Time dependence of series elasticity in tracheal smooth muscle

The stress-strain curve for the series elastic component (SEC) of tracheal smooth muscle was obtained by quick releasing the muscle from isometric tension to various afterloads and measuring the elastic recoils (SEC lengths) at a specific time after stimulation. A family of such curves was obtained by releasing the muscle at different points in time during contraction. Stiffnesses of the SEC (slopes of the stress-strain curves) at a specific stress level calculated from these curves (constant-stress stiffness) showed significant difference from one another. The same difference can also be characterized by the slope of the linear stiffness-stress curve, the constant A. The constant A during a 10-s isometric contraction was maximal at 2 s. It then decreased with time. This stiffness behavior is only seen when the effect of stress is held constant or eliminated. If stress is allowed to increase with time as it does during a tetanus then stiffness appears to increase monotonically. The SEC stiffness during active contraction was found to vary within the boundaries of the stiffness of muscle in rigor (upper limit) and that at resting state (lower limit).     

Theoretical models in mechanics of the left ventricle

Different rheological concepts and theoretical studies have been recently presented using models of myocardial mechanics. Complex analysis of the mechanical behavior of the left ventricular wall have been developed in order to estimate the local stresses and deformations that occur during the heart cycle as well as the ventricular stroke volume and pressure. Theoretical models have taken into account non-linear and viscoelastic passive properties of the myocardium tissue, when subjected to large deformations, through given strain energy functions or stress-strain relations. Different prolate spheroid geometries have been considered for such thick shell cardiac structure. During the active state of the contraction, the rheological behavior of the fibers has been described using different muscle models and relationships between fiber tension and strain, and activation degree. A forthcoming approach for bridging the gap between the knowledge of the muscle fiber microrheological properties and the study of the mechanical behavior of the entire ventricle, consists in including anisotropic and inhomogeneous effects through fiber direction field.     

Mechanical characterization of porcine corneas

An experimental program has been carried out in order to investigate the mechanical behavior of porcine corneas. We report the results of inflation tests on the whole cornea and uniaxial tests on excised corneal strips, performed on 51 fresh porcine eyes. Uniaxial tests have been performed on specimens cut from previously inflated corneas. The cornea behavior is characterized by means of elastic stiffness, measured on both average pressure-apex displacement and average uniaxial stress-strain curves; and by means of transversal contraction coefficient, peak stress, and failure stress measured on uniaxial stress-strain curves. Uniaxial tests performed on excised strips allowed to measure the anisotropy in the corneal stiffness and to compare the stiffness of the cornea with the one of the sclera. Viscous properties of the cornea have been obtained through uniaxial relaxation curves on excised corneal strips. The relevant geometrical parameters have been measured and, with the aid of the elastic thin shell theory, a stress-strain curve has been derived from the average inflation test data and compared with similar data available in the literature. The experimental system has been developed in view of future applications to the mechanical testing of both porcine and human corneas.     

Biaxial vasoactivity of porcine coronary artery

The passive mechanical properties of blood vessel mainly stem from the interaction of collagen and elastin fibers, but vessel constriction is attributed to smooth muscle cell (SMC) contraction. Although the passive properties of coronary arteries have been well characterized, the active biaxial stress-strain relationship is not known. Here, we carry out biaxial (inflation and axial extension) mechanical tests in right coronary arteries that provide the active coronary stress-strain relationship in circumferential and axial directions. Based on the measurements, a biaxial active strain energy function is proposed to quantify the constitutive stress-strain relationship in the physiological range of loading. The strain energy is expressed as a Gauss error function in the physiological pressure range. In K(+)-induced vasoconstriction, the mean ± SE values of outer diameters at transmural pressure of 80 mmHg were 3.41 ± 0.17 and 3.28 ± 0.24 mm at axial stretch ratios of 1.3 and 1.5, respectively, which were significantly smaller than those in Ca(2+)-free-induced vasodilated state (i.e., 4.01 ± 0.16 and 3.75 ± 0.20 mm, respectively). The mean ± SE values of the inner and outer diameters in no-load state and the opening angles in zero-stress state were 1.69 ± 0.04 mm and 2.25 ± 0.08 mm and 126 ± 22°, respectively. The active stresses have a maximal value at the passive pressure of 80-100 mmHg and at the active pressure of 140-160 mmHg. Moreover, a mechanical analysis shows a significant reduction of mean stress and strain (averaged through the vessel wall). These findings have important implications for understanding SMC mechanics.     

Passive tension and stiffness of vertebrate skeletal and insect flight muscles: the contribution of weak cross-bridges and elastic filaments.

Tension and dynamic stiffness of passive rabbit psoas, rabbit semitendinosus, and waterbug indirect flight muscles were investigated to study the contribution of weak-binding cross-bridges and elastic filaments (titin and minititin) to the passive mechanical behavior of these muscles. Experimentally, a functional dissection of the relative contribution of actomyosin cross-bridges and titin and minititin was achieved by 1) comparing mechanically skinned muscle fibers before and after selective removal of actin filaments with a noncalcium-requiring gelsolin fragment (FX-45), and 2) studying passive tension and stiffness as a function of sarcomere length, ionic strength, temperature, and the inhibitory effect of a carboxyl-terminal fragment of smooth muscle caldesmon. Our data show that weak bridges exist in both rabbit skeletal muscle and insect flight muscle at physiological ionic strength and room temperature. In rabbit psoas fibers, weak bridge stiffness appears to vary with both thin-thick filament overlap and with the magnitude of passive tension. Plots of passive tension versus passive stiffness are multiphasic and strikingly similar for these three muscles of distinct sarcomere proportions and elastic proteins. The tension-stiffness plot appears to be a powerful tool in discerning changes in the mechanical behavior of the elastic filaments. The stress-strain and stiffness-strain curves of all three muscles can be merged into one, by normalizing strain rate and strain amplitude of the extensible segment of titin and minititin, further supporting the segmental extension model of resting tension development.     

Evaluation of a combination of continuum and truss finite elements in a model of passive and active muscle tissue

The numerical method of finite elements (FE) is a powerful tool for analysing stresses and strains in the human body. One area of increasing interest is the skeletal musculature. This study evaluated modelling of skeletal muscle tissue using a combination of passive non-linear, viscoelastic solid elements and active Hill-type truss elements, the super-positioned muscle finite element (SMFE). The performance of the combined materials and elements was evaluated for eccentric motions by simulating a tensile experiment from a published study on a stimulated rabbit muscle including three different strain rates. It was also evaluated for isometric and concentric contractions. The resulting stress-strain curves had the same overall pattern as the experiments, with the main limitation being sensitivity to the active force-length relation. It was concluded that the SMFE could model active and passive muscle tissue at constant rate elongations for strains below failure, as well as isometric and concentric contractions.     

Mechanical properties of the heart muscle in the passive state

The viscoelastic behaviour of the heart muscle (papillary muscle) in the passive unstimulated) state is studied by such methods as stress relaxation, creep, vibration and stress-strain testing. The tests are conducted on a newly developed electromechanical muscle testing device which is suitable for conducting active and passive tests on biological materials.     

A mechanics model of the compression of cells with finite initial contact area

The effect of intercellular bonding on the stress-strain behavior of soft plant tissue is considered. In our mechanical model, a conglomerate of identical cells is arranged in a regular array. Each cell is pressurized and bonded across flat contact areas with adjacent cells in the direction of the applied load. The cell wall is a finitely-deformed mechanical membrane bounding an incompressible fluid (the cytoplasm). A nonlinear elastic constitutive law is presented that describes data for apple parenchyma. Results show that intercellular bonding has a strong effect on the macroscopic properties of the whole tissue. A larger intercellular contact area increases tissue stiffness and magnifies the effect of initial turgor pressure on tissue stiffness.     

The possible role of poroelasticity in the apparent viscoelastic behavior of passive cardiac muscle

This paper investigates the contribution of extracellular fluid flow to the apparent viscoelastic behavior of passive cardiac muscle. The muscle is modeled as an incompressible, isotropic, poroelastic solid saturated by an incompressible viscous fluid. Based on Biot's linear and nonlinear consolidation theories, solutions are presented for general time-dependent uniaxial loading of unconfined cylindrical muscle specimens. The nonlinear analysis includes the effects of large strain, material nonlinearity, and strain-dependent permeability. The computed results show that, for axial stretch ratios greater than 1.1, the changing permeability and the loading rate strongly affect the total stress relaxation and the short-time relaxation rate. Comparisons of theoretical and published experimental results show that extracellular fluid flow can account for several observed biomechanical features of passive myocardium, including the insensitivity of stress-strain curves to loading rate and of stress-relaxation curves to the amount of stretch. Theoretical hysteresis loops, however, are too small. Thus, both poroelastic and tissue viscoelastic effects must be considered in studies of passive cardiac muscle.     

Estimation of muscle active state

A method is presented for the estimation of the complete time course of muscle active state. The method is based on the selection of a proper model for the muscle, consisting of linear and non-linear components, and on the estimation of its parameters from a simple experiment. The model's parameters are estimated, using the least square method, from measurements of a tetanized muscle's response to a change of its length. The time course of the active state is calculated from an isometric twitch tension response of the same muscle. The twitch tension response is taken as the system's output, and the active state as its input. The latter can be estimated since the system parameters have already been estimated from the tetanized muscle experiment. Experiments were performed on the gastrocnemius muscle of frogs and cats. Results are given for the whole active state time course of these muscles. The results show that the peak active state force does not reach tetanic value, and a negative force is generated during the relaxation period. Additional experiments were carried out with the purpose of verifying the existence of this force; however, no conclusive results were obtained.This research was supported by the Julius Silver Institute of Bio-Medical Engineering Sciences, Grant 050-304     

Control of human eye movements: I. modelling of extraocular muscle

The properties of extraocular muscle are important in consideration of the control of human eye movements. A proposed model for human extraocular muscle is based on the anatomical and physiological evidence; it considers both the static and dynamic properties of active and passive muscle. The passive parallel elasticity was determined from the length-tension curves for passive muscle, while the active series elasticity was defined utilizing quick stretch results for active muscle. The characteristics of active muscle as the tension generator were computed from length-tension data; the force-velocity relationship was used to describe the viscosity of active muscle. Simulations using the muscle model accurately depicted the quick stretch experiments of both active and passive muscle as well as the isometric development of muscle force to a state of tentanus. The model will be incorporated into an overall representation of the extraocular plant mechanism in the immediately suceeding paper.     

Control of human eye movements: III. dynamic characteristics of the eye tracking mechanism

The properties of extraocular muscle are important in consideration of the control of human eye movements. A proposed model for human extraocular muscle is based on the anatomical and physiological evidence; it considers both the static and dynamic properties of active and passive muscle. The passive parallel elasticity was determined from the length-tension curves for passive muscle, while the active series elasticity was defined utilizing quick stretch results for active muscle. The characteristics of active muscle as the tension generator were computed from length-tension data; the force-velocity relationship was used to describe the viscosity of active muscle. Simulations using the muscle model accurately depicted the quick stretch experiments of both active and passive muscle as well as the isometric development of muscle force to a state of tentanus. The model will be incorporated into an overall representation of the extraocular plant mechanism in the immediately suceeding paper.     

Cardiac mechanoenergetics in silico

The aim of this thesis is to investigate the link between biochemical intracellular processes and mechanical contraction of the cardiac muscle. First, the regulation of intracellular energy fluxes between mitochondria and myofibrils is studied. It is shown, that the experimentally observed metabolic stability of the cardiac muscle is reproducible by a simple feedback regulation mechanism, i.e., ATP consumption in myofibrils and ATP production in mitochondria are balanced by the changes of the high energy phosphate concentrations. Second, an important property of energy transformation from biochemical form to mechanical work in the cardiac muscle, the linear relationship between the oxygen consumption and the stress-strain area, is replicated by a cross-bridge model. Third, by using the developed cross-bridge model, the correlation between ejection fraction of the left ventricle and heterogeneity of sarcomere strain, developed stress and ATP consumption in the left ventricular wall is established. Fourth, an experimentally observed linear relationship between oxygen consumption and the pressure-volume area can be predicted theoretically from a linear relationship between the oxygen consumption and the stress-strain area. Summing up, it is shown how the macrovariables of a cardiac muscle are interwoven with intracellular physiological processes into a whole.     

Muscles as a chain of the Hill three element model for calculating asynchronicity of excitation in assessing the "active state" during isotonic contraction

The muscle is described by the chain of Hill three-element models. The expression is obtained of the index of chemical energy transformation into the mechanical one ("active state") as a function of the velocity of the excitation wave propagation along the chain under isotonic contraction.     

A Modular Fibrinogen Model that Captures the Stress-Strain Behavior of?Fibrin Fibers

We tested what to our knowledge is a new computational model for fibrin fiber mechanical behavior. The model is composed of three distinct elements: the folded fibrinogen core as seen in the crystal structure, the unstructured α-C connector, and the partially folded α-C domain. Previous studies have highlighted the importance of all three regions and how they may contribute to fibrin fiber stress-strain behavior. Yet no molecular model has been computationally tested that takes into account the individual contributions of all these regions. Constant velocity, steered molecular dynamics studies at 0.025 Å/ps were conducted on the folded fibrinogen core and the α-C domain to determine their force-displacement behavior. A wormlike chain model with a persistence length of 0.8 nm (Kuhn length = 1.6 nm) was used to model the mechanical behavior of the unfolded α-C connector. The three components were combined to calculate the total stress-strain response, which was then compared to experimental data. The results show that the three-component model successfully captures the experimentally determined stress-strain behavior of fibrin fibers. The model evinces the key contribution of the α-C domains to fibrin fiber stress-strain behavior. However, conversion of the α-helical coiled coils to β-strands, and partial unfolding of the protein, may also contribute.     

Mechanical properties and composition of mesenteric small arteries of simulated microgravity rats with and without daily -G(x) gravitation

The aim of the present study was to evaluate the active and passive mechanical properties and wall collagen and elastin contents of mesenteric small arteries (MSAs) isolated from rats of 28-day simulated microgravity (SUS), countermeasure [S + D: SUS plus 1 h/d -G(x) to simulate intermittent artificial gravity (IAG)] and control (CON) groups. Three mechanical parameters were calculated: the overall stiffness (β), circumferential stress (σ(θ))-strain (ε(θ)) relationship and pressure-dependent incremental elastic modulus (E(inc,p)). Vessel wall collagen and elastin percentage were quantified by electron microscopy. The results demonstrate that the active mechanical behavior of MSAs differs noticeably among the three groups: the active stress-strain curve of SUS vessels is very close to the passive curve, whereas the active σ(θ)-ε(θ) curves of CON and S + D vessels are shifted leftward and display a parabolic shape, indicating that for MSAs isolated from S + D, but not those from SUS rats, the pressure-induced myogenic constriction can effectively stiffen the vessel wall as the CON vessels. The passive mechanical behavior of MSAs does not show significant differences among the three groups. However, the percentage of collagen is decreased in the wall of SUS and S + D compared with CON vessels in the following order: SUS < S + D < CON. Thus, the relationship between passive mechanical behavior and compositional changes may be complex and yet depends on factors other than the quantity of collagen and elastin. These findings have provided biomechanical data for the understanding of the mechanism of postflight orthostatic intolerance and its gravity-based countermeasure.     

Regional variation of tibialis anterior tendon mechanics is lost following denervation.

Denervation or inactivity is known to decrease the mass and alter the phenotype of muscle. The mechanical response of tendon to inactivity that has been determined experimentally differs from what is reported by patients. We investigated the hypothesis that this difference was the result of artifacts of the testing process and did not represent what occurred in vivo. To test this hypothesis, a novel approach was used to determine the mechanical properties of the tibialis anterior (TA) tendon by optically measuring the end-to-end mechanical strains as well as the local strains at specific regions of excised TA tendon units. When the end-to-end strain of normal TA tendon is determined, stress-strain response curves show considerably more extensibility than when strain is measured across only the midsection of the tendon (mid-tendon). The strain experienced by the region close to the muscle (muscle tendon) is five times greater than the strain in either the mid-tendon or near the bone (bone-tendon). Five weeks of denervation decreased muscle mass by 67%; increased tendon mass by 10%; and changed the entire shape of the nonlinear response curve, including a loss in regional variation in strain, a 3.9-fold increase in end-to-end tangent modulus, and a 70% reduction in the toe region, as a result of a drastic reduction of the extensibility in the muscle-tendon region. The stress-strain response in the mid-tendon region of a normal TA tendon is therefore not indicative of its overall ability to deform in vivo as it transmits forces from muscle to bone.     

The motion of the left ventricle—III

We use the concept of a layered wall, where each separate layer is to be homogeneous, isotropic, and incompressible, to derive stress-strain relations for the middle layer muscle ring at the transverse midsection of the left ventricle; a convenient method of formulation is that based on the elastic potential function. The hoop or circumferential stress in all three layers is found using dimensional and mechanical parameters derived earlier. The various parameters are expressed as Fourier series so that their behavior over a complete ventricular cycle is known analytically. The cases of simple elongation and what we termcurvilinear simple elongation are considered for the middle layer muscle ring strain, and the resulting stress-strain relations are derived. The results are compared with an incompressible rubber-like material known as a Mooney material.     

Pliometric activity of inspiratory muscles: maximal pressure-flow curves

We tested the hypothesis that inspiratory muscles, like other skeletal muscles, would exert greater force under pliometric conditions (being lengthened while active) than under isometric or miometric (active shortening) conditions. Maximal inspiratory pressure-flow curves of the respiratory system are analogous to the force-velocity curves for isolated muscle (Agostoni and Fenn, J. Appl. Physiol. 15:349-353, 1960). We measured esophageal pressure (Pes) and plethysmographic flow (V) at relaxation volume of the respiratory system in six trained subjects inspiring maximally through graded resistors (miometric), against a closed airway (isometric), and while constant expiratory flows were forced by a reduced pressure source at the airway opening (pliometric). Pes varied inversely with V and this trend continued into the pliometric range. In addition we found that the pressure-flow characteristics of the rib cage and of the abdomen are similar to those for the chest wall as a whole. The mechanical and energetic advantages of muscle activity under pliometric conditions may be available to some inspiratory muscles in both normal and pathological situations.