Biomechanics of Cardiac Function

Abstract

The heart pumps blood to maintain circulation and ensure the delivery of oxygenated blood to all the organs of the body. Mechanics play a critical role in governing and regulating heart function under both normal and pathological conditions. Biological processes and mechanical stress are coupled together in regulating myocyte function and extracellular matrix structure thus controlling heart function. Here we offer a brief introduction to the biomechanics of left ventricular function and then summarize recent progress in the study of the effects of mechanical stress on ventricular wall remodeling and cardiac function as well as the effects of wall mechanical properties on cardiac function in normal and dysfunctional hearts. Various mechanical models to determine wall stress and cardiac function in normal and diseased hearts with both systolic and diastolic dysfunction are discussed. The results of these studies have enhanced our understanding of the biomechanical mechanism in the development and remodeling of normal and dysfunctional hearts. Biomechanics provide a tool to understand the mechanism of left ventricular remodeling in diastolic and systolic dysfunction and guidance in designing and developing new treatments.

Introduction

The heart pumps blood and nutrients to all organs to support their normal function. Synchronized contraction of the myocardium generates pressure to drive the blood flow in arteries to distal organs and the constant repetitive pumping action maintains the circulation to all organs. Biomechanical principles play an important role in governing cardiac function.

Many diseases may affect the complex pumping system of the heart, and can be caused by a variety of factors including genetic defects, aging, and environmental stimuli. Left ventricular (LV) myocardial infarction (MI) due to coronary heart disease and diastolic dysfunction due to hypertension and LV hypertrophy are two major forms of heart disease. Biomechanics plays a critical role in regulating cardiac function not only in the normal heart but also in the diseased heart. Knowledge of the biomechanics of the heart is requisite for understanding the causes and consequences of cardiac diseases. For example, mechanical stress plays an important role in the development of cardiomyopathy and LV remodeling post-MI, regulating tissue fibrosis and scar formation. Altering the mechanical stress patterns can provide effective approaches for treatment of MI and improving cardiac function. Increased stresses in the myocardium due to hypertension can also lead to hypertrophy of the ventricles and diastolic heart failure. While heart valve diseases, either stenosis or insufficiency (regurgitation) also have a direct effect on the pumping function of the heart, we intend to primarily focus our discussion on the myocardial wall and LV function. We will provide a brief discussion of the biomechanical studies of the right ventricle, atria and heart valves and refer readers to recent reviews in the fields.

This paper reviews the relevant biomechanical concepts and measurements and summarizes the recent advances in the biomechanics of LV in MI and diastolic dysfunction as well as related treatments. It is concluded that biomechanical knowledge and research are required to fully understand the causes of cardiac dysfunction and develop new treatment devices and techniques.

Biomechanics of Normal Cardiac Function

The heart is a multiscale system that functions at the organ, tissue, cellular, and protein levels. Cardiac function can be evaluated at the cellular, tissue and organ levels, and at each level mechanical stress plays an important role in regulating function. This section will examine the measurement of cardiac function and the role of mechanics in determining cardiac function at each of these length scales in the healthy heart.

Cardiac Function

The primary function of the LV is to pump blood to distal organs and all the extremities of the body. The performance of the pump depends on the contraction force of the myocardium, the loading conditions, ventricular size and shape, and valve function. Heart failure occurs when the LV is unable to meet the demands of the body. Biomechanics is a major determinant of cardiac function. Therefore, it is important to be able to describe and measure cardiac function.

The Ventricular Pressure Volume Relationship

The cardiac cycle, a single beat of the heart, is typically divided into two phases: systole, the period of active contraction, and diastole the period of relaxation and filling. At the onset of the systolic phase the LV of the heart is filled with blood to a pressure of about 8 mm Hg and a pressure of greater than 16 mm Hg being considered abnormal (152, 154). At this point both the mitral valve that leads into the LV and the aortic valve through which blood leaves the chamber are closed. Active contraction of the myocytes in the myocardium of the LV rapidly raises the fluid pressure above the pressure in the aorta. This period of systole is referred to as isovolumic contraction since blood is not flowing into or out of the LV. Once the fluid pressure inside the LV surpasses the pressure in the aorta, the aortic valve opens and the contraction of the myocardium pushes the pressurized blood out of the chamber and into circulation. This phase is known as ejection. As the contractile force generated by the myocytes diminishes the pressure of the blood in the LV chamber again falls below the systemic circulatory pressure and the aortic valve closes marking the end of the ejection phase and the end of systole. Relaxation of the myocytes causes a rapid isovolumic pressure drop in the blood remaining in the LV chamber, during the first phase of diastole known as isovolumic relaxation. When the pressure of the blood in the LV falls below the pressure of the left atria, the mitral valve opens causing the LV chamber to fill with blood. Finally the contraction of the atria forces in the last bit of blood and slightly pressurizes the chamber to its end-diastolic pressure. This phase of the cardiac cycle is referred to as the filling or diastolic filling phase.

The overall performance of the pump depends on the contraction force of the myocardium, the loading conditions, ventricular size and shape, and valve function among others (Table 1).

Table 1. Mechanical Factors that Affect Cardiac Output.

Category	Factors
Preload	venous return, diastolic wall stiffness, filling time, atrial stiffness
Contractility	sarcomere length, inotropic state
Afterload	arterial pressure, arterial resistance, aortic valve function
Heart Rate	activity level

In terms of mechanics, the best way to depict the cardiac cycle is using a pressure-volume diagram (Figure 1.A). The PV diagram depicts the cardiac cycle as a counterclockwise loop. The right and left halves of the loop correspond to the isovolumic contraction and isovolumic relaxation phases while the bottom segment represents the filling phase and the top segment represents the ejection phase. The area contained within the loop is referred to as the stroke work (SW) and represents the amount of energy imparted by the LV into the blood. SW is a measure of how hard the heart is working. Despite being a relatively simple measure SW is often miscalculated in the literature and reported with incorrect units (170). Sarnoff and Berglund were the first to report SW, and they calculated SW as gram-force-meters, but listed the units simply as gram-meters (169). The distinction between grams and grams-force is subtle and has led to much misreporting. The correct units for SW should be units of work such as Joules, or simply mm Hg-ml. The heart is capable of adjusting the amount of work it does in order to match the metabolic demands of the body.

Figure 1. The Pressure Volume Relationship.

A graphical representation of the pressure volume loop depicting the events of the cardiac cycle, and depicting stroke work as the area inside the loop. B. Occlusion of the vena cava reduces LV filling and allows for the determination of the end-diastolic pressure volume relationship (EDPVR) and the end-systolic pressure volume relationship (ESPVR). C. Increased myocardial stiffness leads to a leftward and upward shift of the EDPVR, reducing diastolic filling (red dotted line). Dilation of the LV can be noted as a rightward shift of the EDPVR (blue dotted line).

Plotting different cardiac cycles with varied end-diastolic volumes on one plot allows for two important mechanical relationships to be determined, the end-diastolic pressure volume relationship (EDPVR) and the end-systolic pressure volume relationship (ESPVR) (Figure 1.B). The EDPVR can be measured by varying the amount of diastolic filling through temporarily occluding of the vena cava, a common technique in animal studies (12, 31). The EDPVR represents the relationship between the diastolic pressure and the diastolic volume. Increasing the diastolic volume stretches the myocardial tissue which puts stress on the tissue and increases the pressure of the blood. In this way the curve is a representation of the passive mechanical properties of the myocardial tissue with volume being equivalent to strain and pressure being equivalent to the stress. Diastolic pressure volume curves are typically exponential matching the exponential stress-strain behavior of most biological soft tissues. One of the foundational principles of ventricular mechanics is the Frank-Starling mechanism, also called Starling’s Law of the Heart. This principle states that increasing diastolic filling will increase the stroke volume of the heart (151). This can be seen by looking at the PV curves and seeing that as the volume of blood during diastole increases, the end-diastolic point on the EDPVR moves further away from the ESPVR which increases the stroke volume. From a physiological standpoint this occurs due to the fact that the added diastolic filling stretches the sarcomeres of the myocytes which in turn allows them to generate more force per contraction (71). Diastolic dysfunction can occur when the ventricle becomes too stiff resulting in a leftward and upward shift of the EDPVR and adverse remodeling can lead to dilation of the ventricle which leads to a right shift in the EDPVR (Figure 1.C) (131).

The end-systolic pressure volume relationship represents the amount of blood left in the ventricle for a given aortic blood pressure. The higher the aortic blood pressure, the less blood that is able to leave the LV. The ESPVR is typically a linear relationship and the slope of the ESPVR is called the maximum elastance (168). The maximal elastance is considered a measure of the contractile ability of the LV for a given inotropic state. Changes in the inotropic state which could be due to the influence of signaling hormones such as epinephrine or drugs such as beta blockers alter the maximal elastance which can raise or lower the amount of blood the LV is able to eject (30). Inotropic agents are currently under investigation as potential therapies for heart failure, but trials have been met with mixed success (137).

Stroke Volume and Ejection Fraction

There are many different parameters that are used to quantify the function of the heart (Table 2). However, since the primary function of the heart is to pump blood through the body, the most useful measures quantify the actual volume of blood being pumped. Stroke volume (SV) is defined as the difference between the LV volume at end-diastole (EDV) and end-systole (ESV), or in other words the width of the pressure-volume loop.

$$\mathit{SV}=\mathit{EDV}-\mathit{ESV}$$ (1)

While SV represents how much blood the heart pumps per beat, another parameter, ejection fraction (EF) is often used to describe heart function. EF is defined as

$$\mathit{EF}=\frac{\mathit{SV}}{\mathit{EDV}}\times 100$$ (2)

EF is normalized by the end-diastolic volume so as to normalize the amount of blood to the actual size of the LV, which accounts for differences in size between patients. In humans, ejection fraction is typically between 50 and 80% and readings below this level are a sign of heart failure (35).

Table 2. Measures of Cardiac Function.

Measure	Description
Stroke Volume (SV)	Volume of blood pumped per beat
Ejection Fraction (EF)	Stroke volume normalized by diastolic volume
Cardiac Output (CO)	Volume of blood pumped per unit time
Stroke Work (SW)	Energy imparted to the blood by the myocardium during one beat
Global Longitudinal Strain (GLS)	Measure of longitudinal contractile ability
Global Radial Strain (GRS)	Measure of radial contractile ability
Ratio of mitral inflow velocity to early diastolic annular velocity (E/e’)	Measure of diastolic function, correlated with diastolic filling pressure
dP/dt	The rate of pressure increase during systolic contraction
Time constant of ventricular relaxation (τ)	Measure of the rate of ventricular contraction

Cardiac output is defined as the volume of blood a heart pumps per minute.

$$\mathit{CO}=\mathit{SV}\times \mathit{HR}$$ (3)

Where HR is the heart rate. CO is an important index of overall heart function. CO increases as body demand goes up such as in physical exercise. CO depends on many factors and myocardial contractility is only one of these factors.

Measuring Cardiac Function

There are many options for measuring cardiac function including both invasive and noninvasive methods (Table 3). Clinically, the first choice in measurement techniques is often echocardiography as it is relatively inexpensive, portable and does not rely on ionizing radiation (43). Echocardiography allows for coarse evaluation of cardiac dimensions throughout the cardiac cycle. This allows for the calculation of LV volumes and wall thicknesses. Improvements in echocardiography over the last decade now allow for three dimensional imaging, which can improve the estimate of LV chamber volumes (93). The speed and portability of echocardiography make it well suited to the research lab as well. CT scans are also commonly employed to measure cardiac function, and they may give added resolution as compared to echocardiography. However, they come with added expense and radiation dose to the patient and may not be the first choice for examining LV function. MRIs can offer very detailed geometries of the LV, but due to imaging times, as well as costs may not be the best choice. A Multi Gated Acquisition Scan (MUGA) is another clinical option for measuring cardiac volumes. During this test a radioactive tracer is injected into the blood stream and the LV is imaged with a gamma camera that detects the gamma particles emitted by the tracer. This method is highly accurate but is typically reserved for patients who have already been diagnosed with heart disease. CT, MRI and MUGA all require the use of a gating system which utilizes the patient’s ECG signal to reconstruct accurate LV volumes at various points throughout the cardiac cycle based on several successive cardiac cycles.

Table 3. Methods for Measuring Cardiac Function.

Measurement	Methods
Dimensions and Geometry	Echocardiography, MRI, CT, SPECT, PET, MUGA
Contractile Function and Strain	Tagged MRI, Tissue Doppler Echocardiography, Speckle-Tracking Echocardiography
Pressure-Volume Relationship	Cardiac Catheterization

While, volumetric measurements are a good measure of the overall ventricle function, they do not capture the whole biomechanical picture. Measurement of local myocardial contraction and wall strain has been used as another important index of cardiac function. Early studies relied on the implantation of radiopaque markers on to the surfaces of the LV which allowed for their motion to be tracked by radiographic methods (4, 42, 197) Advances in MRI technology now allow for virtual tags to be placed on the heart and their motion tracked throughout the cardiac cycle in order to examine local tissue deformation (140, 224). Tags can be placed by creating small tissue regions with distinct magnetic properties, which can be achieved through magnetic saturation of these regions or spatial variations in the magnetic field gradient (89). For a review of strain analysis techniques using MRI please see the 2014 article by Jiang, et al (89). Another recent advance is the development of speckle-tracking echocardiography and Doppler tissue imaging which both allow for the calculation of regional tissue strains (1, 66, 186). The use of ultrasonic contrast agents such as microspheres can aid in the measurement of local tissue deformation by more clearly defining the boundary between blood and tissue (129). A nice overview of echocardiograpic strain analysis techniques can be found in the review by Gorcsan et al (56). Local strains of the LV wall during the cardiac cycle give a direct measurement of tissue contractile ability and can identify regions of tissue that are not contracting properly. The global or averaged longitudinal strain has become a widely used clinical measurement (93, 185). In a healthy population longitudinal strain was found to have 95% confidence intervals of −17.0-28.9% while the confidence interval for radial strain was found to be 40.1-82.0% (101). Values that are nearer to 0 are a strong indicator of heart failure (141).

Echocardiographic strain analysis has also allowed for the calculation of strain rates which can provide insight into dynamics of contraction. Speckle tracking echocardiography has also become an important tool in the quantification of LV twist. Twist of the LV is an important component of cardiac function and reduction in LV twist has been associated with several forms of cardiac disease (141). In a cohort of healthy humans, peak LV systolic twist was found to be 6.7 degrees in young patients, 8.0 degrees in middle aged patients, and 10.8 degrees in older patients (183). The rate and amount of untwisting during diastole is also an important measure of diastolic function (4, 23, 183).

Doppler imaging technologies have also allowed for the calculation of mitral inflow velocities as well as the annular velocities of the mitral valve. The variable E is used to represent the peak mitral inflow velocity or peak E wave velocity. The variable e’ is used to denote the annular velocity of the mitral valve during the early, E wave period of diastole. These values are an important measure of diastolic function and the ratio of the mitral inflow velocity to the early diastolic annular velocity (E/e’) is an excellent predictor of the end-diastolic LV pressure (144).

Cardiac catheterization is an invasive technique in which a catheter containing a pressure sensor, or now commonly a pressure and volume sensor is inserted into the heart through the aorta. Guidance of the catheter is often aided by the use of a fluoroscope which can be used to determine the position of the catheter in the heart. This technique can be used to determine the pressure volume loops and can be used to determine if there are any unusual pressure gradients in the LV which could indicate areas of dysfunction (64). Two common measurements determined by cardiac catherization include the dP/dt which is the rate at which the pressure increases during systole and τ which is the time constant of ventricular relaxation. dP/dt is used in diagnosing systolic dysfunction while abnormally high values of τ denote diastolic dysfunction and can be an indicator of hypertrophy (19).

Cardiac catheterization is commonly employed in the research lab. One important test of mechanical function conducted with the use of pressure volume catheters is the occlusion test. During the measurement process, the inferior vena cava is temporarily occluded using a suture. This reduces the amount of filling in the LV which through the Frank-Starling mechanism reduces the amount of contractile force. By recording the PV loops for several different end-diastolic volumes, both the EDPVR and the ESPVR can be measured.

These measurements provide input for further mechanical analysis of cardiac function. Clinically, it provides references for the diagnosis of heart diseases.

Mechanical Properties of the Myocardium

In order to properly discuss the mechanics of the heart, it is necessary to clarify some of the mechanical engineering terms used in this review. Broadly, mechanics refers to the relationship between the forces applied to an object (solid or fluid) and the translation, rotation, and deformation generated as a result of the applied force. Mechanical stress (σ) describes the intensity of the mechanical force (loads) and mechanical strain describes the intensity of the deformation (elongation and angular rotation of a line in an object), thus stress has a unit of force per area while the strain is non-dimensional. Stretch or stretch ratio (λ) is a simple measure of deformation that is defined as the deformed length of a line segment divided by its initial undeformed length. For cardiovascular tissues that undergo large deformations, there are several different methods to define the stress and strain based on the reference configuration chosen. In cardiovascular mechanics, stress is most commonly reported as the Cauchy stress (or true stress) which is defined as the force over a unit area acting in the deformed configuration. Since, real-world mechanical problems are three dimensional, stress and strain are represented as tensors, with nine components. Traditionally, cardiovascular solid mechanics has employed the framework of continuum mechanics, which assumes that the object (solid or fluid) has a continuous distribution of mass, meaning that there are no spaces or gaps in the material. This obviously does not capture the fact that materials are made of atoms and molecules and the use of continuum mechanics in biology is typically limited to the tissue level and larger. The phrase, “mechanical properties” as used in this review refers to the innate relationship between stress and strain of the tissue that governs how that tissue deforms under load. The mechanical properties of a tissue are described by the strain energy density (W) which describes how the mechanical energy in the tissue changes as a result of the deformation of the tissue. Thus it can be used as a measure of how much force or stress is needed to deform the tissue. The equations used to model the strain energy density are termed constitutive equations. The mechanical properties are determined by the structure and organization of the myocardial wall, the properties of both the intracellular and extracellular structural proteins, and the local mechanical stresses.

Ventricular Wall Structure

The ventricular wall is well known for its complex structure. The myofibers wrap around in layered sheets with rotating orientation. Across the wall thickness in the mid-ventricle, from endocardium to epicardium, the fiber direction changes from longitudinal to circumferential and then towards the longitudinal direction again.

Myocytes occur in sheets that are parallel to the epicardial surface of the heart. The myocytes in the sheet nearest to the epicardial surface of the heart tend to align at a negative angle with respect to the circumferential axis, while myocytes in the sheet nearest the endocardial surface tend to align in a direction with a positive angle with respect to circumferential axis. The exact amount of rotation has been shown to vary depending on the exact location within the LV (75). Furthermore, the orientation and amount of rotation of the myocytes varies depending on the location within the heart (60). The heterogeneity of myocyte orientation and the rotation of the myocytes through the thickness of the myocardium has many interesting mechanical implications. First of all it provides the tissue with strength in both the longitudinal and circumferential directions, the two directions that will experience the highest stresses. Secondly, it leads to the generation of ventricular torsion when the myocytes contract and relax (4). This arises because the inner surface of the myocardium is contracting in a different direction than the outer surface. Ventricular torsion is also partially due to differences in the timing of the electrical contraction signal between the subepicardial and subendocardial layers of the LV (22).

Cellular and Extracellular Determinants of Mechanics

The mechanical properties of the left ventricle are determined by both the properties of the cells, primarily the myocytes, and the extracellular matrix. In healthy myocardial tissue the passive mechanical properties are primarily determined by the intracellular protein titin. Titin is a large elastic protein that connects the z-line of the sarcomere to the m-line (Figure 2). The stiffness of the titin molecule prevents overextension of the sarcomere preventing damage to the cells. Given the abundance of myocytes in the myocardial tissue, titin is considered to be the primary determinant of the passive mechanical properties of the healthy LV under low to moderate deformations (76). Interestingly, titin has many isoforms with some variants being significantly less stiff than others, and differences in the expression of these isoforms could play a role the development of diastolic dysfunction and heart failure (208). Further mutations of the titin gene have been associated with a number of various cardiomyopathies (117). Titin also plays an important role in cellular mechanotransduction as well as force generation (116). Phosphorylation of titin has been shown to be a means of altering the passive stiffness of the protein (80).

Figure 2. The Sarcomere of the Cardiac Myocyte.

Titin is an elastic protein that runs from the Z band all the way to the M-line, and provides the sarcomere with its passive strength. Myosin is the motor protein of the sarcomere and its interaction with the actin filament drives cardiomyocyte contraction. Figure adapted from McNally, 2012 with permission of the American Society for Clinical Investigation (134).

Since titin is a fibrous protein, it primarily provides stiffness in the fiber direction (along the length of the sarcomere). This makes myocardial tissue an anisotropic material. However, the myocytes of the heart do not align all in the same direction.

While titin determines the passive mechanical properties of the tissue, the active contractile force is generated by the interaction of the actin and myosin filaments. Myosin is a motor protein consisting of a head domain and a tail domain. The head domain is capable of binding to the actin protein that runs parallel to the myosin along the length of the sarcomere. Powered by the hydrolysis of adenosine triphosphate (ATP), the myosin head undergoes a conformational change that generates tension on the actin fiber. Following this conformational change, the myosin detaches from the actin filament, binds new ATP and then reattaches to the actin filament in a new location. This cyclic process allows for the myosin heads to essentially “walk” down the actin filaments resulting in the contraction of the sarcomere. The stiffness of the myocardial wall during active contraction is largely dictated by the number of myosin actin crossbridges that are engaged (32). The amount of force that can be generated by the sarcomere depends upon three key factors:1. The concentration of calcium ions released in response to the action potential, which activates the myofilaments to trigger contraction, 2. The phosphorylation state of the myosin chains which alters the stiffness of the myosin, 3. The length of the sarcomere which depends on both the preload and afterload placed on the ventricle (132). Both myosin and actin proteins have different isoforms, and changes in the relative amounts of the isoforms can lower contractility and are associated with the development of heart failure (219). Mutations in the genes for myosin are associated with both inherited dilated cardiomyopathy and hypertrophic cardiomyopathy (134). The coupling between the electrical signaling system and the mechanics of the heart is highly complex and was recently discussed in detail by Pfeiffer et al (156).

The extracellular matrix of the myocardium is composed of structural proteins such as collagen and elastin as well as non-structural proteins such as proteoglycans, proteases, and growth factors. From a mechanical standpoint, the most important of these proteins is collagen, which is primarily found as collagen I and collagen III, however collagen I is much stiffer than collagen III and as such is the primary controller of myocardial tissue properties under large deformation (205). Other collagen types, such as collagen IV, V, and VI are present in the ECM as well and although, they don’t directly contribute much to the mechanical properties of the tissue they have been shown to play important roles in collagen fiber formation and cell-matrix interactions (174). Fibronectin is another important ECM protein involved in regulating and facilitating the assembly of collagen I, however fibronectin, on its own, is not a primary determinant of tissue mechanical properties. Fibronectin is an important mediator of LV remodeling (92, 175). Collagen I is a relatively stiff protein with a highly non-linear stress strain profile. Collagen provides little resistance at low amounts of stretch but large amounts of resistance at large stretches (48). Collagen fibers are composed of bundles of collagen proteins that are cross-linked together (Figure 3). Collagen fibers have a coiled structure, that when stretched becomes uncoiled or straight. This shape explains its non-linear stress strain profile. It takes very little force to uncoil the fiber, but very high levels of force to stretch the fiber when it is uncoiled and completely straight.

Figure 3. Collagen Fiber Structure and Assembly.

Procollagen assembles as a triple helix and then has the N and C terminal ends cleaved by proteases. The collagen triple helixes then assemble into larger fibers aided by collagen cross-linking facilitated by lysyl oxidase. Figure adapted from Kadler, 2004 with permission of Elsevier (91).

The primary purpose of collagen in the healthy myocardium is to prevent overstretch and provide surfaces for the myocytes to attach to in order to aid in transmission of contractile force to the tissue. In healthy tissues, the amount of collagen is very low, but due to disease or aging can become elevated through a process known as fibrosis (41, 58, 94, 211). An excess of collagen fibers increases the stiffness of the tissue which reduces the ability of the LV to fill with blood (115, 121). This can be pictured on the pressure volume diagram as an increase in the slope of the EDPVR, which serves to reduce stroke volume. A severe reduction in ventricle function due to impaired filling is termed diastolic heart failure and is a significant clinical problem. Crosslinking of the collagen network, which is largely controlled by the protein lysyl oxidase has been shown to alter the mechanics of myocardial tissue as well (121, 220).

Elastin is another structural protein that is often overlooked when discussing the mechanical properties of the myocardium. Similar to collagen, elastin forms long, thin fibers. These fibers are termed elastic fibers and consist of an elastin core surrounded by a class of proteins termed microfibrils (173). Microfibrils, such as fibulins and fibrillins play an important role in the assembly of the elastic network, contribute to the mechanical properties of the fibers and provide integrin binding sites (196). Elastic fibers, as their name would indicate have an elastic stress-strain behavior, similar to the mechanical properties of titin, which is much more abundant in the healthy myocardium (48, 118). Studies of elastin in the healthy myocardium remain very limited, however elastin is becoming a more active subject of study in left ventricular remodeling and in regenerative medicine which will be discussed later in this review (48, 108, 130, 208).

Proteoglycans serve an important role in regulating the water content of tissues, although little work has been done on understanding their role in the myocardium (48). Proteoglycans contain many negatively charged gylcosaminoglycan (GAG) side chains that attract and retain water molecules (163). The water retained by the GAG side chains can in turn alter the water composition within the collagen and elastic fibers (104). This change in water content can significantly alter the mechanical properties of the tissue by increasing the residual stress and effectively making the tissue stiffer (48, 104). It has been shown that GAG expression varies spatially in arteries corresponding to differences in residual stress at the inner and outer surfaces of the vessel (6). Proteoglycans also play an important role in fibrilogenesis. Work from the lab of Andrew McCulloch has shown that deletion of the genes for the proteoglycans decorin and biglycan leads to variation in collagen fiber ultrastructure and altered tissue mechanics post-myocardial infarction (26, 206). Elevated levels of the proteoglycan syndecan-1 have been associated with myocardial fibrosis and the development of diastolic heart failure (190).

Mechanical Testing

Mechanical testing of the left ventricle has been a topic of research for more than 150 years. The earliest mechanical tests involved ex vivo inflation testing in which the whole LV would be excised from the body and inflated to various volumes and pressures to essentially obtain the EDPVR. Ludwig and Langendorff in the 19^th century developed a method of keeping the heart beating in an ex vivo setting which allowed for the determination of the active properties of the tissue as well as full PV loop analysis (228). The Langendorff perfused heart is still commonly employed in the 21^st century as a cost effective method for studying pharmaceutical agents, cardiac toxicology, and ischemia (177). The downside to whole heart testing is that it is difficult to accurately quantify the local stresses and strains of the tissue, giving only average properties for the ventricle.

Mechanical testing of small, excised pieces of cardiac tissue allow for the determination of more localized mechanical properties. The earliest tests used uniaxial tensile testing to examine the material properties of papillary muscles (157, 158). To better represent the in vivo loading conditions, biaxial mechanical testing was first employed for myocardial tissues in the 1980s (33). The technique in which a flat piece of excised tissue is trimmed, and then pulled in two directions simultaneously allows for accurate quantification of stresses and strains which can be used to determine the anisotropic, non-linear material properties of the myocardial tissue. Slicing the myocardium into several sheets across the thickness, such that each sheet contained myocytes aligned in the same direction allows for calculation of fiber oriented material properties. Having material properties with a localized reference frame is critical in creating highly accurate mathematical models of the LV. Biaxial mechanical studies have also been conducted in which the tissue was subjected to electrical current so that the mechanical properties of the active tissue could be determined. Lin and Yin found a way to tetanize the tissue and conduct biaxial tests so as to measure the contracted mechanical properties (114). Biaxial mechanical testing is still a gold standard in cardiac mechanics testing and has recently been adapted for the study of tissues from small animals including, rats, mice and mole rats (46, 61).

Another newer technique of mechanical testing is isolated myocyte testing. Zile and colleagues isolated cardiomyoctes and seeded them in an agarose gel which was then used in tensile testing (226, 227). They then used a finite element program to estimate the stress on the myocytes and remove the contribution of the gel in the determination of the mechanical properties. Mechanical testing has also been performed on individual myocytes. In these tests, a single myocyte could be subjected to force and the passive and active mechanical properties could be determined (122). Much like isolated whole hearts, isolated individual myocytes offer an excellent platform for studying the effects of pharmaceutical agents making it a commonly employed method in biomechanics studies (17, 78, 161). Moving to even smaller length scales, sarcomeres have been isolated and subjected to mechanical testing (160).

Implantation of sonomicrometer crystals onto the myocardium of live animals has been used as a means of estimating local in vivo stresses and strains (46). This invasive analysis gives insight that is more detailed than the data that can be collected from the non-invasive imaging studies. Further, this data can prove to be very important in validating new imaging modalities such as strain analysis methods (5, 79, 113).

Constitutive Equations Used to Model the Ventricular Wall

The myocardium is a non-linear, anisotropic, heterogeneous, soft tissue that undergoes large deformation. To appropriately model this behavior the framework of continuum mechanics must be employed. The general constitutive equation used to relate stress and strain is typically

$$\mathit{t}=\frac{2}{J}\mathit{F}\frac{\delta W}{\delta C}{\mathit{F}}^T$$ (4)

Where t is the Cauchy stress tensor, F is the deformation gradient, J is the Jacobian of the deformation gradient, C is the right Cauchy Green tensor, and W is the strain energy density function. As shown by this equation, the strain energy density function determines the stress-strain relation of tissues. Various material behavior can be captured by choosing different forms of the strain energy density function and fitting the experimental stress and strain data to this form. The most common strain energy density equation form is the Fung-Type exponential equation originally proposed by Y.C. Fung (50).

$$W=\frac{1}{2}c(e^Q-1)$$ (5)

Where c is a constant, and Q is an equation chosen so as to best model the anisotropic behavior of the material. One of the simplest forms of Q often chosen for biaxial material testing is

$$Q=b_1{E_x}^2+b_2{E_y}^2+2b_4{E}_x{E}_y$$ (6)

Where b1-b4 are constants that govern the mechanical behavior of the material and Ex and Ey are the Green strains in the x and y directions respectively. Typically, the x and y directions are chosen to correspond to the circumferential and longitudinal directions of the heart. High values of c in for the constitutive model described by equations 5 and 6 are characteristic of a more elastic tissue while high values for the b parameters denote a more exponential or non-linear stress-strain behavior, perhaps characteristic of a more collagenous tissue. In general, increasing values of the c and b constants represent increased passive tissue stiffness, which reduces diastolic filling. This model is highly simplistic though and doesn’t capture the heterogeneous nature of the myocardial tissue which has rotating fiber directions. Thus, an alternate form of Q that is based on the local fiber direction of the myocytes is often employed.

$$Q=b_{\mathit{ff}}{E_{\mathit{ff}}}^2+b_{\mathit{xx}}({E_{\mathit{cc}}}^2+{E_{\mathit{rr}}}^2+{E_{\mathit{cr}}}^2+{E_{\mathit{rc}}}^2)+b_{\mathit{fx}}({E_{\mathit{fc}}}^2+{E_{\mathit{cf}}}^2+{E_{\mathit{fr}}}^2+{E_{\mathit{rf}}}^2)$$ (7)

Where b_ff, b_xx, and b_fx are material constants and E_ff, E_cc, E_rr, E_fc, and E_cf are the components of the Green strain tensor with subscripts, f denoting the fiber direction, c, denoting the cross fiber direction, and r denoting the radial direction.

Since myocardial tissue is primarily composed of water, it is often modeled as incompressible. When the assumption of incompressibility is not acceptable, it is common to see the inclusion of a bulk modulus term with equation 5.

$$W=\frac{1}{2}c(e^Q-1)+\frac{1}{2}K{\left(\ln \right(J\left)\right)}^2$$ (8)

Where K is the bulk modulus and J is the jacobian of the deformation gradient. High values of K represent tissue that is highly incompressible.

Recent work has focused on the development of constitutive equations based on the actual cellular and extracellular structure of the left ventricle (202, 203).

Much work has gone into the field of modeling the active contractile forces generated by the myocytes and many different methods for modeling it have been developed. Typically though, the active contractile force is added to the constitutive equation 1 as

$$\mathit{t}=\frac{2}{J}\mathit{F}\frac{\delta W}{\delta C}{\mathit{F}}^T+T(\alpha ,[{\mathit{Ca}}^{2+}\left]\right)\mathit{m}\otimes \mathit{m}$$ (9)

Where T is the active tension developed by the myocyte which is a function of α, the fiber stretch, and [Ca²⁺] the calcium concentration. The active force is only generated along the direction of the fiber m. Through equation 9, the passive mechanical properties and the active mechanical properties become coupled. A form of the calcium dependent tension generation commonly employed in modeling today was proposed by Hunter et al, 1998 (85).

$$T(\alpha ,[{\mathit{Ca}}^{2+}\left]\right)=\frac{{\left[{\mathit{Ca}}^{2+}\right]}^n}{{\left[{\mathit{Ca}}^{2+}\right]}^n+C_{50}^n}{T}_{\mathit{max}}(1+\beta (\alpha -1\left)\right)$$ (10)

Where n is the hill coefficient, typically chosen to be 2, $C_{50}^n$ is the calcium concentration at which the tension generated is half maximal when the fiber is unstretched, T_max is the maximum tension generated from an unstretched fiber, and β is a parameter that captures the fact that the binding of Ca²⁺ is dependent upon the length of the fiber.

The electromechanics of cardiac contraction is an ongoing field with several new models being proposed over the last decade (103, 143, 162). Many of these models aim to capture much of the heterogeneity of both electrical transmission and sarcomere length, both of which are dependent upon the local stresses of the tissue (27). For an overview of several recent electromechanical models see the review article by Trayanova and Rice (189).

Stress Analysis of the Heart

The classic model to estimate the average wall stress in the LV is the membrane-based Laplace law.

$$p=\frac{T_{\theta }}{r_{\theta }}+\frac{T_{\phi }}{r_{\phi }}$$ (11)

Where T and r are wall stress per unit length and the radius of curvature, with subscripts θ and ϕ denote the circumferential direction and the longitudinal (meridional) direction. For uniform wall thickness h, T= t*h with t and h being the mean stress and wall thickness.

A simplified model is the spherical model. The Law of Laplace for the spherical LV wall becomes:

$$t=\frac{\mathit{pr}}{2h}$$ (12a)

Where t is the Cauchy stress in the plane of the wall, P is the pressure inside the ventricle, r is the deformed radius of the ventricle, and h is the thickness of the myocardial wall. This equation may be suitable for roughly estimating the circumferential or longitudinal stresses near the apex of the ventricle.

For mid-ventricular circumferential wall stress, LV is often simplified into a cylindrical model and the Laplace law become

$$t=\frac{\mathit{pr}}{h}$$ (12b)

The stress in the longitudinal direction near the mid-ventricle can still be estimated with equation 12a. While this model is a gross simplification of the actual geometry of the LV it is still used today due to its simplicity. Variations used in membrane models include ellipsoid or prolate spheroidal geometries, which more accurately capture the shape of the LV. For thick-walled ventricles, modified equations have been proposed for mean wall stress estimation for the mid-ventricle of prolate spheroid model

$$t_{\phi }=\frac{\mathit{pb}}{2h};t_{\theta }=\frac{\mathit{pb}}{h}(1-\frac{b^2}{2a^2})$$ (12c)

Where t_φ and t_θ are the stresses in the longitudinal and circumferential directions, and b and a are the minor and major radii. The choice of equation for stress estimation largely depends on the location of interest, the shape and dimensions of the LV, and the accuracy needed. For example, stresses at the mid-ventricle, or near the base may best be calculated using the equations for the cylindrical shape (equation 12a for the longitudinal direction and equation 12b for the circumferential direction), while stresses near the apex may be better approximated using equation 12a for both directions. If the long axis and short axis dimensions are known, equation 12c will give even better estimates.

For even more accurate analysis of ventricular wall stress, finite element analysis (FEA) is the best choice for accurate stress analysis. Finite element analysis is now the method of choice for conducting accurate stress analyses. Geometries can be accurately imported and digitized from CT, or MRI images allowing for the analysis to be conducted for individual patients. Image based finite element models have been used more and more for patient specific stress analysis (55, 62, 199).

Interestingly, the existence of residual stress significantly reduces the stress concentration in the lumen wall and uniformalizes the stress across the wall thickness (49, 146). While the ventricle is a thick-walled structure, it has been shown that the Laplace law gives a reasonable well estimation of the mean wall stress as compared to the complex models using finite element analysis (138, 223). However, when considering the irregular LV structure and wall thickness variations, especially in MI, FEA is necessary to determine the local wall stress (223).

Biomechanics of Cardiac Function Post-MI

Myocardial infarction (MI) occurs when coronary arteries are blocked by atherosclerostic plaques resulting in the death of cardiac myocytes due to ischemia. Coronary heart disease obstructs the blood flow to the myocardial tissue. It reduces the ability of the heart to effectively pump blood and leads to a dynamic wound healing process that alters the mechanics of the LV as well as the mechanical properties of the myocardial tissue.

Current treatment for myocardial infarction consists of a combination of reperfussion surgery which may consist of arterial grafting or angioplasty and stenting of the artherosclerotic arteries, treatment with pharmaceutical anticoagulants, and anti-thrombotics, as well as long term management of diet and blood pressure often including the use of ACE inhibitors and beta blockers (209).

The Wound Healing Response to MI

MI triggers a complex dynamic wound healing process marked initially by inflammatory processes followed by fibrosis and scar formation. An excellent 2005 review by Holmes, Borg, and Covell breaks down both these changes over the course of the wound healing response in terrific detail (83).

The wound healing response can be broken down into four temporal phases based upon the biological changes occurring at the time. The first phase is the acute ischemic phase which lasts for around the first four to six hours following occlusion of the coronary artery. During this period, the contractile ability of the myocardial tissue in the ischemic region is significantly reduced or eliminated altogether. During this time period, a thinning of the infarct region occurs which results in a right shift of the EDPVR, as well as the ESPVR. This shift reduces the EF of the LV. The infarct region itself, has been shown to become slightly more compliant than normal during the first hour after myocardial infarction, but actually increases in stiffness by four hours after occlusion. It is theorized that this early increase in stiffness is due to edema in the ischemic region.

The necrotic phase follows the acute ischemic phase and lasts for around 5-7 days. During this phase, inflammation and necrosis set in and clear the injured myocytes and begin to destroy the existing collagen network. The infarct region continues to thin further contributing to dilation of the LV chamber. During this time period the unstressed length of the infarct region appears to become elongated while the end-diastolic lengths appear to be similar to the pre-occlusion state indicating a tissue that has become stiffer. The increase in unstressed length is likely due to the destruction of titin in the infarct region by macrophages and neutrophils. Since this phase of wound healing occurs before new ECM is produced, the increase in stiffness has again been attributed to edema. One of the major complications seen during this time period is rupture of the infarct wall which results from degradation of the structural proteins of the myocardium (11, 54).

The third phase of the wound healing process is the fibrotic phase during which the production of new ECM begins. This period lasts for roughly two to three weeks following the end of the necrotic phase. The fibrotic phase begins with the initial production of a temporary ECM network composed of proteins such as fibronectin and collagen III, which serves as scaffolding for the assembly of stiffer collagen I networks. While, some thinning and elongation of the infarct region still occurs during the early part of the fibrotic phase, the primary mechanical change is an increase in the stiffness of the infarct, especially along the circumferential direction of the LV matching the principal direction of collagen fiber alignment. The increase in stiffness during the fibrotic phase reduces diastolic filling and can in turn lower the ability of the neighboring healthy tissues to contract through the Frank-Starling mechanism (195).

The final phase is referred to as the remodeling phase. During this phase the scar begins to shrink as it becomes a more mature stable structure. During this phase, collagen density alone is no longer the principal determinant of the infarct mechanical properties. Collagen cross-linking increases greatly during this time period which may aid in scar contraction. Interestingly though the literature is divided on whether the infarct tissue becomes stiffer or more compliant during this time period (46, 65). While in general the remodeling phase may be marked by improved LV function, the changes are highly variable from patient to patient and may be dependent upon several factors. When remodeling leads to complications for the patient it is often referred to as adverse LV remodeling, an area of great research interest. A pictorial overview of LV dilation and fibrosis during the first 28 days post-MI in a mouse model adapted from the work of Zamilpa and Lindsey is presented in Figure 4 (221).

Figure 4. Progression of Left Ventricle Dilation and Remodeling Post-MI.

The inner pictures display the cross-section of a mouse left ventricle stained with 1% 2,3,5-triphenyltetrazolium chloride after myocardial infarction. Significant cavity dilation and wall thinning can be observed. The outer pictures show histological sections stained with picrosirius red for collagen. An increase in collagen is seen around day 7 and by day 28 collagen fibers have become densely packed and highly aligned. Figure adapted from Zamilpa and Lindsey, 2010 with permission of Elsevier (221)

Variation in MI Outcome

Since heart failure following MI is primarily the result of mechanical failures, it is important to understand what variations in the remodeling process lead to these various failures. As mentioned earlier, the most catastrophic complication is rupture of the infarct wall. It has been shown in mice that increased infarct size increases the chances of cardiac rupture, and that male mice are 2-3 times more likely to experience rupture (53, 54). The level of inflammation in the LV also contributes to the risk of cardiac rupture, and the deletion of several inflammatory genes has been shown to reduce the chances of rupture including, MMP-2, MMP-9, and periostin (37, 54, 74, 176). Deletion of the gene for MMP-28 has recently been shown to increase the rate of rupture (124). A comprehensive listing of demographic, clinical presentation, and treatment risk factors for the development of rupture is presented in a 2010 report by Lopez-Sendon et al (120). In their report, they found that the average age of patients who experienced rupture was 74 compared to an average age of 66 for the non-rupture cohort. They also found that 49% of the rupture group was female, while only 33% of the non-rupture group was female, which is an opposite trend from that reported in mice. Patients who experienced cardiac rupture also had lower body weights, were less likely to be smokers, had a reduced incidence of hyperlipidaemia, and were less likely to have had previous cardiovascular events. Diabetes and hypertension were not found to be risk factors. On presentation, patients who went on to experience cardiac rupture were more likely to have ST segment elevation, have reduced systolic blood pressures, and have an increased pulse. Patients who experienced cardiac rupture were also less likely to have been treated with ACE inhibitors, aspirin, thienoppyridine, beta blockers, or statins within the first 24 hours of treatment. Cardiac rupture patients were also more likely to have received thrombolytic treatment, but on average the rupture group was given this treatment at later timepoints following the onset of symptoms.

The development of diastolic heart failure occurs as the result of excessive infarct stiffness preventing the LV from filling. Thus factors that control fibrosis and long term remodeling are also factors in the development of diastolic heart failure. Again, factors such as age, and sex influence the development of heart failure again with women and the elderly being at higher risk (38, 40). Diabetes, which increases LV remodeling, has also been shown to increase the risk for developing diastolic heart failure (3). Increased heart rate and hypertension can also contribute to the risk of developing diastolic heart failure (210).

Systolic heart failure following MI can occur due to the loss of contractile function or can occur as the result of an infarct that is too compliant which can result in infarct bulging (83). LV dilation which increases the load against which the already compromised myocardium must contract worsens the situation. The risk for developing systolic heart failure following myocardial infarction is again associated with age as well as the presence of previous cardiovascular disease, reduced medical intervention and infarct size (133, 187). Interestingly, the risk factors that predict mortality due to systolic heart failure following MI are often reversed, with males and patients with low blood pressure being more likely to die (187). Infarcts located near the apex of the heart were also found to increase the mortality rate (187)

Clearly, there are many factors that play a role in regulating patient outcome post-MI, however many of these factors interact with each other complicating our understanding of the disease progression. A summary of the various factors that contribute to patient outcome are listed in Table 4. Much more research is needed to fully understand the biological causes for the variability in patient outcome.

Table 4. Main Factors Influencing Patient Outcome Post-MI.

Factor in Patient Outcome

Infarct Size

Infarct Thickness (Transmural or Non-Transmural)

Infarct Location

ST Segment Elevation

Reperfussion

Pharmaceutical Treatment

Inflammation Levels

Level of LV Remodeling

Scar Stiffness

LV Wall Stress

Age

Sex

Previous Cardiovascular Disease

Obesity

Diabetes

Hypertension

Hyperlipidaemia

Smoking Status

Role of Mechanical Stress in LV Remodeling and Outcome

The fibrotic and remodeling phases of the MI response are dominated by the production of new ECM proteins. The organization, composition, and assembly of the new ECM material determine the mechanical properties of the tissue which in turn alter the distribution of stress in the tissue as well cardiac function (84). However, the tissue stresses also regulate the production of the new ECM materials in a sort of feedback mechanism (Figure 5). This mechanical feedback system can lead either to the eventual stability of the scar and cardiac function or a progressive deterioration of ventricular function leading to heart failure, referred to as adverse LV remodeling (2). Thus it is important to understand the role that stress plays in regulating the remodeling process.

Figure 5. Regulation of MI Outcome by Mechanical Feedback.

Dilation of the LV due to the loss of cellular structure increases the wall stress which in turn signals for increased inflammation and fibrosis. Inflammation reduces tissue stiffness while fibrosis increases tissue stiffness. Increased tissue stiffness in turn reduces LV stretch and dilation. Unbalances in the feedback system can lead either to systolic heart failure due to infarct expansion and LV dilation, or diastolic heart failure due to over-stiffening of the infarct. The + symbol in the schematic represents a positive correlation between the factors, i.e. increased LV dilation increases wall stresses, while the – symbol denotes a negative correlation.

Mechanical stress leads to deformation of both cells and the ECM which can trigger biological responses through mechanotransduction. Mechanotransduction occurs through several different pathways including the opening of stretch activated ion channels, changes in integrin tension and signaling, the release of proteins from the extracellular matrix, the turnover of intracellular fibers such as actin, the exposure of “hidden” binding domains on cell surface proteins, and changes in spatial chemical gradients (14, 39). Several signaling pathways have been identified as being mechanosensative, including focal adhesion kinases (FAKs) and mitogen activated kinases (MAPKs) such as c-jun N terminal kinase (JNK) and extracellular related kinase (ERK) (39). For an excellent review of mechnotransduction signaling in fibrosis please refer to the 2014 article by Duscher et al (39). For the most part mechanotransudction allows for tissues to modulate their stiffness in order to maintain a mechanical homeostasis. Stress is thought to be a very important factor in the development of the cardiac structure, leading to the helical rotation of the cardiomyocytes as well as the presence of residual stress to balance the total stress across the myocardial wall (181, 188).

In the post-MI environment, the LV has undergone major changes in geometry, including wall thinning and chamber dilation which greatly increase the tissue stresses, especially in the infarct region and border zones (63). The role of mechanical stress in the inflammatory response to MI has not been particularly well studied. Recent work on vascular smooth muscle cells has shown that mechanical stretch increased the levels of both MMP-2 and monocyte chemoattractant protein-1 (214). MMP-13 and ADAMTS-5 both increase in response to mechanical stretch in chondrocytes (184). A study on human foreskin fibroblasts concluded that mechanical stretch does not alter the expression of MMPs but the presence of fibronectin and collagen I does (222). Recent work on rabbit corneal fibroblasts has shown that 5% equibiaxial cyclic stretch results in decreased expression of MMP-2 with a corresponding increase in TIMP-2, while 15% equibiaxial cyclic stretch lead to increased levels of MMP-2 and decreased levels of TIMP-2 (119).

Macrophages play a critical role in the inflammatory response to MI, and these cells are also affected by biomechanical cues (102, 135). Increased stretch of atrial myocytes has been shown to stimulate the recruitment of macrophages (145). The elasticity of macrophages and the mechanical properties of the culture substrate have been shown to alter macrophage function, having effects on phagocytosis, TNF-α production, and altering the transcriptomic profile (150). Further, it was recently shown that elongation of macrophage cell shape, resulted in a transition from the M1 (proinflammatory macrophage phenotype) to the M2 (wound healing macrophage phenotype) (135). Transition to the M2 phenotype has been associated with improved cardiac outcomes post MI (124, 212). Hypoxia has been shown to reduce the ability of macrophages to change their shape and orientation in response to mechanical stretch (148). Much more work is needed to fully understand the contributions of mechanics to the MI inflammatory response.

Neutrophils are another class of leukocytes that play an important role in the inflammatory process post-MI (2, 98). Only a minimal amount of research into mechanotransduction signaling in neutrophils has been conducted, but it has been shown that neutrophils are capable of measuring substrate stiffness and more readily respond to chemotactic gradients when cultured on stiff substrates (87). The proposed mechanism underlying this mechanosensing is by integrin tension. In the blood stream, fluid shear stress has been shown to activate neutrophils and regulate their morphology through G-protein signaling (126, 127). Neutrophils are also producers of MMP-9 which they produce to traverse the basement membrane of tissues and both MMP-2 and MMP-9 have been shown to be upregulated due to increased mechanical stresses in arteries (20, 97). However, it has not been demonstrated that production of MMPs by neutrophils is mechanosensitive.

The role of mechanics in the regulation of the fibrotic process is better understood. Uniaxial mechanical stretch has been shown to increase the ratio of collagen I to collagen III produced by cardiac fibroblasts in culture (29). Cardiac fibroblasts grown under 3% equibiaxial stretch showed an increase in collagen III deposition while those grown under 6% equibiaxial stretch showed decreases in collagen III (105). Mechanical stretch also modulates the production of cyotkines, growth factors, and receptors by cardiac fibroblasts including the production of TGF-β, TNF-α, and angiotensin II receptors as well as their release from the ECM (128, 192, 201). Further, mechanical stress was shown to regulate the transition from fibroblast to myofibroblast, partially by altering the phosphorylation of syndecan-4 (77).

Perhaps most interestingly, mechanical stress and stretch is the primary determinant of collagen organization and alignment in the post-MI environment (47). Fibroblasts have been shown to elongate under stretch and have been shown to orient themselves in the direction of uniaxial stretch in vitro and are thought to orient themselves according to the directions of the principal stretches in vivo (72, 73). Fibroblasts deposit new collagen fibers aligned along the long axis of the cells, and can reorient existing collagen fibers so that they more closely align with the orientation of the cells by establishing focal adhesions that run perpendicular to the direction of stretch (28, 155). The alignment of the collagen fibers not only regulates the anisotropy of the tissue, but it can also impact the migration of other cells through the ECM. A recent study by the Holmes laboratory demonstrated the influence of scar shape and location on collagen formation post-MI in a rat model (47). Their results indicated that the location of the shape of the scar had little effect on the orientation of the collagen fibers, but the location of the scar played a major influence. Collagen was found to be randomly aligned in scars near the apex of the heart where the stresses are nearly uniform in both the longitudinal and circumferential directions. However, scars that were located nearer to the base of the LV had fibers aligned primarily in the circumferential direction. The circumferential direction is the direction of the largest principal stress in the more cylindrical basal region. Another interesting finding from this study is that the alignment of the existing ECM matrix did not have a major effect on the final ECM matrix three weeks post-MI.

Mechanical regulation of the post-MI wound healing response has also been studied with the use of computational models. Rouillard and Holmes developed an agent based computational model to examine the effects of infarct shape, mechanical stretch, and existing ECM structure on the migration of cardiac fibroblasts and the deposition and alignment of new collagen fibrils (165). They found that the effect of infarct shape had a minimal effect on cell alignment but that the direction of stretch played a major role in the development of an oriented collagen network, matching their experimental results. They also noted that chemical guidance of fibroblasts by chemokine gradients did not play a major role in determining the organization of collagen fibers, but did have an effect on the fibers near the border zones where the gradients are large. This modeling study was recently expanded to a finite element coupled model so as to better capture the mechanical loads imparted on the LV (164). Again the results of the computational model correlated with the experimental findings. Furthermore, the model predicted that fibroblast alignment in the direction of the largest principal stretch acts as a negative feedback mechanism that reduces scar anisotropy since increased fiber deposition in the direction of principal stretch reduces that stretch. Further, they showed that structural guidance cues act as a positive feedback mechanism, and in the absence of mechanical feedback would lead to isotropic scar formation, indicating the importance of biomechanics in regulating the remodeling response. While the paper by Rouillard and Holmes offers a nice multi-scale look at the remodeling process, more work is needed, especially in understanding the interaction between the inflammatory and remodeling responses. Computational models such as the cellular interaction models by Jin and colleagues could be extended to include the role of mechanical regulation (90, 217).

Mechanical Models to predict LVEF

We have previously discussed the use of mechanical modeling in stress analysis and LV remodeling, but perhaps most importantly they can be used to predict cardiac function specifically left ventricular EF. Mechanical modeling allows the researcher to readily change model parameters to study the effects of various pathologies and treatments on cardiac function which may otherwise be difficult and costly to study in the lab.

LVEF is one of the most important determinants of long-term prognosis for patients with coronary artery disease (18). Improving cardiac function as indicated by the LVEF is the major goal of coronary revascularization (angioplasty or bypass grafting) although improvement in patient’s symptoms, such as relief of angina pectoris is also important (86).

A pioneering study by Bogen et al, in 1980 used a membrane model to analyze both the systolic and diastolic behavior of the LV post-MI (16). They were able to vary parameters including the size and stiffness of the infarct region. They found that large and compliant infarcts led to lower cardiac performance than more rigid ones. They also identified the presence of large stresses in the border zone regions and a coupling between the mechanical properties of the infarct tissue and the contractile ability of the healthy tissue. In a follow up paper, Bogen et al, used their computational model to study the effect of varying the inotropic state of the contractile tissue, establishing the use of computational modeling to simulate potential therapeutic interventions (15).

Simple membrane models were developed to predict LVEF based on cine MRI from clinical patients (70, 147). The model predicted the post-revascularization LVEF at a very good accuracy. Clinical studies have shown that the dysfunctional myocardium can be either irreversible, as infarcted myocardium, or reversible, as hibernating myocardium, with only the hibernating myocardium potentially able to recover its function once reperfused through revascularization (18). The model estimated the LVEF based on the size and properties of the myocardium measured from cine MR images, prior to revascularization (Figure 6). Thus the model could be used to predict the benefit of the procedure and patient outcome. Later, the model was modified to predict LVEF based on patient echocardiographic images (67-69). Since clinical reports have shown that not all patients benefit from revascularization, prediction of the post-revascularization LVEF would be useful in selecting patients for effective revascularization (18). This will help to eliminate non-beneficial revascularization procedures to reduce patient risks of morbidity and mortality and save patient and medical care cost.

Figure 6. Myocardial viability and LV function.

Schematic illustration of myocardial viability change post-revascularization and a scheme to determine the left ventricular volume from short axis slices. λ with subscript N, H, I, represent the contraction ratio in the normal, hibernating and infarct regions, respectively. The ventricular volume is determined by summation of the area (A) multiplied by slice thickness h.

Guccione and colleagues developed a finite element model of an ovine LV with aneurysm based on MRI images (63). They used their model primarily to look at border zone dysfunction, and the role of infarct stiffness. They determined that border zone dysfunction was the result of changes in contractility in the region rather than increased levels of stress. This work has since been extended in several studies that aim to establish whether surgical intervention such as the Dor procedure can improve border zone contractility and restore cardiac function (142, 198, 207). A recent study by Warwick et al, developed a model to determine what patients would benefit from surgical repair of LV aneurysms or dilated cardiomyopathy, highlighting the potential utility of computational modeling in the clinical setting (204).

Several finite element models have been developed to study the effect of altering the mechanical properties of the infarct region by therapeutic intervention. Fomovsky et al created a model to examine the influence of scar anisotropy on ejection fraction and found that increasing the longitudinal stiffness of the infarct region would improve cardiac function (44). Kortsmit et al, examined the effect of an injectable hydrogel on the mechanics of the infarct region and on cardiac function (99). They found that the presence of the hydrogel did improve cardiac function.

Voorhees and Han developed a cylindrical LV model to study the influence of collagen alignment, density, and mechanics within the infarct region on cardiac function (195). They concluded that a longitudinal alignment of fibers maximizes EF in the post-MI environment by allowing for increased diastolic filling and increasing contractility through the Frank-Starling mechanism.

A recent study by Wall et al developed a computational model of the post-MI LV that included electromechanical coupling (199). Electrical conduction in the infarct region is significantly altered compared to the healthy tissue and understanding the influence of electrical conduction on both tissue mechanics and cardiac function will be important in developing new treatments for MI.

Mechanics of MI Treatment

Biomechanics is already playing a major role in the development of new treatments for MI. The use of mesh wrapping placed around the LV has been investigated as a means of reinforcing the infarct tissue and preventing LV dilation (13, 95). The procedure is highly invasive though, and many researchers are instead attempting to increase the stiffness of the infarct tissue directly through the injection of a wide range of hydrogels and tissue fillers (57). These techniques have been shown to prevent LV dilation and reduce adverse remodeling by reducing the mechanical stresses. One interesting approach is the injection of elastin into the infarct area which also shows promise in preventing LV remodeling (139). A more recent study injected stem cells programmed to overexpress elastin into the infarct area and produced very promising results (108). Based on the findings of their computational model, Fomovsky et al, implanted an anisotropic patch over the infarct region of a canine LV and found that the patch did improve systolic function without impairing diastolic function (45). The Cardiokinetix Parachute is a catheter delivered device that expands in the LV and partitions the healthy and infracted segments of the LV, and reduces the mechanical stresses in the myofibers of the healthy region, reducing the risk of developing of hypertrophy (106).

Cardiac mechanics are also important in the development of surgical techniques designed to restore LV function. The Dor procedure in which the ischemic region of the LV is removed and the ventricle then patched so that the final size and geometry roughly match that of the healthy LV has been used for almost 30 years with success (34, 36). Part of the theory behind why this procedure works is that it reduces the mechanical stresses on the LV. The development of accurate, patient specific computational models can further aid improvements in surgical techniques (100, 223).

Left ventricular assist devices (LVADs) are currently used as a short term bridge to transplant in patients with heart failure, including heart failure due to MI (51). Recent advances in the technology are making LVADs a viable long term destination therapy (9, 111, 112, 213). Clearly, a knowledge of mechanical engineering is needed to design and build these pumps, but it is also important to understand the ways in which LVADs alter the mechanics of the heart. LVADs modulate the wall stresses in the myocardial tissue, but also the flow patterns of the blood through the heart and into the aorta which can lead to clinical complications (21, 88) LVADs decrease the filling pressure and mechanical load on the ventricle which can reduce adverse remodeling (51). It has been shown that LVAD devices can reduce the expression of MMP-1 and MMP-9, increase the expression of TIMP-1 and TIMP-3, and decrease the expression of NF-κB (59, 109), Further, LVAD therapy has been shown to prevent myocyte hypertrophy (8). Current state of the art technology has led to the development of continuous flow LVAD devices which improve patient outcome following implantation (25). The decision on what patients should receive LVAD devices is a difficult one, and biomechanical analyses may be able to aid in the decision making process (123).

Pharmaceutical agents are a major part of the treatment regimen for MI, and many of these agents have effects on blood pressure and the remodeling process which can change the mechanical stresses and deformations of the ventricle wall, altering remodeling (110, 149). Voorhees et al recently showed that deletion of the gene for MMP-9 altered the mechanical properties of the infarct region 7 days post-MI creating a tissue that with increased stiffness (194). The development of computational models focusing on biological and mechanical interaction will be very important in predicting the effects a pharmaceutical agent on both changes in mechanical properties due to remodeling but also in predicting changes in LV function.

The ultimate goal in treatment of myocardial infarction is the generation of new myocardium to replace the dysfunctional myocardium. Advances in regenerative medicine and tissue engineering are making this a possibility. To date, several clinical studies have been performed in which stem cells of various types were delivered to the ischemic myocardium (153). However, there is little evidence in humans that these cells actually differentiated into myocytes. It is known that the differentiation of stem cells into cardiomyocytes is highly regulated by chemical signals such as growth factors and cytokines, electrical signals, and mechanical signals (200). Given the interplay of all these factors, the success of regenerative therapies will likely lie in controlling the mechanical environment of the LV.

Biomechanics in LV hypertrophy and Diastolic Heart Failure

While atherosclerosis in the coronary artery can lead to MI, increased LV pressure due to hypertension, aortic valve stenosis, or stiffening of the arterial walls can lead to LV hypertrophy and diastolic dysfunction. Diastolic heart failure, or heart failure with preserved ejection fraction (HFpEF) has become increasingly studied and is responsible for half of all heart failure hospitalizations (7, 152, 210, 216). Risk factors for HFpEF include aging, diabetes, obesity, and hypertension, and HFpEF has a higher prevalence in women than men.

Patients with HFpEF commonly have an elevated end-diastolic LV pressure as a result of impaired diastolic filling. Aortic valve stenosis reduces the outlet diameter from the ventricle and in turn increases the LV pressures (218). Similarly, peripheral artery stiffening increases the resistance of the circulatory system leading to hypertension and increased LV pressure (215). HFpEF hearts commonly show concentric remodeling characterized by normal LV volume, increased LV mass (thus decreased volume to mass ratio), increased wall thickness, and increased chamber and myocardial stiffness (7). HFpEF hearts undergo hypertrophy with a marked increase in fibrosis, which leads to increased wall stiffness. In fact, it has been shown that both extracellular matrix (MMP, collagen, fibronectin) and titin are altered (117). The increase in wall stiffness prevents both diastolic filling and relaxation. Biomechanically, HFpEF results in a upward and rightward shift of the diastolic pressure-volume curve (225). This means that a high pressure is required to generate a given filling volume.

Diagnosis of HFpEF is often difficult given that there is no change in EF. The current consensus is that diagnosis should be based on either invasive hemodynamic measurements such as LV end-diastolic pressure, mean pulmonary capillary wedge pressure, and τ, or on a combination of tissue Doppler measurements, such as E/e’, and biomarkers such as brain natriuretic peptide (152). It was recently shown strain as measured by speckle tracking echocardiograpy is a predictor of HFpEF patient outcome (178)

Similar to what we have discussed for post-MI remodeling, mechanical stress also plays an important role in the remodeling process that leads to diastolic heart failure. In an early computational model, Segers et al, showed that increased diastolic pressure resulted in LV remodeling that yielded a hypertrophic LV wall (171). Lemmon and Yongathan developed a fluid structure interaction model to examine the role of tissue stiffness on ventricle filling (107). Yang et al, developed a mechanically coupled model of cardiac aging, showing that aging results in increased collagen deposition, increased LV mass, increased LV stiffness, and an increase in LV pressures (217). Many of the models developed so far use simplified geometries, and more work is needed to more fully understand the role of LV tissue properties on the development of HFpEF.

There is currently no proven effective therapy for HFpEF (210). Current treatments aim to control hypertension and heart rate but these therapies cannot reverse remodeling once it has occurred. Several clinical trials have been conducted with minimal success, likely due to the heterogeneity of underlying causes (valve disease, myocyte hypertrophy, fibrosis, atrial fibrillation, etc.) (172). The best outcomes will likely be achieved when therapies are given based on the underlying causes of HFpEF rather than based on the symptoms. Surgery is sometimes an option for treating HFpEF, again depending on the cause of the dysfunction. In general, surgery is not an established option for treating HFpEF, however valve replacement surgery is often prescribed for patients with aortic valve stenosis (218). Understanding the various biomechanical causes of HFpEF will be essential in developing new patient specific therapies and surgical techniques.

Biomechanics of the Right Ventricle, Atria, and Heart Valves

While the focus of this review has been on the cardiac function of the left ventricle, the contributions of the other chambers as well as the function of the valves cannot be discounted.

The right ventricle (RV) of the heart is responsible for pumping blood to the lungs in order to be reoxygenated. While under significantly lower pressures than the LV, the mechanics of the RV are very similar to those of the LV, and RV function can be assessed using many of the same techniques and measurements. Pulmonary hypertension can lead to RV remodeling and the development of RV HF and potentially death (52) A recent article from the Sacks lab, examined the changes in mechanical properties and tissue structure that occur in the RV as a result of pressure overload (81). For a review RV mechanics and function, the reader is directed to the report by the National Heart, Lung, and Blood Institute Working Group on Cellular and Molecular Mechanisms of Right Heart Failure (193).

The atria of the heart are responsible for the filling of the ventricles, and play an important role in cardiac function. Remodeling of the atria is associated with a dilation and stiffening of the chamber similar to that seen in the ventricles and is associated with the development of heart failure (96, 191). These conditions reduce the ability of the atria to fill with blood and act as a reservoir for ventricle filling (82). It has been experimentally shown that the motion of the ventricle during systole alters the dimensions of the atria changing its reservoir capacity, and that changes in the stiffness of the ventricle alters atrial function as well (10). Improving our understanding of atrial mechanics could aid in the development of treatments for diastolic heart failure. For a discussion of atrial mechanics the reader is directed to the review by Vieira et al (191)

There is a tremendous literature on the biomechanics of normal and diseased heart valves. Heart valves remodel in response to both fluid shear stresses and tissue stresses which has effects on both cell and ECM organization and density (24, 136). Increased valve stiffness has been associated with diseases such as aortic valve stenosis. Treatment of valvular disease is typically achieved through surgery and possibly replacement of the valve, and understanding the complex structure and mechanics of the heart valves will improve both surgical technique and the design of new artificial valves (159). The interested reader may refer to the reviews by Sacks (166, 167).

The development of the heart is a complex biological feat that is largely guided by biomechanical forces. The heart starts as a straight tube and then bends into a loop that will form the basis for the mature heart (180). Torsion is thought to be an important factor in the cardiac looping phenomenon (182). Later in development, hemodynamic factors play a major role in regulating myocyte shape and organization as well as ECM production (125). For overviews of biomechanics in the heart development and growth can refer to the papers by Taber et al and a recent review of the role of mechanotransduction in development by Majkut et al (125, 179-182).

Future Perspectives and Directions

Cardiac biomechanics is a broad field and there are many areas that need further study. The following are some of the most pressing issues in the field: 1. We need better constitutive models for myocardial tissue, ideally models that include the effects of cellular proteins like titin, 2. We need improved multi-scale, whole-heart models of cardiac behavior that include the electrical, chemical, cellular, and mechanical factors, 3. We need to further study the role of mechanical stress in the inflammatory period and develop computational models that include this effect in the remodeling process, 4. We need to examine how deletion or over expression of individual genes affects tissue mechanics, 5. We need to use the principles of mechanical analysis to develop effective treatments for diastolic heart failure. Biomechanical analysis will allow us to address these knowledge gaps and improve the way we diagnose and treat future patients.

Conclusion

Biomechanical factors are the primary determinants of cardiac function in both the normal and diseased heart. The mechanical properties of cardiac tissue alter the ability of the ventricles and atria to fill with blood and contract. Biological processes such as inflammation and fibrosis have a direct impact on tissue mechanics and alterations to the local mechanical stresses drive adverse remodeling and contribute to the development heart failure. Recognition of the important role that biomechanics plays in regulating heart function has led to mechanical measures such as tissue strain being used to diagnose cardiac disease. Mechanical stress analysis can allow physicians to determine what patients may benefit from surgical intervention.