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

Understanding heterogeneous mechanisms of heart failure with preserved ejection fraction through cardiorenal mathematical modeling

In contrast to heart failure (HF) with reduced ejection fraction (HFrEF), effective interventions for HF with preserved ejection fraction (HFpEF) have proven elusive, in part because it is a heterogeneous syndrome with incompletely understood pathophysiology. This study utilized mathematical modeling to evaluate mechanisms distinguishing HFpEF and HFrEF. HF was defined as a state of chronically elevated left ventricle end diastolic pressure (LVEDP > 20mmHg). First, using a previously developed cardiorenal model, sensitivities of LVEDP to potential contributing mechanisms of HFpEF, including increased myocardial, arterial, or venous stiffness, slowed ventricular relaxation, reduced LV contractility, hypertension, or reduced venous capacitance, were evaluated. Elevated LV stiffness was identified as the most sensitive factor. Large LV stiffness increases alone, or milder increases combined with either decreased LV contractility, increased arterial stiffness, or hypertension, could increase LVEDP into the HF range without reducing EF. We then evaluated effects of these mechanisms on mechanical signals of cardiac outward remodeling, and tested the ability to maintain stable EF (as opposed to progressive EF decline) under two remodeling assumptions: LV passive stress-driven vs. strain-driven remodeling. While elevated LV stiffness increased LVEDP and LV wall stress, it mitigated wall strain rise for a given LVEDP. This suggests that if LV strain drives outward remodeling, a stiffer myocardium will experience less strain and less outward dilatation when additional factors such as impaired contractility, hypertension, or arterial stiffening exacerbate LVEDP, allowing EF to remain normal even at high filling pressures. Thus, HFpEF heterogeneity may result from a range of different pathologic mechanisms occurring in an already stiffened myocardium. Together, these simulations further support LV stiffening as a critical mechanism contributing to elevated cardiac filling pressures; support LV passive strain as the outward dilatation signal; offer an explanation for HFpEF heterogeneity; and provide a mechanistic explanation distinguishing between HFpEF and HFrEF.

Multiscale simulations of left ventricular growth and remodeling

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

Computational models of cardiac hypertrophy

Cardiac hypertrophy, defined as an increase in mass of the heart, is a complex process driven by simultaneous changes in hemodynamics, mechanical stimuli, and hormonal inputs. It occurs not only during pre- and post-natal development but also in adults in response to exercise, pregnancy, and a range of cardiovascular diseases. One of the most exciting recent developments in the field of cardiac biomechanics is the advent of computational models that are able to accurately predict patterns of heart growth in many of these settings, particularly in cases where changes in mechanical loading of the heart play an import role. These emerging models may soon be capable of making patient-specific growth predictions that can be used to guide clinical interventions. Here, we review the history and current state of cardiac growth models and highlight three main limitations of current approaches with regard to future clinical application: their inability to predict the regression of heart growth after removal of a mechanical overload, inability to account for evolving hemodynamics, and inability to incorporate known growth effects of drugs and hormones on heart growth. Next, we outline growth mechanics approaches used in other fields of biomechanics and highlight some potential lessons for cardiac growth modeling. Finally, we propose a multiscale modeling approach for future studies that blends tissue-level growth models with cell-level signaling models to incorporate the effects of hormones in the context of pregnancy-induced heart growth.

Mathematical modeling of cardiac growth and remodeling

This review provides an overview of the current state of mathematical models of cardiac growth and remodeling (G&R). We concisely describe the experimental observations associated with cardiac G&R and discuss existing mathematical models that describe this process. To facilitate the discussion, we have organized the G&R models in terms of (1) the physical focus (biochemical vs mechanical) and (2) the process that they describe (myocyte hypertrophy vs extracellular matrix remodeling). The review concludes with a discussion of some possible directions that can advance the existing state of cardiac G&R mathematical modeling. WIREs Syst Biol Med 2016, 8:211-226. doi: 10.1002/wsbm.1330 For further resources related to this article, please visit the WIREs website.

Stress and strain adaptation in load-dependent remodeling of the embryonic left ventricle

Altered pressure in the developing left ventricle (LV) results in altered morphology and tissue material properties. Mechanical stress and strain may play a role in the regulating process. This study showed that confocal microscopy, three-dimensional reconstruction, and finite element analysis can provide a detailed model of stress and strain in the trabeculated embryonic heart. The method was used to test the hypothesis that end-diastolic strains are normalized after altered loading of the LV during the stages of trabecular compaction and chamber formation. Stage-29 chick LVs subjected to pressure overload and underload at stage 21 were reconstructed with full trabecular morphology from confocal images and analyzed with finite element techniques. Measured material properties and intraventricular pressures were specified in the models. The results show volume-weighted end-diastolic von Mises stress and strain averaging 50-82 % higher in the trabecular tissue than in the compact wall. The volume-weighted-average stresses for the entire LV were 115, 64, and 147 Pa in control, underloaded, and overloaded models, while strains were 11, 7, and 4 %; thus, neither was normalized in a volume-weighted sense. Localized epicardial strains at mid-longitudinal level were similar among the three groups and to strains measured from high-resolution ultrasound images. Sensitivity analysis showed changes in material properties are more significant than changes in geometry in the overloaded strain adaptation, although resulting stress was similar in both types of adaptation. These results emphasize the importance of appropriate metrics and the role of trabecular tissue in evaluating the evolution of stress and strain in relation to pressure-induced adaptation.

A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload

Adult cardiac muscle adapts to mechanical changes in the environment by growth and remodeling (G&R) via a variety of mechanisms. Hypertrophy develops when the heart is subjected to chronic mechanical overload. In ventricular pressure overload (e.g. due to aortic stenosis) the heart typically reacts by concentric hypertrophic growth, characterized by wall thickening due to myocyte radial growth when sarcomeres are added in parallel. In ventricular volume overload, an increase in filling pressure (e.g. due to mitral regurgitation) leads to eccentric hypertrophy as myocytes grow axially by adding sarcomeres in series leading to ventricular cavity enlargement that is typically accompanied by some wall thickening. The specific biomechanical stimuli that stimulate different modes of ventricular hypertrophy are still poorly understood. In a recent study, based on in-vitro studies in micropatterned myocyte cell cultures subjected to stretch, we proposed that cardiac myocytes grow longer to maintain a preferred sarcomere length in response to increased fiber strain and grow thicker to maintain interfilament lattice spacing in response to increased cross-fiber strain. Here, we test whether this growth law is able to predict concentric and eccentric hypertrophy in response to aortic stenosis and mitral valve regurgitation, respectively, in a computational model of the adult canine heart coupled to a closed loop model of circulatory hemodynamics. A non-linear finite element model of the beating canine ventricles coupled to the circulation was used. After inducing valve alterations, the ventricles were allowed to adapt in shape in response to mechanical stimuli over time. The proposed growth law was able to reproduce major acute and chronic physiological responses (structural and functional) when integrated with comprehensive models of the pressure-overloaded and volume-overloaded canine heart, coupled to a closed-loop circulation. We conclude that strain-based biomechanical stimuli can drive cardiac growth, including wall thickening during pressure overload.

The role of the Frank-Starling law in the transduction of cellular work to whole organ pump function: a computational modeling analysis

We have developed a multi-scale biophysical electromechanics model of the rat left ventricle at room temperature. This model has been applied to investigate the relative roles of cellular scale length dependent regulators of tension generation on the transduction of work from the cell to whole organ pump function. Specifically, the role of the length dependent Ca(2+) sensitivity of tension (Ca(50)), filament overlap tension dependence, velocity dependence of tension, and tension dependent binding of Ca(2+) to Troponin C on metrics of efficient transduction of work and stress and strain homogeneity were predicted by performing simulations in the absence of each of these feedback mechanisms. The length dependent Ca(50) and the filament overlap, which make up the Frank-Starling Law, were found to be the two dominant regulators of the efficient transduction of work. Analyzing the fiber velocity field in the absence of the Frank-Starling mechanisms showed that the decreased efficiency in the transduction of work in the absence of filament overlap effects was caused by increased post systolic shortening, whereas the decreased efficiency in the absence of length dependent Ca(50) was caused by an inversion in the regional distribution of strain.

Age-related cardiac muscle sarcopenia: Combining experimental and mathematical modeling to identify mechanisms

Age-related skeletal muscle sarcopenia has been extensively studied and smooth muscle sarcopenia has been recently described, but age-related cardiac sarcopenia has not been previously examined. Therefore, we evaluated adult (7.5+/-0.5 months; n = 27) and senescent (31.8+/-0.4 months; n = 26) C57BL/6J mice for cardiac sarcopenia using physiological, histological, and biochemical assessments. Mice do not develop hypertension, even into senescence, which allowed us to decouple vascular effects and monitor cardiac-dependent variables. We then developed a mathematical model to describe the relationship between age-related changes in cardiac muscle structure and function. Our results showed that, compared to adult mice, senescent mice demonstrated increased left ventricular (LV) end diastolic dimension, decreased wall thickness, and decreased ejection fraction, indicating dilation and reduced contractile performance. Myocyte numbers decreased, and interstitial fibrosis was punctated but doubled in the senescent mice, indicating reparative fibrosis. Electrocardiogram analysis showed that PR interval and QRS interval increased and R amplitude decreased in the senescent mice, indicating prolonged conduction times consistent with increased fibrosis. Intracellular lipid accumulation was accompanied by a decrease in glycogen stores in the senescent mice. Mathematical simulation indicated that changes in LV dimension, collagen deposition, wall stress, and wall stiffness precede LV dysfunction. We conclude that age-related cardiac sarcopenia occurs in mice and that LV remodeling due to increased end diastolic pressure could be an underlying mechanism for age-related LV dysfunction.

Role of diastolic properties in the transition to failure in a mouse model of the cardiac dilatation

Although the physiological states of hypertrophic remodeling and congestive heart failure have been intensively studied, less is known about the transition from one to the other. The use of genetically engineered murine models of heart failure has proven valuable in characterizing the progression of remodeling and its ultimate decompensation to failure. Mice deficient in the cytoskeletal muscle LIM-only protein (MLP) are known to present with a clinical picture of dilated cardiomyopathy and transition to failure as adults. Longitudinal high-field magnetic resonance (MR) cardiac imaging provided a time course of remodeling where an improvement in ejection fraction and stroke volume (15- vs. 31-wk MLP(-/-) mice; P < 0.0001) was temporally concurrent with an abrupt phase of end-diastolic chamber dilatation. Hemodynamic analysis conducted throughout that dilatation phase showed improved ratio of maximum first derivative of pressure to end-diastolic pressure (dP/dt(max)/EDP; 15- vs. 31-wk MLP(-/-) mice; P < 0.0005), ratio of minimum first derivative of pressure to EDP (dP/dt(min)/EDP; 15- vs. 31-wk MLP(-/-) mice; P < 0.003), and developed pressure (15- vs. 31-wk MLP(-/-) mice; P < 0.0001) levels in the MLP(-/-) mice. Computational modeling techniques were used to estimate the EDP volume relationship, revealing that although MLP hearts possess a stiffer stress-strain relation, chamber compliance increased as a function of dilatation. This detailed physiological characterization during a phase of rapid anatomical remodeling suggests that systolic function in the MLP(-/-) mice may temporarily improve as a result of alterations in chamber compliance, which are mediated by dilatation. In turn, a balance may exist between exploiting the Frank-Starling mechanism and altering chamber compliance that maintains function in the absence of hypertrophic growth. Though initially compensatory, this process may exhaust itself and consequently transition to a maladaptive course.

Determinants of left ventricular shape change during filling

Left ventricular shape and shape change are easy to measure and their analysis has been proposed as a noninvasive method to determine myocardial anisotropy. In preparation for applying this approach to studies of rats with experimentally induced cardiac hypertrophy, the goals of this study were to describe normal shape changes during diastolic filling in the rat and to utilize a finite-element model to estimate the relative importance of three factors that determine left ventricular shape change during filling: global chamber compliance, fiber to crossfiber stiffness ratio, and fiber architecture. The results suggest that left ventricular shape change is least sensitive to fiber to cross fiber stiffness ratio, and that this will likely limit the practical utility of using shape changes to diagnose changes in myocardial anisotropy.

Distribution of stress and strain along the porcine aorta and coronary arterial tree

The existence of a homeostatic state of stresses and strains has been axiomatic in the cardiovascular system. The objective of this study was to determine the distribution of circumferential stress and strain along the aorta and throughout the coronary arterial tree to test this hypothesis. Silicone elastomer was perfused through the porcine aorta and coronary arterial tree to cast the arteries at physiological pressure. The loaded and zero-stress dimensions of the vessels were measured. The aorta (1.8 cm) and its secondary branches were considered down to 1.5 mm diameter. The left anterior descending artery (4.5 mm) and its branches down to 10 microm were also measured. The Cauchy mean circumferential stress and midwall stretch ratio were calculated. Our results show that the stretch ratio and Cauchy stress were lower in the thoracic than in the abdominal aorta and its secondary branches. The opening angle (theta) and midwall stretch ratio (lambda) showed a linear variation with order number (n) as follows: theta = 10.2n + 63.4 (R(2) = 0.989) and lambda = 4.47 x 10(-2)n + 1.1 (R(2) = 0.995). Finally, the stretch ratio and stress varied between 1.2 and 1.6 and between 10 and 150 kPa, respectively, along the aorta and left anterior descending arterial tree. The relative uniformity of strain (50% variation) from the proximal aorta to a 10-microm arteriole implies that the vascular system closely regulates the degree of deformation. This suggests a homeostasis of strain in the cardiovascular system, which has important implications for mechanotransduction and for vascular growth and remodeling.

Candidate mechanical stimuli for hypertrophy during volume overload

A myocyte system that senses and responds to mechanical inputs might be activated by any number of features of the time-varying length or force signals experienced by the myocytes. We therefore characterized left ventricular volume and wall stress signals during early volume overload with high spatial and temporal resolution. Left ventricular pressure and volume were measured in open-chest isoflurane-anesthetized male Sprague-Dawley rats 4 and 7 days after surgical creation of an infrarenal arteriovenous fistula or sham operation. Mean wall stresses were calculated by using a simple thick-walled ellipsoidal model. Consistent with previous reports, this surgical model produced a 66% increase in cardiac output and a 10% increase in left ventricular mass by day 7. A number of features of the time-varying volume signal (maximum, mean, amplitude, rates of rise and fall) were significantly altered during early volume overload, whereas many other proposed hypertrophic stimuli, including peak systolic wall stress and diastolic strain, were not. Treating hemodynamic variables more generally as time-varying signals allowed us to identify a wider range of candidate mechanical stimuli for hypertrophy (including some not previously proposed in the literature) than focusing on standard time points in the cardiac cycle. We conclude that features of the time-varying ventricular volume signal and related local deformations may drive hypertrophy during volume overload and propose that those features of the volume signal that also change during pressure overload might be the most interesting candidates for further exploration.

Low coronary perfusion pressure is associated with endocardial fibrosis in a rat model of volume overload cardiac hypertrophy

Left ventricular hypertrophy following volume overload is regarded as an example of cardiac remodeling without increased fibrosis accumulation. However, infarction is associated with increased fibrosis within the noninfarcted, hypertrophied myocardium, particularly in the subendocardial regions. It is conceivable to suppose that, as also occurs postinfarction, low coronary driving pressure may also interfere with accumulation of myocardial fibrosis following aortocaval fistula. PURPOSE: To investigate the role of acute hemodynamic changes in subsequent deposition of cardiac fibrosis in response to aortocaval fistula. METHOD: Aortocaval fistula were created in 4 groups of Wistar rats that were followed over 4 and 8 weeks: aortocaval fistula 4 and aortocaval fistula 8 (10 rats each) and their respective controls (sham-operated controls - Sh), Sh4 and Sh8 (8 rats each). Hemodynamic measurements were performed 1 week after surgery. Hypertrophy and fibrosis were quantified by myocyte diameter and collagen volume fraction at the end of follow up. RESULT: Compared with Sh4 and Sh8, pulse pressure, left ventricular end-diastolic pressure, and +dP/dt were higher in aortocaval fistula 4 and aortocaval fistula 8, but -dP/dt was similar. Coronary driving pressure (mm Hg), used as an estimate of perfusion pressure, was lower in aortocaval fistula 8 (52.6 ± 4.1) than in Sh8 (100.8 ± 1.3), but comparable between aortocaval fistula 4 (50.0 ± 8.9) and Sh4 (84.8 ± 2.3). Myocyte diameter was greater in aortocaval fistula 8, whereas interstitial and subendocardial fibrosis were greater in aortocaval fistula 4 and aortocaval fistula 8. Coronary driving pressure correlated inversely and independently with subendocardial fibrosis (r² = .86, P <.001), whereas left ventricular systolic pressure (r² = 0.73, P = .004) and end-diastolic pressure (r² = 0.55, P = 012) correlated positively and independently with interstitial fibrosis. CONCLUSION: Coronary driving pressure falls and ventricular pressures increase early after aortocaval fistula and are associated with subsequent myocardial fibrosis deposition.

Pressure overload alters stress-strain properties of the developing chick heart

As a first step in investigating a control mechanism regulating stress and/or strain in the embryonic heart, this study tests the hypothesis that passive mechanical properties of left ventricular (LV) embryonic myocardium change with chronically increased pressure during the chamber septation period. Conotruncal banding (CTB) created ventricular pressure overload in chicks from Hamburger-Hamilton (HH) stage 21 (HH21) to HH27, HH29, or HH31. LV sections were cyclically stretched while biaxial strains and force were measured. Wall architecture was assessed with scanning electron microscopy. In controls, porosity-adjusted stress-strain relations decreased significantly from HH27 to HH31. CTB at HH21 resulted in significantly stiffer stress-strain relations by HH27, with larger increases at HH29 and HH31, and nearly constant wall thickness. Strain patterns, hysteresis, and loading-curve convergence showed few differences after CTB. Trabecular extent decreased with age, but neither extent nor porosity changed significantly after CTB. The stiffened stress-strain relations and constant wall thickness suggest that mechanical load may play a regulatory role in this response.

Modeling Total Heart Function

Computational models of the electrical and mechanical function of the heart are reviewed. These models attempt to explain the integrated function of the heart in terms of ventricular anatomy, the structure and material properties of myocardial tissue, the membrane ion channels, and calcium handling and myofilament mechanics of cardiac myocytes. The models have established the computational framework for linking the structure and function of cardiac cells and tissue to the integrated behavior of the intact heart, but many more aspects of physiological function, including metabolic and signal transduction pathways, need to be included before significant progress can be made in understanding many disease processes.

Glycated collagen cross-linking alters cardiac mechanics in volume-overload hypertrophy

Alteration of hemodynamic loading induces remodeling that includes changes in myocardial properties and extracellular matrix structure. We investigated the hypothesis that cardiac hypertrophy due to volume overload produces changes in myocardial diastolic mechanics and stiffness that are in part due to alterations in advanced glycation end-product (AGE) collagen cross-linking. Rats developed volume overload induced by arteriovenous fistula (AVF). To assess the dependence of AGE cross-linking on mechanics, we prevented AGE formation by administering the drug aminoguanidine (AG) to one group of AVF rats (AG+AVF). Volume overload did not modify collagen concentration. Right ventricular AGE cross-links were modestly elevated in AVF hearts but were significantly reduced by AG. AVF rats exhibited significantly increased septal AGE cross-links that were inhibited in the AG+AVF group. AVF-induced increases in left ventricular longitudinal stiffness and septal circumferential stiffness were prevented in AG+AVF hearts. Volume overload appears to regionally modify AGE collagen cross-linking and stiffness, and AG treatment prevented these increases, demonstrating that AGE cross-linking plays a role in mediating diastolic compliance in volume-overload hypertrophy.

Regional passive ventricular stress-strain relations during development of altered loads in chick embryo

Mechanical load influences embryonic ventricular growth, morphogenesis, and function. However, little is known about changes in regional passive ventricular properties during the development of altered mechanical loading conditions in the embryo. We tested the hypothesis that regional mechanical loads are a critical determinant of embryonic ventricular passive properties. We measured biaxial passive right and left ventricular (RV and LV, respectively) stress-strain relations in chick embryos at Hamburger-Hamilton stages 21 and 27 after conotruncal banding (CTB) to increase biventricular pressure load or left atrial ligation (LAL) to reduce LV volume load and increase RV volume load. In the RV, wall strains at end-diastolic (ED) pressure normalized whereas ED stresses increased after either CTB or LAL during development. In the left ventricle, both ED strain and stress normalized after CTB, whereas both remained reduced with significantly increased myocardial stiffness after LAL. These results suggest that the embryonic ventricle adapts to chronically altered mechanical loading conditions by changing specific RV and LV passive properties. Thus regional mechanical load has a critical role during cardiogenesis.

Muscle LIM protein deficiency leads to alterations in passive ventricular mechanics

Accumulating evidence indicates that cytoskeletal defects may be an important pathway for dilated cardiomyopathy and eventual heart failure. Targeted disruption of muscle LIM protein (MLP) has previously been shown to result in dilated cardiomyopathy with many of the clinical signs of heart failure, although the effects of MLP disruption on passive ventricular mechanics and myocyte architecture are not known. We used the MLP knockout model to examine changes in passive ventricular mechanics and laminar myofiber sheet architecture. Pressure-volume and pressure-strain relations were altered in MLP knockout mice, in general suggesting a less compliant tissue in the dilated hearts. Transmural laminar myocyte structure was also altered in this mouse model, especially near the epicardium. A mathematical model of the heart showed a likely increase in passive tissue stiffness in the MLP-deficient (-/-) heart. These results suggest that the disruption of the cytoskeletal protein MLP results in less compliant passive tissue and concomitant structural alterations in the three-dimensional myocyte architecture that may in part explain the ventricular dysfunction in the dilated heart.

Diastolic wall stress and ANG II in cardiac hypertrophy and gene expression induced by volume overload

We investigated the effects of diastolic wall stress (WS) and angiotensin II (ANG II) on the left ventricular (LV) hypertrophy (LVH) induced by volume overload and on the gene expression of LV adrenomedullin (AM) and atrial natriuretic peptide (ANP) in volume overload. Diastolic WS was pharmacologically manipulated with (candesartan) or without (calcium channel blocker manidipine) inhibition of ANG II type 1 receptors in aortocaval-shunted rats over 6 wk. Diastolic WS reached a plateau at 2 wk and subsequently declined regardless of further LVH. Although diastolic WS was decreased to a similar extent by both compounds, candesartan blunted LVH over 6 wk, whereas manidipine blunted LVH at 2 wk but not after 4 wk. Levels of AM and ANP gene expression increased as LVH developed but were completely suppressed by candesartan over 6 wk. ANP expression level was also attenuated by manidipine over 6 wk, whereas AM expression level was suppressed at 2 wk but not after 4 wk by manidipine. We concluded that diastolic WS and ANG II might be potent stimuli for the LVH and LV AM and ANP gene expression in volume overload and that diastolic WS could be relatively involved in the early LVH and in the gene expression of ANP rather than of AM.

Maturation of end-systolic stress-strain relations in chick embryonic myocardium

The embryonic myocardium increases functional performance geometrically during cardiac morphogenesis. We investigated developmental changes in the in vivo end-systolic stress-strain relations of embryonic chick myocardium in stage 17, 21, and 24 white Leghorn chick embryos (n = 10 for each stage). End-systolic stress-strain relations were linear in all developmental stages. End-systolic strain decreased from 0.50 +/- 0.02 to 0.31 +/- 0.01 (mean +/- SE, P < 0.05), while average end-systolic wall stress was similar at 3.29 +/- 0.34 to 4.19 +/- 0.43 mmHg (P = 0.14) from stage 17 to 24. Normalized end-systolic myocardial stiffness, a load-independent index of ventricular contractility, increased from 2.98 +/- 0.19 to 6.03 +/- 0.39 mmHg from stage 17 to 24 (P < 0.05). Zero-stress midwall volume increased from 0.024 +/- 0.002 to 0.124 +/- 0.004 microl from stage 17 to 24 (P < 0.05). These results suggest that the embryonic ventricle increases normalized ventricular "contractility" while maintaining average end-systolic wall stress over a relatively narrow range during cardiovascular morphogenesis.

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.