Regional myocardial perfusion and mechanics: a model-based method of analysis.

A new parametric model-based method has been developed that allows epicardial strain distributions to be computed on the left ventricular free wall in normal and ischemic myocardium and integrated with the regional distributions of anatomic and physiological measurements so that underlying relationships can be explored. An array of radiopaque markers was sewn on the anterior wall of the left ventricle (LV) in three anesthetized open-chest canines, and their positions were recorded using biplane video fluoroscopy before and 2 min after occlusion of the left anterior descending coronary artery. The three-dimensional (3D) anatomy of the LV and epicardial fiber angles were measured post-mortem using a 3D probe. A prolate spheroidal finite element model was fitted to the epicardial surface points (with <0.2 mm accuracy) and fiber angles (<5 degrees error). Regional myocardial blood flows (MBFs) were measured using fluorescent microspheres and fitted into the model (<0.3 ml min(-1) g(-1) error). Epicardial fiber and cross-fiber strain distributions were computed by allowing the model to deform from end-diastole to end-systole according to the recorded motion of the surface markers. Systolic fiber strain varied from -0.05 to 0.01 within the region of the markers during baseline, and regional MBF varied from 1.5 to 2.0 ml min(-1) g(-1). During 2 min ischemia, regional MBF was less than 0.3 ml min(-1) g(-1) in the ischemic region and 1.0 ml min(-1) g(-1) in the nonischemic region, and fiber strain ranged from 0.05 in the central ischemic zone to -0.025 in the remote nonischemic tissue. This analysis revealed a zone of impaired fiber shortening extending into the normally perfused myocardium that was significantly wider at the base than the apex. A validation analysis showed that a regularizing function can be optimized to minimize both fitting errors and numerical oscillations in the computed strain fields.

A three-dimensional finite element method for large elastic deformations of ventricular myocardium: I--Cylindrical and spherical polar coordinates.

A three-dimensional Galerkin finite element method was developed for large deformations of ventricular myocardium and other incompressible, nonlinear elastic, anisotropic materials. Cylindrical and spherical elements were used to solve axisymmetric problems with r.m.s. errors typically less than 2 percent. Isochoric interpolation and pressure boundary constraint equations enhanced low-order curvilinear elements under special circumstances (69 percent savings in degrees of freedom, 78 percent savings in solution time for inflation of a thick-walled cylinder). Generalized tensor products of linear Lagrange and cubic Hermite polynomials permitted custom elements with improved performance, including 52 percent savings in degrees of freedom and 66 percent savings in solution time for compression of a circular disk. Such computational efficiencies become significant for large scale problems such as modeling the heart.

A three-dimensional finite element method for large elastic deformations of ventricular myocardium: II--Prolate spheroidal coordinates.

A three-dimensional finite element method for nonlinear finite elasticity is presented using prolate spheroidal coordinates. For a thick-walled ellipsoidal model of passive anisotropic left ventricle, a high-order (cubic Hermite) mesh with 3 elements gave accurate continuous stresses and strains, with a 69 percent savings in degrees of freedom (dof) versus a 70-element standard low-order model. A custom mixed-order model offered 55 percent savings in dof and 39 percent savings in solution time compared with the low-order model. A nonsymmetric 3D model of the passive canine LV was solved using 16 high-order elements. Continuous nonhomogeneous stresses and strains were obtained within 1 hour on a laboratory workstation, with an estimated solution time of less than 4 hours to model end-systole. This method represents the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis.

An equibiaxial strain system for cultured cells.

We developed a device that applies homogeneous equibiaxial strains of 0-10% to a cell culture substrate and quantitatively verified transmission of substrate deformation to cultured cardiac cells. Clamped elastic membranes in both single-well and multiwell versions of the device are uniformly stretched by indentation with a plastic ring, resulting in strain that is directly proportional to the pitch-to-radius ratio. Two-dimensional deformations were measured by tracking fluorescent microspheres attached to the substrate and to cultured adult rat cardiac fibroblasts. For nominal stretches up to 18%, strains along circumferential and radial axes were equal in magnitude and homogeneously distributed with negligible shear. For 5% stretch, circumferential and radial strains in the substrate were 0.046 +/- 0.005 and 0.048 +/- 0.004 [not significant (NS)], respectively, and shear strain was 0.001 +/- 0.003 (NS). Calibration of both single-well and multiwell versions permits strain selection by device rotation. The reproducible application and quantification of homogeneous equibiaxial strain in cultured cells provides a quantitative approach for correlating mechanical stimuli to cellular transduction mechanisms.

Comparison of two techniques for measuring two-dimensional strain in rat left ventricles.

Measurements of regional deformation in the left ventricle are needed to understand the structural basis of ventricular function. Two techniques were employed to measure two-dimensional strain in the intact, beating rat heart. Rats were anesthetized and ventilated, and the chest of each rat was opened. Homogeneous two-dimensional strains were measured during the cardiac cycle relative to end diastole with either a triangle of miniature (0.3-0.5 mm) piezoelectric crystals implanted at midwall or with three epicardial surface markers imaged with a 60-Hz video system. Average heart rate was 303 +/- 37 beats/min, end-diastolic pressure was 2 +/- 2 mmHg, and peak-systolic pressure was 106 +/- 31 mmHg in all of the hearts. In general, strains during the cardiac cycle showed similar trends to those previously reported in the dog. The magnitudes of peak systolic cardiac strains on the epicardium and at midwall were -0.076 +/- 0.055, -0.068 +/- 0.014 (circumferential), -0.102 +/- 0.040, -0.082 +/- 0.039 (longitudinal), and 0.065 +/- 0.016, 0.064 +/- 0.043 (in-plane shear). There were mechanical side effects due to the crystal implantation that may limit the usefulness of this technique in its present form in the contracting rat heart. The epicardial surface technique does not have these side effects and will allow measurements of regional systolic cardiac function in rats with pathological interventions or genetic modifications that may alter regional ventricular function.

Distributed mechanics of the canine right ventricle: effects of varying preload.

Fundamental questions in the mechanics of the right ventricle (RV) include: what are the distributions of diastolic and systolic strains across the RV epicardium and how do these strains change with increasing preload? Arrays (approximately 4 x 4 cm) of 25 to 30 lead markers were sutured to the epicardium of the RV anterior free wall in 6 open-chest, anesthetized dogs. Biplane cinéradiography (16 mm, 120 fps) was used to track marker positions throughout the cardiac cycle as loading conditions were altered by intravenous volume infusion. Continuous two-dimensional nonhomogeneous deformations were estimated across the region by fitting high-order finite element surfaces to the three-dimensional marker coordinates in successive ciné frames. End-systolic strains referred to end-diastole did not change with increasing preload, but did exhibit considerable longitudinal variation, e.g. the principal strain associated with maximal shortening (E1) was more than twice as great nearer the apex (E1 = -0.18 +/- 0.08) than in more basal (E1 = -0.09 +/- 0.05) regions. However, large amounts of lengthening occurred during diastolic inflation. End-diastolic extensional strains referred to an unloaded configuration were moderate at low pressure (E2 = 0.13 +/- 0.08) but increased to large values at high preloads (E2 = 0.28 +/- 0.11). End-diastolic strains also showed considerable longitudinal variation, i.e. near the base lengthening (E2 = 0.31 +/- 0.13) tended to be much greater than near the apex (E2 = 0.15 +/- 0.12). These results indicate that both diastolic sarcomere lengths and systolic sarcomere shortening increase in proportion to diastolic loading leaving end-systolic sarcomere strains unchanged.

Effect of coronary artery reperfusion on transmural myocardial remodeling in dogs.

BACKGROUND: The effects of reperfusion after coronary occlusion on transmural remodeling of the ischemic region early and late after nontransmural infarction must importantly affect the recovery of regional function. Accordingly, analysis of local volume and three-dimensional strain was performed using a finite element method to determine regional remodeling. Systolic and remodeling strains were measured using radiographic imaging of three columns (approximately 1 cm apart) of four to six gold beads implanted across the left ventricular posterior wall in 6 dogs. METHODS AND RESULTS: After a control study, infarction was produced by 2 to 4 hours of proximal left circumflex coronary artery occlusion followed by reperfusion. Follow-up studies were performed at 2 days, 3 weeks, and 12 weeks with the dogs under anesthesia and in closed-chest conditions. Biplane cineradiography was performed to obtain the three-dimensional coordinates of the beads. At 2 days, end-systolic strains were akinetic with loss of normal transmural gradients of shortening and thickening. Remodeling strains (RS) were determined by use of a nonhomogeneous finite element method by referring the end-diastolic configuration during follow-up studies to its control state at matched end-diastolic pressures and heart rates. Tissue volume at 2 days increased substantially, more at the endocardium (30 +/- 7%) than at the epicardium (5 +/- 12%, P < .01); the increase was associated with an average RS in the wall-thickening direction of 0.18 +/- 0.15 (P < .01) with all other RS near zero. At 12 weeks systolic function partially recovered, with normal wall thickening in the epicardium (radial strain, 0.081 +/- 0.056 [control] versus 0.113 +/- 0.088 [12 weeks]) but with dysfunction in the endocardium (0.245 +/- 0.108 [control] versus 0.111 +/- 0.074 [P < .01] [12 weeks]). This inability of the inner wall to recover function may be related to increased transmural torsional shear and negative longitudinal-radial transverse shear in the inner wall. Volume loss occurred at 12 weeks in the endocardium (-36 +/- 16%) corresponding to transmural gradients in longitudinal RS and both transverse shear RS. Negative longitudinal RS was greater at the endocardium (-0.20 +/- 0.10) than at the epicardium (-0.06 +/- 0.05, P < .01). CONCLUSIONS: These results indicate the presence of marked subendocardial edema 2 days after reperfusion following 2 to 4 hours of coronary occlusion. At 3 months after reperfusion, however, there was volume loss in the inner wall due to shrinkage along the myofiber direction with reduced transmural function and loss of longitudinal shortening, while both tissue volume and function recovered completely in the outer wall.

Gradients of epicardial strain across the perfusion boundary during acute myocardial ischemia.

To study the mechanical interaction between acutely ischemic and adjacent perfused myocardium, nonhomogeneous distributions of end-systolic epicardial strain were measured using an array of radiopaque beads sewn on the left ventricular free wall of the pig during complete left circumflex coronary artery occlusion. The midwall perfusion boundary, demarcated by postmortem dye injection, was reconstructed over the span of the epicardial array. During ischemia, circumferential and longitudinal shortening remained significantly depressed up to 13 mm outside the ischemic region near the base of the ventricle, up to 8-9 mm at the midventricle, but only 0-1 mm near the apex (P < 0.05). Gradients of circumferential and longitudinal strain across the boundary were significantly different during both baseline conditions and acute ischemia (P = 0.0001). However, gradients of the change in the strain from baseline to ischemia were not different for the two components. These results support the concept that direction-dependent differences in the strain gradients across the boundary during ischemia were due to the preservation of the baseline regional variations of strain combined with a loss of systolic function in the ischemic region.

Scar remodeling and transmural deformation after infarction in the pig.

BACKGROUND: Changes in stress and tissue material properties have been proposed as important mechanical factors that may influence infarct expansion and subsequent healing. Because such changes will be reflected by alterations in the finite deformation of the tissue, we examined the direction and magnitude of myocardial deformation after coronary ligation in the pig. METHODS AND RESULTS: Gold beads were implanted in the left ventricular free wall of five pigs. After ligation of the coronary supply to the region containing the markers, we used biplane cineradiography to reconstruct the three-dimensional deformations of the myocardium during single cardiac cycles as well as the remodeling deformations that occurred over time. Deformations were studied at 1 and 3 weeks after infarction. The analysis of single cardiac cycles revealed permanent loss of systolic shortening immediately after ligation. However, significant passive systolic wall thickening (P < .001) and large shears were observed at 3 weeks in regions composed almost entirely of collagen. The analysis of remodeling deformations at 1 week revealed infarct expansion with a predominant axis that varied widely. At 3 weeks, a 30% to 60% reduction in local tissue volume was measured in the infarct region, with the principal direction of scar shrinkage nearly circumferential in all animals (range, -2 degrees to 35 degrees). CONCLUSIONS: We conclude that infarct expansion and scar shrinkage may be controlled by different factors. In addition, we conclude that measurement of systolic wall thickening alone is not always adequate to assess postinfarction regional contractile function.

Nonhomogeneous ventricular wall strain: analysis of errors and accuracy.

Nonhomogeneous distributions of strains are simulated and utilized to determine two potential errors in the measurement of cardiac strains. First, the error associated with the use of single-plane imaging of myocardial markers is examined. We found that this error ranges from small to large values depending on the assumed variation in stretch. If variations in stretch are not accompanied by substantial regional changes in ventricular radius, the associated error tends to be quite small. However, if the nonuniform stretch field is a result of substantial variations in local curvature from their reference values, large errors in stretch and strain occur. For canine hearts with circumferential radii of 2 to 4 cm, these errors in stretch may be as great as 30 percent or more. Moreover, gradients in stretch may be over- or underestimated by as much as 100 percent. In the second part of this analysis, the influence of random measurement errors in the coordinate positions of markers on strains computed from them is studied. Arrays of markers covering about 16 cm2 of ventricular epicardium are assumed and nonuniform stretches imposed. The reference and deformed positions of the markers are perturbed with Gaussian noise with a standard deviation of 0.1 mm, and then strains are computed using either homogeneous strain theory or a nonhomogeneous finite element method. For the strain distributions prescribed, it is found that the finite element method reduces the error resulting from noise by about 50 percent over most of the region. Accurate measurements of cardiac strain distributions are needed for correlation with and validation of realistic three-dimensional stress analyses of the heart.(ABSTRACT TRUNCATED AT 250 WORDS)

Effect of residual stress on transmural sarcomere length distributions in rat left ventricle.

It has been previously shown that the myocardium in the walls of the unloaded passive left ventricle (LV) is not stress free. To assess the functional significance of residual stress in the ventricular wall, we compared the transmural distributions of sarcomere length (SL) in specimens of rat LV myocardium fixed in the unloaded (residually stressed) and stress-free states. When a cross-sectional ring cut from the equatorial region of the freshly arrested rat hearts was cut radially to relieve residual stress, it sprang open into an arc with a mean opening angle of 45 +/- 15 degrees (SD) (n = 8). During immersion fixation in glutaraldehyde, the opening angle increased 9.3 +/- 7.1 degrees (SD) overall. SLs were measured at 16 equally spaced transmural locations from the free wall in the stress-free tissue sections and were compared with control measurements from adjacent cross-sectional rings in which residual stress had not been relieved. Average SL for the stress-free tissue (n = 11) was 1.84 +/- 0.05 (SD) microns and for the unloaded tissue was 1.83 +/- 0.06 (SD) microns. However, analysis of covariance on the pooled data showed that the transmural distributions were significantly different (P < 0.0001). Whereas SL was uniform across the wall in the stress-free state with a mean gradient of -0.014 +/- 0.044 (SD) microns/total wall thickness, there was a significant decrease (P = 0.001) in SL from epicardium to endocardium in the intact unloaded tissue [slope = -0.114 +/- 0.054 (SD) microns/total wall thickness].(ABSTRACT TRUNCATED AT 250 WORDS)

Mechanics of active contraction in cardiac muscle: Part II--Cylindrical models of the systolic left ventricle.

Models of contracting ventricular myocardium were used to study the effects of different assumptions concerning active tension development on the distributions of stress and strain in the equatorial region of the intact left ventricle during systole. Three models of cardiac muscle contraction were incorporated in a cylindrical model for passive left ventricular mechanics developed previously [Guccione et al. ASME Journal of Biomechanical Engineering, Vol. 113, pp. 42-55 (1991)]. Systolic sarcomere length and fiber stresses predicted by a general "deactivation" model of cardiac contraction [Guccione and McCulloch, ASME Journal of Biomechanical Engineering, Vol. 115, pp. 72-81 (1993)] were compared with those computed using two less complex models of active fiber stress: In a time-varying "elastance" model, isometric tension development was computed from a function of peak intracellular calcium concentration, time after contraction onset and sarcomere length; a "Hill" model was formulated by scaling this isometric tension using the force-velocity relation derived from the deactivation model. For the same calcium ion concentration, the sarcomeres in the deactivation model shortened approximately 0.1 microns less throughout the wall at end-systole than those in the other models. Thus, muscle fibers in the intact ventricle are subjected to rapid length changes that cause deactivation during the ejection phase of a normal cardiac cycle. The deactivation model predicted rather uniform transmural profiles of fiber stress and cross-fiber stress distributions that were almost identical to those of the radial component. These three components were indistinguishable from the principal stresses. Transmural strain distributions predicted at end-systole by the deactivation model agreed closely with experimental measurements from the anterior free wall of the canine left ventricle.

Nonhomogeneous analysis of epicardial strain distributions during acute myocardial ischemia in the dog.

To study the nonuniform mechanical function that occurs in normal and ischemic ventricular myocardium, a new method has been developed and validated. An array of 25 lead markers (approximately 4 x 4 cm) was sewn onto the epicardium of the anterior free wall of the left ventricle in an open-chest, anesthetized canine preparation. Biplane cineradiography was used to track marker positions throughout the cardiac cycle before and during episodes of acute ischemia induced by occlusion of the left anterior descending coronary artery. To estimate two-dimensional nonhomogeneous deformations in the region at risk and its border zone with normally perfused tissue, surfaces defined by bicubic Hermite isoparametric finite element interpolation were fitted by least squares to the three-dimensional marker coordinates in successive cine frames. Global smoothing functions prevented ill-conditioning in areas of low marker density. Continuous distributions of systolic finite strains referred to the end-diastolic state were obtained under normal and ischemic conditions without the conventional assumption of homogeneous strain analysis. Substantial regional variations in epicardial strains were observed in both the normal and ischemic heart. The method was validated in regions of small to moderate strain variations by comparing the continuous distributions of strain components with piecewise-constant measurements made using marker triplets and homogeneous strain theory. The influence of marker density was examined by recomputing strains from surfaces fitted to subsets of the original array. Further validation of moderate to large strain variations was obtained by simulating a nonuniform distribution of stretch across a planar sheet and computing strains both analytically and using the current method. The new method allows for more comprehensive measurements of distributed ventricular function, providing a tool with which to quantify better the nonhomogeneous function associated with regional ischemia.

Passive material properties of intact ventricular myocardium determined from a cylindrical model.

The equatorial region of the canine left ventricle was modeled as a thick-walled cylinder consisting of an incompressible hyperelastic material with homogeneous exponential properties. The anisotropic properties of the passive myocardium were assumed to be locally transversely isotropic with respect to a fiber axis whose orientation varied linearly across the wall. Simultaneous inflation, extension, and torsion were applied to the cylinder to produce epicardial strains that were measured previously in the potassium-arrested dog heart. Residual stress in the unloaded state was included by considering the stress-free configuration to be a warped cylindrical arc. In the special case of isotropic material properties, torsion and residual stress both significantly reduced the high circumferential stress peaks predicted at the endocardium by previous models. However, a resultant axial force and moment were necessary to cause the observed epicardial deformations. Therefore, the anisotropic material parameters were found that minimized these resultants and allowed the prescribed displacements to occur subject to the known ventricular pressure loads. The global minimum solution of this parameter optimization problem indicated that the stiffness of passive myocardium (defined for a 20 percent equibiaxial extension) would be 2.4 to 6.6 times greater in the fiber direction than in the transverse plane for a broad range of assumed fiber angle distributions and residual stresses. This agrees with the results of biaxial tissue testing. The predicted transmural distributions of fiber stress were relatively flat with slight peaks in the subepicardium, and the fiber strain profiles agreed closely with experimentally observed sarcomere length distributions. The results indicate that torsion, residual stress and material anisotropy associated with the fiber architecture all can act to reduce endocardial stress gradients in the passive left ventricle.

Transmural myocardial deformation in the ischemic canine left ventricle.

The myocardium is a complex three-dimensional structure consisting of myocytes interconnected by a dense collagen weave that courses in different directions. Regional ischemia can be expected to produce complex changes in ventricular deformation. In the present study, we examined the effects of ischemia on two- and three-dimensional finite strains during acute transmural myocardial ischemia in 13 open-chest anesthetized dogs. In contrast to systolic deformation observed during the control period in which circumferential shortening exceeded longitudinal shortening, our results indicate that after 5 minutes of acute ischemia, end-systolic in-plane lengthening across the left ventricular wall occurs in approximately equal amounts in the circumferential and longitudinal directions. Along with these changes in extensional strains, there were significant negative transverse shearing deformations during ischemia. Myocardial ischemia also resulted in a loss of the normal end-systolic transmural gradients of shortening and thickening. Three-dimensional end-diastolic strains indicate that the left ventricular wall undergoes a significant passive reconfiguration that varies transmurally with lengthening in the epicardial tangent plane and wall thinning increasing from the epicardium toward the endocardium. The large systolic changes in shearing deformations with ischemia could potentially influence collateral blood flow and certainly indicate that uniaxial measurements of deformation in the ischemic myocardium, which do not account for shearing deformation, are incomplete and must be interpreted with caution. Moreover, normal transmural systolic gradients in deformation, which would be anticipated on geometric grounds, are lost during ischemia, implying that the material properties of ischemic tissue or the loading conditions imposed on the ischemic region by partially impaired adjacent myocardium vary transmurally.

Relation between transmural deformation and local myofiber direction in canine left ventricle.

To determine the relation between local myofiber anatomy and local deformation in the wall of the left ventricle, both three-dimensional transmural deformation and myofiber orientation were examined in the anterior free wall of seven canine left ventricles. Deformation was measured by imaging columns of implanted radiopaque markers with high-speed, biplane cineradiography (16 mm, 120 frames/sec). Hearts were fixed at end diastole and sectioned parallel to the local epicardial tangent plane to determine the transmural distribution of fiber directions at the site of strain measurement. The principal direction of deformation associated with the greatest shortening was compared with the local fiber direction in the outer (21 +/- 8% of the wall thickness from the epicardium) and inner (65 +/- 9%) halves of the wall. Although the fiber direction varied substantially with depth from the epicardium, the principal direction did not. In the outer half of the wall, fiber direction averaged -8 +/- 24 degrees, while the principal direction averaged -33 +/- 24 degrees from circumferential (counterclockwise angles are positive). In the inner half, fiber direction averaged 69 +/- 10 degrees, while the principal direction averaged -22 +/- 21 degrees. Therefore, while fiber and principal directions were not substantially different in the outer half, the greatest shortening occurred orthogonally to the fiber direction in the inner half. Normal and shear strains measured in a cardiac coordinate system (circumferential, longitudinal, and radial coordinates) were rotated (transformed) to "fiber" coordinates in both halves of the wall. In the outer half, normal strains observed in the fiber (-0.09 +/- 0.04) and cross-fiber (-0.04 +/- 0.04) directions were not significantly different (paired t test, p less than 0.05). In the inner half, more than twice as much strain occurred in the cross-fiber (-0.17 +/- 0.03) than in the fiber direction (-0.06 +/- 0.06). Moreover, the only shear strain that remained substantial after transformation was transverse shear in the plane of the fiber and radial coordinates. These results suggest that both reorientation and cross-sectional shape changes of myofibers or the interstitium may contribute to the large wall thickenings observed during contraction, particularly in the inner half of the ventricular wall.

Technique for measuring regional two-dimensional finite strains in canine left ventricle.

We developed a technique to measure regional two-dimensional deformations in the myocardium. Three piezoelectric crystals were implanted in a triangular array in the left ventricular anterior midwall in six anesthetized dogs. Each crystal was used in a dual function, to both transmit and receive ultrasonic signals from the other two crystals. In this manner, the three segment lengths of the crystal triangle throughout the cardiac cycle were simultaneously recorded. The orientation of the crystal triangle with reference to the left ventricular long and minor axes was determined. The orientation and three segment lengths of the crystal triangle were used to calculate the circumferential strain E11, the longitudinal strain E22, the in-plane shear strain E12, and the mutually perpendicular principal strains E1 and E2. Also, the orientation of the first principal direction or the in-plane angle was determined, which was defined as the angle between the first principal direction (E1) and the circumferential direction (0 degree). This information fully describes the regional two-dimensional myocardial deformations. This technique was applied to measure regional myocardial deformations at three different left ventricular end-diastolic pressures (LVEDP) of 2 +/- 1 (mean +/- SD), 8 +/- 1, and 17 +/- 2 mm Hg. The first principal direction at end-systole was oriented away from the circumferential direction at low LVEDP (-43 +/- 21 degrees) but became progressively closer in each animal to the circumferential direction as LVEDP increased to mid (-26 +/- 18 degrees) and high (-14 +/- 13 degrees) levels. The end-systolic ratio E11/E1 was 0.6 +/- 0.2 at low LVEDP, but increased toward unity in each animal to 0.9 +/- 0.1 at mid and high LVEDP. Thus, at low LVEDP, the greatest systolic deformation occurred in a direction different from the circumferential orientation. Therefore, circumferential strain measurements (E11) significantly underestimated the greatest systolic deformation (E1). However, as LVEDP increased, the first principal direction rotated closer toward the circumferential orientation, and circumferential strain measurements adequately estimated the greatest systolic deformation. Nevertheless, the presence of significant amounts of shortening along either the longitudinal (E22) or the second principal direction (E2) in the midwall necessitated the use of the two-dimensional method. The change in end-diastolic configuration as LVEDP increased from 1 +/- 1 to 16 +/- 1 mm Hg was also examined. Unlike the end-systolic data, the end-diastolic first principal direction did not deviate significantly from the circumferential direction at any LVEDP.(ABSTRACT TRUNCATED AT 400 WORDS)

Effects of ventricular pacing on finite deformation in canine left ventricles.

Despite the fact that myofibers would be expected to shorten only along their axes, there is now evidence for substantial deformation away from the local myofiber direction in the left ventricle. To determine if the principal directions of deformation could be altered by a physiological stimulus, we examined local three-dimensional finite deformation in the anterior free wall of the left ventricle during normal atrial activation (AA) and, subsequently, during epicardial ventricular pacing (VP) at the site of deformation measurement in open-chest anesthetized dogs. An analysis of variance by repeated measures revealed the following significant changes (P less than or equal to 0.05) in the overall (average of epicardial and endocardial data) strain variables at end systole. Circumferential strain increased from -0.07 (AA) to 0.14 (VP), radial strain decreased from 0.16 (AA) to 0.01 (VP), shear in the tangent plane of the local epicardium decreased from 0.04 (AA) to -0.02 (VP), shear in the plane of the longitudinal and radial coordinates decreased from 0.03 (AA) to -0.03 (VP). Neither the first (greatest shortening) nor the third (greatest lengthening) principal strain changed significantly, but the direction of the first principal axis of deformation projected on the epicardial tangent plane changed from -51 degrees (AA) to -80 degrees (VP) from circumferential. In addition, substantial tipping of the plane of principal shortening away from the epicardial tangent plane was observed, particularly with ventricular pacing. These data indicate that the principal directions of deformation can be altered substantially by changing the activation sequence. In conjunction with the observed shearing deformations, particularly near the endocardium, they support the concept that locally the heart wall deforms as a unit with significant transmural tethering.

Transmural myocardial deformation in the canine left ventricle. Normal in vivo three-dimensional finite strains.

To examine transmural finite deformation in the wall of the canine left ventricle, closely spaced columns of lead beads were implanted at a single site on the left ventricular free wall. The three-dimensional coordinates of these myocardial markers were obtained with high-speed biplane cineradiography. Any four noncoplanar markers forming small tetrahedral volumes (less than or equal to 0.1 cc) were used to calculate finite normal and shear strains with respect to a cardiac coordinate system at end diastole. Due to the symmetry of the finite strain tensor, the algebraic eigenvalue problem could be solved to compute principal strains and the directions of the principal axes of deformation with respect to the reference coordinates. An examination of the principal strains in a number of tetrahedra in five animals indicates that deformation increases with depth beneath the epicardium. For example, the transmural variation of principal shortening strain averages -0.014 +/- 0.009 per 10% increment in thickness from epicardium to endocardium. Furthermore, shortening and thickening strains at midwall and deeper are too large (0.10 to 0.40) to be described accurately by infinitesimal theory. These strains are often accompanied by substantial in-plane and transverse shears which are not predicted by typical membrane or shell theories, indicating that these theories must be applied with caution when computing indices of regional ventricular performance. The directions of the principal axes of shortening vary substantially less than the fiber direction varies across the wall (20 degrees - 40 degrees compared with 100 degrees - 140 degrees for fiber direction), supporting the concept that there are substantial interactions between neighboring fibers in the left ventricular wall.