Transverse elasticity of myofibrils of rabbit skeletal muscle studied by atomic force microscopy

Surface structure of myofibrils of rabbit skeletal muscle and their transverse elasticity were studied by atomic force microscopy. Images of myofibrils had a periodic structure characteristic of sarcomeres of skeletal muscle fibers. The transverse elasticity distribution in the sarcomere was determined based on force-distance curves measured at various loci of single myofibrils. The Z-line in rigor myofibrils was the most rigid in all the loci of myofibrils studied under various physiological conditions. The overall transverse elasticity of myofibrils decreased in the order in rigor solution > +AMPPNP solution > relaxing solution. The "apparent" transverse Young's modulus of myofibrils estimated at the overlap region between thin and thick filaments was 84.0 +/- 18.1, 37.5 +/- 14.0, and 11.5 +/- 3.5 kPa in rigor, +AMPPNP, and relaxing solution respectively.     

Elasticity of mutant myosin subfragment-1 arranged on a functional silver surface.

Elasticity of a two-dimensionally arranged myosin subfragment-1 (S1) was measured by using a surface forces apparatus. To prepare a two-dimensionally arranged S1-monolayer on a functionalized silver surface, we used genetically engineered Dictyostelium S1 molecules. A highly reactive cysteine residue was fused to the COOH-terminus using the recombinant DNA method. On the other hand, the maleimide groups was self-assembled onto a silver surface. Then the mutant S1 molecules were chemically bound to the functionalized silver surface at its COOH-terminus. This arrangement technique was necessary in order to create a stable S1-monolayer by chemical bond formation onto the silver surface. The occupied area of the single S1 on the silver surface was about 110 nm(2). In the interaction between the S1-monolayer and mica surfaces in aqueous solution, a long-range attractive force was observed. The elastic constants (stiffness and Young's modulus) of myosin S1 were evaluated from force-distance profiles in aqueous solution, using the Hertz theory. We found that the stiffness (or spring constant) and Young's modulus of S1 in the absence of nucleotide are 4.4 +/- 1.0 pN/nm and 0.71 +/- 0.16 GPa, respectively.     

Stiffness and fraction of Myosin motors responsible for active force in permeabilized muscle fibers from rabbit psoas

The stiffness of the single myosin motor (epsilon) is determined in skinned fibers from rabbit psoas muscle by both mechanical and thermodynamic approaches. Changes in the elastic strain of the half-sarcomere (hs) are measured by fast mechanics both in rigor, when all myosin heads are attached, and during active contraction, with the isometric force (T0) modulated by changing either [Ca2+] or temperature. The hs compliance is 43.0+/-0.8 nm MPa-1 in isometric contraction at saturating [Ca2+], whereas in rigor it is 28.2+/-1.1 nm MPa-1. The equivalent compliance of myofilaments is 21.0+/-3.3 nm MPa-1. Accordingly, the stiffness of the ensemble of myosin heads attached in the hs is 45.5+/-1.7 kPa nm-1 in isometric contraction at saturating [Ca2+] (e0), and in rigor (er) it rises to 138.9+/-21.2 kPa nm-1. Epsilon, calculated from er and the lattice molecular dimensions, is 1.21+/-0.18 pN nm-1. epsilon estimated, using a thermodynamic approach, from the relation of T0 at saturating [Ca2+] versus the reciprocal of absolute temperature is 1.25+/-0.14 pN nm-1, similar to that estimated for fibers in rigor. Consequently, the ratio e0/er (0.33+/-0.05) can be used to estimate the fraction of attached heads during isometric contraction at saturating [Ca2+]. If the osmotic agent dextran T-500 (4 g/100 ml) is used to reduce the lateral filament spacing of the relaxed fiber to the value before skinning, both e0 and er increase by approximately 40%. Epsilon becomes approximately 1.7 pN nm-1 and the fraction and the force of myosin heads attached in the isometric contraction remain the same as before dextran application. The finding that the fraction of myosin heads attached to actin in an isometric contraction is 0.33 rules out the hypothesis of multiple mechanical cycles per ATP hydrolyzed.     

Creatine kinase binding and possible role in chemically skinned guinea-pig taenia coli.

The activity and role of creatine kinase (CK) associated with contractile proteins of smooth muscle have been investigated using skinned guinea-pig taenia coli fibers. Total CK activity was 163 +/- 22 IU/g (ww) and agarose electrophoresis showed BB, MB, and MM isoforms (BB-CK being the predominant isoenzyme). After skinning for 1 h with Triton X-100, BB-CK was specifically associated with the myofibrils, representing 22% of the preskinned CK activity. When relaxed fibers were exposed to pCa 9 in the presence of 250 microM ADP, 0 ATP and 12 mM PCr, tension was not significantly different from resting tension, but changing to pCa 4.5 caused the fibers to generate 59.1 +/- 5.2 percent of maximal tension. When a high-tension rigor state was achieved (250 microM ADP, 0 ATP, 0 PCr, and pCa 9), the addition of 12 mM PCr effected significant relaxation. These observations implicate an endogenous form of BB-CK, associated with the myofilaments and capable of producing enough ATP for submaximal tension generation and significant relaxation from rigor conditions. It was also shown that ADP is bound to the myofibrils and available for rephosphorylation by BB-CK. These results suggest co-localization of ATPase, MLCK and CK on the contractile proteins of the taenia coli. This enzymic association may play a role in the compartmentation of adenine nucleotides in smooth muscle.     

Direct measurement of the mechanical properties of lipid phases in supported bilayers

Biological membranes define not only the cell boundaries but any compartment within the cell. To some extent, the functionality of membranes is related to the elastic properties of the lipid bilayer and the mechanical and hydrophobic matching with functional membrane proteins. Supported lipid bilayers (SLBs) are valid biomimetic systems for the study of membrane biophysical properties. Here, we acquired high-resolution topographic and quantitative mechanics data of phase-separated SLBs using a recent atomic force microscopy (AFM) imaging mode based on force measurements. This technique allows us to quantitatively map at high resolution the mechanical differences of lipid phases at different loading forces. We have applied this approach to evaluate the contribution of the underlying hard support in the determination of the elastic properties of SLBs and to determine the adequate indentation range for obtaining reliable elastic moduli values. At ~200 pN, elastic forces dominated the force-indentation response and the sample deformation was <20% of the bilayer thickness, at which the contribution of the support was found to be negligible. The obtained Young's modulus (E) of 19.3 MPa and 28.1 MPa allowed us to estimate the area stretch modulus (k(A)) as 106 pN/nm and 199 pN/nm and the bending stiffness (k(c)) as 18 k(B)T and 57 k(B)T for the liquid and gel phases, respectively.     

Micro-mechanical sensing platform for the characterization of the elastic properties of the ovum via uniaxial measurement

Stiffness is an important parameter in determining the physical properties of living tissue. Recently, considerable biomedical attention has centered on the mechanical properties of living tissues at the single cell level. In the present paper, the Young's modulus of zona pellucida of bovine ovum was calculated using Micro Tactile Sensor (MTS) fabricated using piezoelectric (PZT) material. The sensor consists of a needle-shaped 20-microm transduction point made using a micro-electrode puller and mounted on a micro-manipulator platform. Measurements were made under microscopic control, using a suction pipette to support the ovum in the same horizontal axis as the MTS. Young's modulus of ovum was found to be 25.3+/-7.94 kPa (n=28). This value was indirectly determined based on calibration curves relating change in resonance frequency (Deltaf(0)) of the sensor with tip displacement for gelatin at concentrations of 4%, 6%, and 8%. The regression equation between the rate of change in resonance frequency (versus sensor tip displacement), Deltaf(0)/x and Young's modulus is Deltaf(0)/x (Hz/microm)=0.2992 x Young's modulus (kPa)-1.0363. It is concluded that a reason that the stiffness of ovum measured in the present study is approximately six times larger than previously reported, may be due to the absence of large deformation present in of existing methodologies.     

Alterations in the mechanical properties of the human chondrocyte pericellular matrix with osteoarthritis

In articular cartilage, chondrocytes are surrounded by a pericellular matrix (PCM), which together with the chondrocyte have been termed the "chondron." While the precise function of the PCM is not know there has been considerable speculation that it plays a role in regulating the biomechanical environment of the chondrocyte. In this study, we measured the Young's modulus of the PCM from normal and osteoarthritic cartilage using the micropipette aspiration technique, coupled with a newly developed axisymmetric elastic layered half-space model of the experimental configuration. Viable, intact chondrons were extracted from human articular cartilage using a new microaspiration-based isolation technique. In normal cartilage, the Young's modulus of the PCM was similar in chondrons isolated from the surface zone (68.9 +/- 18.9 kPa) as compared to the middle and deep layers (62.0 +/- 30.5 kPa). However, the mean Young's modulus of the PCM (pooled for the two zones) was significantly decreased in osteoarthritic cartilage (66.5 +/- 23.3 kPa versus 41.3 +/- 21.1 kPa, p < 0.001). In combination with previous theoretical models of cell-matrix interactions in cartilage, these findings suggest that the PCM has an important influence on the stress-strain environment of the chondrocyte that potentially varies with depth from the cartilage surface. Furthermore, the significant loss of PCM stiffness that was observed in osteoarthritic cartilage may affect the magnitude and distribution of biomechanical signals perceived by the chondrocytes.     

The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

The origin of passive force enhancement in skeletal muscle

The aim of the present study was to test whether titin is a calcium-dependent spring and whether it is the source of the passive force enhancement observed in muscle and single fiber preparations. We measured passive force enhancement in troponin C (TnC)-depleted myofibrils in which active force production was completely eliminated. The TnC-depleted construct allowed for the investigation of the effect of calcium concentration on passive force, without the confounding effects of actin-myosin cross-bridge formation and active force production. Passive forces in TnC-depleted myofibrils (n = 6) were 35.0 +/- 2.9 nN/ microm(2) when stretched to an average sarcomere length of 3.4 microm in a solution with low calcium concentration (pCa 8.0). Passive forces in the same myofibrils increased by 25% to 30% when stretches were performed in a solution with high calcium concentration (pCa 3.5). Since it is well accepted that titin is the primary source for passive force in rabbit psoas myofibrils and since the increase in passive force in TnC-depleted myofibrils was abolished after trypsin treatment, our results suggest that increasing calcium concentration is associated with increased titin stiffness. However, this calcium-induced titin stiffness accounted for only approximately 25% of the passive force enhancement observed in intact myofibrils. Therefore, approximately 75% of the normally occurring passive force enhancement remains unexplained. The findings of the present study suggest that passive force enhancement is partly caused by a calcium-induced increase in titin stiffness but also requires cross-bridge formation and/or active force production for full manifestation.     

Tension recovery in permeabilized rat soleus muscle fibers after rapid shortening and restretch

Permeabilized rat soleus muscle fibers were subjected to rapid shortening/restretch protocols (20% muscle length, 20 ms duration) in solutions with pCa values ranging from 6.5 to 4.5. Force redeveloped after each restretch but temporarily exceeded the steady-state isometric tension reaching a maximum value approximately 2.5 s after relengthening. The relative size of the overshoot was <5% in pCa 6.5 and pCa 4.5 solutions but equaled 17% +/- 4% at pCa 6.0 (approximately half-maximal Ca2+ activation). Muscle stiffness was estimated during pCa 6.0 activations by imposing length steps at different time intervals after repeated shortening/restretch perturbations. Relative stiffness and relative tension were correlated (p < 0.001) during recovery, suggesting that tension overshoots reflect a temporary increase in the number of attached cross-bridges. Rates of tension recovery (k(tr)) correlated (p < 0.001) with the relative residual force prevailing immediately after restretch. Force also recovered to the isometric value more quickly at 5.7 < or = pCa < or = 5.9 than at pCa 4.5 (ANOVA, p < 0.05). These results show that k(tr) measurements underestimate the rate of isometric force development during submaximal Ca2+ activations and suggest that the rate of tension recovery is limited primarily by the availability of actin binding sites.     

Heterogeneous nanostructural and nanoelastic properties of pericellular and interterritorial matrices of chondrocytes by atomic force microscopy

Hyaline cartilage consists of sparse chondrocytes and abundant extracellular matrix. There is a paucity of experimental data in support of the notion of conceivable regional differences in the mechanical properties of chondral matrices. Upon visual differentiation of the pericellular and interterritorial matrices in each of 19 fresh growth plate samples with toluidine blue and alizarin red labels, nanoindentation was applied separately to the pericellular matrix and interterritorial matrix to using fluid-phase atomic force microscopy and real-time imaging. The interterritorial matrix demonstrated elongated parallel ridges, whereas the pericellular matrix showed irregular, short-range elevations with characteristic pores and canals. Analysis of surface contours at 600nm(2) scan size revealed that the interterritorial matrix had significantly greater surface roughness (71+/-18nm; mean+/-SE) than the pericellular matrix (24+/-4nm) ( P< 0.001). The average Young's modulus of the interterritorial matrix was 636+/-123 (kPa), significantly greater than the pericellular matrix (265+/-53kPa) (P< 0.001 ). Thus, the interterritorial matrix appears to possess not only distinct microtopographic contours in comparison with the pericellular matrix, but also significantly greater mechanical stiffness. These distinctive nanostructural and nanomechanical properties may have implications in nutrient diffusion and fluid dynamics, both of which are of vital importance for cartilage health and function.     

Ca2+ and cross-bridge-induced changes in troponin C in skinned skeletal muscle fibers: effects of force inhibition

Changes in skeletal troponin C (sTnC) structure during thin filament activation by Ca2+ and strongly bound cross-bridge states were monitored by measuring the linear dichroism of the 5' isomer of iodoacetamidotetramethylrhodamine (5'IATR), attached to Cys98 (sTnC-5'ATR), in sTnC-5'ATR reconstituted single skinned fibers from rabbit psoas muscle. To isolate the effects of Ca2+ and cross-bridge binding on sTnC structure, maximum Ca2+-activated force was inhibited with 0.5 mM AlF4- or with 30 mM 2,3 butanedione-monoxime (BDM) during measurements of the Ca2+ dependence of force and dichroism. Dichroism was 0.08 +/- 0.01 (+/- SEM, n = 9) in relaxing solution (pCa 9.2) and decreased to 0.004 +/- 0.002 (+/- SEM, n = 9) at pCa 4.0. Force and dichroism had similar Ca2+ sensitivities. Force inhibition with BDM caused no change in the amplitude and Ca2+ sensitivity of dichroism. Similarly, inhibition of force at pCa 4.0 with 0.5 mM AlF4- decreased force to 0.04 +/- 0.01 of maximum (+/- SEM, n = 3), and dichroism was 0.04 +/- 0.03 (+/- SEM, n = 3) of the value at pCa 9.2 and unchanged relative to the corresponding normalized value at pCa 4.0 (0.11 +/- 0.05, +/- SEM; n = 3). Inhibition of force with AlF4- also had no effect when sTnC structure was monitored by labeling with either 5-dimethylamino-1-napthalenylsulfonylaziridine (DANZ) or 4-(N-(iodoacetoxy)ethyl-N-methyl)amino-7-nitrobenz-2-oxa-1,3-diazole (NBD). Increasing sarcomere length from 2.5 to 3.6 microm caused force (pCa 4.0) to decrease, but had no effect on dichroism. In contrast, rigor cross-bridge attachment caused dichroism at pCa 9.2 to decrease to 0.56 +/- 0.03 (+/- SEM, n = 5) of the value at pCa 9. 2, and force was 0.51 +/- 0.04 (+/- SEM, n = 6) of pCa 4.0 control. At pCa 4.0 in rigor, dichroism decreased further to 0.19 +/- 0.03 (+/- SEM, n = 6), slightly above the pCa 4.0 control level; force was 0.66 +/- 0.04 of pCa 4.0 control. These results indicate that cross-bridge binding in the rigor state alters sTnC structure, whereas cycling cross-bridges have little influence at either submaximum or maximum activating [Ca2+].     

Mouse zona pellucida dynamically changes its elasticity during oocyte maturation, fertilization and early embryo development

A change in the elasticity of mouse zona pellucida was quantitatively evaluated during oocyte maturation, fertilization and early embryo development. Young's modulus of zona pellucida of germinal vesicle (GV), metaphase-II (MII), pronuclear (PN), 2cell, 4cell, 8cell, morulae (M) and early blastocyst (EB) stages was measured using a micro tactile sensor (MTS) and a chamber exclusively designed for the measurement. The MTS has very high sensitivity and a deformation of only 5 microm was sufficient to calculate the Young's modulus and the oocyte/embryo maintained its original spherical shape during the measurement. The Young's modulus of GV, MII, PN, 2cell, 4cell, 8cell, M and EB was 22.8+/-10.4 kPa (n=30), 8.26+/-5.22 kPa (n=74), 22.3+/-10.5 kPa (n=66), 13.8+/-3.54 kPa (n=41), 12.6+/-3.34 kPa (n=19), 5.97+/-4.97 kPa (n=6), 1.88+/-1.34 kPa (n=8) and 3.39+/-1.86 kPa (n=4), respectively. Experimental results clearly demonstrated that the mouse zona pellucida hardened following fertilization. Interestingly, once the zona pellucida hardened at the PN stage, it gradually softened as the embryo developed (i.e. it was found that the zona hardening is a transient phenomenon). Furthermore, the zona pellucida of the GV oocyte was as hard as that of the PN embryo and became soft as it matured to the MII stage. In addition, the safety of the MTS measurement for oocytes and embryos was discussed both theoretically and experimentally.     

Cooperative effects of rigor and cycling cross-bridges on calcium binding to troponin C

The effects of rigor and cycling cross-bridges on distributions of calcium (Ca) bound within sarcomeres of rabbit psoas muscle fibers were compared using electron probe x-ray microanalysis. Calcium in the overlap region of rigor fibers, after correction for that bound to thick filaments, was significantly higher than in the I-band at all pCa levels tested between 6.9 and 4.8, but the difference was greatest at pCa 6.9. With addition of MgATP, differences were significant at high levels of activation (pCa 5.6 and 4.9); near and below the threshold for activation, Ca was the same in I-band and overlap regions. Comparison of Ca and mass profiles at the A-I junction showed elevation of Ca extending 55-110 nm (up to three regulatory units) into the I-band. Extraction of TnC-reduced I-band and overlap Ca in rigor fibers at pCa 5.6 to the same levels found in unextracted fibers at pCa 8.9, suggesting that variations reported here reflect changes in Ca bound to troponin C (TnC). Taken together, these observations provide evidence for near-neighbor cooperative effects of both rigor and cycling cross-bridges on Ca(2+) binding to TnC.     

Intrinsic mechanical properties of trabecular calcaneus determined by finite-element models using 3D synchrotron microtomography

To determine intrinsic mechanical properties (elastic and failure) of trabecular calcaneus bone, chosen as a good predictor of hip fracture, we looked for the influence of image's size on a numerical simulation. One cubic sample of cancellous bone (9 x 9 x 9 mm(3)) was removed from the body of the calcaneus (6 females, 6 males, 79+/-9 yr). These samples were tested under compressive loading. Before compressive testing, these samples were imaged at 10.13 microm resolution using a 3D microcomputed tomography (muCT) (ESRF, France). The muCT images were converted to finite-element models. Depending on the bone density values (BV/TV), we compared two different finite element models: a linear hexahedral and a linear beam finite element models. Apparent experimental Young's modulus (E(app)(exp)) and maximum apparent experimental compressive stress (sigma(max)(exp)) were significantly correlated with bone density obtained by Archimedes's test (E(app)(exp)=236+/-231 MPa [19-742 MPa], sigma(max)(exp)=2.61+/-1.97 MPa [0.28-5.81 MPa], r>0.80, p<0.001). Under threshold at 40 microm, the size of the numerical samples (5.18(3) and 6.68(3)mm(3)) seems to be an important parameter on the accuracy of the results. The numerical trabecular Young's modulus was widely higher (E(trabecular)(num)=34,182+/-22,830 MPa [9700-87,211 MPa]) for the larger numerical samples and high BV/TV than those found classically by other techniques (4700-15,000 MPa). For rod-like bone samples (BV/TV<12%, n=7), Young's modulus, using linear beam element (E(trabecular)(num-skeleton): 10,305+/-5500 MPa), were closer to the Young's modulus found by other techniques. Those results show the limitation of hexahedral finite elements at 40 microm, mostly used, for thin trabecular structures.     

Reduced cross-bridge dependent stiffness of skinned myocardium from mice lacking cardiac myosin binding protein-C

The role of cardiac myosin binding protein-C (MyBP-C) on myocardial stiffness was examined in skinned papillary muscles of wild-type (WT(+/+)) and homozygous truncated cardiac MyBP-C (MyBP-C(t/t) male mice. No MyBP-C was detected by gel electrophoresis or by Western blots in the MyBP-C(t/t) myocardium. Rigor-bridge dependent myofilament stiffness, i.e., rigor minus relaxed stiffness, in the MyBP-C(t/t) myocardium (281 +/- 44 kN/m2) was 44% that in WT(+/+) (633 +/- 141 kN/m2). The center-to-center spacing between thick filaments as determined by X-ray diffraction in MyBP-C(t/t) (45.0 +/- 1.2 nm) was not significantly different from that in WT(+/+) (43.2 +/- 0.9 nm). The fraction of cross-sectional area comprised of myofibrils, as determined by electron microscopy, was reduced in the MyBP-C(t/t) (39.9%) by 10% compared to WT(+/+) (44.5%). These data suggest that the 56% reduction in rigor-bridge dependent stiffness of the skinned MyBP-C(t/t) myocardium could not be due solely to a 10% reduction in the number of thick filaments per cross-sectional area and must also be due to approximately 50% reduction in the stiffness of the rigor-bridge attached thick filaments lacking MyBP-C.     

Three-axial strain controlled testing applied to bone specimens from the proximal tibial epiphysis

Reproducibility of the determination of Young's modulus and energy absorption along the three axes of trabecular bone cubes was analysed by non-destructive compression to 0.5% strain using different testing protocols. These protocols included testing with and without pre-conditioning to a viscoelastic steady state, and different orders of test directions. Reproducibility of conditioned tests was generally better than that of non-conditioned tests. No major effect of changing the order of the test direction was found. Three-axial conditioned testing of cubes from the proximal tibial epiphysis of five humans revealed a global transverse isotrophy while most cubes showed orthotropy. The ratio between stiffness along the long axis of the tibia and the stiffness in the transverse plane was 3.7 +/- 0.4 (mean +/- 2 SE). The corresponding ratios for elastic energy storage and viscoelastic energy dissipation were 2.5 +/- 0.2. There was no difference between the relative energy loss during a testing cycle (loss tangent) in the three axes.     

Mapping elasticity moduli of atherosclerotic plaque in situ via atomic force microscopy

Several studies have suggested that evolving mechanical stresses and strains drive atherosclerotic plaque development and vulnerability. Especially, stress distribution in the plaque fibrous capsule is an important determinant for the risk of vulnerable plaque rupture. Knowledge of the stiffness of atherosclerotic plaque components is therefore of critical importance. In this work, force mapping experiments using atomic force microscopy (AFM) were conducted in apolipoprotein E-deficient (ApoE(-/-)) mouse, which represents the most widely used experimental model for studying mechanisms underlying the development of atherosclerotic lesions. To obtain the elastic material properties of fibrous caps and lipidic cores of atherosclerotic plaques, serial cross-sections of aortic arch lesions were probed at different sites. Atherosclerotic plaque sub-structures were subdivided into cellular fibrotic, hypocellular fibrotic and lipidic rich areas according to histological staining. Hertz's contact mechanics were used to determine elasticity (Young's) moduli that were related to the underlying histological plaque structure. Cellular fibrotic regions exhibit a mean Young modulus of 10.4±5.7kPa. Hypocellular fibrous caps were almost six-times stiffer, with average modulus value of 59.4±47.4kPa, locally rising up to ～250kPa. Lipid rich areas exhibit a rather large range of Young's moduli, with average value of 5.5±3.5kPa. Such precise quantification of plaque stiffness heterogeneity will allow investigators to have prospectively a better monitoring of atherosclerotic disease evolution, including arterial wall remodeling and plaque rupture, in response to mechanical constraints imposed by vascular shear stress and blood pressure.     

Radial stiffness of frog skinned muscle fibers in relaxed and rigor conditions.

Radial stiffness in various conditions of mechanically skinned fibers of semitendinosus muscle of Rana catesbeiana was determined by compressing the fiber with polyvinylpyrrolidone (PVP K-30, Mr = 40,000) in incubating solution. The change in width (D) of fibers with increasing and decreasing PVP concentrations was highly reproducible at a range 0-6% PVP. Radial stiffness of relaxed fibers was almost independent of the sarcomere length. On the other hand, radial stiffness of rigor fibers showed a linear relation against the sarcomere length. These results indicate that cross-bridge attachment would be a major factor in the increase of the radial stiffness. Radial stiffness of relaxed and rigor fibers was (2.14 +/- 0.52) X 10(4) N/m2 (mean +/- SD) and (8.76 +/- 2.04) X 10(4) N/m2, respectively, at the relative fiber width (D/D0) of 0.92, where D0 denotes the fiber width in the rigor solution at 0% PVP. Radial stiffness of a fiber in a rigor solution containing pyrophosphate (PPi) was between those of relaxed and rigor fibers, i.e., (4.76 +/- 0.86) X 10(4) N/m2 at D/Do of 0.92. In PPi and rigor solutions, radial stiffness reversibly increased to around 150 and 130%, respectively, in the presence of 10(-6) M Ca2+. To explain these results, especially the Ca2+-induced change in the radial stiffness, some factor in addition to the number of attached cross-bridges has to be taken into account. The variation of radial stiffness under various conditions will be discussed in relation to the possible manner of cross-bridge attachment.     

The flexural rigidity of the aortic valve leaflet in the commissural region

Flexure is a major deformation mode of the aortic valve (AV) leaflet, particularly in the commissural region where the upper portion of the leaflet joins the aortic root. However, there are no existing data known on the mechanical properties of leaflet in the commissural region. To address this issue, we quantified the effective stiffness of the commissural region using a cantilever beam method. Ten specimens were prepared, with each specimen flexed in the direction of natural leaflet motion (forward) and against the natural motion (reverse). At a flexure angle (phi) of 30 degrees , the effective forward direction modulus E was 42.63+/-4.44 kPa and the reverse direction E was 75.01+/-14.53 kPa (p=0.049). Further, E-phi response was linear (r(2) approximately 0.9) in both flexural directions. Values for dE/dphi were -2.24+/-0.6 kPa/ degrees and -1.90+/-0.3 kPa/ degrees in the forward and reverse directions, respectively (not statistically different, p=0.424), indicating a consistent decrease in stiffness with increased flexure. In comparison, we have reported that the effective tissue stiffness of AV leaflet belly region was 150-200 kPa [Merryman, W.D., Huang, H.Y.S., Schoen, F.J., Sacks, M.S. (2006). The effects of cellular contraction on AV leaflet flexural stiffness. Journal of Biomechanics 39 (1), 88-96], which was also independent of direction and amount of flexure. Histological studies of the commissure region indicated that tissue buckling was a probable mechanism for decrease in E with increasing flexure. The observed change in E with flexural angle in the commissural region is a subtle aspect of valve function. From a valve design perspective, these findings can be used as design criteria in fabricating prosthetic devices AV resulting in better functional performance.