Computational Cardiovascular Mechanics

The first basic biomechanics modeling step outlined in the introductory chapter is to define the geometric configuration. In Chapters 12 and 14 we demonstrate the application of either simple (i.e., axisymmetric truncated ellipsoid) or complex (i.e., fully 3-D) left ventricular (LV) geometric models or finite element (FE) meshes. This chapter is primarily concerned with an instructive review of the methodology we have used to create both types of FE meshes, which relies on the “parametric” meshing software TrueGrid^®. Since TrueGrid is rather expensive, Section 1.6 describes the use of free software executables available from the Pacific Northwest National Laboratory. The second basic biomechanics modeling step (determine mechanical properties) is addressed in the next three chapters. The third and fourth basic biomechanics modeling steps (governing equations and boundary conditions) are discussed briefly at the end of this chapter.

A precise knowledge of the microstructures of the myocardium such as myocyte organization and myofiber orientation is necessary to better understand material and functional properties of the tissue. By characterizing the diffusion of water exerted by its molecular environment, magnetic resonance diffusion tensor imaging has emerged as a viable alternative to conventional histology for mapping tissue fibers and offers advantages of being nondestructive, relatively convenient, and inherently 3D. This chapter presents assessments and modeling of myocardial structures via diffusion tensor imaging, including their principles, validation, applications, and potential directions for future development.

Of the four basic biomechanics modeling steps outlined in the Introduction, determining the constitutive equations for cardiovascular tissue is often the most difficult step, especially when the tissue properties vary with time and sarcomere length history, as is the case with contracting myocardium. Using a cylindrical model to study transmural variations in stress and strain rather than a finite element model of the entire left ventricle allows for the implementation of a time- and sarcomere length history-dependent constitutive equation. The cylindrical model simulations can then be repeated with progressively simpler constitutive equations and the resulting transmural stress and strain distributions compared to determine under what conditions the most computationally efficient constitutive equations are valid. This chapter is primarily concerned with an instructive review of the constitutive equations we have implemented in cylindrical and finite element models of the passive and beating left ventricle, including that of diseased and surgically treated hearts. The last section of this chapter is concerned with experimental measurements that we have used to validate these models.

The previous chapter includes a computationally efficient strain energy function for describing the three-dimensional relationship between stress and strain in passive myocardial material properties, the material parameters of which were formally optimized using left ventricular pressure and epicardial strain measurements in a cylindrical model. Results from such a model are confined at best to the equatorial region of the left ventricle. A finite element model of the entire left ventricle is required to determine regional variations in myocardial material properties. The most important or at least interesting finding from such a study is that myocardial contractility in the (border zone) region adjacent to a myocardial infarction is much less than (typically only half) that in regions remote from the myocardial infarction. This finding has been confirmed with active stress measurements in skinned muscle fibers dissected from these regions. This chapter is concerned with brief descriptions of the studies from our laboratory that have led up to our current knowledge concerning regional variations of myocardial contractility in infarcted left ventricles.

Models of cardiac electrical activation have been proposed for over 100 years. While the major components of the cardiac source and volume conductor models have not changed over the years, they have become increasingly complex and more robust. Although modeling of body surface potentials (forward model) and cardiac potentials (inverse model) has been a major topic of research, the clinical utility has yet to be fully realized. Integrated cardiac models with electrical, mechanical, neural, metabolic, circulatory, and genetic inputs are currently being developed. These integrated models are likely to provide new insights into cardiac electrical activation during heart failure and generate new hypotheses about multi-system coupling in the heart. The objective of this chapter is to provide an overview of the history, theory, and clinical use of electrical heart models with applications to heart failure.

Biomechanics relates the function of a physiological system to its structure. The objective of biomechanics is to deduce the function of a system from its geometry, material properties, and boundary conditions based on the balance laws of mechanics. Geometry clearly plays a major role in formulation of boundary value problems in biomechanics and is intimately related to function and physiology. Here, we shall provide an overview of the geometric features of the vascular system with special emphasis on the vascular system of the heart (coronary circulation).

The geometry of vascular system is an important determinant of blood flow in health and disease. There is a strong geometric component to atherosclerosis in coronary heart disease since lesions are preferentially located at bifurcation points and regions of high curvature. The influence of these local structures on recirculation and deleterious shear stresses and their role in plaque development is widely accepted. Over time, researchers have turned to MR, CT, or biplane images of vascular trees to faithfully capture these features in the flow simulations. Historically, this has taken the form of labor-intensive manual reconstructions from morphometric measurements based on the centerline, whereby small idealized subsets of vascular trees are developed into computational grids. With improved imaging, image processing, and geometric reconstruction algorithms, researchers have begun to develop geometrically accurate computational models directly from the medical images. This chapter provides an overview of contemporary methods for image processing, centerline detection, boundary condition definition, and grid generation of both clinical and research images of cardiovascular structures.

Coronary heart disease which is a major cause of heart failure in the United States has a focal nature which is due to local hemodynamic disturbances. The computational fluid dynamics (CFD) method has become a powerful approach to understand blood flows in the cardiovascular system and its local features. This chapter outlines the field equations for blood flow and some of the approaches for numerical solutions. Specifically, the text focuses on the finite difference (FD) and finite element (FE) methods with applications to blood flow dynamics in coronary arteries.

The cardiovascular system experiences strong fluid–structure interaction (FSI). This chapter presents the theoretical formulations for two powerful FSI techniques: the arbitrary Lagrangian Eulerian (ALE) and the immersed boundary (IB) methods. Examples of FSI applications to aortic cross-clamping used during surgical treatment of heart failure and valveless pumping are also presented.

Turbulence is a fluid regime characterized by chaotic and stochastic changes of flow. The onset of turbulence can occur under disease conditions and is known to have adverse effects on the function of the cardiovascular (CV) system. This chapter outlines the basic features of turbulence in the CV system. As a specific example, simulation of turbulent flow in an abdominal aortic aneurysm (AAA) is presented. The simulated results show that transition to turbulence occurs in large aneurysms with high Reynolds number. Onset of turbulence is seen to drastically change the distribution of wall shear stress and fluid pressure. The general implications are enumerated.

Left ventricular (LV) remodeling after myocardial infarction (MI) plays an important role in the progression of heart failure (HF). Changes in the shape, size, and function of the LV are caused by altered mechanical properties of the injured myocardium. As the survival rate after MI improves with medical advances, the incidence of HF patients increases. Hence, an accurate depiction of the LV remodeling process facilitates disease surveillance and monitoring of therapeutic efficacy. It may also help determine the choice of treatment, e.g., surgery to remove the infarcted wall segment and reduce the LV cavity size. Traditionally, there are several ways of characterizing LV remodeling: changes in LV diameter, LV volume, ejection fraction, and qualitative or semi-quantitative descriptors of LV shape. In this chapter, we present a new approach to quantify LV shape (in terms of curvedness), wall stress, and function by using computational modeling.

Perhaps the most straightforward clinical application of validated regional ventricular mechanics models for diseased hearts is the simulation of a novel surgical procedure or medical device for treating heart failure or ischemic cardiomyopathy. In each study our cardiac biomechanics laboratory uses one of two different approaches: (1) an axisymmetric truncated ellipsoidal model with left ventricular (LV) cavity and wall volumes typical of the failing human heart or animal model of heart failure to determine efficacy of the surgical procedure or device; or (2) an animal- or patient-specific fully 3-D model of the infarcted LV created using echocardiography or MRI to optimize the design of the surgical procedure or device. This chapter is concerned with brief descriptions of the studies from our laboratory that provide the best examples of these two approaches.

Both myocardial infarction and volume overloading associated with regurgitant valve lesions lead to eccentric left ventricular (LV) hypertrophy. The mechanism is presumed to be positive feedback between diastolic LV wall stress and eccentric LV hypertrophy. Further, in each case, an increase in LV size is an important adverse prognostic finding. The experience with skeletal muscle cardiomyoplasty led to the hypothesis that passive constraint of LV enlargement would interrupt the diastolic stress and eccentric hypertrophy cycle, in addition to halting and possibly reversing the adverse LV remodeling. A number of passive constraint devices such as the Acorn CorCap™ Cardiac Support Device (CSD), Paracor Medical HeartNet™ Ventricular Support System (VSS), and Myocor™ yosplint^® have been used. Most recently, an Adjustable Fluid Filled Balloon CSD was proposed by Ghanta and colleagues. In this chapter we model the effect of passive constraint devices, with the exception of the Paracor Medical HeartNet™ VSS, on the LV stroke volume/end-diastolic pressure (Starling) relationship and regional distributions of stress in the local muscle fiber direction.

In recent years, there has been a significant effort to restore heart function by the addition of stem cells directly into the myocardium. These cells are normally carried in a synthetic extracellular matrix and implanted into the injured heart. While there has been little demonstration of actual tissue regeneration using such methods, there has been long-term improvement from these techniques, and surprisingly, from the implantation of biomaterials alone, without any included cells. This has in fact led to therapies that directly add passive materials into the ventricle to help prevent heart failure. Therefore, theoretically evaluating the addition of passive material volumes into the myocardium is of clinical importance to understand the mechanisms for the improvement of ventricular mechanics and for optimizing such treatments. In this chapter we discuss the role of finite element studies in investigating the direct addition of non-contractile materials into the myocardium.

In recent years, cardiac resynchronization therapy (CRT) has become an effective and popular approach to the treatment of heart failure with a conduction disturbance, but it is unclear why 30% of patients do not respond. With improvements in computer power, diagnostic and therapeutic medical technologies, it is increasingly feasible to apply patient-specific modeling to guide and predict the response to CRT. In this chapter we discuss strategies as to how computational modeling of CRT could be used to try to predict the outcome of this therapy patient-specifically.

Computational modeling is an excellent tool with which to investigate the mechanics of the aortic heart valve. The setting of the heart valve presents complex dynamics and mechanical behavior in which solid structures interact with a fluid domain. There currently exists no standard approach; a variety of strategies have been used to address the different aspects of modeling the heart valve. Simplifications reduce computational costs, but could compromise accuracy. As advancements in modeling techniques are made and utilized, more physiologically relevant models are possible. Computational studies of the aortic valve have contributed to an improved understanding of the mechanics of the normal valve, and insights into the progression of diseased valves.

Coronary artery bypass graft (CABG) is a major therapy for ischemic heart disease which if left untreated can progress to failure of the heart. Restenosis, a leading cause of CABG, can be correlated with the geometric configuration and the hemodynamics of the graft. In this chapter we use computational fluid dynamics (CFD) to investigate the hemodynamics in a 3D out-of-plane sequential bypass graft model. Using a finite volume approach, quasi-steady flow simulations are performed at mid-ejection and at mid-diastole. Plots of velocity vectors, wall shear stress (WSS), and spatial WSS gradient (WSSG) distribution are presented in the aorto-left coronary bypass graft domain. Simulation results reveal a more uniform WSS and spatial WSSG distribution in the side-to-side (sequential graft) anastomosis configuration over the end-to-side (multiple graft) anastomosis. Results for the multiple bypass graft model show the peak magnitudes of the spatial WSSG are higher compared to the sequential bypass graft model. These findings suggest that sequential bypass grafting may be preferable over multiple bypass grafting to avoid non-uniformities of WSS.

A ventricular assist device (VAD) is a pump surgically connected to the heart and aorta in order to boost systemic blood flow in heart failure patients. The design of these devices has evolved over the past 30 years, with improvements and innovations enabled through the synergistic use of experimental research, clinical studies, and computational models. The application of computational fluid dynamics models has allowed the design of VADs to shift from large, bulky devices designed for patients with severe cardiac failure to a variety of smaller devices designed for a range of patients and cardiovascular conditions.