Fiber shortening in the inner layers of the left ventricular wall as assessed from epicardial deformation during normoxia and ischemia

iPSC modeling of young-onset Parkinson's disease reveals a molecular signature of disease and novel therapeutic candidates

Young-onset Parkinson's disease (YOPD), defined by onset at <50 years, accounts for approximately 10% of all Parkinson's disease cases and, while some cases are associated with known genetic mutations, most are not. Here induced pluripotent stem cells were generated from control individuals and from patients with YOPD with no known mutations. Following differentiation into cultures containing dopamine neurons, induced pluripotent stem cells from patients with YOPD showed increased accumulation of soluble α-synuclein protein and phosphorylated protein kinase Cα, as well as reduced abundance of lysosomal membrane proteins such as LAMP1. Testing activators of lysosomal function showed that specific phorbol esters, such as PEP005, reduced α-synuclein and phosphorylated protein kinase Cα levels while increasing LAMP1 abundance. Interestingly, the reduction in α-synuclein occurred through proteasomal degradation. PEP005 delivery to mouse striatum also decreased α-synuclein production in vivo. Induced pluripotent stem cell-derived dopaminergic cultures reveal a signature in patients with YOPD who have no known Parkinson's disease-related mutations, suggesting that there might be other genetic contributions to this disorder. This signature was normalized by specific phorbol esters, making them promising therapeutic candidates.

Prediction of Left Ventricular Mechanics Using Machine Learning

The goal of this paper was to provide a real-time left ventricular (LV) mechanics simulator using machine learning (ML). Finite element (FE) simulations were conducted for the LV with different material properties to obtain a training set. A hyperelastic fiber-reinforced material model was used to describe the passive behavior of the myocardium during diastole. The active behavior of the heart resulting from myofiber contractions was added to the passive tissue during systole. The active and passive properties govern the LV constitutive equation. These mechanical properties were altered using optimal Latin hypercube design of experiments to obtain training FE models with varied active properties (volume and pressure predictions) and varied passive properties (stress predictions). For prediction of LV pressures, we used eXtreme Gradient Boosting (XGboost) and Cubist, and XGBoost was used for predictions of LV pressures, volumes as well as LV stresses. The LV pressure and volume results obtained from ML were similar to FE computations. The ML results could capture the shape of LV pressure as well as LV pressure-volume loops. The results predicted by Cubist were smoother than those from XGBoost. The mean absolute errors were as follows: XGBoost volume: 1.734 ± 0.584 ml, XGBoost pressure: 1.544 ± 0.298 mmHg, Cubist volume: 1.495 ± 0.260 ml, Cubist pressure: 1.623 ± 0.191 mmHg, myofiber stress: 0.334 ± 0.228 kPa, cross myofiber stress: 0.075 ± 0.024 kPa, and shear stress: 0.050 ± 0.032 kPa. The simulation results show ML can predict LV mechanics much faster than the FE method. The ML model can be used as a tool to predict LV behavior. Training of our ML model based on a large group of subjects can improve its predictability for real world applications.

Relationship of Transmural Variations in Myofiber Contractility to Left Ventricular Ejection Fraction: Implications for Modeling Heart Failure Phenotype With Preserved Ejection Fraction

The pathophysiological mechanisms underlying preserved left ventricular (LV) ejection fraction (EF) in patients with heart failure and preserved ejection fraction (HFpEF) remain incompletely understood. We hypothesized that transmural variations in myofiber contractility with existence of subendocardial dysfunction and compensatory increased subepicardial contractility may underlie preservation of LVEF in patients with HFpEF. We quantified alterations in myocardial function in a mathematical model of the human LV that is based on the finite element method. The fiber-reinforced material formulation of the myocardium included passive and active properties. The passive material properties were determined such that the diastolic pressure-volume behavior of the LV was similar to that shown in published clinical studies of pressure-volume curves. To examine changes in active properties, we considered six scenarios: (1) normal properties throughout the LV wall; (2) decreased myocardial contractility in the subendocardium; (3) increased myocardial contractility in the subepicardium; (4) myocardial contractility decreased equally in all layers, (5) myocardial contractility decreased in the midmyocardium and subepicardium, (6) myocardial contractility decreased in the subepicardium. Our results indicate that decreased subendocardial contractility reduced LVEF from 53.2 to 40.5%. Increased contractility in the subepicardium recovered LVEF from 40.5 to 53.2%. Decreased contractility transmurally reduced LVEF and could not be recovered if subepicardial and midmyocardial contractility remained depressed. The computational results simulating the effects of transmural alterations in the ventricular tissue replicate the phenotypic patterns of LV dysfunction observed in clinical practice. In particular, data for LVEF, strain and displacement are consistent with previous clinical observations in patients with HFpEF, and substantiate the hypothesis that increased subepicardial contractility may compensate for subendocardial dysfunction and play a vital role in maintaining LVEF.

Transmural gradients of myocardial structure and mechanics: Implications for fiber stress and strain in pressure overload

Although a truly complete understanding of whole heart activation, contraction, and deformation is well beyond our current reach, a significant amount of effort has been devoted to discovering and understanding the mechanisms by which myocardial structure determines cardiac function to better treat patients with cardiac disease. Several experimental studies have shown that transmural fiber strain is relatively uniform in both diastole and systole, in contrast to predictions from traditional mechanical theory. Similarly, mathematical models have largely predicted uniform fiber stress across the wall. The development of this uniform pattern of fiber stress and strain during filling and ejection is due to heterogeneous transmural distributions of several myocardial structures. This review summarizes these transmural gradients, their contributions to fiber mechanics, and the potential functional effects of their remodeling during pressure overload hypertrophy.

Optimization-Based Speckle Tracking Algorithm for Left Ventricle Strain Estimation: A Feasibility Study

Speckle tracking echocardiography (STE) is a widespread method for calculating myocardial strains and estimating left ventricle function. Since echocardiographic clips are corrupted by speckle decorrelation noise, resulting in irregular, nonphysiological tissue displacement fields, smoothing is performed on the displacement data, affecting the strain results. Thus, strain results may depend on the specific implementations of 2-D STE, as well as other systems' characteristics of the various vendors. A novel algorithm (called K-SAD) is introduced, which integrates the physiological constraint of smoothness of the displacement field into an optimization process. Simulated B-mode clips, modeling healthy and abnormal cases, were processed by K-SAD. Peak global and subendocardial longitudinal strains, as well as regional strains, were calculated. In addition, 410 healthy subjects were also processed. The results of K-SAD are compared with those of one of the leading commercial product. K-SAD provides global mid-wall strain values, as well as subendocardial and regional strain values, all in good agreement with the ground-truth-simulated phantom data. K-SAD peak global longitudinal systolic strain values for 410 healthy subjects are quite similar for the different regions: - 17.02 ± 4.02%, - 19.00 ± 3.45%, and - 19.72 ± 5.06% at the basal, mid, and apical regions, respectively. Improved performance under noisy conditions was demonstrated by comparing a subgroup of 40 subjects with the best image quality with the remaining 370 cohort: K-SAD provides statistically similar global and regional results for the two cohorts. Our study indicates that the sensitivity of strain values to speckle noise, caused by the post block-matching weighted smoothing, can be significantly reduced and accuracy enhanced by employing an integrated one-stage, physiologically constrained optimization process.

Computational analysis of the myocardial structure: adaptation of cardiac myofiber orientations through deformation

Deformation and structure of the cardiac wall can be assessed non-invasively by imaging techniques such as magnetic resonance imaging. Understanding the (patho-)physiology that underlies the observed deformation and structure is critical for clinical diagnosis. However, much about the genesis of deformation and structure is unknown. In the present computational model study, we hypothesize that myofibers locally adapt their orientation to achieve minimal fiber-cross fiber shear strain during the cardiac cycle. This hypothesis was tested in a 3D finite element model of left ventricular (LV) mechanics by computation of tissue deformations and subsequent adaptation of initial myofiber orientations towards those in the deformed tissue. As a consequence of adaptation, local tissue peak stress, strain during ejection and stroke work density were all found to increase by at least 10%, as well as to become 50% more homogeneous throughout the wall. Global LV work (peak systolic pressure, stroke volume and stroke work) increased significantly as well (>9%). The model-predicted myofiber orientations were found to be similar to those in experiments. To the best of our knowledge the presented model is the first that is able to simultaneously predict a realistic myocardial structure as well as to account for the experimentally observed homogeneity in local mechanics.

Regional assessment of left ventricular torsion by CMR tagging

PURPOSE

To introduce a standardized method for calculation of left ventricular torsion by CMR tagging and to determine the accuracy of torsion analysis in regions using an analytical model.

METHODS

Torsion between base and apex, base and mid, and mid and apex levels was calculated using CSPAMM tagging and Harmonic Phase tracking. The accuracy of torsion analysis on a regional basis (circumferential segments and transmural layers) was analyzed using an analytical model of a deforming cylinder with a displaced axis of rotation (AoR). Regional peak torsion values from twelve healthy volunteers calculated by the described method were compared to literature.

RESULTS

The deviation from the analytical torsion per % AoR-displacement (of the radius) was 0.90 +/- 0.44% for the circumferential segments and only 0.05% for the transmural layers. In the subjects, circumferentially, anterolateral torsion was larger than inferior (12.4 +/- 3.9 degrees vs. 5.0 +/- 3.3 degrees , N.S.). Transmurally, endocardial torsion was smaller than epicardial (7.5 +/- 1.3 degrees vs. 8.0 +/- 1.5 degrees , p < 0.001).

CONCLUSION

Variability in the position of the AoR causes a large variability in torsion in circumferential segments. This effect was negligible for global torsion, and torsion calculated in transmural layers. Results were documented for the healthy human heart and are in agreement with data from literature.

Clinical applications of strain rate imaging

Myocardial strain (epsilon) is a dimensionless index of change in myocardial length in response to an applied force. epsilon Rate (SR) is the rate of change of length and is usually obtained as the time derivative of the epsilon signal. In echocardiography, SR is calculated as the difference between 2 velocities normalized to the distance between the 2 velocities. SR imaging (SRI) has a theoretic advantage over Doppler tissue imaging in that SRI is relatively immune to cardiac translational motion and tethering. Therefore, SRI may be superior to Doppler tissue imaging in quantitative assessment of regional myocardial function and may find clinical application in the interrogation of coronary artery disease. The high frame rates of SRI have also renewed interest in timings of global and regional mechanical events, and their potential clinical applications. The high temporal resolution allows SRI to depict regional systolic and diastolic asynchrony. Ongoing clinical trials will determine the sensitivity, specificity, and accuracy of SRI parameters for a variety of clinical conditions. Potential clinical applications include investigation of ischemia (at rest and with stress), myocardial viability, and altered global and regional systolic and diastolic function in cardiomyopathies. Suboptimal signal quality remains a major limitation of strain imaging, and advances in data acquisition and postprocessing capabilities will help determine its future incorporation into standard regional myocardial assessment.

Relation between torsion and cross-sectional area change in the human left ventricle

During the ejection phase, motion of the left ventricular (LV) wall is such that all myocardial fibers shorten to the same extent. In a mathematical model of LV mechanisms it was found that this condition could be satisfied only if torsion around the long axis followed a unique function of the ratio of cavity volume to wall volume. When fiber shortening becomes non-uniform due to cardiac pathology, this pathology may be reflected in aberration of the torsional motion pattern. In the present study we investigated whether the predicted regular motion pattern could be found in nine healthy volunteers, using Magnetic Resonance Tagging. In two parallel short-axis cross-sections, displacement, rotation, and area ejection were derived from the motion of tags, attached non-invasively to the myocardium. Information from both sections was combined to determine area ejection, quantified as the change in the logarithm of the ratio of cavity area to wall area, and torsion, represented by the shear angle on the epicardium. Linear regression was applied to torsion as a function of area ejection. The slope thus found (-0.173 +/- 0.024 rad, mean +/- S.D.) was similar to the slope as predicted by the model of LV mechanics (-0.194 +/- 0.026 rad). In conclusion, the relation between area ejection and torsion could be assessed noninvasively in humans. In healthy volunteers, the relation was close to what was predicted by a mathematical model of LV mechanics, and also close to what was found earlier in experiments on animals.

Effects of ischemia on left ventricular apex rotation. An experimental study in anesthetized dogs

BACKGROUND

Left ventricular (LV) twist has been defined as the counterclockwise rotation of the ventricular apex with respect to the base during systole. We recently showed that, since base rotation is minimal, measurement of apex rotation reflects the dynamics of LV twist. Since ischemia is known to affect endocardial and epicardial fiber force and shortening and therefore the transmural balance of torsional moments, we hypothesized that ischemia has a significant effect on apex-rotation amplitude and on untwisting during the isovolumic relaxation (IVR) period.

METHODS AND RESULTS

With an optical device coupled to the LV apex, apex rotation was recorded simultaneously with LV pressure, ECG, LV segment length, and minor-axis diameters in 16 open-chest dogs. Ischemia was caused by a 1- to 2-minute snare occlusion of either the left anterior descending (LAD) or circumflex (LCx) arteries. LAD ischemia had a pronounced effect on apex rotation: an increase in apex-rotation amplitude attributed to subendocardial dysfunction at 10 seconds of ischemia; maximum apex rotation occurring later (during the IVR period) throughout the ischemia; a paradoxical relaxation pattern of initial untwisting followed by twisting and untwisting during the IVR period with ischemia; and a decrease in the amplitude of apex rotation with ischemia, possibly due to transmural dysfunction. LCx occlusion had similar effects on apex rotation, except that apex-rotation amplitude was not increased at 10 seconds of occlusion and the amplitude of apex rotation did not decrease with severe ischemia. Under control preischemic conditions, a linear relationship between apex rotation and segment length was observed during ejection and a different, steeper relationship during IVR. With regionally ischemic segments, this relationship became nonlinear for both ejection and IVR.

CONCLUSIONS

Both LAD and LCx ischemia had profound effects on the dynamics of apex rotation. A paradoxical relaxation pattern occurred with ischemia. We suggest that these observations are due to changes in the dynamic transmural balance of torsional moments that determine LV twist.

Distribution of myocardial strains: an MRI study

Quantification of myocardial strains is essential for understanding cardiac mechanics. Previous techniques for assessing regional myocardial strains have been mainly limited to invasive procedures. A technique by which tagging can be added to magnetic resonance images (MRI) has recently been introduced and allows for noninvasive measurement of myocardial deformations. We have applied MRI tagging to two sets of orthogonal planes and have obtained three dimensional (3D) reconstructions of 24 myocardial cuboids at end-diastole (ED) and at end-systole (ES). Applying finite strain analysis to these cuboids we were able to study the longitudinal distribution of the endocardial and epicardial principal strains (PS) in the normal canine heart. In addition we have calculated the longitudinal distribution of the left ventricular (LV) transmural thickening using a 3D approach. Our results show similarity in the longitudinal distribution of endocardial PS and transmural thickening. These results imply that endocardial strains are determined not only by endocardial fiber deformations but mainly by geometrical coupling through transmural thickening.

The relationship between regional blood flow and contractile function in normal, ischemic, and reperfused myocardium

The prevailing paradigm of coronary physiology and pathophysiology is that a balance between blood flow (i.e., supply) and function (i.e., demand) exists under normal conditions and that an imbalance between supply and demand occurs during ischemia. However, this paradigm is derived largely from studies relating changes in total coronary inflow to global ventricular function. The present article examines the relationship between myocardial blood flow and function on a regional level and proposes that a change may be needed in the current paradigm of coronary pathophysiology. In normal myocardium, considerable heterogeneity of regional blood flow exists, indicating either similar heterogeneity of metabolic demand and function or questioning the precision of metabolic coupling between flow and function. After the onset of ischemia, a transient imbalance between the reduced blood flow and function may exist. However, myocardial function rapidly declines and during early steady-state ischemia regional myocardial blood flow and function are once again evenly matched. Such supply-demand balance may persist over prolonged periods of ischemia enabling the myocardium to remain viable through reduction of energy expenditure for contractile function, i.e., to "hibernate". Whereas in "hibernating" ischemic myocardium, regional myocardial blood flow and function are both reduced but appropriately matched to one another, flow and function appear to be largely uncoupled in reperfused "stunned" myocardium. The clinical identification of viable but ischemic (hibernating) and postischemic (stunned) myocardium is of utmost importance in patients undergoing reperfusion procedures. A new paradigm of coronary and myocardial pathophysiology, encompassing a regional as well as a global view of perfusion and function, will have to include explanations for phenomena such as myocardial hibernation and myocardial stunning.

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.

Discrepancies between myocardial blood flow and fiber shortening in the ischemic border zone as assessed with video mapping of epicardial deformation

Myocardial function around the border of ischemia was investigated in eight open-chest dogs using video mapping of epicardial deformation. With this method, 40-60 white markers attached to the left ventricular epicardium were traced in time automatically. Before and 5-10 min after coronary artery occlusion, blood flow and epicardial deformation were determined in 30-40 regions with a spatial resolution of about 5 mm. Epicardial deformation was expressed as subepicardial fiber shortening and surface area decrease during the ejection phase. The latter indicates local contribution to stroke volume. The absolute values of these variables were normalized relative to the central ischemic (= 0%) and remote non-ischemic area (= 100%). The 50% contour line of a variable was defined as its border. The average distance between the borders of perfusion and function was not significantly different from zero, due to considerable variation in this distance both within one heart (+/- 5.7 mm) and between mean distances for different hearts (+/- 4.4 mm). The width of the transition zone (distance between the 20% and 80% contour lines) of surface area decrease and subepicardial fiber shortening was significantly larger (20.5 and 15.0 mm, respectively) than those of transmural and subepicardial blood flow (8.5 and 9.5 mm, respectively). The present results demonstrate that in a 20-mm zone around the border of ischemia, major discrepancies are present between perfusion and deformation.

Relation between longitudinal, circumferential, and oblique shortening and torsional deformation in the left ventricle of the transplanted human heart

The present study was designed to investigate the anisotropy of systolic chord shortening in the lateral, inferior, septal, and anterior regions of the human left ventricle. At the time of surgery, 12 miniature radiopaque markers were implanted into the left ventricular midwall of the donor heart in 15 cardiac transplant recipients. Postoperative biplane cineradiograms were computer-analyzed to yield the three-dimensional coordinates of these markers at 16.7-msec intervals. In each of the four left ventricular regions, chords were constructed from a central marker to outlying markers, and the percent systolic shortening of each chord was calculated. In each region, chord angles were measured with respect to the circumferential direction (positive angles counterclockwise) and each chord was assigned to one of four angular groups: I. oblique, -45 +/- 22.5 degrees or 135 +/- 22.5 degrees; II. circumferential, 0 +/- 22.5 degrees or 180 +/- 22.5 degrees; III. oblique, 45 +/- 22.5 degrees or -135 +/- 22.5 degrees; or IV. longitudinal, 90 +/- 22.5 degrees. In the lateral, inferior, and septal regions, respectively, systolic shortening (mean +/- SD%) was significantly greater in Group I chords (19 +/- 5%, 17 +/- 5%, and 15 +/- 4%) than those in Group II (15 +/- 5%, 12 +/- 4%, and 11 +/- 4%), Group III (12 +/- 4%, 12 +/- 5%, and 11 +/- 4%), or Group IV (13 +/- 5%, 13 +/- 6%, and 12 +/- 5%). The anterior region was unique in exhibiting equal shortening in both Group I and Group II chords (16 +/- 5%), although the shortening of these chords was significantly greater than that of Group III and Group IV (12 +/- 5%) in this region. A cylindrical mathematical model was developed to relate longitudinal, circumferential, and oblique systolic shortening to torsional deformation about the long axis of the left ventricle. Torsional deformations measured in these 15 hearts were of sufficient magnitude and correct sense to agree with model predictions. These data suggest that torsional deformations of the left ventricle are of fundamental importance in linking the one-dimensional contraction of the helically wound myocytes to the three-dimensional anisotropic systolic shortening encountered in the transplanted human heart.

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.

The effect of diltiazem on myocardial recovery after regional ischemia in dogs

The effect of diltiazem on post-ischemic metabolic and functional recovery was investigated in regionally ischemic dog hearts. The duration of ischemia was 60 min, followed by 60 min of reperfusion. Diltiazem (bolus injection of 0.1 mg X kg-1 body weight prior to ischemia, followed by a continuous infusion of 0.1 mg X kg-1 X h-1) had no effect on residual coronary flow in the centre of the ischemic area, but blunted the reactive hyperemia response after restoration of flow. The drug partially prevented the depletion of ATP and glycogen in the severely underperfused subendocardial layers, i.e. when residual flow was below 0.1 ml X min-1 X g-1. Reduction of the content of these substances in the subepicardial layers was moderate and not influenced by diltiazem. Segment shortening in the subepicardial layers disappeared whereas segment lengthening was observed in the subendocardial layers during the ischemic period. Diltiazem did not prevent the loss of contractile function. Despite an initial restoration of contractile function within 10 min after reperfusion, no significant beneficial effect of diltiazem treatment on mechanical function of the reperfused area was present thereafter.

Mapping of epicardial deformation using a video processing technique

A method has been developed to measure deformation of the canine epicardium during the cardiac cycle simultaneously in a number (eight) of small regions (1 X 1 cm2). Approximately 50 white markers (diameter 1.5 mm) are attached to the epicardium and their motion is recorded on tape by a video camera. Marker positions are detected by computer processing of the digitized images. In each region the three deformation parameters are calculated from the displacements of all markers in that region by means of a least-squares criterium. In the experimental situation in the center of the area of the epicardium analyzed the accuracy of measuring circumferential strain, base-to-apex strain and shear is +/- 0.005, +/- 0.005 and +/- 0.002 rad, respectively. The method has been applied in an experiment in which local ischemia of the left ventricular wall was induced by occluding the anterior descending branch of the left coronary artery. Healthy and ischemic regions could clearly be distinguished by the differences in deformation.

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.

Dissociation between epicardial and transmural function during acute myocardial ischemia

The relationship between epicardial and transmural function (measured with sonomicrometers) was examined in 13 anesthetized open-chest dogs. Systolic wall thickening was used as a standard of integrated transmural function to compare with epicardial function measured as segment shortening parallel to surface fibers. Three levels of coronary inflow restriction were produced by using decrements in systolic wall thickening as an index of changes in the transmural distribution of myocardial blood flow (microspheres) in myocardium perfused by the left anterior descending artery (anterior-apical group, n = 7) or circumflex artery (posterior-basal group, n = 6). Levels 1 and 2 were characterized by reductions in systolic wall thickening of 35% and 80%, respectively, and marked decreases in deep myocardial blood flow. In the subepicardium, myocardial blood flow was minimally affected at levels 1 and 2 and there was no change in posterior-basal epicardial segment shortening, but anterior segment shortening decreased significantly (by 21% and 37%, respectively). At level 3 myocardial blood flow was reduced transmurally, producing systolic wall thinning and marked epicardial dysfunction in both groups. Parallel epicardial segment shortening underestimated the extent of transmural dysfunction in both groups at levels 1 and 2 but the degree of underestimation was greatest in the posterior-basal group. Anterior-apical segment shortening was impaired at levels 1 and 2, whereas posterior-basal segment shortening was unaffected, suggesting that significant regional variability exists in the epicardial response to nontransmural ischemia.