Epicardial suction: a new approach to mechanical testing of the passive ventricular wall

The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to introduce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlinear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and second, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocardium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechanics.     

Adaptation of passive rat left ventricle in diastolic dysfunction.

This article deals with providing a theoretical explanation for quantitative changes in the geometry, the opening angle and the deformation parameters of the rat ventricular wall during adaptation of the passive left ventricle in diastolic dysfunction. A large deformation theory is applied to analyse transmural stress and strain distribution in the left ventricular wall considering it to be made of homogeneous, incompressible, transversely isotropic, non-linear elastic material. The basic assumptions made for computing stress distributions are that the average circumferential stress and strain for the adaptive ventricle is equal to the average circumferential stress and strain in the normotensive ventricle, respectively.All the relevant parameters, such as opening angle, twist per unit length, axial extension, internal and external radii and others, in the stress-free, unloaded and loaded states of normotensive, hypertensive and adaptive left ventricle are determined. The circumferential stress and strain distribution through the ventricular wall are also computed. Our analysis predicts that during adaptation, wall thickness and wall mass of the ventricle increase. These results are consistent with experimental findings and are the indications of initiation of congestive heart failure.     

Transmural mechanics at left ventricular epicardial pacing site

Left ventricular (LV) epicardial pacing acutely reduces wall thickening at the pacing site. Because LV epicardial pacing also reduces transverse shear deformation, which is related to myocardial sheet shear, we hypothesized that impaired end-systolic wall thickening at the pacing site is due to reduction in myocardial sheet shear deformation, resulting in a reduced contribution of sheet shear to wall thickening. We also hypothesized that epicardial pacing would reverse the transmural mechanical activation sequence and thereby mitigate normal transmural deformation. To test these hypotheses, we investigated the effects of LV epicardial pacing on transmural fiber-sheet mechanics by determining three-dimensional finite deformation during normal atrioventricular conduction and LV epicardial pacing in the anterior wall of normal dog hearts in vivo. Our measurements indicate that impaired end-systolic wall thickening at the pacing site was not due to selective reduction of sheet shear, but rather resulted from overall depression of fiber-sheet deformation, and relative contributions of sheet strains to wall thickening were maintained. These findings suggest lack of effective end-systolic myocardial deformation at the pacing site, most likely because the pacing site initiates contraction significantly earlier than the rest of the ventricle. Epicardial pacing also induced reversal of the transmural mechanical activation sequence, which depressed sheet extension and wall thickening early in the cardiac cycle, whereas transverse shear and sheet shear deformation were not affected. These findings suggest that normal sheet extension and wall thickening immediately after activation may require normal transmural activation sequence, whereas sheet shear deformation may be determined by local anatomy.     

Time-dependent remodeling of transmural architecture underlying abnormal ventricular geometry in chronic volume overload heart failure

To test the hypothesis that the abnormal ventricular geometry in failing hearts may be accounted for by regionally selective remodeling of myocardial laminae or sheets, we investigated remodeling of the transmural architecture in chronic volume overload induced by an aortocaval shunt. We determined three-dimensional finite deformation at apical and basal sites in left ventricular anterior wall of six dogs with the use of biplane cineradiography of implanted markers. Myocardial strains at end diastole were measured at a failing state referred to control to describe remodeling of myofibers and sheet structures over time. After 9 +/- 2 wk (means +/- SE) of volume overload, the myocardial volume within the marker sets increased by >20%. At 2 wk, the basal site had myofiber elongation (0.099 +/- 0.030; P <0.05), whereas the apical site did not [P=not significant (NS)]. Sheet shear at the basal site increased progressively toward the final study (0.040 +/- 0.003 at 2 wk and 0.054 +/- 0.021 at final; both P <0.05), which contributed to a significant increase in wall thickness at the final study (0.181 +/- 0.047; P < 0.05), whereas the apical site did not (P=NS). We conclude that the remodeling of the transmural architecture is regionally heterogeneous in chronic volume overload. The early differences in fiber elongation seem most likely due to a regional gradient in diastolic wall stress, whereas the late differences in wall thickness are most likely related to regional differences in the laminar architecture of the wall. These results suggest that the temporal progression of ventricular remodeling may be anatomically designed at the level of regional laminar architecture.     

Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study.

The dependence of local left ventricular (LV) mechanics on myocardial muscle fiber orientation was investigated using a finite element model. In the model we have considered anisotropy of the active and passive components of myocardial tissue, dependence of active stress on time, strain and strain rate, activation sequence of the LV wall and aortic afterload. Muscle fiber orientation in the LV wall is quantified by the helix fiber angle, defined as the angle between the muscle fiber direction and the local circumferential direction. In a first simulation, a transmural variation of the helix fiber angle from +60 degrees at the endocardium through 0 degrees in the midwall layers to -60 degrees at the epicardium was assumed. In this simulation, at the equatorial level maximum active muscle fiber stress was found to vary from about 110 kPa in the subendocardial layers through about 30 kPa in the midwall layers to about 40 kPa in the subepicardial layers. Next, in a series of simulations, muscle fiber orientation was iteratively adapted until the spatial distribution of active muscle fiber stress was fairly homogeneous. Using a transmural course of the helix fiber angle of +60 degrees at the endocardium, +15 degrees in the midwall layers and -60 degrees at the epicardium, at the equatorial level maximum active muscle fiber stress varied from 52 kPa to 55 kPa, indicating a remarkable reduction of the stress range. Moreover, the change of muscle fiber strain with time was more similar in different parts of the LV wall than in the first simulation. It is concluded that (1) the distribution of active muscle fiber stress and muscle fiber strain across the LV wall is very sensitive to the transmural distribution of the helix fiber angle and (2) a physiological transmural distribution of the helix fiber angle can be found, at which active muscle fiber stress and muscle fiber strain are distributed approximately homogeneously across the LV wall.     

Ventricular mechanics in diastole: material parameter sensitivity

Models of ventricular mechanics have been developed over the last 20 years to include finite deformation theory, anisotropic and inhomogeneous material properties and an accurate representation of ventricular geometry. As computer performance and the computational efficiency of the models improve, clinical application of these heart mechanics models is becoming feasible. One such application is to estimate myocardial material properties by adjusting the constitutive parameters to match wall deformation from MRI or ultrasound measurements, together with a measurement (or estimate) of ventricular pressure. Pigs are now the principal large animal model for these studies and in this paper we present the development of a new three-dimensional finite element model of the heart based on measurements of the geometry and the fibre and sheet orientations of pig hearts. The end-diastolic deformation of the model is computed using the "pole-zero" constitutive law which we have previously used to model the mechanics of passive myocardial tissue specimens. The sensitivities of end-diastolic fibre-sheet material strains and heart shape to changes in the material parameters are computed for the parameters of the pole-zero law in order to assess the utility of the models for inverse material property determination.     

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes. The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation. In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola-Kirchhoff active stress tensor. As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.     

A two-phase finite element model of the diastolic left ventricle

A porous medium finite element model of the passive left ventricle is presented. The model is axisymmetric and allows for finite deformation, including torsion about the axis of symmetry. An anisotropic quasi-linear viscoelastic constitutive relation is implemented in the model. The model accounts for changing fibre orientation across the myocardial wall. During passive filling, the apex rotates in a clockwise direction relative to the base for an observer looking from apex to base. Within an intraventricular pressure range of 0-3 kPa the rotation angle of all nodes remained below 0.1 rad. Diastolic viscoelasticity of myocardial tissue is shown to reduce transmural differences of preload-induced sarcomere stretch and to generate residual stresses in an unloaded ventricular wall, consistent with the observation of opening angles seen when the heart is slit open. It is shown that the ventricular model stiffens following an increase of the intracoronary blood volume. At a given left ventricular volume, left ventricular pressure increases from 1.5 to 2.0 kPa when raising the intracoronary blood volume from 9 to 14 ml (100 g)-1 left ventricle.     

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes.

The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation.

In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola–Kirchhoff active stress tensor.

As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.     

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.     

Sarcomere length changes in a 3D mathematical model of the pig ventricles

Measurements of the geometry and fibrous-sheet structure of the left and right ventricles of the pig heart are fitted with a finite element model. Mechanical changes during the heart cycle are computed by solving the equations of motion under specified ventricular boundary conditions and using experimentally defined constitutive laws for the active and passive material properties of myocardial tissue. The resulting patterns of deformation, such as axial torsion and changes in wall thickness and base-apex length, are consistent with experimental observations. The model can therefore be used to predict sarcomere length changes and other strain patterns throughout the myocardium and throughout the cardiac cycle. Here we present sarcomere length changes at a limited number of material points within the wall. Sarcomere length typically varies by 10% above and below the unloaded length; although under the boundary conditions imposed in the current model the midwall circumferentially oriented sarcomere lengths increased by up to 20% at end diastole. We provide web-access details for a downloadable software program designed to provide more extensive information on mechanical deformation, such as the principal strains and muscle fibre cross-sectional area changes during the cardiac cycle.     

Finite-element analysis of left ventricular myocardial stresses

A versatile method of finite-element analysis is presented for the determination of the stress distributions in the left ventricular myocardial wall. The instantaneous shapes of the left ventricular myocardial wall, measured at 0,5 mm intervals and at a rate 0f 60 images/sec during a cardiac cycle, are approximated by axisymmetric shells following the approach of Gould et al. and analysed by the method of incremental loadings to account for the changing transmural pressure. The ventricular wall is mathematically divided up into coaxial rings of triagular cross sections so that determination of the stresses at any point within the wall can be achieved by assigning increased number of nodes across the wall thickness in the regions of the left ventricular wall where particular attention is needed. Appropriate boundary conditions are defined at the base of the left ventricle so that it can be treated as a shell with an open end. The computer program, which implements all the stress calculations involved, depends on the dimensions of the left ventricular wall measured from an operator-interactive roengen videometry system. It carries out the sequential formation of the nodes and elements and includes a CALCOMP subroutine to plot the finite-element partitioning of the instantaneous shape. Illustrative results of the end-diastolic stress distributions within the myocardial wall of a metabolically-supported, isolated, working canine left ventricle are given. This technique predicts higher endocardial meridional and hoop wall stresses relative to the stresses in the middle and epicardial region than those obtained with previous models.     

Role of tissue structure on ventricular wall mechanics

It is well known that systolic wall thickening in the inner half of the left ventricular (LV) wall is of greater magnitude than predicted by myofiber contraction alone. Previous studies have related the deformation of the LV wall to the orientation of the laminar architecture. Using this method, wall thickening can be interpreted as the sum of contributions due to extension, thickening, and shearing of the laminar sheets. We hypothesized that the thickening mechanics of the ventricular wall are determined by the structural organization of the underlying tissue, and may not be influenced by factors such as loading and activation sequence. To test this hypothesis, we calculated finite strains from biplane cineradiography of transmural markers implanted in apical (n = 22) and basal (n = 12) regions of the canine anterior LV free wall. Strains were referred to three-dimensional laminar microstructural axes measured by histology. The results indicate that sheet angle is of opposite sign in the apical and basal regions, but absolute value differs only in the subepicardium. During systole, shearing and extension of the laminae contribute the most to wall thickening, accounting for >90% (transmural average) at both apex and base. These two types of deformation are also most prominent during diastolic inflation. Increasing afterload has no effect on the pattern of systolic wall thickening, nor does reversing transmural activation sequence. The pattern of wall thickening appears to be a function of the orientation of the laminar sheets, which vary regionally and transmurally. Thus, acute interventions do not appear to alter the contributions of the laminae to wall thickening, providing further evidence that the structural architecture of the ventricular wall is the dominant factor for its regional mechanical function.     

Relating myocardial laminar architecture to shear strain and muscle fiber orientation

Cardiac myofibers are organized into laminar sheets about four cells thick. Recently, it has been suggested that these layers coincide with the plane of maximum shear during systole. In general, there are two such planes, which are oriented at +/-45 degrees to the main principal strain axes. These planes do not necessarily contain the fiber axis. In the present study, we explicitly added the constraint that the sheet planes should also contain the muscle fiber axis. In a mathematical analysis of previously measured three-dimensional transmural systolic strain distributions in six dogs, we computed the planes of maximum shear, adding the latter constraint by using the also-measured muscle fiber axis. Generally, for such planes two solutions were found, suggesting that two populations of sheet orientation may exist. The angles at which the predicted sheets intersected transmural tissue slices, cut along left ventricular short- or long-axis planes, were strikingly similar to experimentally measured values. In conclusion, sheets coincide with planes of maximum systolic shear subject to the constraint that the muscle fiber axis is contained in this plane. Sheet orientation is not a unique function of the transmural location but occurs in two distinct populations.     

Transmural left ventricular mechanics underlying torsional recoil during relaxation

Early relaxation in the cardiac cycle is characterized by rapid torsional recoil of the left ventricular (LV) wall. To elucidate the contribution of the transmural arrangement of the myofiber to relaxation, we determined the time course of three-dimensional fiber-sheet strains in the anterior wall of five adult mongrel dogs in vivo during early relaxation with biplane cineangiography (125 Hz) of implanted transmural markers. Fiber-sheet strains were found from transmural fiber and sheet orientations directly measured in the heart tissue. The strain time course was determined during early relaxation in the epicardial, midwall, and endocardial layers referenced to the end-diastolic configuration. During early relaxation, significant circumferential stretch, wall thinning, and in-plane and transverse shear were observed (P < 0.05). We also observed significant stretch along myofibers in the epicardial layers and sheet shortening and shear in the endocardial layers (P < 0.01). Importantly, predominant epicardial stretch along the fiber direction and endocardial sheet shortening occurred during isovolumic relaxation (P < 0.05). We conclude that the LV mechanics during early relaxation involves substantial deformation of fiber and sheet structures with significant transmural heterogeneity. Predominant epicardial stretch along myofibers during isovolumic relaxation appears to drive global torsional recoil to aid early diastolic filling.     

Effects of transmural electrical heterogeneities and electrotonic interactions on the dispersion of cardiac repolarization and action potential duration: A simulation study

It has been shown in the literature that myocytes isolated from the ventricular walls at various intramural depths have different action potential durations (APDs). When these myocytes are embedded in the ventricular wall, their inhomogeneous properties affect the sequence of repolarization and the actual distribution of the APDs in the entire wall. In this article, we implement a mathematical model to simulate the combined effect of (a) the non-homogeneous intrinsic membrane properties (in particular the non-homogeneous APDs) and (b) the electrotonic currents that modulate the APDs when the myocytes are embedded in the ventricular myocardium. In particular, we study the effect of (a) and (b) on the excitation and repolarization sequences and on the distribution of APDs in the ventricles. We implement a Monodomain tissue representation that includes orthotropic anisotropy, transmural fiber rotation and homogeneous or heterogeneous transmural intrinsic membrane properties, modeled according to the phase I Luo-Rudy membrane ionic model. Three-dimensional simulations are performed in a cartesian slab with a parallel finite element solver employing structured isoparametric trilinear finite elements in space and a semi-implicit adaptive method in time. Simulations of excitation and repolarization sequences elicited by epicardial or endocardial pacing show that in a homogeneous slab the repolarization pathways approximately follow the activation sequence. Conversely, in the heterogeneous cases considered in this study, we observed two repolarization wavefronts that started from the epi and the endocardial faces respectively and collided in the thickness of the wall and in one case an additional repolarization wave starting from an intramural site. Introducing the heterogeneities along the transmural epi-endocardial direction affected both the repolarization sequence and the APD dispersion, but these effects were clearly discernible only in transmural planes. By contrast, in planes parallel to epi- and endocardium the APD distribution remained remarkably similar to that observed in the homogeneous model. Therefore, the patterns of the repolarization sequence and APD dispersion on the epicardial surface (or any other intramural surface parallel to it) do not reveal the uniform transmural heterogeneity.     

Evaluation of transmural distribution of viable muscle by myocardial strain profile and dobutamine stress echocardiography

Transmural distribution of viable myocardium in the ischemic myocardium has not been quantified and fully elucidated. To address this issue, we evaluated transmural myocardial strain profile (TMSP) in dogs with myocardial infarction using a newly developed tissue strain imaging. TMSP was obtained from the posterior wall at the epicardial left ventricular short-axis view in 13 anesthetized open-chest dogs. After control measurements, the left circumflex coronary artery was occluded for 90 min to induce subendocardial infarction (SMI). Subsequently, latex microbeads (90 microm) were injected in the same artery to create transmural infarction (TMI). In each stage, measurements were done before and after dobutamine challenge (10 microg.kg(-1).min(-1) for 10 min) to estimate transmural myocardial viability. Strain in the subendocardium in the control stage increased by dobutamine (from 53.6 +/- 17.1 to 73.3 +/- 21.8%, P < 0.001), whereas that in SMI and TMI stages was almost zero at baseline and did not increase significantly by dobutamine [from 0.8 +/- 8.8 to 1.3 +/- 7.0%, P = not significant (NS) for SMI, from -3.9 +/- 5.6 to -1.9 +/- 6.0%, P = NS for TMI]. Strain in the subepicardium increased by dobutamine in the control stage (from 23.9 +/- 6.1 to 26.3 +/- 6.4%, P < 0.05) and in the SMI stage (from 12.4 +/- 7.3 to 27.1 +/- 8.8%, P < 0.005), whereas that in the TMI stage did not change (from -1.0 +/- 7.8 to -0.7 +/- 8.3%, P = NS). In SMI, the subendocardial contraction was lost, but the subepicardium showed a significant increase in contraction with dobutamine. However, in TMI, even the subepicardial increase was not seen. Assessment of transmural strain profile using tissue strain imaging was a new and useful method to estimate transmural distribution of the viable myocardium in myocardial infarction.     

Right ventricular regional wall curvedness and area strain in patients with repaired tetralogy of Fallot

A quantitative understanding of right ventricular (RV) remodeling in repaired tetralogy of Fallot (rTOF) is crucial for patient management. The objective of this study is to quantify the regional curvatures and area strain based on three-dimensional (3-D) reconstructions of the RV using cardiac magnetic resonance imaging (MRI). Fourteen (14) rTOF patients and nine (9) normal subjects underwent cardiac MRI scan. 3-D RV endocardial surface models were reconstructed from manually delineated contours and correspondence between end-diastole (ED) and end systole (ES) was determined. Regional curvedness (C) and surface area at ED and ES were calculated as well as the area strain. The RV shape and deformation in rTOF patients differed from normal subjects in several respects. Firstly, the curvedness at ED (mean for 13 segments, 0.030 ± 0.0076 vs. 0.029 ± 0.0065 mm(-1); P < 0.05) and ES (mean for 13 segments, 0.040 ± 0.012 vs. 0.034 ± 0.0072 mm(-1); P < 0.001) was decreased by chronic pulmonary regurgitation. Secondly, the surface area increased significantly at ED (mean for 13 segments, 982 ± 192 vs. 1,397 ± 387 mm(2); P < 0.001) and ES (mean for 13 segments, 576 ± 130 vs. 1,012 ± 302 mm(2); P < 0.001). In particular, rTOF patients had significantly larger surface area than that in normal subjects in the free wall but not for the septal wall. Thirdly, area strain was significantly decreased (mean for 13 segments, 56 ± 6 vs. 34 ± 7%; P < 0.0001) in rTOF patients. Fourthly, there were increases in surface area at ED (5,726 ± 969 vs. 6,605 ± 1,122 mm(2); P < 0.05) and ES (4,280 ± 758 vs. 5,569 ± 1,112 mm(2); P < 0.01) and decrease in area strain (29 ± 8 vs. 18 ± 8%; P < 0.001) for RV outflow tract. These findings suggest significant geometric and strain differences between rTOF and normal subjects that may help guide therapeutic treatment.     

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.     

Asynchrony of ventricular activation affects magnitude and timing of fiber stretch in late-activated regions of the canine heart

Abnormal electrical activation of the left ventricle results in mechanical dyssynchrony, which is in part characterized by early stretch of late-activated myofibers. To describe the pattern of deformation during "prestretch" and gain insight into its causes and sequelae, we implanted midwall and transmural arrays of radiopaque markers into the left ventricular anterolateral wall of open-chest, isoflurane-anesthetized, adult mongrel dogs. Biplane cineradiography (125 Hz) was used to determine the time course of two- and three-dimensional strains while pacing from a remote, posterior wall site. Strain maps were generated as a function of time. Electrical activation was assessed with bipolar electrodes. Posterior wall pacing generated prestretch at the measurement site, which peaked 44 ms after local electrical activation. Overall magnitudes and transmural gradients of strain were reduced when compared with passive inflation. Fiber stretch was larger at aortic valve opening compared with end diastole (P < 0.05). Fiber stretch at aortic valve opening was weakly but significantly correlated with local activation time (r(2) = 0.319, P < 0.001). With a short atrioventricular delay, fiber lengths were not significantly different at the time of aortic valve opening during ventricular pacing compared with atrial pacing. However, ejection strain did significantly increase (P < 0.05). We conclude that the majority of fiber stretch occurs after local electrical activation and mitral valve closure and is different from passive inflation. The increased shortening of these regions appears to be because of a reduced afterload rather than an effect of length-dependent activation in this preparation.