Potential applications of computational fluid dynamics to biofluid analysis

Computational fluid dynamics was developed to the stage where it has become an indispensable part of aerospace research and design. In view of advances made in aerospace applications, the computational approach can be used for biofluid mechanics research. Several flow simulation methods developed for aerospace problems are briefly discussed for potential applications to biofluids, especially to blood flow analysis

Simulating Cardiac Fluid Dynamics in the Human Heart

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin, flexible valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions. However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the cardiac valves are limited in their abilities to predict valve performance, resolve fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac fluid dynamics in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart's microstructure. Further, it is the first fluid-structure interaction model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and predicts fine-scale flow features. None of these outputs are prescribed; instead, they emerge from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical devices or clinical interventions. They also can serve as platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients

The LifeV library: engineering mathematics beyond the proof of concept

LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testing of new methods, one distinguishing feature of LifeV is its use on real world problems and it is intended to provide a tool for many engineering applications. It has been actually used in computational hemodynamics, including cardiac mechanics and fluid-structure interaction problems, in porous media, ice sheets dynamics for both forward and inverse problems. In this paper we give a short overview of the features of LifeV and its coding paradigms on simple problems. The main focus is on the parallel environment which is mainly driven by domain decomposition methods and based on external libraries such as MPI, the Trilinos project, HDF5 and ParMetis. Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar

Finite Element Modelling of Pulsatile Blood Flow in Idealized Model of Human Aortic Arch: Study of Hypotension and Hypertension

A three-dimensional computer model of human aortic arch with three branches is reproduced to study the pulsatile blood flow with Finite Element Method. In specific, the focus is on variation of wall shear stress, which plays an important role in the localization and development of atherosclerotic plaques. Pulsatile pressure pulse is used as boundary condition to avoid flow entry development, and the aorta walls are considered rigid. The aorta model along with boundary conditions is altered to study the effect of hypotension and hypertension. The results illustrated low and fluctuating shear stress at outer and inner wall of aortic arch, proximal wall of branches, and entry region. Despite the simplification of aorta model, rigid walls and other assumptions results displayed that hypertension causes lowered local wall shear stresses. It is the sign of an increased risk of atherosclerosis. The assessment of hemodynamics shows that under the flow regimes of hypotension and hypertension, the risk of atherosclerosis localization in human aorta may increase

Modelling mitral valvular dynamics–current trend and future directions

Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed

Modelling the Human Cardiac Fluid Mechanics. 4th ed

With the Karlsruhe Heart Model (KaHMo) we aim to share our vision of integrated computational simulation across multiple disciplines of cardiovascular research, and emphasis yet again the importance of Modelling the Human Cardiac Fluid Mechanics within the framework of the international STICH study. The focus of this work is on integrated cardiovascular fluid mechanics, and the potential benefits to future cardiovascular research and the wider bio-medical community

Integrated Heart - Coupling multiscale and multiphysics models for the simulation of the cardiac function

Mathematical modelling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a complex multiscale system involving interacting phenomena at the molecular, cellular, tissue, and organ levels. This article addresses the numerical modelling of many aspects of heart function, including the interaction of the cardiac electrophysiology system with contractile muscle tissue, the sub-cellular activation-contraction mechanisms, as well as the hemodynamics inside the heart chambers. Resolution of each of these sub-systems requires separate mathematical analysis and specially developed numerical algorithms, which we review in detail. By using specific sub-systems as examples, we also look at systemic stability, and explain for example how physiological concepts such as microscopic force generation in cardiac muscle cells, translate to coupled systems of differential equations, and how their stability properties influence the choice of numerical coupling algorithms. Several numerical examples illustrate three fundamental challenges of developing multiphysics and multiscale numerical models for simulating heart function, namely: (i) the correct upscaling from single-cell models to the entire cardiac muscle, (ii) the proper coupling of electrophysiology and tissue mechanics to simulate electromechanical feedback, and (iii) the stable simulation of ventricular hemodynamics during rapid valve opening and closure

Fluid-structure interaction analysis of the aortic valve in young healthy, ageing and post treatment conditions

Optimal aortic valve function, limitation of blood damage, and frequency of thromboembolic events are all dependent upon the haemodynamics within the aortic root. Improved understanding of the young healthy physiological state via investigation of the fluid dynamics around and through the aortic valve is essential to identify detrimental changes leading to pathologies and develop novel therapeutic procedures. The aim of this study is to develop a numerical model that can support a better comprehension of the valve function and serve as a reference to identify the changes produced by specific pathologies and treatments. A Fluid-structure interaction (FSI) numerical model was developed and adapted to accurately replicate the conditions of a previous in vitro investigation into aortic valve dynamics, performed by means of particle image velocimetry (PIV). The model was validated on equivalent physical settings, in a pulse duplicator replicating the physiological healthy flow and pressure experienced in the left heart chambers. The resulting velocity fields and hydrodynamic valve performance indicators of the two analyses were qualitatively and quantitatively compared to validate the numerical model. The validated FSI model was then used to describe realistic young healthy, ageing and post treatment conditions, by eliminating the experimental and methodological limitations and approximations. In detail, in terms of treatments, both surgical and transcatheter valve replacement procedures were investigated. In terms of pathologies, typical alterations frequently due to ageing, namely thickening of the valve leaflets and progressive dilation of the aortic chamber, were studied. The analysis was performed by comparing the data obtained for the ageing and post treatment configurations with those of the young healthy root environment. The results were analysed in terms of leaflets kinematics, flow dynamics, pressure and valve performance parameters. The study suggests a new operating mechanism for the young healthy aortic valve leaflets considerably different from what reported in the literature to date and largely more efficient in terms of hydrodynamic performance

A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with ad- hoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors

Use of Machine Learning for Automated Convergence of Numerical Iterative Schemes

Convergence of a numerical solution scheme occurs when a sequence of increasingly refined iterative solutions approaches a value consistent with the modeled phenomenon. Approximations using iterative schemes need to satisfy convergence criteria, such as reaching a specific error tolerance or number of iterations. The schemes often bypass the criteria or prematurely converge because of oscillations that may be inherent to the solution. Using a Support Vector Machines (SVM) machine learning approach, an algorithm is designed to use the source data to train a model to predict convergence in the solution process and stop unnecessary iterations. The discretization of the Navier Stokes (NS) equations for a transient local hemodynamics case requires determining a pressure correction term from a Poisson-like equation at every time-step. The pressure correction solution must fully converge to avoid introducing a mass imbalance. Considering time, frequency, and time-frequency domain features of its residual’s behavior, the algorithm trains an SVM model to predict the convergence of the Poisson equation iterative solver so that the time-marching process can move forward efficiently and effectively. The fluid flow model integrates peripheral circulation using a lumped-parameter model (LPM) to capture the field pressures and flows across various circulatory compartments. Machine learning opens the doors to an intelligent approach for iterative solutions by replacing prescribed criteria with an algorithm that uses the data set itself to predict convergence