A 2D Finite Element Model of the Interventricular Septum Under Normal and Abnormal Loading

Abstract

The interventricular septum is the structure that separates the left and right ventricles of the heart. Under normal loading conditions, it is concave to the left ventricle, but under abnormal loading the septum flattens and occasionally inverts. In the past, the septum has frequently been modelled as integral to the left ventricle with the effects of pressure from the right ventricle being ignored. Under abnormal loading, the septum has been described as behaving equivalent to a “flapping sail”. There has been no consideration of structural behaviour under these conditions. A 2-D plane stress FE model of the septum was used to investigate the difference in structural behaviour of the septum during diastole between normal and abnormal loading. The biaxial stress patterns that develop are distinctively disparate. Under normal loading, the septum behaves much like a thick-walled cylinder subject to internal and external pressure, with the resulting stresses being circumferential tension and radial compression, both varying with radius. These stresses are very low throughout most of diastole. However, under abnormal loading, the septum behaves in an arch-like fashion, with high compressive stresses almost circumferential in direction, combined with radial compression. We conclude that right ventricular pressures cause bending effects in the wall of the heart, and that under abnormal loading, the compressive stresses that develop in the septum may lead to an understanding of certain, previously unexplained, pathological conditions.     

Compression of interventricular septum during right ventricular pressure loading

The interventricular septum, which flattens and inverts in conditions such as pulmonary hypertension, is considered by many to be an unstressed membrane, in that its position is assumed to be determined solely by the transseptal pressure gradient. A two-dimensional finite element model was developed to investigate whether compression and bending moments (behavior incompatible with a membrane) exist in the septum during diastole under abnormal loading, i.e., pulmonary artery (PA) constriction. Hemodynamic and echocardiographic data were obtained in six open-chest anesthetized dogs. For both control and PA constriction, the measured left ventricular and right ventricular pressures were applied to a residually stressed mesh. Adjustments were made to the stiffness and end-bending moments until the deformed and loaded residually stressed mesh matched the observed configuration of the septum. During PA constriction, end-bending moments were required to obtain satisfactory matches but not during control. Furthermore, substantial circumferential compressive stresses developed during PA constriction. Such stresses might impede septal blood flow and provoke the unexplained ischemia observed in some conditions characterized by abnormal septal motion.     

Anatomic features of postmortem experimental ruptures of the human heart

Comparison of postmortem performed experimental cardiac ruptures with post-infarction lesions reveals uniformity of their localization. The ruptures are found to occur at places of a sharp change in the relief of the cardiac internal surface. These areas should be considered as concentrators of strain, promoting cardiac ruptures. In the left ventricle six concentrators of strain are revealed. They are: the place where the anterior part of the interventricular septum passes into the anterior wall of the left ventricle, the right edge of the papillary muscle, the left edge of the anterior papillary muscle, the left edge of the posterior papillary muscle, the right edge of the posterior papillary muscle, the place where the posterior part of the interventricular septum passes into the posterior wall of the left ventricle. Frequency of the experimental ruptures of the interventricular septum, under loading of the left ventricle, is demonstrated to depend on pressure in the right cardiac part.     

A 2D FE model of the heart demonstrates the role of the pericardium in ventricular deformation

During pulmonary artery constriction (PAC), an experimental model of acute right ventricular (RV) pressure overload, the interventricular septum flattens and inverts. Finite element (FE) analysis has shown that the septum is subject to axial compression and bending when so deformed. This study examines the effects of acute PAC on the left ventricular (LV) free wall and the role the pericardium may play in these effects. In eight open-chest anesthetized dogs, LV, RV, aortic, and pericardial pressures were recorded under control conditions and with PAC. Model dimensions were derived from two-dimensional echocardiography minor-axis images of the heart. At control (pericardium closed), FE analysis showed that the septum was concave to the LV; stresses in the LV, RV, and septum were low; and the pericardium was subject to circumferential tension. With PAC, RV end-diastolic pressure exceeded LV pressure and the septum inverted. Compressive stresses developed circumferentially in the septum out to the RV insertion points, forming an arch-like pattern. Sharp bending occurred near the insertion points, accompanied by flattening of the LV free wall. With the pericardium open, the deformations and stresses were different. The RV became much larger, especially with PAC. With PAC, the arch-like circumferential stresses still developed in the septum, but their magnitudes were reduced, compared with the pericardium-closed case. There was no free wall inversion and flattening was less. From these FE results, the pericardium has a significant influence on the structural behavior of the septum and the LV and RV free walls. Furthermore, the deformation of the heart is dependent on whether the pericardium is open or closed.     

Compressive and tensile mechanical properties of the porcine nasal septum

The expanding nasal septal cartilage is believed to create a force that powers midfacial growth. In addition, the nasal septum is postulated to act as a mechanical strut that prevents the structural collapse of the face under masticatory loads. Both roles imply that the septum is subject to complex biomechanical loads during growth and mastication. The purpose of this study was to measure the mechanical properties of the nasal septum to determine (1) whether the cartilage is mechanically capable of playing an active role in midfacial growth and in maintaining facial structural integrity and (2) if regional variation in mechanical properties is present that could support any of the postulated loading regimens. Porcine septal samples were loaded along the horizontal or vertical axes in compression and tension, using different loading rates that approximate the in vivo situation. Samples were loaded in random order to predefined strain points (2–10%) and strain was held for 30 or 120 seconds while relaxation stress was measured. Subsequently, samples were loaded until failure. Stiffness, relaxation stress and ultimate stress and strain were recorded. Results showed that the septum was stiffer, stronger and displayed a greater drop in relaxation stress in compression compared to tension. Under compression, the septum displayed non-linear behavior with greater stiffness and stress relaxation under faster loading rates and higher strain levels. Under tension, stiffness was not affected by strain level. Although regional variation was present, it did not strongly support any of the suggested loading patterns. Overall, results suggest that the septum might be mechanically capable of playing an active role in midfacial growth as evidenced by increased compressive residual stress with decreased loading rates. However, the low stiffness of the septum compared to surrounding bone does not support a strut role. The relatively low stiffness combined with high stress relaxation under fast loading rates suggests that the nasal septum is a stress dampener, helping to absorb and dissipate loads generated during mastication.     

Some unusual considerations about vessel walls and wall stresses

The "zero-stress state" of blood vessels is usually defined with respect to the atmospheric pressure p(a) ( approximately 750 mmHg). As a consequence, circumferential and axial wall stresses due to a positive transmural pressure can only be positive and thus, by definition, only tensile. If the zero-stress state were defined with respect to vacuum pressure (0 mmHg), the compressive stress -p(a) generated by p(a) everywhere in the wall would, however, be included so that negative (=compressive) wall stresses would formally become possible. In order to examine the consequences this alternative definition would have for arteries, we have compared radial, circumferential, and axial stresses calculated "conventionally" to the values they take when the zero-stress state is defined "correctly" by reference to the vacuum pressure. It turns out that, under normal physiologic conditions, axial stress and perhaps also circumferential stress might well be compressive in many elastic and conductance arteries, contrary to the intuitive conviction of many people. Since the type of stresses a vessel wall is submitted to may be highly relevant for its structure and mechanical properties, this unconventional way of considering wall stresses may reveal unsuspected relationships between wall stresses on one side, and wall structure, vessel growth, adaptation and repair processes, atherosclerosis, angioplasty or stenting on the other side. Similar considerations might also prove useful with regard to cardiac hypertrophy.     

The echocardiographic study of the rabbit heart left ventricle morpho-functional parameters

Morphometric and functional parameters of the heart left ventricle in rabbits during systole and diastole were investigated by the method of echocardiography. Morphometric parameters were studied on three levels: the mitral valve, the papillary muscles and the apical level. The internal dimension of the left ventricle uniformly decreases in three parallel planes during systole, its maximal reduction being observed on the apical level. During the contraction phase, the posterior wall thickness of the left ventricular and the interventricular septum thickness increases on the basal level to a greater extent than on the apical one. During systole, the interventricular septum movement is greater than the left ventricular posterior wall motion. During the heart cycle, the form of the left ventricular cavity changes from an ellipsoid in diastole to elliptic paraboloid in systole.     

Relationship of pulmonary vein flow to left ventricular short-axis epicardial displacement in diastole: model-based prediction with in vivo validation

Previous studies in healthy humans have established that the (approximately 850 ml) volume enclosed by the pericardial sac is nearly constant over the cardiac cycle, exhibiting a transient approximately 5% decrease (approximately 40 ml) from end diastole to end systole. This volume decrease manifests as a "crescent" at the ventricular free wall level when short-axis MRI images of the epicardial surface acquired at end systole and end diastole are superimposed. On the basis of the (near) constant-volume property of the four-chambered heart, the volume decrease ("crescent effect") must be restored during subsequent early diastolic filling via the left atrial conduit volume. Therefore, volume conservation-based modeling predicts that pulmonary venous (PV) Doppler D-wave volume must be causally related to the radial displacement of the epicardium (Delta) (i.e., magnitude of "crescent effect" in the radial direction). We measured Delta from M-mode echocardiographic images and measured D-wave velocity-time integral (VTI) from Doppler PV flow of the right superior PV in 11 subjects with catheterization-determined normal physiology. In accordance with model prediction, high correlation was observed between Delta and D-wave VTI (r=0.86) and early D-wave VTI measured to peak D-wave velocity (r=0.84). Furthermore, selected subjects with various pathological conditions had values of Delta that differed significantly. These observations demonstrate the volume conservation-based causal relationship between radial pericardial displacement of the left ventricle and the PV D-wave-generated filling volume in healthy subjects as well as the potential role of the M-mode echo-derived radial epicardial displacement index Delta as a regional (radial) parameter of diastolic function.     

Differential expression of the cardiac ryanodine receptor in normal and arrhythmogenic right ventricular cardiomyopathy canine hearts

Arrhythmogenic right ventricular cardiomyopathy (ARVC) is a form of cardiomyopathy characterized by ventricular tachyarrhythmias and a fibrofatty infiltrate that is believed to preferentially affect the right ventricle. Mutations in the cardiac ryanodine receptor (RyR2) gene have been identified in some human families with a unique form of ARVC, ARVC2. Although the RyR2 has significant importance in excitation–contraction coupling across the ventricles, mutations in the gene encoding for it appear to have the greatest impact on the right ventricle in ARVC2. Using a canine model (boxer), the RyR2 protein and message RNA in the right ventricle, left ventricle and interventricular septum from normal dogs and dogs with ARVC were investigated by immunoblotting and real time PCR. The cardiac RyR2 message and protein expression were differentially expressed across the cardiac walls in the normal heart, with the lowest concentration expressed in the right ventricle (P < 0.05). The message and protein expression of the RyR2 were reduced in all chambers in the canine model of ARVC. We propose that the increased susceptibility of the right ventricle to ARVC may be associated with the lower baseline protein concentration of RyR2 in the normal right ventricle compared to the left ventricle and interventricular septum and that all three areas are equally affected in this canine model of ARVC. Using this naturally occurring model of canine ARVC, we may have provided new insights into the pathogenesis of this cardiomyopathy.     

Compression induced by RV pressure overload decreases regional coronary blood flow in anesthetized dogs

Pulmonary artery constriction (PAC), a model of right ventricular (RV) pressure overload, flattens or inverts the septum and may flatten the left ventricular (LV) free wall. Finite element (FE) analysis predicts that such deformations may cause substantial compression. This study tests the hypothesis that deformation-induced myocardial compressive stress impedes coronary blood flow (CBF). Colored microspheres ( approximately 2 x 10(6)) were injected into the left atrium of 13 open-chest, anesthetized dogs under control conditions and during PAC, which decreased the end-diastolic transseptal pressure gradient (LV - RV) from 1.6 +/- 1.3 to -3.4 +/- 1.7 mmHg. Septal and LV deformation was assessed with the use of two-dimensional echocardiography, and by FE analysis, the hydrostatic component of stress was assessed. Postmortem, a 2.5-cm wide, LV equatorial ring was divided into 16 endocardial and epicardial samples. PAC decreased CBF in the FE-predicted compression zones, areas with the greatest compression having the greatest reductions in CBF. During PAC, compression reached a maximum of 25.3 +/- 1.8 mmHg on the (LV) endocardial sides of the RV insertion points, areas that saw CBF decrease from 1.05 +/- 0.08 to 0.68 +/- 0.05 ml.min(-1).g(-1) (P < 0.001), more than 30%. CBF decreased (from 1.08 +/- 0.07 to 0.81 +/- 0.07 ml.min(-1).g(-1); P < 0.001) on the RV side of the midseptum, an area with as much as 16.0 +/- 1.0 mmHg of compression. Overall, average compressions of 10 mmHg decreased CBF by approximately 30%. We conclude that acute RV pressure overload deforms the septum and LV and induces compressive stresses that reduce CBF substantially. This may help explain why some patients with pulmonary hypertension and no critical coronary disease have chest discomfort indistinguishable from angina pectoris.     

Deformation behaviour and damage accumulation of cortical bone specimens from the equine tibia under cyclic loading

Despite its clinical importance, the fatigue behaviour of cortical bone has not been examined as widely as its static behaviour. In the present study, specimens from the tibiae of horses have been subjected to load-controlled single step tests. The cyclic deformation behaviour was described by the development of stress-strain hysteresis parameters over the lifetime. The fatigue behaviour of bone is characterised by cyclic softening which is most distinctive towards the end of the lifetime. The microstructural damage accumulated during cyclic loading results in a loss of stiffness, asymmetrical deformation of the bone in tension and compression in cyclic creep. As shown by light and scanning electron microscopy, microcrack formation and growth is the main damage mechanism. The crack growth behaviour is strongly influenced by the microstructure, the stress components and the absolute value of the local stresses. Lower local stresses and/or compressive mean stresses lead to a dominant influence of the shear stress components with shear failure at inner interfaces. With increasing crack length, that is, higher local stress amplitudes, or tensile mean stresses, the microstructure is more and more ignored and failure occurs primarily under the influence of the normal stress components. This can be clearly seen on the fracture and specimen surfaces.     

Changes in myosin isozyme expression during cardiac hypertrophy in hyperthyroid rabbits

The myosin isozyme distribution in the left ventricle and in the interventricular septum of rabbits was studied after 3, 7, 11, 14 and 21 days of L-thyroxine (500 micrograms/kg/day) administration. Histochemical procedures were employed to identify V1 and V3 by their Ca2+ ATPase activity and their proportions were quantified through polyacrylamide gel electrophoresis. In the left ventricle, the subepicardium was the first to show the shift from V3 to V1, followed by the subendocardium. The intermediate region became heterogeneous by 11 days and remained so until 21 days. The right subendocardial and the intermediate regions of the interventricular septum were heterogeneous in the normal rabbit and hyperthyroidism resulted in a shift from V3 to V1 in both the right and left subendocardial regions of the septum. Like the left ventricle, the intermediate region of the interventricular septum remained heterogeneous. Localized accumulations of collagen were seen in all regions of the left ventricle and interventricular septum. From these results we conclude that in thyrotoxic myocardial hypertrophy the isozymic shift from V3 to V1 is progressive, region-specific and is directly correlated with the period of hyperthyroidism in the first 2 weeks. Prolonged hyperthyroidism results in localized accumulation of collagen which does not exhibit any regional specificity.     

Pericardial heterograft valves: An assessment of leaflet stresses and their implications for heart valve design

Bovine pericardium, stabilized with glutaraldehyde, is used widely in the construction of heart valve substitutes, but the design and construction of valve substitutes from this material are empirically based. Collagenous tissue can support tension, but experimental evidence indicates that flexure-induced compressive stresses can lead to fatigue failure. This study uses experimental results obtained from cyclic uniaxial load tests to predict the type and magnitude of operational stresses which occur in pericardial heterograft leaflets. Both Young's modulus and Poisson's ratio varied with uniaxial loading in pericardium, chemically modified free of tension. Leaflet stresses were analysed by using effective incremental representations of these parameters. In leaflets with unrestricted rotation at the point of attachment to the stent, the mid-plane tensions always exceeded the bending stresses, and no zones of leaflet compression were predicted. In contrast, with totally restricted leaflet rotation induced by clamping (possibly between a male and female frame) the bending stresses were greater than the mid-plane tensions at the hinge line and significant compressive stresses were predicted at this site. If elastic boundary conditions were introduced at the stent (possibly by wrapping the stent in pericardium) then the compressive stresses were reduced as the degree of elasticity was increased. Glutaraldehyde fixation of the pericardium under load produced a stiffer material; higher compressive stresses at the stent and significant increases in total stress were predicted for this tissue. The application of elevated pressure loading also increased the compressive and total stresses in the leaflet. Finally, it was shown that bicuspid leaflets were likely to experience higher stresses than tricuspid leaflets. This simple stress analysis should help valve designers of pericardial heterografts to identify those conditions which lead to tissue compression, high total stress, and ultimately material fatigue.     

A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole

In this work, we introduce a modified Holzapfel-Ogden hyperelastic constitutive model for ventricular myocardium that accounts for residual stresses, and we investigate the effects of residual stresses in diastole using a magnetic resonance imaging–derived model of the human left ventricle (LV). We adopt an invariant-based constitutive modelling approach and treat the left ventricular myocardium as a non-homogeneous, fibre-reinforced, incompressible material. Because in vivo images provide the configuration of the LV in a loaded state even in diastole, an inverse analysis is used to determine the corresponding unloaded reference configuration. The residual stress in this unloaded state is estimated by two different methods. One is based on three-dimensional strain measurements in a local region of the canine LV, and the other uses the opening angle method for a cylindrical tube. We find that including residual stress in the model changes the stress distributions across the myocardium and that whereas both methods yield qualitatively similar changes, there are quantitative differences between the two approaches. Although the effects of residual stresses are relatively small in diastole, the model can be extended to explore the full impact of residual stress on LV mechanical behaviour for the whole cardiac cycle as more experimental data become available. In addition, although not considered here, residual stresses may also play a larger role in models that account for tissue growth and remodelling.     

State of the capillary network of rat myocardium in the presence of hypertrophy and physical loading

Morphofunctional state of the capillary network in various myocardial parts was studied in white rats under normal conditions, myocardial hypertrophy of different degree and under physical loading. It was demonstrated that density, metabolic surface and capacity of the capillary bed is larger in the right ventricle than in the left one. The capillary blood supply in hypertrophied myocardium, increasing simultaneously with hypertrophy, at the state of rest corresponds to its increasing mass. On the contrary, under maximal physical loading functioning of the capillary part in the myocardium becomes unadequate that is evident from a decreasing activity of the test animals.     

Heterogeneity of the myocardium. Function of the left and right ventricle under normal and pathological conditions

A number of important differences can be found between the left ventricle (LV) and right ventricle (RV) of the heart under physiological conditions. In anatomy, the most important is probably the architecture of the atrioventricular valve and its annulus. The LV has a mitral valve (with two cusps) and a firm annulus, while the RV has a tricuspid valve with a greater total area, but relatively small cuspid areas, and an elastic annulus. The difference in the blood supply is important. Owing to high intramural pressure, the coronary flow in the wall of the LV occurs only during the diastole; in the RV it is limited only in the presence of a significant increase in intracavitary pressure. The LV myocardium is functionally "accustomed" to short-term marked changes in the systolic load (in extreme static exercise the arterial pressure rises for a short time to three times the normal value), while the RV is adapted to changes in the diastolic load (marked filling changes associated with deep breathing, for instance). The difference in the response to a long-term volume load is difficult to evaluate: between a defect of the interatrial septum and aortic insufficiency there are too many differences. A long-term pressure load seems to be tolerated better by the right ventricle: patients with severe pulmonary stenosis and a pressure six times higher than the physiological value have lived 25 years and patients with isolated corrected L-transposition of the great arteries can reach 35 years without any signs of impaired RV function.(ABSTRACT TRUNCATED AT 250 WORDS)     

Measurement of strain in the left ventricle during diastole with cine-MRI and deformable image registration

The assessment of regional heart wall motion (local strain) can localize ischemic myocardial disease, evaluate myocardial viability, and identify impaired cardiac function due to hypertrophic or dilated cardiomyopathies. The objectives of this research were to develop and validate a technique known as hyperelastic warping for the measurement of local strains in the left ventricle from clinical cine-magnetic resonance imaging (MRI) image datasets. The technique uses differences in image intensities between template (reference) and target (loaded) image datasets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target image. To validate the technique, MRI image datasets representing two deformation states of a left ventricle were created such that the deformation map between the states represented in the images was known. A beginning diastolic cine-MRI image dataset from a normal human subject was defined as the template. A second image dataset (target) was created by mapping the template image using the deformation results obtained from a forward FE model of diastolic filling. Fiber stretch and strain predictions from hyperelastic warping showed good agreement with those of the forward solution (R2=0.67 stretch, R2=0.76 circumferential strain, R2=0.75 radial strain, and R2=0.70 in-plane shear). The technique had low sensitivity to changes in material parameters (deltaR2= -0.023 fiber stretch, deltaR2=-0.020 circumferential strain, deltaR2=-0.005 radial strain, and deltaR2=0.0125 shear strain with little or no change in rms error), with the exception of changes in bulk modulus of the material. The use of an isotropic hyperelastic constitutive model in the warping analyses degraded the predictions of fiber stretch. Results were unaffected by simulated noise down to a signal-to-noise ratio (SNR) of 4.0 (deltaR2= -0.032 fiber stretch, deltaR2=-0.023 circumferential strain, deltaR2=-0.04 radial strain, and deltaAR2=0.0211 shear strain with little or no increase in rms error). This study demonstrates that warping in conjunction with cine-MRI imaging can be used to determine local ventricular strains during diastole.     

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.     

Contribution of collagen fibers to the compressive stiffness of cartilaginous tissues

Cartilaginous tissues such as the intervertebral disk are predominantly loaded under compression. Yet, they contain abundant collagen fibers, which are generally assumed to contribute to tensile loading only. Fiber tension is thought to originate from swelling of the proteoglycan-rich nucleus. However, in aged or degenerate disk, proteoglycans are depleted, whereas collagen content changes little. The question then rises to which extend the collagen may contribute to the compressive stiffness of the tissue. We hypothesized that this contribution is significant at high strain magnitudes and that the effect depends on fiber orientation. In addition, we aimed to determine the compression of the matrix. Bovine inner and outer annulus fibrosus specimens were subjected to incremental confined compression tests up to 60 % strain in radial and circumferential direction. The compressive aggregate modulus was determined per 10 % strain increment. The biochemical composition of the compressed specimens and uncompressed adjacent tissue was determined to compute solid matrix compression. The stiffness of all specimens increased nonlinearly with strain. The collagen-rich outer annulus was significantly stiffer than the inner annulus above 20 % compressive strain. Orientation influenced the modulus in the collagen-rich outer annulus. Finally, it was shown that the solid matrix was significantly compressed above 30 % strain. Therefore, we concluded that collagen fibers significantly contribute to the compressive stiffness of the intervertebral disk at high strains. This is valuable for understanding the compressive behavior of collagen-reinforced tissues in general, and may be particularly relevant for aging or degenerate disks, which become more fibrous and less hydrated.     

Dynamic and quasi-static compressive response of porcine muscle

Research and application activities in impact biomechanics require dynamic response of biological tissues under high-rate loading. However, experimental difficulties have limited the characterization of soft tissues under such loading conditions. In this paper, we identify these technical challenges in dynamic compression experiments using a split Hopkinson pressure bar (SHPB) and present the remedies to overcome them. In order to subject the specimens to valid dynamic testing conditions, in addition to developing new pulse-shaping techniques and incorporating highly sensitive load-measuring transducers, annular thin-disc specimens radically different from regular solid specimens were used to minimize radial inertia effects that may overshadow the intrinsic material properties. By using this modified SHPB, the compressive stress-strain behavior of soft porcine muscle tissue was obtained along and perpendicular to the muscle fiber direction from quasi-static to dynamic strain rates. The results show that the non-linear compressive stress-strain responses in both directions are strongly strain-rate sensitive.