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.

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.

Impact of Pressure Guidewire on Model-Based FFR Prediction.

INTRODUCTION: Fractional Flow Reserve (FFR) is used to characterize the functional significance of coronary artery stenoses. FFR is assessed under hyperemic conditions by invasive measurements of trans-stenotic pressure thanks to the insertion of a pressure guidewire across the coronary stenosis during catheterization. In order to overcome the potential risk related to the invasive procedure and to reduce the associated high costs, three-dimensional blood flow simulations that incorporate clinical imaging and patient-specific characteristics have been proposed. PURPOSE: Most CCTA-derived FFR models neglect the potential influence of the guidewire on computed flow and pressure. Here we aim to quantify the impact of taking into account the presence of the guidewire in model-based FFR prediction. METHODS: We adopt a CCTA-derived FFR model and perform simulations with and without the guidewire for 18 patients with suspected stable CAD. RESULTS: Presented results show that the presence of the guidewire leads to a tendency to predict a lower FFR value. The FFR reduction is prominent in cases of severe stenoses, while the influence of the guidewire is less pronounced in cases of moderate stenoses. CONCLUSION: From a clinical decision-making point of view, including of the pressure guidewire is potentially relevant only for intermediate stenosis cases.

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.

Personalized Pressure Conditions and Calibration for a Predictive Computational Model of Coronary and Myocardial Blood Flow.

Predictive modeling of hyperemic coronary and myocardial blood flow (MBF) greatly supports diagnosis and prognostic stratification of patients suffering from coronary artery disease (CAD). In this work, we propose a novel strategy, using only readily available clinical data, to build personalized inlet conditions for coronary and MBF models and to achieve an effective calibration for their predictive application to real clinical cases. Experimental data are used to build personalized pressure waveforms at the aortic root, representative of the hyperemic state and adapted to surrogate the systolic contraction, to be used in computational fluid-dynamics analyses. Model calibration to simulate hyperemic flow is performed in a "blinded" way, not requiring any additional exam. Coronary and myocardial flow simulations are performed in eight patients with different clinical conditions to predict FFR and MBF. Realistic pressure waveforms are recovered for all the patients. Consistent pressure distribution, blood velocities in the large arteries, and distribution of MBF in the healthy myocardium are obtained. FFR results show great accuracy with a per-vessel sensitivity and specificity of 100% according to clinical threshold values. Mean MBF shows good agreement with values from stress-CTP, with lower values in patients with diagnosed perfusion defects. The proposed methodology allows us to quantitatively predict FFR and MBF, by the exclusive use of standard measures easily obtainable in a clinical context. This represents a fundamental step to avoid catheter-based exams and stress tests in CAD diagnosis.

Assessing turbulent effects in ascending aorta in presence of bicuspid aortic valve.

Aortic valves with bicuspids have two rather than three leaflets, which is a congenital heart condition. About 0.5-2% of people have a bicuspid aortic valve. Blood flow through the aorta is commonly believed to be laminar, although aortic valve disorders can cause turbulent transitions. Understanding the impact of turbulence is crucial for foreseeing how the disease will progress. The study's objective was use large eddy simulation to provide a thorough analysis of the turbulence in bicuspid aortic valve dysfunction. Using a large eddy simulation, the blood flow patterns of the bicuspid and tricuspid aortic valves were compared, and significant discrepancies were found. The velocity field in flow in bicuspid configurations was asymmetrically distributed toward the ascending aorta. In tricuspid aortic valve (TAV) the flow, on the other hand, was symmetrical within the same aortic segment. Moreover, we looked into standard deviation, Q-criterion, viscosity ratio and wall shear stresses for each cases to understand transition to turbulence. Our findings indicate that in the bicuspid aortic valve (BAV) case, the fluid-dynamic abnormalities increase. The global turbulent kinetic energy and time-averaged wall shear stress for the TAV and BAV scenarios were also examined. We discovered that the global turbulent kinetic energy was higher in the BAV case compared to TAV, in addition to the increased wall shear stress induced by the BAV in the ascending aorta.

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.

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

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

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.

A Computational Study of Blood Flow Dynamics in the Pulmonary Arteries.

In this work we study the blood dynamics in the pulmonary arteries by means of a 3D-0D geometric multiscale approach, where a detailed 3D model for the pulmonary arteries is coupled with a lumped parameters (0D) model of the cardiovascular system. We propose to investigate three strategies for the numerical solution of the 3D-0D coupled problem: the Splitting-Explicit and Implicit algorithms, where information are exchanged between 3D and 0D models at each time step at the interfaces, and the One-Way algorithm, where the 0D is solved first off-line. In our numerical experiments performed in a realistic patient-specific 3D domain with a physiologically calibrated 0D model, we discuss first the issue on instabilities that may arise when not suitable connections are considered between 3D and 0D models; second we compare the performance and accuracy of the three proposed numerical strategies. Finally, we report a comparison between a healthy and a hypertensive case, providing a preliminary result highlighting how our method could be used in future for clinical purposes.

Fluid structure interaction analysis to stratify the behavior of different atheromatous carotid plaques.

BACKGROUND: In asymptomatic carotid stenosis (ACS), different plaque types, i.e. lipidic (LP), fibrous (FP), and calcific (CP), could have different hemodynamic and structural behaviors. METHODS: Different carotid plaques, reconstructed from medical imaging of ACS >70%, were analyzed by computing fluid structure interaction (FSI), modeling the spatial distribution of wall shear stresses (WSS), plaque displacements (D), von Mises stresses (VMS), and absorbed elastic energy (AEE) together with their maximum-in-space values at the systole (WSSsyst, Dsyst, VMSsyst and AEEsyst). RESULTS: WSS resulted significantly higher in CP, whereas D and VMS showed the highest values for LP. Regarding AEEsyst stored by the plaques, LP absorbed in average 2320 J/m3, FP 408 J/m3 (470%) and CP 99 J/m3 (2240%), (P<0.01, P<0.01, and P<0.01, respectively). CONCLUSIONS: Depending upon their nature, plaques store different deformations and inner distributions of forces, thus potentially influencing their vulnerability.

Computational electrophysiology of the coronary sinus branches based on electro-anatomical mapping for the prediction of the latest activated region.

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.

Prediction of myocardial blood flow under stress conditions by means of a computational model.

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.

Computational Fluid-Structure Interaction Study of a New Wave Membrane Blood Pump.

PURPOSE: Wave membrane blood pumps (WMBP) are novel pump designs in which blood is propelled by means of wave propagation by an undulating membrane. In this paper, we computationally studied the performance of a new WMBP design (J-shaped) for different working conditions, in view of potential applications in human patients. METHODS: Fluid-structure interaction (FSI) simulations were conducted in 3D pump geometries and numerically discretized by means of the extended finite element method (XFEM). A contact model was introduced to capture membrane-wall collisions in the pump head. Mean flow rate and membrane envelope were determined to evaluate hydraulic performance. A preliminary hemocompatibility analysis was performed via calculation of fluid shear stress. RESULTS: Numerical results, validated against in vitro experimental data, showed that the hydraulic output increases when either the frequency or the amplitude of membrane oscillations were higher, with limited increase in the fluid stresses, suggesting good hemocompatibility properties. Also, we showed better performance in terms of hydraulic power with respect to a previous design of the pump. We finally studied an operating point which achieves physiologic flow rate target at diastolic head pressure of 80 mmHg. CONCLUSION: A new design of WMBP was computationally studied. The proposed FSI model with contact was employed to predict the new pump hydraulic performance and it could help to properly select an operating point for the upcoming first-in-human trials.

Hemodynamics and remodeling of the portal confluence in patients with malignancies of the pancreatic head: a pilot study towards planned and circumferential vein resections.

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.

Modeling the cardiac response to hemodynamic changes associated with COVID-19: a computational study.

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.

Extended finite element method for fluid-structure interaction in wave membrane blood pump.

Numerical simulations of cardiac blood pump systems are integral to the optimization of device design, hydraulic performance and hemocompatibility. In wave membrane blood pumps, blood propulsion arises from the wave propagation along an oscillating immersed membrane, which generates small pockets of fluid that are pushed towards the outlet against an adverse pressure gradient. We studied the Fluid-Structure Interaction between the oscillating membrane and the blood flow via three-dimensional simulations using the Extended Finite Element Method (XFEM), an unfitted numerical technique that avoids remeshing by using a fluid fixed mesh. Our three-dimensional numerical simulations in a realistic pump geometry highlighted, for the first time in this field of application, that XFEM is a reliable strategy to handle complex industrial problems. Moreover, they showed the role of the membrane deformation in promoting a blood flow towards the outlet despite an adverse pressure gradient. We also simulated the pump system at different pressure conditions and we validated the numerical results against in-vitro experimental data.