particularly challenging to capture as it arises from the interaction of several parts of the model. [ABSTRACT FROM AUTHOR]

In this paper we consider the numerical solution of the three-dimensional fluid-structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, obtained from semi-implicit approximations, which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non-linearities. We show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact (implicit) scheme. To do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics. We also provide an error analysis for a simple differential model problem when a BDF method is considered for the time discretization and only few Newton iterations are performed at each temporal instant. [ABSTRACT FROM AUTHOR]

Background: We designed a retrospective computational study to evaluate the effects of hemodynamics on portal confluence remodeling in real models of patients with malignancies of the pancreatic head. Methods: Patient-specific models were created according to computed tomography data. Fluid dynamics was simulated by using finite-element methods. Computational results were compared to morphological findings. Results: Five patients underwent total pancreatectomy, one had duodenopancreatectomy. Vein resection was performed en-bloc with the specimen. Histopathological findings showed that in patients without a vein stenosis and a normal hemodynamics, the three-layered wall of the vein was preserved. In patients with a stenosis > 70% of vein diameter and modified hemodynamics, the three-layered structure of the resected vein was replaced by a dense inflammatory infiltrate in absence of tumor infiltration. Conclusions: The portal confluence involved by malignancies of the pancreatic head undergoes a remodeling that is not mainly due to a wall infiltration by the tumor but instead to a persistent pathological hemodynamics that disrupts the balance between eutrophic remodeling and degradative process of the vein wall that can lead to the complete upheaval of the three-layered vein wall. This finding can have useful surgical application in planning resection of the vein involved by tumor growth. [ABSTRACT FROM AUTHOR]

In this work we consider the Optimized Schwarz Method for the three-dimensional (3D) diffusion-reaction problem. In particular, we treat the case of cylindrical interfaces between the subdomains, and we provide a convergence analysis of the Schwarz method, both in the case of Dirichlet interface conditions and in that of general transmission conditions. This allows us to recover, for the latter case, optimal symbols for the interface conditions, which are supposed to work well for geometries which feature cylindrical interfaces. Moreover, starting from these optimal symbols, we propose effective and easily computable constant interface parameters, derived both from Taylor expansions and from an optimization procedure. We finally present several 3D numerical results aiming at validating the theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract: In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general criterion based on energy balance for the proper choice of coupling conditions between models. We also propose a way to include in the 1D model the effect of the external tissue surrounding the vessel and we discuss its importance whenever this effect is considered in the 3D model. Finally, we propose several numerical results in real human carotids, studying different configurations for the 1D model and highlighting the best one in view of the physical consistency. [Copyright &y& Elsevier]

Estimation of the stiffness of a biological soft tissue is useful for the detection of pathologies such as tumors or atherosclerotic plaques. Elastography is a method based on the comparison between two images before and after a forced deformation of the tissue of interest. An inverse elasticity problem is then solved for Young's modulus estimation. In the case of arteries. no forced deformation is required, since vessels naturally move under the action of blood. Young's modulus can therefore be estimated by solving a coupled inverse fluid-structure interaction problem. In this paper we locus on the mathematical properties of this problem and its numerical solution. We give some well posedness analysis and some preliminary results based on a synthetic data set, i.e., test cases where the exact Young's modulus is known and the displacement dataset is numerically generated by solving a forward fluid-structure interaction problem. We address the problem of the presence of the noise in the measured displacement and of the proper sampling frequency for obtaining reliable estimates. [ABSTRACT FROM AUTHOR]

In the solution of fluid-structure interaction (FSI) problems, partitioned procedures are modular algorithms that involve separate fluid and structure solvers that interact ill an iterative framework through the exchange of suitable transmission conditions at the FS interface. In this work we study, using Fourier analysis, the convergence of partitioned algorithms based on Robin transmission conditions. We derive, for different models of the fluid and the structure, a frequency-dependent reduction factor at each iteration of the partitioned algorithm, which is minimized by choosing optimal values of the coefficients in the Robin transmission conditions. Two-dimensional numerical results are also reported, which highlight the effectiveness of the optimization procedure. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain. As well known, in this case there is the problem of prescribing realistic boundary data on the artificial sections, when only partial data are available. This problem has been investigated extensively for the rigid case. In this work we start considering the compliant case, by focusing on the flow rate conditions for the fluid. We propose three formulations of this problem, different algorithms for its numerical solution and carry out several 2D numerical simulations with the aim of comparing the performances of the different algorithms. [Copyright &y& Elsevier]

Abstract: In this work, we propose a Robin–Robin preconditioner combined with Krylov iterations for the solution of the interface system arising in fluid–structure interaction (FSI) problems. It can be seen as a partitioned FSI procedure and in this respect it generalizes the ideas introduced in [S. Badia, F. Nobile, C. Vergara, J. Comput. Phys. 227 (2008) 7027–7051]. We analyze the convergence of GMRES iterations with the Robin–Robin preconditioner on a model problem and compare its efficiency with some existing algorithms. The method is shown to be very efficient for many challenging fluid–structure interaction problems, such as those characterized by a large added-mass effect or by enclosed fluids. In particular, the possibility to solve balloon-type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches. [Copyright &y& Elsevier]

We consider the incompressible Navier-Stokes equations where on a part of the boundary flow rate and mean pressure boundary conditions are prescribed. There are basically two strategies for solving these defective boundary problems: the variational approach (see J. Heywood, R. Rannacher, and S. Turek, Internat. J. Numer. Methods Fluids, 22 (1996), pp. 325-352) and the augmented formulation (see L. Formaggia, J. F. Gerbeau, F. Nobile, and A. Quarteroni, SIAM J. Numer. Anal., 40 (2002), pp. 376-401, and A. Veneziani and C. Vergara, Internat. J. Numer. Methods Fluids, 47 (2005), pp. 803-816). However, both of these approaches present some drawbacks. For the flow rate problem, the former resorts to nonstandard functional spaces, which are quite difficult to discretize. On the other hand, for the mean pressure problem, it yields exact solutions only in very special cases. The latter is applicable only to the flow rate problem, since for the mean pressure problem it provides unfeasible boundary conditions. In this paper, we propose a new strategy based on a reformulation of the problems at hand in terms of the minimization of an appropriate functional. This approach allows us to treat the two kinds of problems (flow rate and mean pressure) successfully within the same framework, which can be useful in view of a mixed problem where the two conditions are simultaneously prescribed on different artificial boundaries. Moreover, it is more versatile, being prone to be extended to other kinds of defective conditions. We analyze the problems obtained with this approach and propose some algorithms for their numerical solution. Several numerical results are presented supporting the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Abstract: In this article we design new partitioned procedures for fluid–structure interaction problems, based on Robin-type transmission conditions. The choice of the coefficient in the Robin conditions is justified via simplified models. The strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane, as in hemodynamics applications. We analyze theoretically the new iterative procedures on a model problem, which represents a simplified blood-vessel system. In particular, the Robin–Neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures. The theoretical results are checked using numerical experimentation. [Copyright &y& Elsevier]