Fast Simulation of Mechanical Heterogeneity in the Electrically Asynchronous Heart Using the MultiPatch Module

Cardiac electrical asynchrony occurs as a result of cardiac pacing or conduction disorders such as left bundle-branch block (LBBB). Electrically asynchronous activation causes myocardial contraction heterogeneity that can be detrimental for cardiac function. Computational models provide a tool for understanding pathological consequences of dyssynchronous contraction. Simulations of mechanical dyssynchrony within the heart are typically performed using the finite element method, whose computational intensity may present an obstacle to clinical deployment of patient-specific models. We present an alternative based on the CircAdapt lumped-parameter model of the heart and circulatory system, called the MultiPatch module. Cardiac walls are subdivided into an arbitrary number of patches of homogeneous tissue. Tissue properties and activation time can differ between patches. All patches within a wall share a common wall tension and curvature. Consequently, spatial location within the wall is not required to calculate deformation in a patch. We test the hypothesis that activation time is more important than tissue location for determining mechanical deformation in asynchronous hearts. We perform simulations representing an experimental study of myocardial deformation induced by ventricular pacing, and a patient with LBBB and heart failure using endocardial recordings of electrical activation, wall volumes, and end-diastolic volumes. Direct comparison between simulated and experimental strain patterns shows both qualitative and quantitative agreement between model fibre strain and experimental circumferential strain in terms of shortening and rebound stretch during ejection. Local myofibre strain in the patient simulation shows qualitative agreement with circumferential strain patterns observed in the patient using tagged MRI. We conclude that the MultiPatch module produces realistic regional deformation patterns in the asynchronous heart and that activation time is more important than tissue location within a wall for determining myocardial deformation. The CircAdapt model is therefore capable of fast and realistic simulations of dyssynchronous myocardial deformation embedded within the closed-loop cardiovascular system.     

Structural finite deformation model of the left ventricle during diastole and systole

A model of left ventricular function is developed based on morphological characteristics of the myocardial tissue. The passive response of the three-dimensional collagen network and the active contribution of the muscle fibers are integrated to yield the overall response of the left ventricle which is considered to be a thick wall cylinder. The deformation field and the distributions of stress and pressure are determined at each point in the cardiac cycle by numerically solving three equations of equilibrium. Simulated results in terms of the ventricular deformation during ejection and isovolumic cycles are shown to be in good qualitative agreement with experimental data. It is shown that the collagen network in the heart has considerable effect on the pressure-volume loops. The particular pattern of spatial orientation of the collagen determines the ventricular recoil properties in early diastole. The material properties (myocardial stiffness and contractility) are shown to affect both the pressure-volume loop and the deformation pattern of the ventricle. The results indicate that microstructural consideration offer a realistic representation of the left ventricle mechanics.     

Theoretical models in mechanics of the left ventricle

Different rheological concepts and theoretical studies have been recently presented using models of myocardial mechanics. Complex analysis of the mechanical behavior of the left ventricular wall have been developed in order to estimate the local stresses and deformations that occur during the heart cycle as well as the ventricular stroke volume and pressure. Theoretical models have taken into account non-linear and viscoelastic passive properties of the myocardium tissue, when subjected to large deformations, through given strain energy functions or stress-strain relations. Different prolate spheroid geometries have been considered for such thick shell cardiac structure. During the active state of the contraction, the rheological behavior of the fibers has been described using different muscle models and relationships between fiber tension and strain, and activation degree. A forthcoming approach for bridging the gap between the knowledge of the muscle fiber microrheological properties and the study of the mechanical behavior of the entire ventricle, consists in including anisotropic and inhomogeneous effects through fiber direction field.     

Towards a biomechanics-based technique for assessing myocardial contractility: an inverse problem approach

This work presents the initial development and implementation of a novel 3D biomechanics-based approach to measure the mechanical activity of myocardial tissue, as a potential non-invasive tool to assess myocardial function. This technique quantifies the myocardial contraction forces developed within the ventricular myofibers in response to electro-physiological stimuli. We provide a 3D finite element formulation of a contraction force reconstruction algorithm, along with its implementation using magnetic resonance (MR) data. Our algorithm is based on an inverse problem solution governed by the fundamental continuum mechanics principle of conservation of linear momentum, under a first-order approximation of elastic and isotropic material conditions. We implemented our technique using a subject-specific ventricle model obtained by extracting the left ventricular anatomical features from a set of high-resolution cardiac MR images acquired throughout the cardiac cycle using prospective electrocardiographic gating. Cardiac motion information was extracted by non-rigid registration of the mid-diastole reference image to the remaining images of a 4D dataset. Using our technique, we reconstructed dynamic maps that show the contraction force distribution superimposed onto the deformed ventricle model at each acquired frame in the cardiac cycle. Our next objective will consist of validating this technique by showing the correlation between the presence of low contraction force patterns and poor myocardial functionality.     

In vivo porcine left atrial wall stress: Computational model

Most computational models of the heart have so far concentrated on the study of the left ventricle, mainly using simplified geometries. The same approach cannot be adopted to model the left atrium, whose irregular shape does not allow morphological simplifications. In addition, the deformation of the left atrium during the cardiac cycle strongly depends on the interaction with its surrounding structures. We present a procedure to generate a comprehensive computational model of the left atrium, including physiological loads (blood pressure), boundary conditions (pericardium, pulmonary veins and mitral valve annulus movement) and mechanical properties based on planar biaxial experiments. The model was able to accurately reproduce the in vivo dynamics of the left atrium during the passive portion of the cardiac cycle. A shift in time between the peak pressure and the maximum displacement of the mitral valve annulus allows the appendage to inflate and bend towards the ventricle before the pulling effect associated with the ventricle contraction takes place. The ventricular systole creates room for further expansion of the appendage, which gets in close contact with the pericardium. The temporal evolution of the volume in the atrial cavity as predicted by the finite element simulation matches the volume changes obtained from CT scans. The stress field computed at each time point shows remarkable spatial heterogeneity. In particular, high stress concentration occurs along the appendage rim and in the region surrounding the pulmonary veins.     

Energetics of ventricular contraction as traced in the pressure-volume diagram

The pressure-volume (P-V) relationship of the canine left ventricle can reasonably be simulated by a time-varying elastance model. In this model the total mechanical energy generated by a contraction can be determined theoretically from the change in the elastance. Applying this theory to the actual left ventricle, we have found that the area in the P-V diagram circumscribed by the end-systolic P-V relation line, the end-diastolic P-V relation curve, and the systolic segment of the P-V trajectory is equivalent to the total mechanical energy generated by ventricular contraction. We call this area the systolic P-V area (PVA). We have studied experimentally the correlation between the PVA and myocardial oxygen consumption (VO2) in the canine left ventricle. VO2 was linearly correlated with PVA regardless of the contraction mode and loading conditions in a given left ventricle. The VO2-PVA relation parallel shifted upward with positive inotropic agents. This shift comprised a significant increase in VO2 component for the unloaded contraction. We therefore consider that further analyses of the VO2-PVA relationship will greatly promote our understanding of cardiac energetics.     

Cardiopulmonary resuscitation in a rat model of chronic myocardial ischemia.

Our group has developed a rat model of cardiac arrest and cardiopulmonary resuscitation (CPR). However, the current rat model uses healthy adult animals. In an effort to more closely reproduce the event of cardiac arrest and CPR in humans with chronic coronary disease, a rat model of coronary artery constriction was investigated during cardiac arrest and CPR. Left coronary artery constriction was induced surgically in anesthetized, mechanically ventilated Sprague-Dawley rats. Echocardiography was used to measure global cardiac performance before surgery and 4 wk postsurgery. Coronary constriction provoked significant decreases in ejection fraction, increases in left ventricular end-diastolic volume, and increases left ventricular end-systolic volume at 4 wk postintervention, just before induction of ventricular fibrillation (VF). After 6 min of untreated VF, CPR was initiated on three groups: 1) coronary artery constriction group, 2) sham-operated group, and 3) control group (without preceding surgery). Defibrillation was attempted after 6 min of CPR. All the animals were resuscitated. Postresuscitation myocardial function as measured by rate of left ventricular pressure increase at 40 mmHg and the rate of left ventricular pressure decline was more significantly impaired and left ventricular end-diastolic pressure was greater in the coronary artery constriction group compared with the sham-operated group and the control group. There were no differences in the total shock energy required for successful resuscitation and duration of survival among the groups. In summary, this rat model of chronic myocardial ischemia was associated with ventricular remodeling and left ventricular myocardial dysfunction 4 wk postintervention and subsequently with severe postresuscitation myocardial dysfunction. This model would suggest further clinically relevant investigation on cardiac arrest and CPR.     

Alteration of collagenous protein profile in congestive heart failure secondary to myocardial infarction

The rat model of myocardial infarction is characterized by progressive cardiac hypertrophy and failure. Rats with infarcts greater than 30% of the left ventricle exhibited early and moderate, stages of heart failure 4 and 8 weeks after the occlusion of the left coronary artery, respectively. As heart failure is usually associated with remodeling of the extracellular matrix, a histological and biochemical study of cardiac collagenous proteins was carried out using failing hearts. Total collagen content in the right ventricle increased at 2, 4, and 8 weeks following occlusion of the left coronary artery whereas such a change in viable left ventricle was seen after 4 and 8 weeks. Total cardiac hydroxyproline concentration was increased in both right and left ventricular samples from the infarcted animals when compared to those of control; this increase was due to elevation of pepsin-insoluble collagen fraction. The myocardial noncollagenous/collagenous protein ratio was decreased in experimental right and left ventricular samples when compared to control samples. These findings suggest that an increase in cross-linking of cardiac collagen as well as disparate synthesis of collagenous and noncollagenous proteins occurs in this model of congestive heart, failure.     

Renin-angiotensin system and sympathetic nervous system in cardiac pressure-overload hypertrophy

Angiotensin II and norepinephrine (NE) have been implicated in the neurohumoral response to pressure overload and the development of left ventricular hypertrophy. The purpose of this study was to determine the temporal sequence for activation of the renin-angiotensin and sympathetic nervous systems in the rat after 3-60 days of pressure overload induced by aortic constriction. Initially on pressure overload, there was transient activation of the systemic renin-angiotensin system coinciding with the appearance of left ventricular hypertrophy (day 3). At day 10, there was a marked increase in AT(1) receptor density in the left ventricle, increased plasma NE concentration, and elevated cardiac epinephrine content. Moreover, the inotropic response to isoproterenol was reduced in the isolated, perfused heart at 10 days of pressure overload. The affinity of the beta(2)-adrenergic receptor in the left ventricle was decreased at 60 days. Despite these alterations, there was no decline in resting left ventricular function, beta-adrenergic receptor density, or the relative distribution of beta(1)- and beta(2)-receptor sites in the left ventricle over 60 days of pressure overload. Thus activation of the renin-angiotensin system is an early response to pressure overload and may contribute to the initial development of cardiac hypertrophy and sympathetic activation in the compensated heart.     

Coupled pacing improves cardiac efficiency during acute atrial fibrillation with or without cardiac dysfunction

Coupled pacing (CP), a method for controlling ventricular rate during atrial fibrillation (AF), consists of a single electrical stimulation applied to the ventricles after each spontaneous activation. CP results in a mechanical contraction rate approximately one-half the rate during AF. Paired stimulation in which two electrical stimuli are delivered to the ventricles has also been proposed as a therapy for heart failure. Although paired stimulation enhances contractility, it greatly increases energy consumption. The primary hypothesis of the present study is that CP improves cardiac function during acute AF without a similar increase in energy consumption because of the reduced rate of ventricular contractions. In a canine model, CP was applied during four stages: sinus rhythm (SR), acute AF, cardiac dysfunction (CD), and AF in the presence of cardiac dysfunction. The rate of ventricular contraction decreased in all four stages as the result of CP. In addition, we determined the changes in external cardiac work, myocardial oxygen consumption, and myocardial efficiency in the each of four stages. CP partially reversed the effects of AF and CD on external cardiac work, whereas myocardial oxygen consumption increased only moderately. In all stages but SR, CP increased myocardial efficiency because of the marked increases in cardiac work compared with the moderate increases in total energy consumed. Thus this pacing therapy may be a viable therapy for patients with concurrent atrial fibrillation and heart failure.     

Acidaemia reduces cardiac output and left ventricular contractility in conscious lambs

We studied the effects of HCI-induced metabolic acidaemia on cardiac output, contractile function, myocardial blood flow, and myocardial oxygen consumption in nine unanaesthetized newborn lambs. Through a left thoracotomy, catheters were placed in the aorta, left atrium and coronary sinus. A pressure transducer was placed in the left ventricle. Three to four days after surgery, we measured cardiac output, dP/dt, left ventricular end diastolic and aortic mean blood pressures, heart rate, aortic and coronary sinus blood oxygen contents, and left ventricular myocardial blood flow during a control period, during metabolic acidaemia, and after the aortic pH was restored to normal. We calculated systemic vascular resistance, myocardial oxygen consumption and left ventricular work. Acidaemia was associated with reduction in cardiac output, maximal dP/dt, and aortic mean blood pressure. Left ventricular end diastolic pressure and systemic vascular resistance increased, and heart rate did not change significantly. The reduction in myocardial blood flow and oxygen consumption was accompanied by fall in cardiac work. Cardiac output returned to control levels after the pH had been normalized but maximal dP/dt was incompletely restored. Myocardial blood flow and oxygen consumption increased beyond control levels. This study demonstrates that HCI-induced metabolic acidaemia in conscious newborn lambs is associated with a reduction in cardiac output which could have been mediated by the reduction in contractile function and/or the increase in systemic vascular resistance. The decreases in myocardial blood flow and oxygen consumption appear to reflect diminished cardiac work. The restoration of a normal cardiac output after normalization of the pH appears to have resulted from the increases in heart rate and left ventricular filling pressures in conjunction with an incomplete restoration of contractile function.     

Theoretical analysis of the effects of a radial activation wave and twisting motion on the mechanics of the left ventricle

The mechanical effects resulting from the normal transmural delay of electrical depolarization of the myocardium are investigated. An activation sequence having a finite radial propagation velocity is introduced into the equations of ventricular mechanics. The resulting system of coupled integral equations is solved using a perturbation method based on the small ratio of transmural propagation time to cardiac period. Numerical calculations are performed using cavity pressure and volume waveforms characteristic of the canine left ventricle (LV), for both simultaneous and delayed activation of fiber layers. The results show that a finite transmural electrical propagation velocity tends to: (i) equalize the transmural distribution of sarcomere length during systole; (ii) equalize the transmural distribution of fiber external work/vol; and (iii) insignificantly affect myocardial tissue pressure. Calculations are also performed to investigate the mechanical effects resulting from the application of an externally applied moment that prevents LV torsion. Those results are highly dependent on the transmural distribution of sarcomere length in the stress-free reference state (unloaded diastole). When we assume a uniform distribution, then normal torsion acting with normal activation delay tends to: (i) increase the magnitude of fiber strain in the subendocardium and decrease it in the subepicardium; (ii) equalize the transmural distribution of fiber external work/vol; and (iii) lower myocardial tissue pressure. The normally occurring transmural delay of activation tends to lessen endocardial O2 demand, while the normally occurring torsion further lessens that demand and improves O2 supply.     

Electrical Wave Propagation in an Anisotropic Model of the Left Ventricle Based on Analytical Description of Cardiac Architecture

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher–Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation.     

Predominant activation of endothelin-dependent cardiac hypertrophy by norepinephrine in rat left ventricle

Locally released endothelin (ET)-1 has been recently identified as an important mediator of cardiac hypertrophy. It is still unclear, however, which primary stimulus specifically activates ET-dependent signaling pathways. We therefore examined in adult rats (n = 51) the effects of a selective ET(A) receptor antagonist in experimental models of cardiac hypertrophy, in which myocardial growth is predominantly initiated by a single primary stimulus. Rats were exposed to mechanical overload (ascending aortic stenosis), increased levels of circulating ANG II (ANG II infusion combined with hydralazine), or adrenergic stimulation (infusion of norepinephrine in a subpressor dose) for 7 days. All experimental treatments significantly increased left ventricular weight/body weight ratios compared with untreated rats, whereas systolic left ventricular peak pressure was increased only after ascending aortic stenosis. ET(A) receptor blockade exclusively reduced norepinephrine-induced cardiac hypertrophy and atrial natriuretic peptide gene expression. Blood pressure levels and heart rates remained unaffected during ET(A) receptor blockade in all experimental groups. These data indicate that in rat left ventricle, the ET-dependent signaling pathway leading to early development of cardiac hypertrophy and fetal gene expression is primarily activated by norepinephrine.     

Structure of the cardiac systole in mammals and birds

The comparative analysis of the contractile function of the heart left ventricle in four species of homoeothermic tetrapods (chicken, quail, rat, sheep) who differ in their spatio-temporal pattern of ventricular excitation, heart rate, and heart weight was performed. The analysis of cardiac cycle structure was performed on the basis of synchronous recording of ECG, phonocardiogram, and apex cardiogram. Indices of myocardial contractility of the left ventricle calculated on the basis of the analysis of the cardiac dynamics indicate disadvantageous contractile function of the left ventricle in rodents and non-flying birds in comparison with sheep. The functioning of the left ventricle in male rats is more strained than in female rats. One fundamental factor determining a more strained functioning of the left ventricle in birds in comparison with mammals is the heart rate. The relative weight and activation pattern of the left ventricular myocardium govern the contractile function of the left ventricle to a lesser extent.     

Real-time pressure-volume diagrams for the evaluation of ventricular function

Using three intraventricular diameter signals obtained from ultrasonic distance gauges and applying the general ellipsoid model to the left ventricle, it was possible to obtain the left ventricular volume signal Implanting a miniature transducer in the left ventricle the pressure signal was attained. With these two signals the pressure-volume diagrams were constructed on line, and ventricular function during load manoeuvres could be studied from them. Because the whole process was done on line, using a microcomputer, the performance of the left ventricle to load manoeuvres in different conditions could be seen instantly.     

Dynamic geometry of the intact left ventricle

Knowledge of left ventricular chamber dynamics is central to our understanding of cardiac physiology. The complicated changes in left ventricular geometry observed in the dog during various phases of the cardiac cycle can be represented as distinct linear relationships between chamber eccentricity and intracavitary volume during diastole and ejection, and probably represent structural properties of the ventricular wall. Chamber geometry of the left ventricle is a major determinant of overall myocardial function. The slope of the radius of curvature (r) to wall thickness (h) relationship is a geometric constant that determines the mural force at any given transmural pressure. Chronic pressure and volume overload produce changes in this geometric relationship as a result of increased mural force resisting ejection. The adaptive mechanism of ventricular hypertrophy in this setting alters the r/h ratio and returns systolic mural force toward normal. Coronary occlusion induces acute changes in regional geometry characterized by holosystolic wall bulging and systolic wall thinning, which shift the r/h relationship upward and to the left. The geometric alteration during ischemia probably increases systolic mural force and could adversely affect myocardial function. Recent studies with patients have shown the r/h ratio to be of value in distinguishing between reversible and irreversible impairment of myocardial performance. Because most myocardial diseases produce major alterations in the structure of the ventricular wall, analysis of dynamic chamber geometry may prove of prognostic value in assessing patients with cardiac disorders.     

Mechanics of the left ventricular myocardial interstitium: effects of acute and chronic myocardial edema

Myocardial interstitial edema forms as a result of several disease states and clinical interventions. Acute myocardial interstitial edema is associated with compromised systolic and diastolic cardiac function and increased stiffness of the left ventricular chamber. Formation of chronic myocardial interstitial edema results in deposition of interstitial collagen, which causes interstitial fibrosis. To assess the effect of myocardial interstitial edema on the mechanical properties of the left ventricle and the myocardial interstitium, we induced acute and chronic interstitial edema in dogs. Acute myocardial edema was generated by coronary sinus pressure elevation, while chronic myocardial edema was generated by chronic pulmonary artery banding. The pressure-volume relationships of the left ventricular myocardial interstitium and left ventricular chamber for control animals were compared with acutely and chronically edematous animals. Collagen content of nonedematous and chronically edematous animals was also compared. Generating acute myocardial interstitial edema resulted in decreased left ventricular chamber compliance compared with nonedematous animals. With chronic edema, the primary form of collagen changed from type I to III. Left ventricular chamber compliance in animals made chronically edematous was significantly higher than nonedematous animals. The change in primary collagen type secondary to chronic left ventricular myocardial interstitial edema provides direct evidence for structural remodeling. The resulting functional adaptation allows the chronically edematous heart to maintain left ventricular chamber compliance when challenged with acute edema, thus preserving cardiac function over a wide range of interstitial fluid pressures.     

A mathematical derivation of the P-V relation at end-systole

A dynamical model of the left ventricle as a thick-walled cylinder contracting radially is used to derive the P-V (pressure-volume) relation in the left ventricular cavity during contraction. It is shown how the mathematical results derived could apply to experimental results.