Differential mechanical response and microstructural organization between non-human primate femoral and carotid arteries

Unique anatomic locations and physiologic functions predispose different arteries to varying mechanical responses and pathologies. However, the underlying causes of these mechanical differences are not well understood. The objective of this study was to first identify structural differences in the arterial matrix that would account for the mechanical differences between healthy femoral and carotid arteries and second to utilize these structural observations to perform a microstructurally motivated constitutive analysis. Femoral and carotid arteries were subjected to cylindrical biaxial loading and their microstructure was quantified using two-photon microscopy. The femoral arteries were found to be less compliant than the carotid arteries at physiologic loads, consistent with previous studies, despite similar extracellular compositions of collagen and elastin ( \(P> 0.05\) ). The femoral arteries exhibited significantly less circumferential dispersion of collagen fibers ( \(P< 0.05\) ), despite a similar mean fiber alignment direction as the carotid arteries. Elastin transmural distribution, in vivo axial stretch, and opening angles were also found to be distinctly different between the arteries. Lastly, we modeled the arteries’ mechanical behaviors using a microstructural-based, distributed collagen fiber constitutive model. With this approach, the material parameters of the model were solved using the experimental microstructural observations. The findings of this study support an important role for microstructural organization in arterial stiffness.     

Contributions of Glycosaminoglycans to Collagen Fiber Recruitment in Constitutive Modeling of Arterial Mechanics

The contribution of glycosaminoglycans (GAGs) to the biological and mechanical functions of biological tissue has emerged as an important area of research. GAGs provide structural basis for the organization and assembly of extracellular matrix (ECM). The mechanics of tissue with low GAG content can be indirectly affected by the interaction of GAGs with collagen fibers, which have long been known to be one of the primary contributors to soft tissue mechanics. Our earlier study showed that enzymatic GAG depletion results in straighter collagen fibers that are recruited at lower levels of stretch, and a corresponding shift in earlier arterial stiffening (Mattson et al., 2016). In this study, the effect of GAGs on collagen fiber recruitment was studied through a structure-based constitutive model. The model incorporates structural information, such as fiber orientation distribution, content, and recruitment of medial elastin, medial collagen, and adventitial collagen fibers. The model was first used to study planar biaxial tensile stress-stretch behavior of porcine descending thoracic aorta. Changes in elastin and collagen fiber orientation distribution, and collagen fiber recruitment were then incorporated into the model in order to predict the stress-stretch behavior of GAG depleted tissue. Our study shows that incorporating early collagen fiber recruitment into the model predicts the stress-stretch response of GAG depleted tissue reasonably well (rms = 0.141); considering further changes of fiber orientation distribution does not improve the predicting capability (rms = 0.149). Our study suggests an important role of GAGs in arterial mechanics that should be considered in developing constitutive models.     

Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues

Structural constitutive models integrate information on tissue composition and structure, avoiding ambiguities in material characterization. However, critical structural information (such as fiber orientation) must be modeled using assumed statistical distributions, with the distribution parameters estimated from fits to the mechanical test data. Thus, full realization of structural approaches continues to be limited without direct quantitative structural information for direct implementation or to validate model predictions. In the present study, fiber orientation information obtained using small angle light scattering (SALS) was directly incorporated into a structural constitutive model based on work by Lanir (J. Biomech., v. 16, pp. 1-12, 1983). Demonstration of the model was performed using existing biaxial mechanical and fiber orientation data for native bovine pericardium (Sacks and Chuong, ABME, v.26, pp. 892-902, 1998). The structural constitutive model accurately predicted the complete measured biaxial mechanical response. An important aspect of this approach is that only a single equibiaxial test to determine the effective fiber stress-strain response and the SALS-derived fiber orientation distribution were required to determine the complete planar biaxial mechanical response. Changes in collagen fiber crimp under equibiaxial strain suggest that, at the meso-scale, fiber deformations follow the global tissue strains. This result supports the assumption of affine strain to estimate the fiber strains. However, future evaluations will have to be performed for tissue subjected to a wider range of strain to more fully validate the current approach.     

A microstructurally driven model for pulmonary artery tissue

A new constitutive model for elastic, proximal pulmonary artery tissue is presented here, called the total crimped fiber model. This model is based on the material and microstructural properties of the two main, passive, load-bearing components of the artery wall, elastin, and collagen. Elastin matrix proteins are modeled with an orthotropic neo-Hookean material. High stretch behavior is governed by an orthotropic crimped fiber material modeled as a planar sinusoidal linear elastic beam, which represents collagen fiber deformations. Collagen-dependent artery orthotropy is defined by a structure tensor representing the effective orientation distribution of collagen fiber bundles. Therefore, every parameter of the total crimped fiber model is correlated with either a physiologic structure or geometry or is a mechanically measured material property of the composite tissue. Further, by incorporating elastin orthotropy, this model better represents the mechanics of arterial tissue deformation. These advancements result in a microstructural total crimped fiber model of pulmonary artery tissue mechanics, which demonstrates good quality of fit and flexibility for modeling varied mechanical behaviors encountered in disease states.     

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.     

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.     

Mechanical identification of layer-specific properties of mouse carotid arteries using 3D-DIC and a hyperelastic anisotropic constitutive model

The role of mechanics is known to be of primary order in many arterial diseases; however, determining mechanical properties of arteries remains a challenge. This paper discusses the identifiability of the passive mechanical properties of a mouse carotid artery, taking into account the orientation of collagen fibres in the medial and adventitial layers. On the basis of 3D digital image correlation measurements of the surface strain during an inflation/extension test, an inverse identification method is set up. It involves a 3D finite element mechanical model of the mechanical test and an optimisation algorithm. A two-layer constitutive model derived from the Holzapfel model is used, with five and then seven parameters. The five-parameter model is successfully identified providing layer-specific fibre angles. The seven-parameter model is over parameterised, yet it is shown that additional data from a simple tension test make the identification of refined layer-specific data reliable.     

A novel constitutive model for passive right ventricular myocardium: evidence for myofiber–collagen fiber mechanical coupling

The function of right ventricle (RV) is recognized to play a key role in the development of many cardiopulmonary disorders, such as pulmonary arterial hypertension (PAH). Given the strong link between tissue structure and mechanical behavior, there remains a need for a myocardial constitutive model that accurately accounts for right ventricular myocardium architecture. Moreover, most available myocardial constitutive models approach myocardium at the length scale of mean fiber orientation and do not explicitly account for different fibrous constituents and possible interactions among them. In the present work, we developed a fiber-level constitutive model for the passive mechanical behavior of the right ventricular free wall (RVFW). The model explicitly separates the mechanical contributions of myofiber and collagen fiber ensembles, and accounts for the mechanical interactions between them. To obtain model parameters for the healthy passive RVFW, the model was informed by transmural orientation distribution measurements of myo- and collagen fibers and was fit to the mechanical testing data, where both sets of data were obtained from recent experimental studies on non-contractile, but viable, murine RVFW specimens. Results supported the hypothesis that in the low-strain regime, the behavior of the RVFW is governed by myofiber response alone, which does not demonstrate any coupling between different myofiber ensembles. At higher strains, the collagen fibers and their interactions with myofibers begin to gradually contribute and dominate the behavior as recruitment proceeds. Due to the use of viable myocardial tissue, the contribution of myofibers was significant at all strains with the predicted tensile modulus of \(\sim \)32 kPa. This was in contrast to earlier reports (Horowitz et al. 1988) where the contribution of myofibers was found to be insignificant. Also, we found that the interaction between myo- and collagen fibers was greatest under equibiaxial strain, with its contribution to the total stress not exceeding 20 %. The present model can be applied to organ-level computational models of right ventricular dysfunction for efficient diagnosis and evaluation of pulmonary hypertension disorder.     

Topological remodeling of cultured endothelial cells by characterized cyclic strains

Evaluation of mechanical environment on cellular function is a major field of study in cellular engineering. Endothelial cells lining the entire vascular lumen are subjected to pulsatile blood pressure and flow. Mechanical stresses caused by such forces determine function of arteries and their remodeling. Critical values of mechanical stresses contribute to endothelial damage, plaque formation and atherosclerosis. A device to impose cyclic strain on cultured cells inside an incubator was designed and manufactured operating with different load amplitudes, frequencies, numbers of cycles and ratios of extension to relaxation. Endothelial cells cultured on collagen coated silicon scaffolds were subjected to cyclic loading. Effects of mechanical loading on cell morphology were quantified using image processing methods. Results showed change in cell orientation from a randomly oriented before the test up to 80 degrees alignment from load axis after loading. Endothelial cells were elongated with shape index reductions up to 47% after cyclic stretch. By increase of strain amplitude, loading frequency and number of cycles, significant decrease in shape index and significant increase in orientation angle were observed. Change of load waveform similar to arterial pulse pressure waveform resulted in alteration of cell alignment with 9.7% decrease in shape index, and 10.8% increase in orientation angle. Results of cyclic loading tests in a disturbed environment with elevated PH showed lack of remodeling. It was concluded that tensile loading of endothelial cells influences cell morphology and alignment, a mechanism for structural regulation, functional adaptation and remodeling. Disturbed environment results in endothelial dysfunction and injury.     

The effect of collagenase on the critical buckling pressure of arteries

The stability of arteries is essential to normal arterial functions and loss of stability can lead to arterial tortuosity and kinking. Collagen is a main extracellular matrix component that modulates the mechanical properties of arteries and collagen degradation at pathological conditions weakens the mechanical strength of arteries. However, the effects of collagen degradation on the mechanical stability of arteries are unclear. The objective of this study was to investigate the effects of collagen degradation on the critical buckling pressure of arteries. Arterial specimens were subjected to pressurized inflation testing and fitted with nonlinear thick-walled cylindrical model equations to determine their stress strain relationships. The arteries were then tested for the critical buckling pressure at a set of axial stretch ratios. Then, arteries were divided into three groups and treated with Type III collagenase at three different concentrations (64, 128, and 400 U/ml). Mechanical properties and buckling pressures of the arteries were determined after collagenase treatment. Additionally, the theoretical buckling pressures were also determined using a buckling equation. Our results demonstrated that the buckling pressure of arteries was lower after collagenase treatment. The difference between pre- and post- treatment was statistically significant for the highest concentration of 400U/ml but not at the lower concentrations. The buckling equation was found to yield a fair estimation to the experimental critical pressure measurements. These results shed light on the role of matrix remodeling on the mechanical stability of arteries and developments of tortuous arteries.     

The Effect of Collagenase on the Critical Buckling Pressure of Arteries^*

The stability of arteries is essential to normal arterial functions and loss of stability can lead to arterial tortuosity and kinking. Collagen is a main extracellular matrix component that modulates the mechanical properties of arteries and collagen degradation at pathological conditions weakens the mechanical strength of arteries. However, the effects of collagen degradation on the mechanical stability of arteries are unclear. The objective of this study was to investigate the effects of collagen degradation on the critical buckling pressure of arteries. Arterial specimens were subjected to pressurized inflation testing and fitted with nonlinear thick-walled cylindrical model equations to determine their stress strain relationships. The arteries were then tested for the critical buckling pressure at a set of axial stretch ratios. Then, arteries were divided into three groups and treated with Type III collagenase at three different concentrations (64, 128, and 400U/ml). Mechanical properties and buckling pressures of the arteries were determined after collagenase treatment. Additionally, the theoretical buckling pressures were also determined using a buckling equation. Our results demonstrated that the buckling pressure of arteries was lower after collagenase treatment. The difference between pre- and post- treatment was statistically significant for the highest concentration of 400U/ml but not at the lower concentrations. The buckling equation was found to yield a fair estimation to the experimental critical pressure measurements. These results shed light on the role of matrix remodeling on the mechanical stability of arteries and developments of tortuous arteries.     

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress.     

A computational model for understanding the micro-mechanics of collagen fiber network in the tunica adventitia

Abdominal aortic aneurysm is a prevalent cardiovascular disease with high mortality rates. The mechanical response of the arterial wall relies on the organizational and structural behavior of its microstructural components, and thus, a detailed understanding of the microscopic mechanical response of the arterial wall layers at loads ranging up to rupture is necessary to improve diagnostic techniques and possibly treatments. Following the common notion that adventitia is the ultimate barrier at loads close to rupture, in the present study, a finite element model of adventitial collagen network was developed to study the mechanical state at the fiber level under uniaxial loading. Image stacks of the rabbit carotid adventitial tissue at rest and under uniaxial tension obtained using multi-photon microscopy were used in this study, as well as the force–displacement curves obtained from previously published experiments. Morphological parameters like fiber orientation distribution, waviness, and volume fraction were extracted for one sample from the confocal image stacks. An inverse random sampling approach combined with a random walk algorithm was employed to reconstruct the collagen network for numerical simulation. The model was then verified using experimental stress–stretch curves. The model shows the remarkable capacity of collagen fibers to uncrimp and reorient in the loading direction. These results further show that at high stretches, collagen network behaves in a highly non-affine manner, which was quantified for each sample. A comprehensive parameter study to understand the relationship between structural parameters and their influence on mechanical behavior is presented. Through this study, the model was used to conclude important structure–function relationships that control the mechanical response. Our results also show that at loads close to rupture, the probability of failure occurring at the fiber level is up to 2%. Uncertainties in usually employed rupture risk indicators and the stochastic nature of the event of rupture combined with limited knowledge on the microscopic determinants motivate the development of such an analysis. Moreover, this study will advance the study of coupling microscopic mechanisms to rupture of the artery as a whole.

     

Computational analyses of mechanically induced collagen fiber remodeling in the aortic heart valve

To optimize the mechanical properties and integrity of tissue-engineered aortic heart valves, it is necessary to gain insight into the effects of mechanical stimuli on the mechanical behavior of the tissue using mathematical models. In this study, a finite-element (FE) model is presented to relate changes in collagen fiber content and orientation to the mechanical loading condition within the engineered construct. We hypothesized that collagen fibers aligned with principal strain directions and that collagen content increased with the fiber stretch. The results indicate that the computed preferred fiber directions run from commissure to commissure and show a strong resemblance to experimental data from native aortic heart valves.     

Ex-vivo observation of calcification process in chick tibia slice: Augmented calcification along collagen fiber orientation in specimens subjected to static stretch

Bone formation through matrix synthesis and calcification in response to mechanical loading is an essential process of the maturation in immature animals, although how mechanical loading applied to the tissue increases the calcification and improves mechanical properties, and which directions the calcification progresses within the tissue are largely unknown. To address these issues, we investigated the calcification of immature chick bone under static tensile stretch using a newly developed real-time observation bioreactor system. Bone slices perpendicular to the longitudinal axis obtained from the tibia in 2- to 4-day-old chick legs were cultured in the system mounted on a microscope, and their calcification was observed up to 24 h while they were stretched in the direction parallel to the slice. Increase in the calcified area, traveling distance and the direction of the calcification and collagen fiber orientation in the newly calcified region were analyzed. There was a significant increase in calcified area in the bone explant subjected to tensile strain over ∼3%, which corresponds to the threshold strain for collagen fibers showing alignment in the direction of stretch, indicating that the fiber alignment may enhance tissue calcification. The calcification progressed to a greater distance to the stretching direction in the presence of the loading. Moreover, collagen fiber orientation in the calcified area in the loaded samples was coincided with the progression angle of the calcification. These results clearly show that the application of static tensile strain enhanced tissue calcification, which progresses along collagen fibers aligned to the loading direction.     

Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model

The collagen network in skin is largely responsible for the nonlinear mechanical stress-strain response of skin. We hypothesize that the force-stretch response of collagen is governed by the entropics of long-chain molecules. We show that a constitutive model derived from the statistical mechanics of long-chain molecules, corresponding to the fibrous collagen network in skin, captures the mechanical response of skin. A connection between the physiologically meaningful parameters of network molecular chain density and free length of collagen fibers and the constitutively significant parameters of initial modulus and limiting stretch is thus established. The relevant constitutive law is shown to have predictive capabilities related to skin histology by replicating in vivo and in vitro experimental results. From finite element simulations, this modeling approach predicts that the collagen network in hypertrophic scars is more dense and the constituent collagen fibers have shorter free lengths than in healthy skin. Additionally, the model is shown to predict that as rat skin ages, collagen network density increases and fiber free length decreases. The importance of knowledge of the in situ stress state for analyzing skin response and validating constitutive laws is also demonstrated.     

Computational modeling of the arterial wall based on layer-specific histological data

Arterial walls typically have a heterogeneous structure with three different layers (intima, media, and adventitia). Each layer can be modeled as a fiber-reinforced material with two families of relatively stiff collagenous fibers symmetrically arranged within an isotropic soft ground matrix. In this paper, we present two different modeling approaches, the embedded fiber (EF) approach and the angular integration (AI) approach, to simulate the anisotropic behavior of individual arterial wall layers involving layer-specific data. The EF approach directly incorporates the microscopic arrangement of fibers that are synthetically generated from a random walk algorithm and captures material anisotropy at the element level of the finite element formulation. The AI approach smears fibers in the ground matrix and treats the material as homogeneous, with material anisotropy introduced at the constitutive level by enhancing the isotropic strain energy with two anisotropic terms. Both approaches include the influence of fiber dispersion introduced by fiber angular distribution (departure of individual fibers from the mean orientation) and take into consideration the dispersion caused by fiber waviness, which has not been previously considered. By comparing the numerical results with the published experimental data of different layers of a human aorta, we show that by using histological data both approaches can successfully capture the anisotropic behavior of individual arterial wall layers. Furthermore, through a comprehensive parametric study, we establish the connections between the AI phenomenological material parameters and the EF parameters having straightforward physical or geometrical interpretations. This study provides valuable insight for the calibration of phenomenological parameters used in the homogenized modeling based on the fiber microscopic arrangement. Moreover, it facilitates a better understanding of individual arterial wall layers, which will eventually advance the study of the structure–function relationship of arterial walls as a whole.     

A method for three-dimensional quantification of vascular smooth muscle orientation: application in viable murine carotid arteries

When studying in vivo arterial mechanical behaviour using constitutive models, smooth muscle cells (SMCs) should be considered, while they play an important role in regulating arterial vessel tone. Current constitutive models assume a strictly circumferential SMC orientation, without any dispersion. We hypothesised that SMC orientation would show considerable dispersion in three dimensions and that helical dispersion would be greater than transversal dispersion. To test these hypotheses, we developed a method to quantify the 3D orientation of arterial SMCs. Fluorescently labelled SMC nuclei of left and right carotid arteries of ten mice were imaged using two-photon laser scanning microscopy. Arteries were imaged at a range of luminal pressures. 3D image processing was used to identify individual nuclei and their orientations. SMCs showed to be arranged in two distinct layers. Orientations were quantified by fitting a Bingham distribution to the observed orientations. As hypothesised, orientation dispersion was much larger helically than transversally. With increasing luminal pressure, transversal dispersion decreased significantly, whereas helical dispersion remained unaltered. Additionally, SMC orientations showed a statistically significant (\(p < 0.05\)) mean right-handed helix angle in both left and right arteries and in both layers, which is a relevant finding from a developmental biology perspective. In conclusion, vascular SMC orientation (1) can be quantified in 3D; (2) shows considerable dispersion, predominantly in the helical direction; and (3) has a distinct right-handed helical component in both left and right carotid arteries. The obtained quantitative distribution data are instrumental for constitutive modelling of the artery wall and illustrate the merit of our method.     

Influence of left-ventricular shape on passive filling properties and end-diastolic fiber stress and strain

Passive filling is a major determinant for the pump performance of the left ventricle and is determined by the filling pressure and the ventricular compliance. In the quantification of the passive mechanical behaviour of the left ventricle and its compliance, focus has been mainly on fiber orientation and constitutive parameters. Although it has been shown that the left-ventricular shape plays an important role in cardiac (patho-)physiology, the dependency on left-ventricular shape has never been studied in detail. Therefore, we have quantified the influence of left-ventricular shape on the overall compliance and the intramyocardial distribution of passive fiber stress and strain during the passive filling period. Hereto, fiber stress and strain were calculated in a finite element analysis of passive inflation of left ventricles with different shapes, ranging from an elongated ellipsoid to a sphere, but keeping the initial cavity volume constant. For each shape, the wall volume was varied to obtain ventricles with different wall thickness. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry along the muscle fiber directions. A realistic transmural distribution in fiber orientation was assumed. We found that compliance was not altered substantially, but the transmural distribution of both passive fiber stress and strain was highly dependent on regional wall curvature and thickness. A low curvature wall was characterized by a maximum in the transmural fiber stress and strain in the mid-wall region, while a steep subendocardial transmural gradient was present in a high curvature wall. The transmural fiber stress and strain gradients in a low and high curvature wall were, respectively, flattened and steepened by an increase in wall thickness.