MRI-based finite-element analysis of left ventricular aneurysm

Tagged MRI and finite-element (FE) analysis are valuable tools in analyzing cardiac mechanics. To determine systolic material parameters in three-dimensional stress-strain relationships, we used tagged MRI to validate FE models of left ventricular (LV) aneurysm. Five sheep underwent anteroapical myocardial infarction (25% of LV mass) and 22 wk later underwent tagged MRI. Asymmetric FE models of the LV were formed to in vivo geometry from MRI and included aneurysm material properties measured with biaxial stretching, LV pressure measurements, and myofiber helix angles measured with diffusion tensor MRI. Systolic material parameters were determined that enabled FE models to reproduce midwall, systolic myocardial strains from tagged MRI (630 +/- 187 strain comparisons/animal). When contractile stress equal to 40% of the myofiber stress was added transverse to the muscle fiber, myocardial strain agreement improved by 27% between FE model predictions and experimental measurements (RMS error decreased from 0.074 +/- 0.016 to 0.054 +/- 0.011, P < 0.05). In infarct border zone (BZ), end-systolic midwall stress was elevated in both fiber (24.2 +/- 2.7 to 29.9 +/- 2.4 kPa, P < 0.01) and cross-fiber (5.5 +/- 0.7 to 11.7 +/- 1.3 kPa, P = 0.02) directions relative to noninfarct regions. Contrary to previous hypotheses but consistent with biaxial stretching experiments, active cross-fiber stress development is an integral part of LV systole; FE analysis with only uniaxial contracting stress is insufficient. Stress calculations from these validated models show 24% increase in fiber stress and 115% increase in cross-fiber stress at the BZ relative to remote regions, which may contribute to LV remodeling.     

Characterization of the normal cardiac myofiber field in goat measured with MR-diffusion tensor imaging

Cardiac myofiber orientation is a crucial determinant of the distribution of myocardial wall stress. Myofiber orientation is commonly quantified by helix and transverse angles. Accuracy of reported helix angles is limited. Reported transverse angle data are incomplete. We measured cardiac myofiber orientation postmortem in five healthy goat hearts using magnetic resonance-diffusion tensor imaging. A novel local wall-bound coordinate system was derived from the characteristics of the fiber field. The transmural course of the helix angle corresponded to data reported in literature. The mean midwall transverse angle ranged from -12 +/- 4 degrees near the apex to +9.0 +/- 4 degrees near the base of the left ventricle, which is in agreement with the course predicted by Rijcken et al. (18) using a uniform load hypothesis. The divergence of the myofiber field was computed, which is a measure for the extent to which wall stress is transmitted through the myofiber alone. It appeared to be <0.07 mm(-1) throughout the myocardial walls except for the fusion sites between the left and right ventricles and the insertion sites of the papillary muscles.     

Myofiber angle distributions in the ovine left ventricle do not conform to computationally optimized predictions

Recent computational models of optimized left ventricular (LV) myofiber geometry that minimize the spatial variance in sarcomere length, stress, and ATP consumption have predicted that a midwall myofiber angle of 20 degrees and transmural myofiber angle gradient of 140 degrees from epicardium to endocardium is a functionally optimal LV myofiber geometry. In order to test the extent to which actual fiber angle distributions conform to this prediction, we measured local myofiber angles at an average of nine transmural depths in each of 32 sites (4 short-axis levels, 8 circumferentially distributed blocks in each level) in five normal ovine LVs. We found: (1) a mean midwall myofiber angle of -7 degrees (SD 9), but with spatial heterogeneity (averaging 0 degrees in the posterolateral and anterolateral wall near the papillary muscles, and -9 degrees in all other regions); and (2) an average transmural gradient of 93 degrees (SD 21), but with spatial heterogeneity (averaging a low of 51 degrees in the basal posterior sector and a high of 130 degrees in the mid-equatorial anterolateral sector). We conclude that midwall myofiber angles and transmural myofiber angle gradients in the ovine heart are regionally non-uniform and differ significantly from the predictions of present-day computationally optimized LV myofiber models. Myofiber geometry in the ovine heart may differ from other species, but model assumptions also underlie the discrepancy between experimental and computational results. To test the predictive capability of the current computational model would we propose using an ovine specific LV geometry and comparing the computed myofiber orientations to those we report herein.     

Why SIT Works: Normal Function Despite Typical Myofiber Pattern in Situs Inversus Totalis (SIT) Hearts Derived by Shear-induced Myofiber Reorientation

The left ventricle (LV) of mammals with Situs Solitus (SS, normal organ arrangement) displays hardly any interindividual variation in myofiber pattern and experimentally determined torsion. SS LV myofiber pattern has been suggested to result from adaptive myofiber reorientation, in turn leading to efficient pump and myofiber function. Limited data from the Situs Inversus Totalis (SIT, a complete mirror image of organ anatomy and position) LV demonstrated an essential different myofiber pattern, being normal at the apex but mirrored at the base. Considerable differences in torsion patterns in between human SIT LVs even suggest variation in myofiber pattern among SIT LVs themselves. We addressed whether different myofiber patterns in the SIT LV can be predicted by adaptive myofiber reorientation and whether they yield similar pump and myofiber function as in the SS LV. With a mathematical model of LV mechanics including shear induced myofiber reorientation, we predicted myofiber patterns of one SS and three different SIT LVs. Initial conditions for SIT were based on scarce information on the helix angle. The transverse angle was set to zero. During reorientation, a non-zero transverse angle developed, pump function increased, and myofiber function increased and became more homogeneous. Three continuous SIT structures emerged with a different location of transition between normal and mirrored myofiber orientation pattern. Predicted SIT torsion patterns matched experimentally determined ones. Pump and myofiber function in SIT and SS LVs are similar, despite essential differences in myocardial structure. SS and SIT LV structure and function may originate from same processes of adaptive myofiber reorientation.     

Regional left ventricular myocardial contractility and stress in a finite element model of posterobasal myocardial infarction

Recently, a noninvasive method for determining regional myocardial contractility, using an animal-specific finite element (FE) model-based optimization, was developed to study a sheep with anteroapical infarction (Sun et al., 2009, "A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm," ASME J. Biomech. Eng., 131(11), p. 111001). Using the methodology developed in the previous study (Sun et al., 2009, "A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm," ASME J. Biomech. Eng., 131(11), p. 111001), which incorporates tagged magnetic resonance images, three-dimensional myocardial strains, left ventricular (LV) volumes, and LV cardiac catheterization pressures, the regional myocardial contractility and stress distribution of a sheep with posterobasal infarction were investigated. Active material parameters in the noninfarcted border zone (BZ) myocardium adjacent to the infarct (T(max_B)), in the myocardium remote from the infarct (T(max_R)), and in the infarct (T(max_I)) were estimated by minimizing the errors between FE model-predicted and experimentally measured systolic strains and LV volumes using the previously developed optimization scheme. The optimized T(max_B) was found to be significantly depressed relative to T(max_R), while T(max_I) was found to be zero. The myofiber stress in the BZ was found to be elevated, relative to the remote region. This could cause further damage to the contracting myocytes, leading to heart failure.     

Contribution of myocardium overlying the anterolateral papillary muscle to left ventricular deformation

Previous studies of transmural left ventricular (LV) strains suggested that the myocardium overlying the papillary muscle displays decreased deformation relative to the anterior LV free wall or significant regional heterogeneity. These comparisons, however, were made using different hearts. We sought to extend these studies by examining three equatorial LV regions in the same heart during the same heartbeat. Therefore, deformation was analyzed from transmural beadsets placed in the equatorial LV myocardium overlying the anterolateral papillary muscle (PAP), as well as adjacent equatorial LV regions located more anteriorly (ANT) and laterally (LAT). We found that the magnitudes of LAT normal longitudinal and radial strains, as well as major principal strains, were less than ANT, while those of PAP were intermediate. Subepicardial and midwall myofiber angles of LAT, PAP, and ANT were not significantly different, but PAP subendocardial myofiber angles were significantly higher (more longitudinal as opposed to circumferential orientation). Subepicardial and midwall myofiber strains of ANT, PAP, and LAT were not significantly different, but PAP subendocardial myofiber strains were less. Transmural gradients in circumferential and radial normal strains, and major principal strains, were observed in each region. The two main findings of this study were as follows: 1) PAP strains are largely consistent with adjacent LV equatorial free wall regions, and 2) there is a gradient of strains across the anterolateral equatorial left ventricle despite similarities in myofiber angles and strains. These findings point to graduated equatorial LV heterogeneity and suggest that regional differences in myofiber coupling may constitute the basis for such heterogeneity.     

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

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

Structure and torsion in the normal and situs inversus totalis cardiac left ventricle. II. Modeling cardiac adaptation to mechanical load

Mathematical models provide a suitable platform to test hypotheses on the relation between local mechanical stimuli and responses to cardiac structure and geometry. In the present model study, we tested hypothesized mechanical stimuli and responses in cardiac adaptation to mechanical load on their ability to estimate a realistic myocardial structure of the normal and situs inversus totalis (SIT) left ventricle (LV). In a cylindrical model of the LV, 1) mass was adapted in response to myofiber strain at the beginning of ejection and to global contractility (average systolic pressure), 2) cavity volume was adapted in response to fiber strain during ejection, and 3) myofiber orientations were adapted in response to myofiber strain during ejection and local misalignment between neighboring tissue parts. The model was able to generate a realistic normal LV geometry and structure. In addition, the model was also able to simulate the instigating situation in the rare SIT LV with opposite torsion and transmural courses in myofiber direction between the apex and base [Delhaas et al. (6)]. These results substantiate the importance of mechanical load in the formation and maintenance of cardiac structure and geometry. Furthermore, in the model, adapted myocardial architecture was found to be insensitive to fiber misalignment in the transmural direction, i.e., myofiber strain during ejection was sufficient to generate a realistic transmural variation in myofiber orientation. In addition, the model estimates that, despite differences in structure, global pump work and the mass of the normal and SIT LV are similar.     

Effects of dihydroergotamine on hemodynamic molsidomine actions in anesthetized dogs

In pentobarbital-anesthetized mongrel dogs the intravenous actions of 0.50 mg/kg molsidomine on pulmonary artery and left ventricular (LV) end-diastolic pressures and internal heart dimensions (preload), left ventricular systolic and peripheral blood pressures, and total peripheral resistance (afterload), as well as on heart rate, dP/dt, stroke volume, and cardiac output (heart performance) were studied for 2 h. Hemodynamic molsidomine effects were influenced by increasing amounts of intravenously infused dihydroergotamine solution (DHE, 1-64 micrograms X kg-1 X min-1). Molsidomine decreased preload, stroke volume, and cardiac output for over 2 h but decreased ventricular and peripheral pressures for 45 min. Systemic vascular resistance showed a tendency to decrease while heart rate and LV dP/dtmax were not altered. DHE infusion reversed molsidomine effects on the preload and afterload of the heart. The diminished stroke volume was elevated so that cardiac output also increased. Total peripheral resistance increased while heart rate fell in a dose-dependent fashion. The LV dP/dtmax remained unchanged until the highest dose of 64 micrograms X kg-1 X min-1 DHE elevated the isovolumic myocardial contractility. These experiments indicate that DHE can reverse the intravenous molsidomine effects on hemodynamics. Most likely, this is mediated through peripheral vasoconstriction of venous capacitance vessels, thereby affecting molsidomine's action on postcapillary beds of the circulation.     

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

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

Cardiac resynchronization therapy modulation of exercise left ventricular function and pulmonary O₂ uptake in heart failure

To better understand the mechanisms contributing to improved exercise capacity with cardiac resynchronization therapy (CRT), we studied the effects of 6 mo of CRT on pulmonary O(2) uptake (Vo(2)) kinetics, exercise left ventricular (LV) function, and peak Vo(2) in 12 subjects (age: 56 ± 15 yr, peak Vo(2): 12.9 ± 3.2 ml·kg(-1)·min(-1), ejection fraction: 18 ± 3%) with heart failure. We hypothesized that CRT would speed Vo(2) kinetics due to an increase in stroke volume secondary to a reduction in LV end-systolic volume (ESV) and that the increase in peak Vo(2) would be related to an increase in cardiac output reserve. We found that Vo(2) kinetics were faster during the transition to moderate-intensity exercise after CRT (pre-CRT: 69 ± 21 s vs. post-CRT: 54 ± 17 s, P < 0.05). During moderate-intensity exercise, LV ESV reserve (exercise - resting) increased 9 ± 7 ml (vs. a 3 ± 9-ml decrease pre-CRT, P < 0.05), and steady-state stroke volume increased (pre-CRT: 42 ± 8 ml vs. post-CRT: 61 ± 12 ml, P < 0.05). LV end-diastolic volume did not change from rest to steady-state exercise post-CRT (P > 0.05). CRT improved heart rate, measured as a lower resting and steady-state exercise heart rate and as faster heart rate kinetics after CRT (pre-CRT: 89 ± 12 s vs. post-CRT: 69 ± 21 s, P < 0.05). For peak exercise, cardiac output reserve increased significantly post-CRT and was 22% higher at peak exercise post-CRT (both P < 0.05). The increase in cardiac output was due to both a significant increase in peak and reserve stroke volume and to a nonsignificant increase in heart rate reserve. Similar patterns in LV volumes as moderate-intensity exercise were observed at peak exercise. Cardiac output reserve was related to peak Vo(2) (r = 0.48, P < 0.05). These findings demonstrate the chronic CRT-mediated cardiac factors that contribute, in part, to the speeding in Vo(2) kinetics and increase in peak Vo(2) in clinically stable heart failure patients.     

Cardiac assist with a twist: apical torsion as a means to improve failing heart function

Changes in muscle fiber orientation across the wall of the left ventricle (LV) cause the apex of the heart to turn 10-15 deg in opposition to its base during systole and are believed to increase stroke volume and lower wall stress in healthy hearts. Studies show that cardiac torsion is sensitive to various disease states, which suggests that it may be an important aspect of cardiac function. Modern imaging techniques have sparked renewed interest in cardiac torsion dynamics, but no work has been done to determine whether mechanically augmented apical torsion can be used to restore function to failing hearts. In this report, we discuss the potential advantages of this approach and present evidence that turning the cardiac apex by mechanical means can displace a clinically significant volume of blood from failing hearts. Computational models of normal and reduced-function LVs were created to predict the effects of applied apical torsion on ventricular stroke work and wall stress. These same conditions were reproduced in anesthetized pigs with drug-induced heart failure using a custom apical torsion device programmed to rotate over various angles during cardiac systole. Simulations of applied 90 deg torsion in a prolate spheroidal computational model of a reduced-function pig heart produced significant increases in stroke work (25%) and stroke volume with reduced fiber stress in the epicardial region. These calculations were in substantial agreement with corresponding in vivo measurements. Specifically, the computer model predicted torsion-induced stroke volume increases from 13.1 to 14.4 mL (9.9%) while actual stroke volume in a pig heart of similar size and degree of dysfunction increased from 11.1 to 13.0 mL (17.1%). Likewise, peak LV pressures in the computer model rose from 85 to 95 mm Hg (11.7%) with torsion while maximum ventricular pressures in vivo increased in similar proportion, from 55 to 61 mm Hg (10.9%). These data suggest that: (a) the computer model of apical torsion developed for this work is a fair and accurate predictor of experimental outcomes, and (b) supra-physiologic apical torsion may be a viable means to boost cardiac output while avoiding blood contact that occurs with other assist methods.     

Determinants of biventricular cardiac function: a mathematical model study on geometry and myofiber orientation

In patient-specific mathematical models of cardiac electromechanics, usually a patient-specific geometry and a generic myofiber orientation field are used as input, upon which myocardial tissue properties are tuned to clinical data. It remains unclear to what extent deviations in myofiber orientation and geometry between model and patient influence model predictions on cardiac function. Therefore, we evaluated the sensitivity of cardiac function for geometry and myofiber orientation in a biventricular (BiV) finite element model of cardiac mechanics. Starting out from a reference geometry in which myofiber orientation had no transmural component, two new geometries were defined with either a 27 % decrease in LV short- to long-axis ratio, or a 16 % decrease of RV length, but identical LV and RV cavity and wall volumes. These variations in geometry caused differences in both local myofiber and global pump work below 6 %. Variation of fiber orientation was induced through adaptive myofiber reorientation that caused an average change in fiber orientation of \({\sim }8^\circ \) predominantly through the formation of a component in transmural direction. Reorientation caused a considerable increase in local myofiber work \(({\sim }18\,\%)\) and in global pump work \(({\sim }17\,\%)\) in all three geometries, while differences between geometries were below 5 %. The findings suggest that implementing a realistic myofiber orientation is at least as important as defining a patient-specific geometry. The model for remodeling of myofiber orientation seems a useful approach to estimate myofiber orientation in the absence of accurate patient-specific information.

     

Regional ventricular wall thickening reflects changes in cardiac fiber and sheet structure during contraction: quantification with diffusion tensor MRI

Dynamic changes of myocardial fiber and sheet structure are key determinants of regional ventricular function. However, quantitative characterization of the contraction-related changes in fiber and sheet structure has not been reported. The objective of this study was to quantify cardiac fiber and sheet structure at selected phases of the cardiac cycle. Diffusion tensor MRI was performed on isolated, perfused Sprague-Dawley rat hearts arrested or fixed in three states as follows: 1) potassium arrested (PA), which represents end diastole; 2) barium-induced contracture with volume (BV+), which represents isovolumic contraction or early systole; and 3) barium-induced contracture without volume (BV-), which represents end systole. Myocardial fiber orientations at the base, midventricle, and apex were determined from the primary eigenvectors of the diffusion tensor. Sheet structure was determined from the secondary and tertiary eigenvectors at the same locations. We observed that the transmural distribution of the myofiber helix angle remained unchanged as contraction proceeded from PA to BV+, but endocardial and epicardial fibers became more longitudinally orientated in the BV- group. Although sheet structure exhibited significant regional variations, changes in sheet structure during myocardial contraction were relatively uniform across regions. The magnitude of the sheet angle, which is an index of local sheet slope, decreased by 23 and 44% in BV+ and BV- groups, respectively, which suggests more radial orientation of the sheet. In summary, we have shown for the first time that geometric changes in both sheet and fiber orientation provide a substantial mechanism for radial wall thickening independent of active components due to myofiber shortening. Our results provide direct evidence that sheet reorientation is a primary determinant of myocardial wall thickening.     

An Inverse Finite Element Method for Determining the Tissue Compressibility of Human Left Ventricular Wall during the Cardiac Cycle

The determination of the myocardium’s tissue properties is important in constructing functional finite element (FE) models of the human heart. To obtain accurate properties especially for functional modeling of a heart, tissue properties have to be determined in vivo. At present, there are only few in vivo methods that can be applied to characterize the internal myocardium tissue mechanics. This work introduced and evaluated an FE inverse method to determine the myocardial tissue compressibility. Specifically, it combined an inverse FE method with the experimentally-measured left ventricular (LV) internal cavity pressure and volume versus time curves. Results indicated that the FE inverse method showed good correlation between LV repolarization and the variations in the myocardium tissue bulk modulus K (K = 1/compressibility), as well as provided an ability to describe in vivo human myocardium material behavior. The myocardium bulk modulus can be effectively used as a diagnostic tool of the heart ejection fraction. The model developed is proved to be robust and efficient. It offers a new perspective and means to the study of living-myocardium tissue properties, as it shows the variation of the bulk modulus throughout the cardiac cycle.     

Maternal Treatment with Agonistic Autoantibodies against Type-1 Angiotensin II Receptor in Late Pregnancy Increases Apoptosis of Myocardial Cells and Myocardial Susceptibility to Ischemia-Reperfusion Injury in Offspring Rats

Epidemiological studies have demonstrated that offspring born to mothers preeclampsia (PE) are at increased risk for developing cardiovascular diseases after birth, but the underlying mechanism is unknown. Angiotensin II receptor type 1 autoantibody (AT1-AA), an agonist acting via activation of the AT1 receptor, is believed to be involved in the pathogenesis of both PE and fetal growth restriction. The aim of the present study was to confirm the hypothesis that prenatal AT1-AA exposure increases the heart susceptibility to ischemia/reperfusion injury (IRI) in the offspring in an AT1-AA-induced animal model of PE, and determine whether or not the increase of maternal AT1-AA level is a factor contributing to sustained abnormalities of the heart structure during infancy. The hearts of 45-day-old offspring rats were studied using Langendorff preparation to determine the susceptibility of the heart to IRI. The results showed that the body weight of the maternal rats was not significantly different between the study and control groups, but the body weight of their offspring in AT1-AA group was decreased slightly at day 21 of gestational age, and at day 3 after birth. Although the heart weight index was not significantly affected at all ages examined, AT1-AA significantly increased the size of myocardial cells of the left ventricle (LV) at the age of 45 days. AT1-AA gained access to fetal circulation via the placenta and induced apoptosis of fetal myocardial cells. AT1-AA also significantly delayed recovery from IRI and affected the LV function of 45-day-old offspring. This was associated with a significant increase in IRI-induced LV myocardial infarct size. These results suggest that AT1-AA induced abnormal apoptosis of fetal myocardial cells during the fetal period and increased the cardiac susceptibility to IRI in adult offspring.     

Structure and torsion of the normal and situs inversus totalis cardiac left ventricle. I. Experimental data in humans

In 1926, the famous American pediatric cardiologist, Dr. Helen B. Taussig, observed that in situs inversus totalis (SIT) main gross anatomical structures and the deep muscle bundles of the ventricles were a mirror image of the normal structure, while the direction of the superficial muscle bundles remained unchanged (H. B. Taussig, Bull Johns Hopkins Hosp 39: 199-202, 1926). She and we wondered about the implication of this observation for left ventricular (LV) deformation in SIT. We used magnetic resonance tagging to obtain information on LV deformation, rotation, and torsion from a series of tagged images in five evenly distributed, parallel, short-axis sections of the heart of nine controls and eight persons with SIT without other structural (cardiac) defect. In the controls, during ejection, the apex rotated counterclockwise with respect to the base, when looking from the apex. Furthermore, the base-to-apex gradient in rotation (torsion) was negative and similar at all longitudinal levels of the LV. In SIT hearts, torsion was positive near the base, indicating mirrored myofiber orientations compared with the normal LV. Contrary to expectations, torsion in the apical regions of SIT LVs was as in normal ones, reflecting a normal internal myocardial architecture. The transition zone with zero torsion, found between the apex and base, suggests that the heart structure in SIT is essentially different from that in the normal heart. This provides a unique possibility to study regulatory mechanisms for myocardial fiber orientation and mechanical load, which has been dealt with in the companion paper by Kroon et al.     

A finite element model of myocardial infarction using a composite material approach

Computational models are effective tools to study cardiac mechanics under normal and pathological conditions. They can be used to gain insight into the physiology of the heart under these conditions while they are adaptable to computer assisted patient-specific clinical diagnosis and therapeutic procedures. Realistic cardiac mechanics models incorporate tissue active/passive response in conjunction with hyperelasticity and anisotropy. Conventional formulation of such models leads to mathematically-complex problems usually solved by custom-developed non-linear finite element (FE) codes. With a few exceptions, such codes are not available to the research community. This article describes a computational cardiac mechanics model developed such that it can be implemented using off-the-shelf FE solvers while tissue pathologies can be introduced in the model in a straight-forward manner. The model takes into account myocardial hyperelasticity, anisotropy, and active contraction forces. It follows a composite tissue modeling approach where the cardiac tissue is decomposed into two major parts: background and myofibers. The latter is modelled as rebars under initial stresses mimicking the contraction forces. The model was applied in silico to study the mechanics of infarcted left ventricle (LV) of a canine. End-systolic strain components, ejection fraction, and stress distribution attained using this LV model were compared quantitatively and qualitatively to corresponding data obtained from measurements as well as to other corresponding LV mechanics models. This comparison showed very good agreement.     

Optimizing ventricular fibers: uniform strain or stress,but not ATP consumption,leads to high efficiency

The aim of this study was to investigate the influence of fiber orientation in the left ventricular (LV) wall on the ejection fraction, efficiency, and heterogeneity of the distributions of developed fiber stress, strain and ATP consumption. A finite element model of LV mechanics was used with active properties of the cardiac muscle described by the Huxley-type cross-bridge model. The computed variances of sarcomere length (SL(var)), developed stress (DS(var)), and ATP consumption (ATP(var)) have several minima at different transmural courses of helix fiber angle. We identified only one region in the used design space with high ejection fraction, high efficiency of the LV and relatively small SL(var), DS(var), and ATP(var). This region corresponds to the physiological distribution of the helix fiber angle in the LV wall. Transmural fiber angle can be predicted by minimizing SL(var) and DS(var), but not ATP(var). If ATP(var) was minimized, then the transverse fiber angle was considerably underestimated. The results suggest that ATP consumption distribution is not regulating the fiber orientation in the heart.