Stress Distribution in the Canine Left Ventricle during Diastole and Systole

A model is proposed for stress analysis of the left ventricular wall (LV wall) based on the realistic assumption that the myocardium is essentially composed of fiber elements which carry only axial tension and vary in orientation through the wall. Stress analysis based on such a model requires an extensive study of muscle fiber orientation and curvature through the myocardium. Accordingly, the principal curvatures were studied at a local site near the equator in ten dog hearts rapidly fixed in situ at end diastole and end systole; the fiber orientation for these hearts had already been established in a previous study. The principal radii of curvature were (a) measured by fitting templates to the endocardial and epicardial wall surfaces in the circumferential and longitudinal directions and (b) computed from measured lengths of semiaxes of ellipsoids of revolution representing the LV wall (“ellipsoid” data). The wall was regarded as a tethered set of nested shells, each having a unique fiber orientation. Results indicate the following. (a) Fiber curvature, k, is maximum at midwall at end systole; this peak shifts towards endocardium at end diastole. (b) The pressure or radial stress through the wall decreases more rapidly near the endocardium than near the epicardium at end diastole and at end systole when a constant tension is assumed for each fiber through the wall. (c) At end diastole the curve for the circumferential stress vs. wall thickness is convex with a maximum at midwall. In the longitudinal direction the stress distribution curve is concave with a minimum at midwall. Similar distributions are obtained at end systole when a constant tension is assumed for each fiber through the wall. (d) The curvature and stress distributions obtained by direct measurements at a selected local site agree well with those computed from “ellipsoid” data.     

Mitral leaflet modeling: Importance of in vivo shape and material properties

The anterior mitral leaflet (AML) is a thin membrane that withstands high left ventricular (LV) pressure pulses 100,000 times per day. The presence of contractile cells determines AML in vivo stiffness and complex geometry. Until recently, mitral valve finite element (FE) models have neglected both of these aspects. In this study we assess their effect on AML strains and stresses, hypothesizing that these will differ significantly from those reported in literature. Radiopaque markers were sewn on the LV, the mitral annulus, and AML in sheep hearts, and their four-dimensional coordinates obtained with biplane video fluoroscopy. Employing in vivo data from three representative hearts, AML FE models were created from the marker coordinates at the end of isovolumic relaxation assumed as the unloaded reference state. AML function was simulated backward through systole, applying the measured trans-mitral pressure on AML LV surface and marker displacements on AML boundaries. Simulated AML displacements and curvatures were consistent with in vivo measurements, confirming model accuracy. AML circumferential strains were mostly tensile (1-3%), despite being compressive (-1%) near the commissures. Radial strains were compressive in the belly (-1 to -0.2%), and tensile (2-8%) near the free edge. These results differ significantly from those of previous FE models. They reflect the synergy of high tissue stiffness, which limits tensile circumferential strains, and initial compound curvature, which forces LV pressure to compress AML radially. The obtained AML shape may play a role not only in preventing mitral regurgitation, but also in optimizing LV outflow fluid dynamics.     

Biomechanical and morphological properties in rat large intestine

Intestinal stress-strain distributions are important determinants of intestinal function and are determined by the mechanical properties of the intestinal wall, the physiological loading conditions and the zero-stress state of the intestine. In this study the distribution of morphometric measures, residual circumferential strains and stress-strain relationships along the rat large intestine were determined in vitro. Segments from four parts of the large intestine were excised, closed at both ends, and inflated with pressures up to 2kPa. The outer diameter and length were measured. The zero-stress state was obtained by cutting rings of large intestine radially. The geometric configuration at the zero-stress state is of fundamental importance because it is the basic state with respect to which the physical stresses and strains are defined. The outer and inner circumferences, wall thickness and opening angle were measured from digitised images. Subsequently, residual strain and stress-strain distributions were calculated. The wall thickness and wall thickness-to-circumference ratio increased in the distal direction. The opening angle varied between approximately 40 and approximately 125 degrees with the highest values in the beginning of proximal colon (F=1.739, P<0.05). The residual strain at the inner surface was negative indicating that the mucosa-submucosal layers of the large intestine in no-load state are in compression. The four segments showed stress-strain distributions that were exponential. All segments were stiffer in longitudinal direction than in the circumferential direction (P<0.05). The transverse colon seemed stiffest both in the circumferential and longitudinal directions. In conclusion, significant variations were found in morphometric and biomechanical properties along the large intestine. The circumferential residual strains and passive elastic properties must be taken into account in studies of physiological problems in which the stress and strain are important, e.g. large intestinal bolus transport function.     

Regional variation in the mechanical role of knee meniscus glycosaminoglycans

High compressive properties of cartilaginous tissues are commonly attributed to the sulfated glycosaminoglycan (GAG) fraction of the extracellular matrix (ECM), but this relationship has not been directly measured in the knee meniscus, which shows regional variation in GAG content. In this study, biopsies from each meniscus region (outer, middle, and inner) were either subjected to chondroitinase ABC (CABC) to remove all sulfated GAGs or not. Compressive testing revealed that GAG depletion in the inner and middle meniscus regions caused a significant decrease in modulus of relaxation (58% and 41% decreases, respectively, at 20% strain), and all regions exhibited a significant decrease in viscosity (outer: 29%; middle: 58%; inner: 62% decrease). Tensile properties following CABC treatment were unaffected for outer and middle meniscus specimens, but the inner meniscus displayed significant increases in Young's modulus (41% increase) and ultimate tensile stress (40% increase) following GAG depletion. These findings suggest that, in the outer meniscus, GAGs contribute to increasing tissue viscosity, whereas in the middle and inner meniscus, where GAGs are most abundant, these molecules also enhance the tissue's ability to withstand compressive loads. GAGs in the inner meniscus also contribute to reducing the circumferential tensile properties of the tissue, perhaps due to the pre-stress on the collagen network from increased hydration of the ECM. Understanding the mechanical role of GAGs in each region of the knee meniscus is important for understanding meniscus structure-function relationships and creating design criteria for functional meniscus tissue engineering efforts.     

Cardiac mechanics in the stage-16 chick embryo.

A theoretical model is presented for the tubular heart of the stage-16 chick embryo (2.3 days of a 21-day incubation period). The model is a thick-walled, pseudoelastic cylindrical shell composed of three isotropic layers: the endocardium, the cardiac jelly, and the myocardium. The analysis is based on a shell theory that accounts for large deformation, material nonlinearity, residual strain, and muscle activation, with material properties inferred from available experimental data. We also measured epicardial strains from recorded motions of microspheres on the primitive right ventricles of stage-16 white Leghorn chick embryos. Relative to end diastole, peak axial and circumferential Lagrange strains occurred near end systole and had similar values. The magnitudes of these strains varied along the longitudinal axis of the heart (-0.16 +/- 0.08), being larger near the ends of the primitive right ventricle and smaller near midventricle. The in-plane shear strain was less than 0.05. Comparison of theoretical and experimental strains during the cardiac cycle shows generally good agreement. In addition, the model gives strong stress concentrations in the myocardial layer at end systole.     

Material properties and residual stress in the stage 12 chick heart during cardiac looping

During the morphogenetic process of cardiac looping, the initially straight cardiac tube bends and twists into a curved tube. The biophysical mechanisms that drive looping remain unknown, but the process clearly involves mechanical forces. Hence, it is important to determine mechanical properties of the early heart, which is a muscle-wrapped tube consisting primarily of a thin outer layer of myocardium surrounding a thick extracellular matrix compartment known as cardiac jelly. In this work, we used microindentation experiments and finite element modeling, combined with an inverse computational method, to determine constitutive relations for the myocardium and cardiac jelly at the outer curvature of stage 12 chick hearts. Material coefficients for exponential strain-energy density functions were found by fitting force-displacement and surface displacement data near the indenter Residual stress in the myocardium also was estimated. These results should be useful for computational models of the looping heart.     

Presence of functional sarcoplasmic reticulum in the developing heart and its confinement to chamber myocardium

During development fast-contracting atrial and ventricular chambers develop from a peristaltic-contracting heart tube. This study addresses the question of whether chamber formation is paralleled by a matching expression of the sarcoplasmic reticulum (SR) Ca(2+) pump. We studied indo-1 Ca(2+) transients elicited by field stimulation of linear heart tube stages and of explants from atria and outflow tracts of the prototypical preseptational E13 rat heart. Ca(2+) transients of H/H 11+ chicken hearts, which constitute the prototypic linear heart tube stage, were sensitive to verapamil only, indicating a minor contribution of Ca(2+)-triggered SR Ca(2+) release. Outflow tract transients displayed sensitivity to the inhibitors similar to that of the linear heart tube stages. Atrial Ca(2+) transients disappeared upon addition of ryanodine, tetracaine, or verapamil, indicating the presence of Ca(2+)-triggered SR Ca(2+) release. Quantitative radioactive in situ hybridization on sections of E13 rat hearts showed approximately 10-fold higher SERCA2a mRNA levels in the atria compared to nonmyocardial tissue and approximately 5-fold higher expression in compact ventricular myocardium. The myocardium of atrioventricular canal, outflow tract, inner curvature, and ventricular trabecules displayed weak expression. Immunohistochemistry on sections of rat and human embryos showed a similar pattern. The significance of these findings is threefold. (i) A functional SR is present long before birth. (ii) SR development is concomitant with cardiac chamber development, explaining regional differences in cardiac function. (iii) The pattern of SERCA2a expression underscores a manner of chamber development by differentiation at the outer curvature, rather than by segmentation of the linear heart tube.     

In vivo dynamic strains of the ovine anterior mitral valve leaflet

Understanding the mechanics of the mitral valve is crucial in terms of designing and evaluating medical devices and techniques for mitral valve repair. In the current study we characterize the in vivo strains of the anterior mitral valve leaflet. On cardiopulmonary bypass, we sew miniature markers onto the leaflets of 57 sheep. During the cardiac cycle, the coordinates of these markers are recorded via biplane fluoroscopy. From the resulting four-dimensional data sets, we calculate areal, maximum principal, circumferential, and radial leaflet strains and display their profiles on the averaged leaflet geometry. Average peak areal strains are 13.8±6.3%, maximum principal strains are 13.0±4.7%, circumferential strains are 5.0±2.7%, and radial strains are 7.8±4.3%. Maximum principal strains are largest in the belly region, where they are aligned with the circumferential direction during diastole switching into the radial direction during systole. Circumferential strains are concentrated at the distal portion of the belly region close to the free edge of the leaflet, while radial strains are highest in the center of the leaflet, stretching from the posterior to the anterior commissure. In summary, leaflet strains display significant temporal, regional, and directional variations with largest values inside the belly region and toward the free edge. Characterizing strain distribution profiles might be of particular clinical significance when optimizing mitral valve repair techniques in terms of forces on suture lines and on medical devices.     

Regional dependency of the vascular smooth muscle cell contribution to the mechanical properties of the pig ascending aortic tissue

BackgroundDilation and dissection of aneurysmal ascending aortic tissues occur preferentially at the outer curvature of the vessel. In this study we hypothesize that the density and contractile properties of the vascular smooth muscle cells (VSMCs) of the pig ascending aorta (AA) are heterogeneous and could explain the non-uniform remodeling and weakening of the AA during aneurysm formation.MethodsEleven pig AA rings were collected. Two square samples of 15×15 mm were taken from each ring from the inner and outer curvature of the AA. Each sample was subjected to equi-biaxial tensile testing in Krebs–Ringer solution maintained at 37 °C. Each test consisted of 8 cycles of preconditioning followed by one experimental run from 0% to 30% strain. Phenylephrine (10^?5 M) was added to contract VSMCs. After biaxial testing, samples were paraffin-embedded and stained with hematoxylin–phloxine–saffron (HPS) to quantify VSMC density.ResultsSignificant differences in cell density, maximum contractile stress resultant magnitude (MCSRM) and orientation (θ_MCSR) were found between the inner and outer curvature. The inner curvature had the greatest contraction. The outer curvature had the highest VSMC density with the maximum contraction stress resultant oriented towards the axial direction.ConclusionVSMC activation with phenylephrine had a significant effect on the stiffness of the pig AA. This effect was independent of location and direction. However, cell orientation, density and contractile properties were dependent on location and suggest variations in the remodeling capabilities, tissue strain and cell phenotype between locations.     

Sound-evoked radial strain in the hearing organ

The hearing organ contains sensory hair cells, which convert sound-evoked vibration into action potentials in the auditory nerve. This process is greatly enhanced by molecular motors that reside within the outer hair cells, but the performance also depends on passive mechanical properties, such as the stiffness, mass, and friction of the structures within the organ of Corti. We used resampled confocal imaging to study the mechanical properties of the low-frequency regions of the cochlea. The data allowed us to estimate an important mechanical parameter, the radial strain, which was found to be 0.1% near the inner hair cells and 0.3% near the third row of outer hair cells during moderate-level sound stimulation. The strain was caused by differences in the motion trajectories of inner and outer hair cells. Motion perpendicular to the reticular lamina was greater at the outer hair cells, but inner hair cells showed greater radial vibration. These differences led to deformation of the reticular lamina, which connects the apex of the outer and inner hair cells. These results are important for understanding how the molecular motors of the outer hair cells can so profoundly affect auditory sensitivity.     

Biomechanical properties of the layered oesophagus and its remodelling in experimental type-1 diabetes

Passive biomechanical properties in term of the stress-strain relationship and the shear modulus were studied in separated muscle layer and mucosa-submucosa layer in the oesophagus of normal and STZ (streptozotocin)-induced diabetic rats. The mucosa-submucosa and muscle layers were separated using microsurgery and studied in vitro using a self-developed test machine. Stepwise elongation and inflation plus continuous twist were applied to the samples. A constitutive equation based on a strain energy function was used for the stress-strain analysis. Five material constants were obtained for both layers. The mucosa-submucosa layer was significantly stiffer than the muscle layer in longitudinal, circumferential and circumferential-longitudinal shear direction. The mechanical constants of the oesophagus show that the oesophageal wall was anisotropic, the stiffness in the longitudinal direction was higher than in the circumferential direction in the intact oesophagus (P < 0.001) and in the muscle layer (P < 0.05). Diabetes-induced pronounced increase in the outer perimeter, inner perimeter and lumen area in both the muscle and mucosa-submucosa layer. The growth of the mucosa-submucosa layer (P < 0.001) was more pronounced than the muscle layer (P < 0.05). Furthermore, the circumferential stiffness of the mucosa-submucosa layer increased 28 days after STZ treatment. In conclusion, the oesophagus is a non-homogeneous anisotropic tube. Thus, the mechanical properties differed between layers as well as in different directions. Morphological and biomechanical remodelling is prominent in the diabetic oesophagus.     

Right and left ventricular wall deformation patterns in normal and left heart hypoplasia chick embryos

The vertebrate embryonic ventricle transforms from a smooth-walled single tube to trabeculated right ventricular (RV) and left ventricular (LV) chambers during cardiovascular morphogenesis. We hypothesized that ventricular contraction patterns change from globally isotropic to chamber-specific anisotropic patterns during normal morphogenesis and that these deformation patterns are influenced by experimentally altered mechanical load produced by chronic left atrial ligation (LAL). We measured epicardial RV and LV wall strains during normal development and left heart hypoplasia produced by LAL in Hamburger-Hamilton stage 21, 24, 27, and 31 chick embryos. Normal RV contracted isotropically until stage 24 and then contracted preferentially in the circumferential direction. Normal LV contracted isotropically at stage 21, preferentially in the longitudinal direction at stages 24 and 27, and then in the circumferential direction at stage 31. LAL altered both RV and LV strain patterns, accelerated the onset of preferential RV circumferential strain patterns, and abolished preferential LV longitudinal strain (P < 0.05 vs. normal). Mature patterns of anisotropic RV and LV deformation develop coincidentally with morphogenesis, and changes in these deformation patterns reflect altered cardiovascular function and/or morphogenesis.     

Filamentous bacterial viruses. XI. Molecular architecture of the class II (Pf1, Xf) virion

The diffraction patterns of the Pf 1 and Xf strains of filamentous bacterial viruses (class II) can be interpreted in terms of a simple helix of protein subunits with 15Åpitch, having 22 units in five turns. The protein subunits are each elongated in an axial direction, and also slope radially, so as to overlap each other, giving an arrangement of subunits reminiscent of scales on a fish. The protein helix forms a tube with inner diameter about 20Åand outer diameter about 60Å. The single-stranded circular DNA is contained within this tube, with two DNA strands running the length of the tube.The diffraction patterns of fd, If 1 and IKe (class I) can be interpreted in terms of a perturbed version of the class II simple helix.     

Variations in cortical material properties throughout the human dentate mandible

Material properties and their variations in individual bone organs are important for understanding bone adaptation and quality at a tissue level, and are essential for accurate mechanical models. Yet material property variations have received little systematic study. Like all other material property studies in individual bone organs, studies of the human mandible are limited by a low number of both specimens and sampled regions. The aims of this study were to determine: 1) regional variability in mandibular material properties, 2) the effect of this variability on the modeling of mandibular function, and 3) the relationship of this variability to mandibular structure and function. We removed 31 samples on both facial and lingual cortices of 10 fresh adult dentate mandibles, measured cortical thickness and density, determined the directions of maximum stiffness with a pulse transmission ultrasonic technique, and calculated elastic properties from measured ultrasonic velocities. Results showed that each of these elastic properties in the dentate human mandible demonstrates unique regional variation. The direction of maximum stiffness was near parallel to the occlusal plane within the corpus. On the facial ramus, the direction of maximum stiffness was more vertically oriented. Several sites in the mandible did not show a consistent direction of maximum stiffness among specimens, although all specimens exhibited significant orthotropy. Mandibular cortical thickness varied significantly (P < 0.001) between sites, and decreased from 3.7 mm (SD = 0.9) anteriorly to 1.4 mm posteriorly (SD = 0.1). The cortical plate was also significantly thicker (P < 0.003) on the facial side than on the lingual side. Bone was 50-100% stiffer in the longitudinal direction (E(3), 20-30 GPa) than in the circumferential or tangential directions (E(2) or E(1); P < 0.001). The results suggest that material properties and directional variations have an important impact on mandibular mechanics. The accuracy of stresses calculated from strains and average material properties varies regionally, depending on variations in the direction of maximum stiffness and anisotropy. Stresses in some parts of the mandible can be more accurately calculated than in other regions. Limited evidence suggests that the orientations and anisotropies of cortical elastic properties correspond with features of cortical bone microstructure, although the relationship with functional stresses and strains is not clear.     

Finite Element Modeling Predictions of Region-specific Cell-matrix Mechanics in the Meniscus

The knee meniscus exhibits significant spatial variations in biochemical composition and cell morphology that reflect distinct phenotypes of cells located in the radial inner and outer regions. Associated with these cell phenotypes is a spatially heterogeneous microstructure and mechanical environment with the innermost regions experiencing higher fluid pressures and lower tensile strains than the outer regions. It is presently unknown, however, how meniscus tissue mechanics correlate with the local micromechanical environment of cells. In this study, theoretical models were developed to study mechanics of inner and outer meniscus cells with varying geometries. The results for an applied biaxial strain predict significant regional differences in the cellular mechanical environment with evidence of tensile strains along the collagen fiber direction of ~0.07 for the rounded inner cells, as compared to levels of 0.02–0.04 for the elongated outer meniscus cells. The results demonstrate an important mechanical role of extracellular matrix anisotropy and cell morphology in regulating the region-specific micromechanics of meniscus cells, that may further play a role in modulating cellular responses to mechanical stimuli.     

A fiduciary marker-based framework to assess heterogeneity and anisotropy of right ventricular epicardial strains in the beating ovine heart

Quantifying ventricular deformation in health and disease is critical to our understanding of normal heart function, heart disease mechanisms, and the effect of medical treatments. Imaging modalities have been developed that can measure ventricular deformation non-invasively. However, because of the small thickness, complex shape, and anatomic position of the right ventricle, using these technologies to determine its deformation remains challenging. Here we develop a first fiduciary marker-based method to assess heterogeneity and anisotropy of right ventricular epicardial strain across the entire free wall. To this end, we combine a high-density array of sonomicrometry crystals implanted across the entire right ventricular epicardial surface with a subdivision surface algorithm and a large deformation kinematics framework. We demonstrate our approach on four beating ovine hearts and present a preliminary regional analysis of circumferential, longitudinal, and areal strain. Moreover, we illustrate maps of the same strains across the entire right ventricular epicardial surface to highlight their spatial heterogeneity and anisotropy. We observe in these animals that RV epicardial strains vary throughout the cardiac cycle, are heterogeneous across the RV free wall, and are anisotropic with larger compressive strains, i.e., contraction, in the longitudinal direction than in the circumferential direction. Average peak compressive strains vary by region between −3.34% and −8.29% in circumferential direction, and −4.02% and −10.57% in longitudinal direction. In summary, we introduce an experimental framework that will allow us to study disease- and device-induced deformations, and long-term consequences of these deformations, including heterogeneous and anisotropic effects.     

Human complement subcomponent C2: purification and proteolytic cleavage in fluid phase by C1s, C1r2-C1s2 and C1

Photosynthetic membranes contain considerable regions of high surface curvature, notably at their margins, where the average radius of curvature is about 10 nm. The proportion of total membrane lipid in the outer and inner thylakoid margin monolayers is estimated at 21% and 13%, respectively. The major thylakoid lipid, monogalactosyldiacylglycerol, is roughly cone-shaped and will not form complete lamellar bilayer phases, even in combination with other thylakoid lipids. It is proposed that this galactolipid plays a role in: (a) stabilising regions of concave curvature in thylakoids; and (b) packaging hydrophobic proteins in planar bilayer regions by means of inverted micelles. This model predicts substantial asymmetries in the distribution of lipids both across and along the thylakoid bilayer plane.     

Morphology and stress-strain properties along the small intestine in the rat

The stress-strain relationship is determined by the inherent mechanical properties of the intestinal wall, the geometric configurations, the loading conditions and the zero-stress state of the segment. The purpose of this project was to provide morphometric and biomechanical data for rat duodenum, jejunum and ileum. The circumferential strains were referenced to the zero-stress state. Large morphometric variations were found along the small intestine with an increase in the outer circumferential length and luminal area and a decrease in wall thickness in distal direction. The serosal residual strain was tensile and decreased in distal direction (P < 0.05). The mucosal residual strain was compressive and the absolute value decreased in distal direction (P < 0.001). The stress-strain experiments showed that the duodenum was stiffest. All segments were stiffest in longitudinal direction (P < 0.05). In conclusion, axial variation in morphometric and biomechanical properties was found in the small intestine. The zero-stress state must be considered in future biomechanical studies in the gastrointestinal tract.     

Structure of the nucleosome core particle at 8 A resolution

The x-ray crystallographic structure of the nucleosome core particle has been determined using 8 A resolution diffraction data. The particle has a mean diameter of 106 A and a maximum thickness of 65 A in the superhelical axis direction. The longest chord through the histone core measures 85 A and is in a non-axial direction. The 1.87 turn superhelix consists of B-DNA with about 78 base pairs or 7.6 helical repeats per superhelical turn. The mean DNA helical repeat contains 10.2 +/- 0.05 base pairs and spans 35 A, slightly more than standard B-DNA. The superhelix varies several Angstroms in radius and pitch, and has three distinct domains of curvature (with radii of curvature of 60, 45 and 51 A). These regions are separated by localized sharper bends +/- 10 and +/- 40 base pairs from the center of the particle, resulting in an overall radius of curvature about 43 A. Compression of superhelical DNA grooves on the inner surface and expansion on the outer surface can be seen throughout the DNA electron density. This density has been fit with a double helical ribbon model providing groove width estimates of 12 +/- 1 A inside vs. 19 +/- 1 A outside for the major groove, and 8 +/- 1 A inside vs. 13 +/- 1 A outside for the minor groove. The histone core is primarily contained within the bounds defined by the superhelical DNA, contacting the DNA where the phosphate backbone faces in toward the core. Possible extensions of density between the gyres have been located, but these are below the significance level of the electron density map. In cross-section, a tripartite organization of the histone octamer is apparent, with the tetramer occupying the central region and the dimers at the extremes. Several extensions of histone density are present which form contacts between nucleosomes in the crystal, perhaps representing flexible or "tail" histone regions. The radius of gyration of the histone portion of the electron density is calculated to be 30.4 A (in reasonable agreement with solution scattering values), and the histone core volume in the map is 93% of its theoretical volume.