Caveolae in ventricular myocytes are required for stretch-dependent conduction slowing

Mechanical stretch of cardiac muscle modulates action potential propagation velocity, causing potentially arrhythmogenic conduction slowing. The mechanisms by which stretch alters cardiac conduction remain unknown, but previous studies suggest that stretch can affect the conformation of caveolae in myocytes and other cell types. We tested the hypothesis that slowing of action potential conduction due to cardiac myocyte stretch is dependent on caveolae. Cardiac action potential propagation velocities, measured by optical mapping in isolated mouse hearts and in micropatterned mouse cardiomyocyte cultures, decreased reversibly with volume loading or stretch, respectively (by 19±5% and 26±4%). Stretch-dependent conduction slowing was not altered by stretch-activated channel blockade with gadolinium or by GsMTx-4 peptide, but was inhibited when caveolae were disrupted via genetic deletion of caveolin-3 (Cav3 KO) or membrane cholesterol depletion by methyl-β-cyclodextrin. In wild-type mouse hearts, stretch coincided with recruitment of caveolae to the sarcolemma, as observed by electron microscopy. In myocytes from wild-type but not Cav3 KO mice, stretch significantly increased cell membrane capacitance (by 98±64%), electrical time constant (by 285±149%), and lipid recruitment to the bilayer (by 84±39%). Recruitment of caveolae to the sarcolemma during physiologic cardiomyocyte stretch slows ventricular action potential propagation by increasing cell membrane capacitance.

Cardiac resynchronization: insight from experimental and computational models

Cardiac resynchronization therapy (CRT) is a promising therapy for heart failure patients with a conduction disturbance, such as left bundle branch block. The aim of CRT is to resynchronize contraction between and within ventricles. However, about 30% of patients do not respond to this therapy. Therefore, a better understanding is needed for the relation between electrical and mechanical activation. In this paper, we focus on to what extent animal experiments and mathematical models can help in order to understand the pathophysiology of asynchrony to further improve CRT.

Complex distributions of residual stress and strain in the mouse left ventricle: experimental and theoretical models

Most soft biological tissues, including ventricular myocardium, are not stress free when all external loads are removed. Residual stress has implications for mechanical performance of the heart, and may be an indicator of patterns of regional growth and remodeling. Cross-sectional rings of arrested ventricles opened up when a radial cut was made (initial mean opening angles were 64 +/- 17 degrees), but further circumferential cuts revealed the presence of additional residual stresses in the tissue with further opening of the rings. In normal mouse hearts, the inner half of a short-axis ring opened more than the outer half, and this change was dependent on apex-base location. At the apex the inner section vs. outer section opening angles were 226 +/- 47 degrees vs. 89 +/- 28 degrees, while at the base the same two angles were 160 +/- 30 degrees vs. 123 +/- 35 degrees. A simple theoretical cylindrical shell model with incompressible hyperelastic material properties was used to model the experimental deformations based on the cutting experiments. The model predicts different residual stress fields depending on the nature of the opening after the circumferential cut (which is done after the conventional radial cut). The observed opening angles were consistent with steep stress gradients near the endocardium compared with those predicted if the first cut was assumed to relieve all residual stresses. These results imply a more complex distribution of residual stress and strain in ventricular myocardium than previously thought.

Regional septal dysfunction in a three-dimensional computational model of focal myofiber disarray

MLC2v/ras transgenic mice display a phenotype characteristic of hypertrophic cardiomyopathy, with septal hypertrophy and focal myocyte disarray. Experimental measurements of septal wall mechanics in ras transgenic mice have previously shown that regions of myocyte disarray have reduced principal systolic shortening, torsional systolic shear, and sarcomere length. To investigate the mechanisms of this regional dysfunction, a three-dimensional prolate spheroidal finite-element model was used to simulate filling and ejection in the hypertrophied mouse left ventricle with septal disarray. Focally disarrayed septal myocardium was modeled by randomly distributed three-dimensional regions of altered material properties based on measured statistical distributions of muscle fiber angular dispersion. Material properties in disarrayed regions were modeled by decreased systolic anisotropy derived from increased fiber angle dispersion and decreased systolic tension development associated with reduced sarcomere lengths. Compared with measurements in ras transgenic mice, the model showed similar heterogeneity of septal systolic strain with the largest reductions in principal shortening and torsional shear in regions of greatest disarray. Average systolic principal shortening on the right ventricular septal surface of the model was -0.114 for normal regions and -0.065 for disarrayed regions; for torsional shear, these values were 0.047 and 0.019, respectively. These model results suggest that regional dysfunction in ras transgenic mice may be explained in part by the observed structural defects, including myofiber dispersion and reduced sarcomere length, which contributed about equally to predicted dysfunction in the disarrayed myocardium.

Transmural distribution of three-dimensional systolic strains in stunned myocardium

BACKGROUND

Regional function in stunned myocardium is usually thought to be more depressed in the endocardium than the epicardium. This has been attributed to the greater loss of blood flow at the endocardium during ischemia.

METHODS AND RESULTS

We measured transmural distributions of 3D systolic strains relative to local myofiber axes in open-chest anesthetized dogs before 15 minutes of left anterior descending coronary artery occlusion and during 2 hours of reperfusion. During ischemia, regional myocardial blood flow was reduced 84% at the endocardium and 32% at the epicardium (P<0.005, n=7), but changes in end-systolic fiber length from baseline were transmurally uniform. Relative to baseline, radial segments in stunned tissue were significantly thinner at the endocardium than the epicardium at end systole (24+/-5% versus 16+/-3%; P<0.05, n=8), consistent with previous reports. Unlike radial and cross-fiber segments, however, the increase of end-systolic fiber lengths in stunned myocardium had no significant transmural gradient (23+/-8% epicardium versus 21+/-4% endocardium). We also observed significant 3D diastolic dysfunction in the ischemic-reperfused region transmurally.

CONCLUSIONS

Myocardial ischemia/reperfusion in the dog results in a significant transmural gradient of dysfunction between epicardial and endocardial layers in radial and cross-fiber segments, but not for fiber segments, despite a gradient in blood flow reduction during ischemia. Perhaps systolic fiber dysfunction rather than the degree of perfusion deficit during the preceding ischemic period may be the main determinant of myocardial dysfunction during reperfusion.

Age-Associated Cardiac Dysfunction in Drosophila melanogaster

Abstract —The fruit fly, Drosophila melanogaster , has served as a valuable model/organism for the study of aging and was the first organism possessing a circulatory system to have its genome completely sequenced. However, little is known about the function of the heartlike organ of flies during the aging process. We have developed methods for studying cardiac function in vivo in adult flies. Using 2 different cardiovascular stress methods (elevated ambient temperature and external electrical pacing), we found that maximal heart rate is significantly and reproducibly reduced with aging in Drosophila , analogous to observations in elderly humans. We also describe for the first time several other aspects of the cardiac physiology of young adult and aging Drosophila , including an age-associated increase in rhythm disturbances. These observations suggest that the study of declining cardiac function in aging flies may serve as a genetically tractable model for genome-wide mutational screening for genes that participate in or protect against cardiac aging and disease.

Myocardial mechanics and collagen structure in the osteogenesis imperfecta murine (oim)

Because the amount and structure of type I collagen are thought to affect the mechanics of ventricular myocardium, we investigated myocardial collagen structure and passive mechanical function in the osteogenesis imperfecta murine (oim) model of pro-alpha2(I) collagen deficiency, previously shown to have less collagen and impaired biomechanics in tendon and bone. Compared with wild-type littermates, homozygous oim hearts exhibited 35% lower collagen area fraction (P:<0.05), 38% lower collagen fiber number density (P:<0.05), and 42% smaller collagen fiber diameter (P:<0.05). Compared with wild-type, oim left ventricular (LV) collagen concentration was 45% lower (P:<0.0001) and nonreducible pyridinoline cross-link concentration was 22% higher (P:<0.03). Mean LV volume during passive inflation from 0 to 30 mm Hg in isolated hearts was 1.4-fold larger for oim than wild-type (P:=NS). Uniaxial stress-strain relations in resting right ventricular papillary muscles exhibited 60% greater strains (P:<0.01), 90% higher compliance (P:=0.05), and 64% higher nonlinearity (P:<0.05) in oim. Mean opening angle, after relief of residual stresses in resting LV myocardium, was 121+/-9 degrees in oim compared with 45+/-4 degrees in wild-type (P:<0.0001). Mean myofiber angle in oim was 23+/-8 degrees greater than wild-type (P:<0.02). Decreased myocardial collagen diameter and amount in oim is associated with significantly decreased fiber and chamber stiffness despite modestly increased collagen cross-linking. Altered myofiber angles and residual stress may be beneficial adaptations to these mechanical alterations to maintain uniformity of transmural fiber strain. In addition to supporting and organizing myocytes, myocardial collagen contributes directly to ventricular stiffness at high and low loads and can influence stress-free state and myofiber architecture.

Model-based analysis of optically mapped epicardial activation patterns and conduction velocity

A novel parametric model-based method was developed to quantify epicardial conduction patterns and velocity in an isolated Langendorff-perfused rabbit heart. The method incorporated geometric and anatomical features of the left and right ventricles into the analysis. Optical images of propagation were obtained using the voltage-sensitive dye DI-4-ANEPPS, and a high-speed digital camera. Activation maps were extracted from these images and interpolated onto a three-dimensional finite-element model of epicardial geometry and fiber structure. Activation time was expressed as a function of local parametric coordinates, and a conduction velocity vector field was computed from the gradient of the scalar field. Activation times measured using bipolar electrodes did not differ significantly from times measured using the optical mapping technique. The method was able to detect a 34% decrease in average fiber velocity and a 28% decrease in average cross-fiber velocity following the addition of 0.5 mM heptanol into the perfusate. The combination of optical mapping with a three-dimensional geometric model of the ventricles provides a new tool to quantify wave-front propagation relative to anatomy at a relatively high spatial resolution.

Structural basis of regional dysfunction in acutely ischemic myocardium

OBJECTIVE

Impaired systolic function in the normally perfused myocardium adjacent to an ischemic region - the functional border zone - is thought to result from mechanical interactions across the perfusion boundary. We investigated how segment orientation and vessel involved affect regional strains in the functional border zone and whether altered stresses associated with a step transition in contractility can explain the functional border zone.

METHODS AND RESULTS

Regional epicardial strain distributions were obtained from measured displacements of radiopaque markers in open-chest anesthetized canines, and related to local myofiber angles and blood flows. The functional border zone for fiber strain was significantly narrower than that for cross-fiber strain and significantly wider for left anterior descending (LAD) than left circumflex (LCx) coronary occlusion (1.23 vs. 0.45 cm). A detailed three-dimensional computational model with a one-to-one relation between perfusion and myofilament activation and no transitional zone of intermediate contractility showed close agreement with these observations and significantly elevated stresses in the border zone. Differences between LAD and LCx occlusions in the model were due to differences in left ventricular systolic pressure and not to differences in perfusion boundary or muscle fiber orientation. The border zone was narrower for fiber strain than cross-fiber strain because systolic stiffness is greatest along the muscle fiber direction.

CONCLUSION

Abnormal regional mechanics in the acute ischemic border arise from increased wall stresses without a transitional zone of intermediate contractility. Perfusion is more tightly coupled to fiber than cross-fiber strain, and a wider functional border zone of fiber strain during LAD than LCx occlusion is primarily due to higher regional wall stresses rather than anatomic variations.

Regional dysfunction correlates with myofiber disarray in transgenic mice with ventricular expression of ras

A hallmark of certain cardiac diseases such as familial hypertrophic cardiomyopathy is focal myofiber disarray. Regional ventricular dysfunction occurs in human subjects with hypertrophic cardiomyopathy; however, no direct evidence exists to correlate regional dysfunction with myofiber disarray. We used a transgenic mouse, which exhibits regional myofiber disarray via ventricular expression of the human oncogene ras, to investigate the relationship between myofiber disarray and septal surface strain. An isolated ejecting mouse heart preparation was used to record deformation of markers on the septal surface and to determine nonhomogeneous septal surface strain maps. Myofiber disarray made in histological tissue sections was correlated with gradients in surface systolic shortening. Significantly smaller maximum principal shortening was associated with disarray located near the right ventricle (RV) septal surface. There was also significantly smaller surface shear strain associated with disarray located either near the RV surface or at the midwall. Because surface shear is a local indicator of torsion, we conclude that myofiber disarray is associated with reduced septal torsion and reduced surface shortening.

Structural and mechanical factors influencing infarct scar collagen organization

Although large collagen fibers in myocardial infarct scar are highly organized, little is known about mechanisms controlling this organization. The preexisting extracellular matrix may act as a scaffold along which fibroblasts migrate. Conversely, deformation within the ischemic area could guide fibroblasts so new collagen is oriented to counteract the stretch. To investigate these potential mechanisms, we infarcted three groups of pigs. Group 1 served as infarct controls. Group 2 had the endocardium slit longitudinally to alter local systolic deformation. Group 3 had a plug sectioned from ischemic tissue and rotated 90 degrees. The slit altered systolic deformation in the infarcted tissue, changing circumferential strain from expansion to compression and increasing radial strain and shears and the variability of collagen fiber angles but not the mean angle. In the plug pigs, when deformation, matrix orientation, and continuity are altered in the infarct area, the result is complete disarray in the organization of collagen within the infarct scar.

Measurement of orientation and distribution of cellular alignment and cytoskeletal organization

Endothelial cells elongate and align with the direction of applied fluid shear stress. Previously, automated methods for analysis of cell orientation distribution have used Fourier- or fractal-based methods. We used intensity gradients in images of control and sheared endothelial cells to measure orientation distributions. Automated measurements of mean orientation and angular deviation compared favorably with manual measurements. There was a significantly greater angular deviation in images of control cells compared with sheared cells. Automated methods were also used to quantify organization of cytoskeletal fibers using the local angular deviation and a measure of the local coalignment of fibers called the coalignment ratio. The local angular deviation of microtubules and microfilaments was significantly smaller in sheared cells compared with control. The coalignment of cytoskeletal fibers was significantly greater in sheared cells. We conclude that image intensity gradients can be used rapidly, accurately, and objectively to measure cell orientation distributions and cytoskeletal filament organization.

Automated measurement of myofiber disarray in transgenic mice with ventricular expression of ras

Quantitative assessment of myofiber disarray associated with diseases such as familial hypertrophic cardiomyopathy (FHC) can be performed by estimating local angular deviation of fiber orientation in histologic sections. The large number of measurements required to estimate angular deviation prohibits manual measurement. We describe methods for automated measurement of local orientation and angular deviation in tissue sections from transgenic mice with ventricular expression of ras, proposed as a model of FHC. Images of histologic tissue sections from normal and transgenic mice were analyzed using image processing techniques to estimate local orientation of myofibers. Results from the automated methods were compared with manual measurements. Automated methods estimated differing mean orientation in 7-20% of normal sections and 17-29% of transgenic tissue sections with differing dispersions in 23-30% of normal sections and 25% of transgenic tissue sections. Automated methods estimate 24.47+/-13.03% of total ventricular mass affected by disarray that is comparable to a previous estimate of 21.7% in the same mouse model. Automated methods are a rapid and accurate alternative to manual measurement for estimation of mean orientation and angular deviation in myocardial tissue sections. Differences between manual and automated methods may be attributed to the substantially larger number of measurements made by automated methods. Automated methods are particularly appropriate for use in determining local variation in orientation such as focal myofiber disarray associated with FHC. The generality of these methods suggests they may have use in other biological fields such as quantifying cellular alignment.

Residual strain in ischemic ventricular myocardium

Structural remodeling during acute myocardial infarction affects ventricular wall stress and strain. To see whether acute myocardial infarction alters residual stress and strain in the left ventricle (LV), we measured opening angles in rat hearts after 30 minutes of left coronary artery occlusion. The mean opening angle in 18 ischemic hearts (51 +/- 20 deg) was significantly greater than in five sham-operated controls (29 +/- 11 deg, P < 0.05). To determine whether these alterations in residual strain may be associated with strain softening caused by systolic overstretch of the noncontracting ischemic tissue, we also measured opening angles in isolated hearts that had been passively inflated to high LV pressures (120 mmHg). The mean opening angle of the strain-softened hearts was not significantly different from the sham-operated hearts (34 +/- 27 deg, P = 0.74). Mean collagen area fractions in the myocardium were not significantly different between ischemic hearts (0.027 +/- 0.014) and the nonischemic group (0.022 +/- 0.011). Although there were significant differences in opening angles measured with ischemia, they do not appear to be a result of altered extracellular collagen content or softening associated with overstretch. Thus, there is a significant change in residual strain associated with acute ischemia that may be related to changes in collagen fiber structure, myocyte structure, or metabolic state.

Left ventricular geometric remodeling and residual stress in the rat heart

Theoretical considerations and observations of residual stress suggest that geometric remodeling in the heart may also alter residual stress and strain. We investigated whether changes in left ventricular geometry during physiologic growth were associated with corresponding changes in myocardial residual strain. In anesthetized rats from eight age groups ranging from 2-25+ weeks, the heart was arrested and isolated, and equatorial slices were obtained. The geometry of the intact, unloaded state was recorded, as well as the "opening angle" of the stress-free configuration after radial resection of the tissue slice. The tissue was fixed and embedded for histological examination of collagen area fraction. Heart weight increased 10-fold with age and unloaded internal radius increased almost 4-fold. However, wall thickness increased only 66 percent, so that the ratio of wall thickness to internal radius decreased significantly from 2.22 +/- 0.29 (mean +/- SD) at 2 weeks to 0.81 +/- 0.47 at 25 weeks. Opening angle of the stress-free slice decreased significantly from 87 +/- 16 deg at 2 weeks to 51 +/- 16 deg, and correlated linearly with wall thickness/radius ratio. Collagen area fraction increased with age. Hence physiologic ventricular remodeling in rats decreases myocardial residual strain in proportion to the relative reduction in wall thickness-radius ratio.

Stress and strain as regulators of myocardial growth

The response of the heart to altered hemodynamic loading is growth or remodeling of myocytes and the extracellular matrix. In order to describe and mathematically model this dynamic and complex system of growing and resorbing tissue, the stimulating factor for tissue growth must be found, and up to now is not known. Most evidence, both in tissue and at the cellular level, points to a mechanical factor as the stimulus, and most likely a deformation signal is transduced to initiate protein synthesis. At the cellular level mechanotransduction likely takes place at the cellular membrane, although multiple biochemical and mechanical pathways have been proposed which induce transcription in the nucleus and eventual protein upregulation. The results of a recent mathematical analysis based on experimental data suggest that end-diastolic fiber strain at the tissue level may be the stimulus to one mode of tissue growth: volume-overload hypertrophy. This is the only mechanical factor that we found to be normalized after volume overload hypertrophy. But other studies do not agree with this result, and other modes of hypertrophy may be regulated by different factors or combinations of factors.

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.

Flow-function relations during graded coronary occlusions in the dog: effects of transmural location and segment orientation

OBJECTIVE

The sensitive relationship between regional myocardial perfusion and local systolic deformation during acute myocardial ischemia is not independent of the transmural location or segment orientation. The aim of this study was to determine the effects of fiber orientation and transmural location on the relationships between regional myocardial flow and three-dimensional systolic wall strain during graded coronary artery occlusions.

METHODS

Transmural distributions of three-dimensional strain (by biplane radiography of implanted radiopaque markers) and myocardial blood flows (using fluorescent microspheres) were measured in the ischemic region during graded left anterior descending (LAD) coronary artery occlusions in 12 anesthetized dogs.

RESULTS

Occlusion of the coronary artery did not significantly alter mean heart rate or end-systolic pressure. As flow decreased during graded occlusions, ischemia significantly changed systolic circumferential, longitudinal, radial, fiber and cross-fiber strains (p < 0.004). There was a significant effect of transmural position on circumferential, cross-fiber and radial strains, but not on fiber or longitudinal strains. Ischemia significantly altered all normal strains: circumferential, longitudinal, fiber, cross-fiber and radial. There was a strong interaction effect between transmural location and blood flow for circumferential, cross-fiber and radial strains, but not fiber or longitudinal strains.

CONCLUSION

During non-transmural ischemia, there is evidence of strong transmural tethering in the cross-fiber direction, whereas the fiber-strain flow relation is independent of transmural position. Thus, whether the relationship between local myocardial bloodflow and systolic strain during acute ischemia is dependent on transmural location, depends on segment orientation.

Protection against myocardial dysfunction after a brief ischemic period in transgenic mice expressing inducible heat shock protein 70

Brief ischemic periods lead to myocardial dysfunction without myocardial infarction. It has been shown that expression of inducible HSP70 in hearts of transgenic mice leads to decreased infarct size, but it remains unclear if HSP70 can also protect against myocardial dysfunction after brief ischemia. To investigate this question, we developed a mouse model in which regional myocardial function can be measured before and after a temporary ischemic event in vivo. In addition, myocardial function was determined after brief episodes of global ischemia in an isolated Langendorff heart. HSP70-positive mice and transgene negative littermates underwent 8 min of regional myocardial ischemia created by occlusion of the left descending coronary artery, followed by 60 min of reperfusion. This procedure did not result in a myocardial infarction. Regional epicardial strain was used as a sensitive indicator for changes in myocardial function after cardiac ischemia. Maximum principal strain was significantly greater in HSP70-positive mice with 88+/-6% of preischemic values vs. 58+/-6% in transgene-negative mice (P < 0.05). Similarly, in isolated Langendorff perfused hearts of HSP70-positive and transgene-negative littermates exposed to 10 min of global ischemia and 90 min of reperfusion, HSP70 transgenic hearts showed a better-preserved ventricular peak systolic pressure. Thus, we conclude that expression of HSP70 protects against postischemic myocardial dysfunction as shown by better preserved myocardial function.

Three-dimensional residual strain in midanterior canine left ventricle

All previous studies of residual strain in the ventricular wall have been based on one- or two-dimensional measurements. Transmural distributions of three-dimensional (3-D) residual strains were measured by biplane radiography of columns of lead beads implanted in the midanterior free wall of the canine left ventricle (LV). 3-D bead coordinates were reconstructed with the isolated arrested LV in the zero-pressure state and again after local residual stress had been relieved by excising a transmural block of tissue. Nonhomogeneous 3-D residual strains were computed by finite element analysis. Mean +/- SD (n = 8) circumferential residual strain indicated that the intact unloaded myocardium was prestretched at the epicardium (0.07 +/- 0.06) and compressed in the subendocardium (-0.04 +/- 0.05). Small but significant longitudinal shortening and torsional shear residual strains were also measured. Residual fiber strain was tensile at the epicardium (0.05 +/- 0.06) and compressive in the subendocardium (-0.01 +/- 0.04), with residual extension and shortening, respectively, along structural axes parallel and perpendicular to the laminar myocardial sheets. Relatively small residual shear strains with respect to the myofiber sheets suggest that prestretching in the plane of the myocardial laminae may be a primary mechanism of residual stress in the LV.

Mechanical regulation of myocardial growth during volume-overload hypertrophy in the rat

Alteration of hemodynamic preload leads to ventricular growth and remodeling, but the specific diastolic mechanical factors, such as myocardial stress or strain, that regulate the hypertrophic response remain unclear. To assess the relative importance of these factors in a model of volume-overload hypertrophy, we measured passive pressure-strain relationships by using ultrasonic crystals in the left ventricle (LV) midwall of rats at 1, 2, 4, and 6 wk after an arteriovenous fistula (AVF). Compared with baseline, mean strain in the muscle fiber direction (Eff) at an end-diastolic (ED) pressure corresponding to the acute elevation in hemodynamic load with AVF increased by 96% from 0.056 +/- 0.028 to 0.110 +/- 0.044 (P < 0.05). Eff returned to normal levels after 6 wk of remodeling (0.045 +/- 0.029). Fiber stress at ED pressure, computed from an optimized prolate spheroidal finite-element model for each group, increased by 82% in the acute response, rose to 5.8 times normal level at 1 wk, and remained substantially elevated (5.2 times) at 6 wk. Concurrently, stiffness in both fiber and cross-fiber directions was increased in all groups and reached a maximum of 10 times normal values by 6 wk. Collagen area fraction, as measured in picrosirius-stained sections of the LV free wall, was not different between 6 wk and control. Thus we conclude that ED strain, rather than stress, is normalized during volume hypertrophy through changes in ventricular geometry and wall stiffness that appear unrelated to changes in collagen content.

Biaxial mechanics of the passively overstretched left ventricle

Overstretching the intact ventricle increases global compliance as a function of maximum previously experienced load and may have an important role in the diseased heart, but the corresponding changes in local myocardial mechanics and structure are unknown. Therefore, we measured two-dimensional strain on the left ventricular (LV) epicardium in isolated arrested rat hearts sequentially inflated to increasing cavity pressures of 10, 30, and 120 mmHg. Strains at matched LV pressures increased significantly (P < 0.002) as the maximum pressure previously experienced by the LV (Pmax) increased. Compared with Pmax = 10 mmHg, relative increases in fiber strain for Pmax = 30 and 120 mmHg (100 and 149%, respectively) were significantly greater (P < 0.001) than the corresponding increases in cross-fiber (51 and 78%, respectively) and fiber shear (57 and 86%, respectively) strains. Using an optimized prolate spheroidal finite-element model of the rat LV that reliably reproduced experimental strains, we estimated progressive decreases in epicardial biaxial wall stiffness up to 87% with increasing Pmax that were not different in the fiber and cross-fiber directions. Thus, although passive ventricular overloading causes direction-dependent increases in epicardial strain, these changes are the consequence of local myocardial softening that is actually independent of direction.

Strain softening in rat left ventricular myocardium

We investigated whether strain softening (or the Mullins effect) may explain the reduced left ventricular stiffness previously associated with the strain-history-dependent preconditioning phenomenon. Passive pressure-volume relations were measured in the isolated, arrested rat heart during LV balloon inflation and deflation cycles. With inflation to a new higher maximum pressure, the pressure-volume relation became less stiff, particularly in the low (diastolic) pressure range, without a significant change in unloaded ventricular volume. In five different loading protocols in which the maximum passive cycle pressure ranged from 10 to 120 mmHg, we measured increases at 10 mmHg in LV volume up to 350 percent of unloaded volume that depended significantly on the history (p < 0.05) and magnitude (p < 0.01) of maximum previous pressure. Although a quasi-linear viscoelastic model based on the pressure-relaxation response could produce a nonlinear pressure-volume relation with hysteresis, it was unable to show any significant change in ventricular stiffness with new maximum pressure. We incorporated a strain softening theory proposed by Johnson and Beatty (1992) into the model by modifying the elastic response with a volume-amplification factor that depended on the maximum previous pressure. This model more accurately reproduced the experimentally observed behavior. Thus, the preconditioning behavior of the myocardium is better explained by strain softening rather than viscoelasticity and may be due to damage to elastic components, rather than the effect of viscous tissue components.

Relationship between passive tissue strain and collagen uncoiling during healing of infarcted myocardium

OBJECTIVE

The structure of the collagen scar during healing of a myocardial infarction is a determinant of the function of the remodeled tissue. We hypothesize that the passive deformations of both scar and normal tissue are related to the underlying collagen uncoiling as the tissue stretches, and that the unloaded tortuosity of the collagen may be a determinant of tissue stiffness at low ventricular pressure. Hence collagen uncoiling and tissue strain were measured during passive loading in normal tissue, and in healing infarct tissue.

METHODS

Left ventricles of rats were infarcted by ligation of the left anterior descending artery for 2 weeks. Surface strains were measured during passive inflation in the scar region in one set of excised hearts, and other arrested hearts were fixed at different ventricular pressures, after which collagen tortuosity was measured in the infarcted and normal tissue.

RESULTS

Passive loading strains were smaller in the scar in both the fiber and cross-fiber directions. Tortuosity decreased with load in normal and infarcted tissue, with fibrils tending to straighten more in the scar tissue at higher pressures (1.056 +/- 0.009 vs. 1.024 +/- 0.009 at P = 20 mmHg) with similar tortuosities at zero pressure (1.110 +/- 0.012 vs. 1.098 +/- 0.019). The decrease in tortuosity with strain was greater for the infarcted tissue.

CONCLUSIONS

The greater stiffness of infarcted tissue at low pressure is not due to 'straightened' collagen fibers, and there may be a different three-dimensional structure of infarct vs. normal coiled collagen fibers which can affect the material properties of these tissues.

Transmural changes in stress-free myocyte morphology during pressure overload hypertrophy in the rat

Cellular hypertrophy can alter the distribution of residual stress in the myocardium, hence can affect active and passive ventricular mechanics. It is hypothesized that an increase in stress-free cell cross-sectional area will tend to increase residual stresses. Therefore transmural distributions of myocyte cross-sectional areas and global ventricular dimensions in young rats 0-21 days following thoracic aortic handling with sham-operated and unoperated control groups were measured in tissue free of all external and residual stresses. Cell cross-sectional area increased in the stress-free state and was uniform across the wall except at 21 days when there was a transmural gradient with cells at the endocardium 46% larger in diameter than those in the outer wall. Cell area increased from a mean of 156 +/- 30 microM2 at 0 days to a mean of 627 +/- 164 microM2 at 21 days, although during this time there were no statistical changes in the opening angles of stress-free tissue sections. Because the time course of opening angle did not follow the changes in cell thickening, the cellular growth measured in this study is probably not the only factor responsible for the distribution of residual stress.

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.

Left ventricular perimysial collagen fibers uncoil rather than stretch during diastolic filling

The collagen fibers in the myocardium are initially wavy, suggesting that they may not be directly stretched for a portion of diastolic filling. To test whether the fibers gradually straighten and at what left ventricular (LV) pressure they become straight, 24 isolated, arrested rat hearts were fixed at physiologic diastolic LV pressures and changes in collagen structure were examined. As LV pressure increased, mean ( +/- SE) sarcomere length increased (1.80 +/- 0.02 to 1.88 +/- 0.02 from 0 mmHg to 26.3 +/- 4.1 mmHg) while the tortuosity of the perimysial fibers (fiber length/midline length) decreased (1.088 +/- 0.014 to 1.031 +/- 0.006 from 0 mmHg to 26.3 +/- 4.1 mmHg). Transmural variations in collagen structure paralleled the trends in sarcomere length (epicardial regions had longer sarcomeres and straighter collagen fibers than endocardial regions). These results indicate that there is a tight coupling between perimysial collagen fibers and myocytes, consistent with the nonlinear pressure-volume and pressure-sarcomere length relationships.

Transmural distribution of capillary morphology as a function of coronary perfusion pressure in the resting canine heart

Changes in coronary perfusion pressure lead to alterations in intracoronary myocardial volume that may be associated with regionally altered microvascular morphology. Transmural variations in coronary capillary geometry were quantified as a function of coronary perfusion pressure in glutaraldehyde-fixed canine hearts. Capillary volume fractions, diameter, numerical density, anisotropy, and sarcomere length were measured using computer analysis of light microscopic images of sections taken transverse or longitudinal to the muscle fiber axis. Capillary volume was 4-6% of myocardial wall volume and exhibited a significant transmural gradient, increasing from epicardium to endocardium. Vessels 4 to 5 microns in diameter with a density of 2900 mm-2 appear to increase in diameter and alter their cross-sectional shape with increasing pressure, rather than increasing in number, suggesting an effective distensibility of approximately 0.007 mm Hg-1. Quantification of vessel anisotropy was directly related to cross-sectional shape and demonstrated that the capillaries are highly oriented. These findings indicate that intramyocardial capacitance is at least in part associated with nonhomogeneous changes in coronary capillary morphology with altered perfusion pressure.

Effects of pressure overload on the passive mechanics of the rat left ventricle

Both myocyte growth and changes in the extracellular matrix may affect the passive mechanics of the left ventricle (LV). Pressure-volume (PV) relationships and midwall two-dimensional strains versus passive loading were measured in isolated rat hearts 2 and 6 weeks after ascending aortic banding. Collagen area fractions and perimysial fibril orientations were determined with picrosirius-polarization microscopy, and the equatorial region of the LV was modeled with finite element analysis of a transversely isotropic cylinder with the same material properties in hypertrophy and control. Compared with weight-matched shams, heart weight increased at 2 (19%) and 6 (22%) weeks, as did LV wall thickness (6% and 31%, respectively). The PV curve became less compliant with hypertrophy; only circumferential strain decreased after hypertrophy. Collagen area fractions were not different at either subendocardium or subepicardium (3.37 +/- 1.06 versus 3.96 +/- 0.76 at 2 weeks and 3.61 +/- 1.30 versus 4.22 +/- 1.50 at 6 weeks for banded and sham, respectively; subendocardium). Collagen and muscle fiber orientations also did not change with hypertrophy. The finite element model predicted trends in the strains similar to those found experimentally. Thus, in this model of pressure-overload hypertrophy, the decreases in compliance and circumferential strain of the passive LV are not due to changes in the percentage of extracellular matrix, but rather to global geometric changes.

Myocardial remodeling in hypertensive Ren-2 transgenic rats

Rats harboring the mouse Ren-2 transgene develop hypertension despite low levels of plasma renin. We determined the extent of left ventricular remodeling present in Ren-2 rats at 16 weeks of age by measuring blood pressure, ratio of heart weight to body weight, left ventricular wall thickness, passive (diastolic) left ventricular compliance, and left ventricular collagen content using hydroxyproline and collagen area fraction. Changes in perivascular fibronectin and collagen type I and III were examined with immunohistochemistry. Blood pressure values at time of death were 244 +/- 15 mm Hg for Ren-2 rats (mean +/- SD, n = 5). Ratios of heart weight to body weight (grams per kilogram) for Ren-2 animals were 4.1 +/- 0.2 versus 3.1 +/- 0.1 for controls (n = 6, P < .001). Wall thickness values for control animals were 2.6 +/- 0.1 versus 4.1 +/- 0.4 mm for Ren-2 animals (P < .001). Left ventricular Ren-2 hydroxyproline measurements were significantly decreased (3.4 +/- 0.2 versus 4.7 +/- 0.9 mg/g dry wt for controls). Significant decreases of approximately 30% were also observed in collagen area fraction in Ren-2 rats. Immunohistochemical and picrosirius red staining indicated increased amounts of perivascular fibrosis in all Ren-2 animals (when compared with controls) with enhanced levels of perivascular fibronectin and type I and type III collagen proteins. Left ventricular compliance measurements indicated a decrease in left ventricular volume for all left ventricular pressures (P = .07).(ABSTRACT TRUNCATED AT 250 WORDS)

Three-dimensional transmural mechanical interaction between the coronary vasculature and passive myocardium in the dog

The "garden hose" effect of coronary perfusion on diastolic left ventricular (LV) mechanics has been proposed to cause changes in systolic function by altering diastolic sarcomere length. We measured transmural distributions of three-dimensional shape change using radiopaque markers implanted in the LV free wall of eight isolated arrested canine hearts as functions of coronary arterial perfusion pressure (Pp) and LV pressure (PLV) and related these deformations to the local muscle fiber architecture. Increased Pp from 0 to 110 mm Hg produced a 10% reduction in LV chamber volume (P < .01) and 25% to 40% decreases in local three-dimensional wall strain at matched PLV, indicating myocardial stiffening. Significant decreases in the magnitudes of local deformation occurred preferentially in the cross-fiber and radial directions (P < .02), with no change in fiber strain. This suggests that changing coronary Pp does not alter diastolic fiber length; hence, the Frank-Starling law may not mediate the Gregg effect. Since the myocardial microvessels are primarily oriented parallel to the muscle fibers, the observed myocardial stiffening occurs in the directions transverse to the microvessels rather than along their length. Local myocardial wall volume in the unloaded LV demonstrated a uniform 5% increase from the unperfused state to Pp of 50 mm Hg. With further increases in Pp up to 110 mm Hg, the change in regional wall volume from the unperfused state developed a substantial transmural gradient increasing by 7% at the epicardium and 15% at the subendocardium. This reflects a significant increase (P < .02) in intramyocardial coronary capacitance from epicardium to endocardium, which may be related to a transmural gradient in coronary distensibility or vascularity.

Contribution of collagen matrix to passive left ventricular mechanics in isolated rat hearts

Although it makes up only 2-6% of left ventricular dry weight, collagen is thought to be the major structural protein determining passive ventricular stiffness. However, the relationship between structure of the extracellular matrix and passive mechanics is not understood. Hence, to deplete the collagen matrix, 16 rat hearts were perfused with bacterial collagenase for 60 min. Quantitative morphology using picrosirius red revealed a 36% decrease in collagen area fraction predominantly in the medium-sized fibers. Scanning electron microscopy revealed damage to the endomysial struts. Passive pressure-volume curves showed increases in left ventricular volume at all pressures (from 0.203 +/- 0.061 to 0.265 +/- 0.061 ml at 5 mmHg, P < 0.0001). Strain during loading, calculated from lengths obtained from a triplet of piezoelectric crystals, was unchanged with collagen depletion. However, remodeling strain computed from the collagenase-treated state referred to the Krebs solution-treated state at the same ventricular pressure showed both circumferential (0.145 +/- 0.166 to 0.170 +/- 0.158) and longitudinal (0.070 +/- 0.120 to 0.068 +/- 0.069) stretching. Sarcomere lengths increased at all depths (5.2% at midwall). Thus alterations in the extracellular matrix lead to increased ventricular volume and sarcomere lengths without altering ventricular compliance.

Passive ventricular mechanics in tight-skin mice

Although changes in the extracellular matrix have been associated with changes in ventricular compliance in certain diseased states, this relationship has not been entirely established. Accordingly, we studied passive ventricular mechanics in the tight-skin (TSk) mouse, a mutant strain known to have increased cardiac collagen. In the arrested left ventricle, we determined the pressure-volume relationship and the stress-free state, as defined by the "opening angle" of an equatorial ring with a radial cut. The results showed the mean opening angle in the TSk mouse to be smaller than that in phenotypic negative controls (7 +/- 6 vs. 21 +/- 9 degrees), and there was no statistical difference in the pressure-volume curves. Histological quantification of the transmural collagen showed a uniform increase of collagen area fraction across the wall in TSk mouse, and a significantly thicker superficial epicardial collagen layer (4.68 +/- 0.87 vs. 3.34 +/- 0.76 micron). Thus, although there appears to be a decrease of residual stress in the TSk mouse heart, which may be related to the thicker epicardial collagen layer, the combination of increased myocardial collagen and the change in stress-free state did not seem to affect the passive pressure-volume relationship of the left ventricle.

Measurement of strain and analysis of stress in resting rat left ventricular myocardium

A technique has been developed for measuring two-dimensional strains in the left ventricle of the isolated arrested rat heart subjected to passive ventricular loading. The pressure-volume relationship was found in eight hearts during inflation of a left ventricular balloon. With the zero-pressure state as reference, in-plane strain components were determined using a triangle of ultrasonic dimension transducers (0.6-0.8 mm diameter) placed 3-6 mm apart in the midwall of the left ventricle. Mean circumferential (fiber) strain was larger than longitudinal (cross-fiber) strain (0.108 +/- 0.045, 0.055 +/- 0.045, respectively, at 11 mmHg), and shear strain (-0.048 +/- 0.029) was negative, consistent with left-handed torsion. The in-plane angle of greatest stretch was uniform with inflation (range = -26.5 degrees to -34.5 degrees). The equatorial region of the left ventricle was modeled with finite element analysis of a transversely isotropic thick-walled cylindrical shell subjected to internal loading and axial forces. The material parameters of an exponential strain energy function were optimized so that the least-squares difference between the predicted and the measured midwall strains was minimized. Material properties, stress and strain in the rat heart were compared to values predicted for the dog. In both species the tissue was stiffer in the fiber direction than in the cross-fiber direction. The ratio of fiber to cross-fiber stiffness was lower in the rat (2.50) than in the dog (5.24) at low loads and approximately equal at higher loads (1.63 and 1.39, respectively). The computational and experimental analyses showed that the larger shear strain and more nonuniform in-plane extension in the rat may be an indication of significantly different anisotropic material properties in these two species, and implies differences in the collagen ultrastructure.

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)

Transmural distribution of three-dimensional strain in the isolated arrested canine left ventricle

Three-dimensional myocardial strains in seven isolated, potassium-arrested dog hearts were measured by biplane radiography of 3 transmural columns of 4-6 radiopaque beads implanted in the midanterior left ventricular free wall. Transmural distributions of strain during inflation of a left ventricular balloon to 20-30 mmHg were computed with respect to the zero pressure state. Magnitudes of the 3 principal strains increased in proportion to ventricular volume (0.0088, 0.0037, and -0.0059 ml-1). At a left ventricular pressure of 8 +/- 4 mmHg, mean circumferential (E11) and longitudinal strains (E22) were similar, increasing from epicardium (0.058 +/- 0.055 and 0.036 +/- 0.024) to subendocardium (0.139 +/- 0.102 and 0.120 +/- 0.084) as did the transmural (wall thinning) strain E33 (-0.053 +/- 0.071 to -0.128 +/- 0.083). Negative in-plane shear E12 was small (-0.008 to -0.052), consistent with a left-handed torsion of the left ventricular wall. Mean transverse shear strains E13 and E23 were small (-0.029 to 0.007) but showed considerable variability between hearts. Fiber strain had no significant transmural variation (P = 0.57). The principal axis of greatest strain was close to the fiber orientation on the epicardium (-15 degrees) but closer to the cross-fiber direction near the endocardium (-40 degrees). Therefore, the end-diastolic fiber lengths are maximized on the epicardium and minimized on the endocardium.

Transmural distribution of myocardial tissue growth induced by volume-overload hypertrophy in the dog

BACKGROUND

Although chronic volume overload is thought to induce uniform cardiac enlargement, the stimulus for tissue growth has not been defined. Changes in diastolic and systolic stress or strain have been proposed as mechanical factors that may stimulate hypertrophy. Since there are thought to be transmural variations in these stresses and strains, three-dimensional patterns of myocardial tissue growth may provide insight into the role of these factors.

METHODS AND RESULTS

To assess the transmural variation in tissue growth after volume overload, the configurations of three columns of four to six gold beads (1-mm diameter) implanted in the left ventricular anterior free wall were recorded in five dogs before and after cardiac enlargement induced by creating a systemic arteriovenous fistula. Data were obtained with end-diastolic pressures adjusted to the same level in the control and hypertrophic states. End-diastolic wall thickness remained constant, whereas left ventricular diameter increased. Small increases in transmural systolic strain were seen. The volumes defined by four beads (a tetrahedron) at end diastole showed increases in myocardial mass of 20-27% after 3.6 (mean) weeks of hypertrophy and were uniform across the wall of the left ventricle. The edges of single bilinear-quadratic finite elements were fitted to the three columns of the bead set at end diastole in control and at end diastole after hypertrophy at equal end-diastolic pressures. Thus, continuous transmural strain distribution were obtained at the hypertrophic state with respect to the control state. The transmural distributions of these end-diastolic growth strains were uniform and positive for both the circumferential and longitudinal components measured in a cardiac coordinate system, with small radial growth strain indicating that growth was predominantly parallel to the epicardial tangent plane. Moreover, when strains were transformed (rotated) to fiber coordinates, in-plane fiber and cross-fiber growth strains were both positive at all locations across the wall and approximately equal in magnitude, indicating considerable growth in the cross-fiber direction.

CONCLUSIONS

These results indicate that the stimulus for volume-overload hypertrophy may be constant across the wall and that substantial cross-fiber growth occurs during volume-overload hypertrophy.

Non-homogeneous analysis of three-dimensional transmural finite deformation in canine ventricular myocardium

A new method has been developed for analyzing transmural distributions of finite deformation in canine ventricular myocardium without the need to assume that the strain in a finite volume of the wall is homogeneous. The three-dimensional nodal geometric parameters of bilinear-cubic or bilinear-quadratic finite elements are fitted by least squares to the measured coordinates of 12-18 radiopaque markers implanted in the left ventricular free wall. For six dog hearts, root-mean-squared errors in the fitted in-plane coordinates ranged from 0.079-0.556 mm in the end-diastolic reference state and 0.142-0.622 mm at end-systole. The corresponding error ranges in the radial coordinate were 0.042-0.264 mm at end-diastole and 0.106-0.279 mm at end-systole. Smoothly continuous transmural profiles of wall strain computed as the element deformed during the cardiac cycle from end-diastole to end-systole showed good agreement with the discrete results of conventional homogeneous analysis. Using the kinematics of a thick-walled incompressible cylinder, overall absolute errors due to the non-homogeneity of myocardial deformation were found to be reduced in the new analysis by 30-35% for typical experimental parameters. Overall relative errors were also reduced (from 23 to 20%). Since measurement errors in the reconstructed marker coordinates were spatially smoothed by the fitting procedure, noise in the computed deformations was also substantially attenuated, and transmural gradients of three-dimensional strain components could be obtained with improved accuracy. Hence physiological factors affected by transmural stress and strain distributions, such as myocardial blood flow, ischemia and hypertrophy, may be better understood.

Residual strain in rat left ventricle

Residual stress in an organ is defined as the stress that remains when all external loads are removed. Residual stress has generally been ignored in published papers on left ventricular wall stress. To take residual stress into account in the analysis of stress distributions in a beating heart, one must first measure the residual strain in the no-load state of the heart. Residual strains in equatorial cross-sectional rings (2-3 mm thick) of five potassium-arrested rat left ventricles were measured. The effects of friction and external loading were reduced by submersing the specimen in fluid, and a hypothermic, hyperkalemic arresting solution containing nifedipine and EGTA was used to delay the onset of ischemic contracture. Stainless steel microspheres (60-100 microns) were lightly imbedded on the surface of the slices, and the coordinates of the microspheres were digitized from photographs taken before and after a radial cut was made through the left ventricular free wall. Two-dimensional strains computed from the deformation of a slice after one radial cut were defined as the residual strains in that slice. It was found that the distributions of the principal residual stretch ratios were asymmetric with respect to the radial cut: in areas where substantial transmural strain gradients existed, the distributions of strain components were different on the two sides of the radial cut. A second radial cut produced deformations significantly smaller than those produced from the first radial cut. Hence, a slice with one radial cut may be considered stress free.(ABSTRACT TRUNCATED AT 250 WORDS)