A patient-specific aortic valve model based on moving resistive immersed implicit surfaces

Image-Based Computational Fluid Dynamics to Compare Two Repair Techniques for Mitral Valve Prolapse

OBJECTIVE : The treatment of mitral valve prolapse involves two distinct repair techniques: chordal replacement (Neochordae technique) and leaflet resection (Resection technique). However, there is still a debate in the literature about which is the optimal one. In this context, we performed an image-based computational fluid dynamic study to evaluate blood dynamics in the two surgical techniques. METHODS : We considered a healthy subject (H) and two patients (N and R) who underwent surgery for prolapse of the posterior leaflet and were operated with the Neochordae and Resection technique, respectively. Computational Fluid Dynamics (CFD) was employed with prescribed motion of the entire left heart coming from cine-MRI images, with a Large Eddy Simulation model to describe the transition to turbulence and a resistive method for managing valve dynamics. We created three different virtual scenarios where the operated mitral valves were inserted in the same left heart geometry of the healthy subject to study the differences attributed only to the two techniques. RESULTS : We compared the three scenarios by quantitatively analyzing ventricular velocity patterns and pressures, transition to turbulence, and the ventricle ability to prevent thrombi formation. From these results, we found that the operative techniques affected the ventricular blood dynamics in different ways, with variations attributed to the reduced mobility of the Resection posterior leaflet. Specifically, the Resection technique resulted in turbulent forces, related with the risk of hemolysis formation, up to 640 Pa, while the other two scenarios exhibited a maximum of 240 Pa. Moreover, in correspondence of the ventricular apex, the Resection technique reduced the areas with low velocity to 15%, whereas the healthy case and the Neochordae case maintained these areas at 30 and 48%, respectively. Our findings suggest that the Neochordae technique developed a more physiological flow with respect to the Resection technique. CONCLUSION: Resection technique gives rise to a different direction of the mitral jet during diastole increasing the ability to washout the ventricular apex preventing from thrombi formation, but at the same time it promotes turbulence formation that is associated with ventricular effort and risk of hemolysis.

Computational haemodynamics for pulmonary valve replacement by means of a reduced fluid-structure interaction model

Pulmonary valve replacement (PVR) consists of substituting a patient's original valve with a prosthetic one, primarily addressing pulmonary valve insufficiency, which is crucially relevant in Tetralogy of Fallot repairment. While extensive clinical and computational literature on aortic and mitral valve replacements is available, PVR's post-procedural haemodynamics in the pulmonary artery and the impact of prosthetic valve dynamics remain significantly understudied. Addressing this gap, we introduce a reduced Fluid-Structure Interaction (rFSI) model, applied for the first time to the pulmonary valve. This model couples a three-dimensional computational representation of pulmonary artery haemodynamics with a one-degree-of-freedom model to account for valve structural mechanics. Through this approach, we analyse patient-specific haemodynamics pre and post PVR. Patient-specific geometries, reconstructed from CT scans, are virtually equipped with a template valve geometry. Boundary conditions for the model are established using a lumped-parameter model, fine-tuned based on clinical patient data. Our model accurately reproduces patient-specific haemodynamic changes across different scenarios: pre-PVR, six months post-PVR, and a follow-up condition after a decade. It effectively demonstrates the impact of valve implantation on sustaining the diastolic pressure gradient across the valve. The numerical results indicate that our valve model is able to reproduce overall physiological and/or pathological conditions, as preliminary assessed on two different patients. This promising approach provides insights into post-PVR haemodynamics and prosthetic valve effects, shedding light on potential implications for patient-specific outcomes.

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

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

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

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

Current progress toward isogeometric modeling of the heart biophysics

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

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.

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.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

A parametric geometry model of the aortic valve for subject-specific blood flow simulations using a resistive approach

Cardiac valves simulation is one of the most complex tasks in cardiovascular modeling. Fluid-structure interaction is not only highly computationally demanding but also requires knowledge of the mechanical properties of the tissue. Therefore, an alternative is to include valves as resistive flow obstacles, prescribing the geometry (and its possible changes) in a simple way, but, at the same time, with a geometry complex enough to reproduce both healthy and pathological configurations. In this work, we present a generalized parametric model of the aortic valve to obtain patient-specific geometries that can be included into blood flow simulations using a resistive immersed implicit surface (RIIS) approach. Numerical tests are presented for geometry generation and flow simulations in aortic stenosis patients whose parameters are extracted from ECG-gated CT images.

Impact of atrial fibrillation on left atrium haemodynamics: A computational fluid dynamics study

We analyse the haemodynamics of the left atrium, highlighting differences between healthy individuals and patients affected by atrial fibrillation. The computational study is based on patient-specific geometries of the left atria to simulate blood flow dynamics. We design a novel procedure to compute the boundary data for the 3D haemodynamic simulations, which are particularly useful in absence of data from clinical measurements. With this aim, we introduce a parametric definition of atrial displacement, and we use a closed-loop lumped parameter model of the whole cardiovascular circulation conveniently tuned on the basis of the patient's characteristics. We evaluate several fluid dynamics indicators for atrial haemodynamics, validating our numerical results in terms of clinical measurements; we investigate the impact of geometric and clinical characteristics on the risk of thrombosis. To highlight the correlation of thrombus formation with atrial fibrillation, according to medical evidence, we propose a novel indicator: age stasis. It arises from the combination of Eulerian and Lagrangian quantities. This indicator identifies regions where slow flow cannot properly rinse the chamber, accumulating stale blood particles, and creating optimal conditions for clots formation.

Computational Methods for Fluid-Structure Interaction Simulation of Heart Valves in Patient-Specific Left Heart Anatomies

Given the complexity of human left heart anatomy and valvular structures, the fluid–structure interaction (FSI) simulation of native and prosthetic valves poses a significant challenge for numerical methods. In this review, recent numerical advancements for both fluid and structural solvers for heart valves in patient-specific left hearts are systematically considered, emphasizing the numerical treatments of blood flow and valve surfaces, which are the most critical aspects for accurate simulations. Numerical methods for hemodynamics are considered under both the continuum and discrete (particle) approaches. The numerical treatments for the structural dynamics of aortic/mitral valves and FSI coupling methods between the solid Ωs and fluid domain Ωf are also reviewed. Future work toward more advanced patient-specific simulations is also discussed, including the fusion of high-fidelity simulation within vivo measurements and physics-based digital twining based on data analytics and machine learning techniques.

Image-Based Computational Hemodynamics Analysis of Systolic Obstruction in Hypertrophic Cardiomyopathy

Hypertrophic Cardiomyopathy (HCM) is a pathological condition characterized by an abnormal thickening of the myocardium. When affecting the medio-basal portion of the septum, it is named Hypertrophic Obstructive Cardiomyopathy (HOCM) because it induces a flow obstruction in the left ventricular outflow tract. In any type of HCM, the myocardial function can become compromised, possibly resulting in cardiac death. In this study, we investigated with computational analysis the hemodynamics of patients with different types of HCM. The aim was quantifying the effects of this pathology on the intraventricular blood flow and pressure gradients, and providing information potentially useful to guide the indication and the modality of the surgical treatment (septal myectomy). We employed an image-based computational approach, integrating fluid dynamics simulations with geometric and functional data, reconstructed from standard cardiac cine-MRI acquisitions. We showed that with our approach we can better understand the patho-physiological behavior of intraventricular blood flow dynamics due to the abnormal morphological and functional aspect of the left ventricle. The main results of our investigation are: (a) a detailed patient-specific analysis of the blood velocity, pressure and stress distribution associated to HCM; (b) a computation-based classification of patients affected by HCM that can complement the current clinical guidelines for the diagnosis and treatment of HOCM.

Computational fluid dynamics of blood flow in an idealized left human heart

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.

Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function

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.

Using Discrete Multiphysics Modelling to Assess the Effect of Calcification on Hemodynamic and Mechanical Deformation of Aortic Valve

This study proposes a 3D particle-based (discrete) multiphysics approach for modelling calcification in the aortic valve. Different stages of calcification (from mild to severe) were simulated, and their effects on the cardiac output were assessed. The cardiac flow rate decreases with the level of calcification. In particular, there is a critical level of calcification below which the flow rate decreases dramatically. Mechanical stress on the membrane is also calculated. The results show that, as calcification progresses, spots of high mechanical stress appear. Firstly, they concentrate in the regions connecting two leaflets; when severe calcification is reached, then they extend to the area at the basis of the valve.

An image-based computational hemodynamics study of the Systolic Anterior Motion of the mitral valve

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.

Augmented resistive immersed surfaces valve model for the simulation of cardiac hemodynamics with isovolumetric phases

In order to reduce the complexity of heart hemodynamics simulations, uncoupling approaches are often considered for the modeling of the immersed valves as an alternative to complex fluid-structure interaction (FSI) models. A possible shortcoming of these simplified approaches is the difficulty to correctly capture the pressure dynamics during the isovolumetric phases. In this work, we propose an enhanced resistive immersed surfaces (RIS) model of cardiac valves, which overcomes this issue. The benefits of the model are investigated and tested in blood flow simulations of the left heart where the physiological behavior of the intracavity pressure during the isovolumetric phases is recovered without using fully coupled fluid-structure models and without important alteration of the associated velocity field.

Hemodynamic effects of support modes of LVADs on the aortic valve

As the alternative treatment for heart failure, left ventricular assist devices (LVADs) have been widely applied to clinical practice. However, the effects of the support modes of LVADs on the biomechanical states of the aortic valve are still poorly understood. Hence, the present study investigates such effects and proposes a novel fluid-structure interaction (FSI) approach that combines the lattice Boltzmann method (LBM) and finite element (FE) method. Two support modes of LVADs, namely constant speed mode and constant flow mode, which have been widely applied to clinical practice, are also designed. Results demonstrate that the support modes of LVADs could significantly affect the biomechanical states of the aortic valve and the blood flow pattern of the ascending aorta. Compared with those in the constant flow mode, the leaflets in the constant speed mode could achieve better dynamic performance and lower stress during the systolic phase. The max radial displacement of the leaflets in the constant speed mode is at 8 mm, whereas that in the constant flow mode is at 0.8 mm. Furthermore, the outflow of LVADs directly impacts the aortic surfaces of the leaflets during the diastolic phase by increasing the level of wall shear stress of the leaflets. The leaflets in the constant speed mode receive less impact than those in the constant flow mode. The condition with such minimal impact is conducive to maintaining the normal structure of leaflets and benefits the reduction of the risk of valvular diseases. In sum, the support modes of LVADs exert a crucial effect on the biomechanical environment of the aortic valve. The constant speed mode is better than the constant flow mode in terms of providing a good hemodynamic environment for the aortic valve.

Detection of arterial wall abnormalities via Bayesian model selection

Patient-specific modelling of haemodynamics in arterial networks has so far relied on parameter estimation for inexpensive or small-scale models. We describe here a Bayesian uncertainty quantification framework which makes two major advances: an efficient parallel implementation, allowing parameter estimation for more complex forward models, and a system for practical model selection, allowing evidence-based comparison between distinct physical models. We demonstrate the proposed methodology by generating simulated noisy flow velocity data from a branching arterial tree model in which a structural defect is introduced at an unknown location; our approach is shown to accurately locate the abnormality and estimate its physical properties even in the presence of significant observational and systemic error. As the method readily admits real data, it shows great potential in patient-specific parameter fitting for haemodynamical flow models.

Fluid-Structure Interaction Models of Bicuspid Aortic Valves: The Effects of Nonfused Cusp Angles

Bicuspid aortic valve (BAV) is the most common type of congenital heart disease, occurring in 0.5-2% of the population, where the valve has only two rather than the three normal cusps. Valvular pathologies, such as aortic regurgitation and aortic stenosis, are associated with BAVs, thereby increasing the need for a better understanding of BAV kinematics and geometrical characteristics. The aim of this study is to investigate the influence of the nonfused cusp (NFC) angle in BAV type-1 configuration on the valve's structural and hemodynamic performance. Toward that goal, a parametric fluid-structure interaction (FSI) modeling approach of BAVs is presented. Four FSI models were generated with varying NFC angles between 120 deg and 180 deg. The FSI simulations were based on fully coupled structural and fluid dynamic solvers and corresponded to physiologic values, including the anisotropic hyper-elastic behavior of the tissue. The simulated angles led to different mechanical behavior, such as eccentric jet flow direction with a wider opening shape that was found for the smaller NFC angles, while a narrower opening orifice followed by increased jet flow velocity was observed for the larger NFC angles. Smaller NFC angles led to higher concentrated flow shear stress (FSS) on the NFC during peak systole, while higher maximal principal stresses were found in the raphe region during diastole. The proposed biomechanical models could explain the early failure of BAVs with decreased NFC angles, and suggests that a larger NFC angle is preferable in suture annuloplasty BAV repair surgery.

Complex blood flow patterns in an idealized left ventricle: A numerical study

In this paper, we study the blood flow dynamics in a three-dimensional (3D) idealized left ventricle of the human heart whose deformation is driven by muscle contraction and relaxation in coordination with the action of the mitral and aortic valves. We propose a simplified but realistic mathematical treatment of the valves function based on mixed time-varying boundary conditions (BCs) for the Navier-Stokes equations modeling the flow. These switchings in time BCs, from natural to essential and vice versa, model either the open or the closed configurations of the valves. At the numerical level, these BCs are enforced by means of the extended Nitsche's method (Tagliabue et al., Int. J. Numer. Methods Fluids, 2017). Numerical results for the 3D idealized left ventricle obtained by means of Isogeometric Analysis are presented, discussed in terms of both instantaneous and phase-averaged quantities of interest and validated against those available in the literature, both experimental and computational. The complex blood flow patterns are analysed to describe the characteristic fluid properties, to show the transitional nature of the flow, and to highlight its main features inside the left ventricle. The sensitivity of the intraventricular flow patterns to the mitral valve properties is also investigated.