Adjustable passive length-tension curve in rabbit detrusor smooth muscle.

Until the 1990s, the passive and active length-tension (L-T) relationships of smooth muscle were believed to be static, with a single passive force value and a single maximum active force value for each muscle length. However, recent studies have demonstrated that the active L-T relationship in airway smooth muscle is dynamic and adapts to length changes over a period of time. Furthermore, our prior work showed that the passive L-T relationship in rabbit detrusor smooth muscle (DSM) is also dynamic and that in addition to viscoelastic behavior, DSM displays strain-softening behavior characterized by a loss of passive stiffness at shorter lengths following a stretch to a new longer length. This loss of passive stiffness appears to be irreversible when the muscle is not producing active force and during submaximal activation but is reversible on full muscle activation, which indicates that the stiffness component of passive force lost to strain softening is adjustable in DSM. The present study demonstrates that the passive L-T curve for DSM is not static and can shift along the length axis as a function of strain history and activation history. This study also demonstrates that adjustable passive stiffness (APS) can modulate total force (35% increase) for a given muscle length, while active force remains relatively unchanged (4% increase). This finding suggests that the structures responsible for APS act in parallel with the contractile apparatus, and the results are used to further justify the configuration of modeling elements within our previously proposed mechanical model for APS.     

ROK-induced cross-link formation stiffens passive muscle: reversible strain-induced stress softening in rabbit detrusor

Passive mechanical properties of strips of rabbit detrusor smooth muscle were examined and found by cyclic loading in a calcium-free solution to display viscoelastic softening and strain-induced stress softening (strain softening). Strain softening, or the Mullins effect, is a loss of stiffness attributed to the breakage of cross-links, and appeared irreversible in detrusor even after the return of spontaneous rhythmic tone during 120 min of incubation in a calcium-containing solution. However, 3 min of KCl or carbachol (CCh)-induced contraction permitted rapid regeneration of the passive stiffness lost to strain softening, and 3 microM of the RhoA kinase (ROK) inhibitor Y-27632 prevented this regeneration. The degree of ROK-induced passive stiffness was inversely dependent on muscle length over a length range where peak CCh-induced force was length independent. Thus rabbit detrusor displayed variable passive stiffness both strain- and activation-history dependent. In conclusion, activation of ROK by KCl or CCh increased passive stiffness softened by muscle strain and thereby attributed to cross-links that remained stable during tissue incubation in a calcium-free solution. Degradation of this signaling system could potentially contribute to urinary incontinence.     

Trabeculated embryonic myocardium shows rapid stress relaxation and non-quasi-linear viscoelastic behavior

Passive viscoelastic behavior is important in embryonic cardiovascular function, influencing the rate and magnitude of contraction and relaxation. We hypothesized that if viscoelastic behavior is influenced by interstitial fluid flow, then the stage-21 (312d) and stage-24 (4d) chick myocardium with large intertrabecular spaces will exhibit much different viscoelastic behavior than stage-16 (212d) and stage-18 (3d) compact myocardium and a non-quasi-linear response. Excised left ventricular sections were tested with ramp-and-hold stress relaxation tests at axial stretch ratios of 1.05:1.1:1.2:1.3. The measured stress relaxation was much more rapid than previously observed in the compact, non-trabeculated myocardium. The reduced relaxation curves depended significantly on the stretch level. A continuous-spectrum quasi-linear relaxation function described their shape well but the model-fit parameters also depended on the stretch level. Sinusoidal stretching of ventricular sections at rates from 0.2 to 25Hz showed that the steepening of stress-strain curves with increasing strain rate was half as much as predicted by a quasi-linear model. Hysteresis ranged from 25-35%, varied little with loading rate from 0.2 to 8Hz, and was twice that predicted from a quasi-linear model. Doubling the viscosity of the perfusate in stress-relaxation tests produced increased stiffness and decreased relaxation rate. These results demonstrate that the passive viscoelastic behavior of the trabeculated embryonic myocardium is markedly different from that of younger, compact myocardium and is not quasi-linear.     

Adjustable passive stiffness in mouse bladder: regulated by Rho kinase and elevated following partial bladder outlet obstruction

Detrusor smooth muscle (DSM) contributes to bladder wall tension during filling, and bladder wall deformation affects the signaling system that leads to urgency. The length-passive tension (L-T(p)) relationship in rabbit DSM can adapt with length changes over time and exhibits adjustable passive stiffness (APS) characterized by a L-T(p) curve that is a function of both activation and strain history. Muscle activation with KCl, carbachol (CCh), or prostaglandin E(2) at short muscle lengths can increase APS that is revealed by elevated pseudo-steady-state T(p) at longer lengths compared with prior T(p) measurements at those lengths, and APS generation is inhibited by the Rho Kinase (ROCK) inhibitor H-1152. In the current study, mouse bladder strips exhibited both KCl- and CCh-induced APS. Whole mouse bladders demonstrated APS which was measured as an increase in pressure during passive filling in calcium-free solution following CCh precontraction compared with pressure during filling without precontraction. In addition, CCh-induced APS in whole mouse bladder was inhibited by H-1152, indicating that ROCK activity may regulate bladder compliance during filling. Furthermore, APS in whole mouse bladder was elevated 2 wk after partial bladder outlet obstruction, suggesting that APS may be relevant in diseases affecting bladder mechanics. The presence of APS in mouse bladder will permit future studies of APS regulatory pathways and potential alterations of APS in disease models using knockout transgenetic mice.     

Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells

Force development in smooth muscle, as in skeletal muscle, is believed to reflect recruitment of force-generating myosin cross-bridges. However, little is known about the events underlying cross-bridge recruitment as the muscle cell approaches peak isometric force and then enters a period of tension maintenance. In the present studies on single smooth muscle cells isolated from the toad (Bufo marinus) stomach muscularis, active muscle stiffness, calculated from the force response to small sinusoidal length changes (0.5% cell length, 250 Hz), was utilized to estimate the relative number of attached cross-bridges. By comparing stiffness during initial force development to stiffness during force redevelopment immediately after a quick release imposed at peak force, we propose that the instantaneous active stiffness of the cell reflects both a linearly elastic cross-bridge element having 1.5 times the compliance of the cross-bridge in frog skeletal muscle and a series elastic component having an exponential length-force relationship. At the onset of force development, the ratio of stiffness to force was 2.5 times greater than at peak isometric force. These data suggest that, upon activation, cross-bridges attach in at least two states (i.e., low-force-producing and high-force-producing) and redistribute to a steady state distribution at peak isometric force. The possibility that the cross-bridge cycling rate was modulated with time was also investigated by analyzing the time course of tension recovery to small, rapid step length changes (0.5% cell length in 2.5 ms) imposed during initial force development, at peak force, and after 15 s of tension maintenance. The rate of tension recovery slowed continuously throughout force development following activation and slowed further as force was maintained. Our results suggest that the kinetics of force production in smooth muscle may involve a redistribution of cross-bridge populations between two attached states and that the average cycling rate of these cross-bridges becomes slower with time during contraction.     

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.     

Nonlinear muscles, passive viscoelasticity and body taper conspire to create neuromechanical phase lags in anguilliform swimmers

Locomotion provides superb examples of cooperation among neuromuscular systems, environmental reaction forces, and sensory feedback. As part of a program to understand the neuromechanics of locomotion, here we construct a model of anguilliform (eel-like) swimming in slender fishes. Building on a continuum mechanical representation of the body as an viscoelastic rod, actuated by a traveling wave of preferred curvature and subject to hydrodynamic reaction forces, we incorporate a new version of a calcium release and muscle force model, fitted to data from the lamprey Ichthyomyzon unicuspis, that interactively generates the curvature wave. We use the model to investigate the source of the difference in speeds observed between electromyographic waves of muscle activation and mechanical waves of body curvature, concluding that it is due to a combination of passive viscoelastic and geometric properties of the body and active muscle properties. Moreover, we find that nonlinear force dependence on muscle length and shortening velocity may reduce the work done by the swimming muscles in steady swimming.     

Effect of exercise training on passive stiffness in locomotor skeletal muscle: role of extracellular matrix

The purpose ofthis study was to evaluate the effect of endurance exercise training onboth locomotor skeletal muscle collagen characteristics and passivestiffness properties in the young adult and old rat. Young(3-mo-old) and senescent (23-mo-old) male Fischer 344 rats wererandomly assigned to either a control or exercise training group[young control (YC), old control (OC), young trained (YT), oldtrained (OT)]. Exercise training consisted of treadmill runningat ~70% of maximal oxygen consumption (45 min/day, 5 days/wk, for 10 wk). Passive stiffness (stress/strain) of the soleus (Sol) muscle fromall four groups was subsequently measured in vitro at 26°C.Stiffness was significantly greater for Sol muscles in OC rats comparedwith YC rats, but in OT rats exercise training resulted in muscles withstiffness characteristics not different from those in YC rats. Solmuscle collagen concentration and the level of the nonreduciblecollagen cross-link hydroxylysylpyridinoline (HP) significantlyincreased from young adulthood to senescence. Although training had noeffect on Sol muscle collagen concentration in either age group, itresulted in a significant reduction in the level of Sol muscle HP in OTrats. In contrast, exercise had no effect on HP in the YT animals.These findings indicate that 10 wk of endurance exercise significantlyalter the passive viscoelastic properties of Sol muscle in old but notin young adult rats. The coincidental reduction in the principalcollagen cross-link HP also observed in response to training in OTmuscle highlights the potential role of collagen in influencing passivemuscle viscoelastic properties.

     

A nonlinear model of passive muscle viscosity

The material properties of passive skeletal muscle are critical to proper function and are frequently a target for therapeutic and interventional strategies. Investigations into the passive viscoelasticity of muscle have primarily focused on characterizing the elastic behavior, largely neglecting the viscous component. However, viscosity is a sizeable contributor to muscle stress and extensibility during passive stretch and thus there is a need for characterization of the viscous as well as the elastic components of muscle viscoelasticity. Single mouse muscle fibers were subjected to incremental stress relaxation tests to characterize the dependence of passive muscle stress on time, strain and strain rate. A model was then developed to describe fiber viscoelasticity incorporating the observed nonlinearities. The results of this model were compared with two commonly used linear viscoelastic models in their ability to represent fiber stress relaxation and strain rate sensitivity. The viscous component of mouse muscle fiber stress was not linear as is typically assumed, but rather a more complex function of time, strain and strain rate. The model developed here, which incorporates these nonlinearities, was better able to represent the stress relaxation behavior of fibers under the conditions tested than commonly used models with linear viscosity. It presents a new tool to investigate the changes in muscle viscous stresses with age, injury and disuse.     

Strain softening is not present during axial extensions of rat intact right ventricular trabeculae in the presence or absence of 2,3-butanedione monoxime

Recent studies of passive myocardial mechanics have shown that strain softening behavior is present during both inflation of isolated whole rat hearts and shearing of tissue blocks taken from the left ventricular free wall in pigs. Strain softening is typically manifested by a stiffer force-extension relation in the first deformation cycle relative to subsequent cycles and is distinguished from viscoelasticity by a lack of recovery of stiffness, even after several hours of rest. The causes of this behaviour are unknown. We investigated whether strain softening is observed in uniaxial extensions of intact, viable, rat right ventricular (RV) cardiac trabeculae. Stretch and release cycles of 5%, 10%, and 15% muscle length were applied at a constant velocity at 26 degrees C. Muscles were tested in random order in the presence and absence of 50 mM 2,3-butanedione monoxime (BDM). Whereas strain softening was displayed by nonviable trabeculae, it was not observed in viable preparations undergoing physiologically relevant extensions whether in the presence or absence of BDM. BDM also had no effect on passive compliance. There was a reversible increase of muscle compliance between the first and subsequent cycles, with recovery after 30 s of rest, independent of the presence of BDM. We conclude that strain softening is neither intrinsic to viable rat RV trabeculae nor influenced by BDM and that passive trabeculae compliance is not altered by the addition of BDM.     

The frequency response of smooth muscle stiffness during Ca2+-activated contraction

To investigate the mechanism of smooth muscle contraction, the frequency response of the muscle stiffness of single beta-escin permeabilized smooth muscle cells in the relaxed state was studied. Also, the response was continuously monitored for 3 min from the beginning of the exchange of relaxing solution to activating solution, and then at 5-min intervals for up to 20 min. The frequency response (30 Hz bandwidth, 0.33 Hz (or 0.2 Hz) resolution) was calculated from the Fourier-transformed force and length sampled during a 3-s (or 5-s) constant-amplitude length perturbation of increasing-frequency (1-32 Hz) sine waves. In the relaxed state, a large negative phase angle was observed, which suggests the existence of attached energy generating cross-bridges. As the activation progressed, the muscle stiffness and phase angle steadily increased; these increases gradually extended to higher frequencies, and reached a steady state by 100 s after activation or approximately 40 s after stiffness began to increase. The results suggest that a fixed distribution of cross-bridge states was reached after 40 s of Ca2+ activation and the cross-bridge cycling rate did not change during the period of force maintenance.     

Regulatable stiffness in relaxed airway smooth muscle: a target for asthma treatment?

The airway smooth muscle (ASM) layer within the airway wall modulates airway diameter and distensibility. Even in the relaxed state, the ASM layer possesses finite stiffness and limits the extent of airway distension by the radial force generated by parenchymal tethers and transmural pressure. Airway stiffness has often been attributed to passive elements, such as the extracellular matrix in the lamina reticularis, adventitia, and the smooth muscle layer that cannot be rapidly modulated by drug intervention such as ASM relaxation by β-agonists. In this study, we describe a calcium-sensitive component of ASM stiffness mediated through the Rho-kinase signaling pathway. The stiffness of ovine tracheal smooth muscle was assessed in the relaxed state under the following conditions: 1) in physiological saline solution (Krebs solution) with normal calcium concentration; 2) in calcium-free Krebs with 2 mM EGTA; 3) in Krebs with calcium entry blocker (SKF-96365); 4) in Krebs with myosin light chain kinase inhibitor (ML-7); and 5) in Krebs with Rho-kinase inhibitor (Y-27632). It was found that a substantial portion of the passive stiffness could be abolished when intracellular calcium was removed; this calcium-sensitive stiffness appeared to stem from intracellular source and was not sensitive to ML-7 inhibition of myosin light chain phosphorylation, but was sensitive to Y-27632 inhibition of Rho kinase. The results suggest that airway stiffness can be readily modulated by targeting the calcium-sensitive component of the passive stiffness within the muscle layer.     

Tissue softening of guinea pig oesophagus tested by the tri-axial test machine

Tissue softening is commonly reported during mechanical testing of biological tissues in vitro. The loss of stiffness may be due to viscoelasticity-induced softening (the time-history of load-caused softening) and strain-induced stress softening (the maximum previous load-caused softening). However, the knowledge about tissue softening behaviour is presently poor. The aims of this study were to distinguish whether the loss of the stiffness during preconditioning was due to strain softening or viscoelasticity and to test the tissue softening in circumferential and longitudinal direction in the guinea pig oesophagus. Eight repeated pressure controlled ramp distensions and eight uniaxial tensile-release ramp stretches in three series were done on eight guinea pig oesophagi. The stress–strain curves were used to display the time-dependency (viscoelasticity) and the maximum previous load-caused softening (strain softening) in circumferential and longitudinal directions. For both the longitudinal and the circumferential softening, the peak stress and stiffness produced during the first loading were bigger than those produced in the remaining loadings. The stress loss due to strain softening was about three times more than that due to viscoelasticity in the longitudinal direction. The strain increased more than two times between the strain softening and viscoelastic softening in the circumferential direction. With a stress level of 20 kPa, the stiffness in the circumferential direction lost more than that in the longitudinal direction (P<0.05), indicating the anisotropic softening properties in the oesophagus. In conclusion, the stiffness loss during preconditioning is mainly attributed to strain softening, appears irreversible and is anisotropic.     

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.     

Tension in frog single muscle fibers while shortening actively and passively at velocities near Vu.

Experiments were undertaken to determine the contribution of passive tension to total tension during rapid shortening in a stimulated muscle fiber. Results were obtained by applying shortening movements at constant velocities slightly less than Vu (the velocity of unloaded shortening) to intact twitch fibers isolated from the frog (Rana temporaria). The tension maintained by unstimulated fibers during such shortening movements ("dynamic passive tension") from moderately long lengths was greater than zero but much less than the passive tension measured under static conditions ("static passive tension") at the same lengths. Fibers maximally activated by electrical stimulation and then shortened at the same velocity over the same range of average sarcomere lengths maintained tension that was greater than zero but less than the dynamic passive tension. For average sarcomere lengths up to approximately 3.1 microns, the dynamic passive tension appeared to be substantially abolished by activation. The onset of the apparent disappearance of dynamic passive tension was studied by initiating the stimulation and the shortening movement simultaneously. The resulting tension response exhibited a latency relaxation that was increased in amplitude compared with the isometric case, followed by a brief tension rise, giving way to a steady tension level equal to that expected if stimulation had been initiated well before the release. These changes are qualitatively explained in terms of the establishment of a steady state distribution of deformations of attached cross-bridges.     

The role of passive structures in force enhancement of skeletal muscles following active stretch

We recently found that force enhancement following active stretch in skeletal muscles is accompanied by an increase in passive force following deactivation (J. Exp. Biol. 205 (2002) 1275). However, it is not known if this increase in passive force contributes to the force enhancement observed in the active muscle, and if it is observed at all muscle lengths. The purposes of this study were to quantify the amount of passive force increase as a function of muscle lengths, and to determine if this passive force contributes to the force enhancement observed in the active muscle. Experiments were performed on cat soleus (n = 24) using techniques published previously (J. Biomech. 30(9) (1997) 865). Conceptually, tests involved comparisons of force enhancement and passive force increase for a variety of stretch tests in soleus. Furthermore, in one test, activation of the soleus was interrupted for 1s in the force-enhanced state, and soleus was then re-activated. We found that total force enhancement and passive force increase were positively correlated for all test conditions, that passive force increase following stretch of the active soleus only occurred at muscle lengths corresponding to the descending limb of the force-length relationship, that increases in passive force for a given stretch magnitude became greater at long muscle lengths, and that upon reactivation, there was a remnant passive force enhancement. We conclude from these results that the passive force enhancement following stretch of an active muscle contributes to the total force enhancement, that this passive contribution increases with increasing muscle length, and that there must be at least one other factor than passive force increase that contributes to the total force enhancement, as the passive force increase was always smaller than the total force enhancement. A by-product of this investigation was that we observed a shift in the passive force-length relationship that was dependent on muscle activation, stretch magnitude and muscle length. Therefore, the passive force-length relationship is not a constant property of skeletal muscle, but depends critically on the muscle's contractile history.     

Mapping motor neuron activity to overt behavior in the leech

As an initial step in constructing a quantitative biomechanical model of the medicinal leech (Hirudo medicinalis), we determined the passive properties of its body wall over the physiological range of dimensions. The major results of this study were:

1. The ellipsoidal cross section of resting leeches is maintained by tonic muscle activation as well as forces inherent in the structure of the body wall (i.e., residual stress).
2. The forces required for longitudinal and circumferential stretch to maximum physiological dimensions were similar in magnitude. Cutting out pieces of body wall did not affect the passive longitudinal or circumferential properties of body wall away from the edges of the cut.
3. The strain (i.e., the percentage change in dimension) of different body segments when subject to the same force was identical, despite differences in muscle crosssections.
4. Serotonin, a known modulator of tension in leech muscles, affected passive forces at all physiological muscle lengths. This suggests that the longitudinal muscle is responsible for at least part of the passive tension of the body wall.
5. We propose a simple viscoelastic model of the body wall. This model captures the dynamics of the passive responses of the leech body wall to imposed step changes in length. Using steady-state passive tensions predicted by the viscoelastic model we estimate the forces required to maintain the leech at any given length over the physiological range.

     

Active and passive components in the length-dependent stiffness of tracheal smooth muscle during isotonic shortening.

Contraction of smooth muscle tissue involves interactions between active and passive structures within the cells and in the extracellular matrix. This study focused on a defined mechanical behavior (shortening-dependent stiffness) of canine tracheal smooth muscle tissues to evaluate active and passive contributions to tissue behavior. Two approaches were used. In one, mechanical measurements were made over a range of temperatures to identify those functions whose temperature sensitivity (Q(10)) identified them as either active or passive. Isotonic shortening velocity and rate of isometric force development had high Q(10) values (2.54 and 2.13, respectively); isometric stiffness showed Q(10) values near unity. The shape of the curve relating stiffness to isotonic shortening lengths was unchanged by temperature. In the other approach, muscle contractility was reduced by applying a sudden shortening step during the rise of isometric tension. Control contractions began with the muscle at the stepped length so that properties were measured over comparable length ranges. Under isometric conditions, redeveloped isometric force was reduced, but the ratio between force and stiffness did not change. Under isotonic conditions beginning during force redevelopment at the stepped length, initial shortening velocity and the extent of shortening were reduced, whereas the rate of relaxation was increased. The shape of the curve relating stiffness to isotonic shortening lengths was unchanged, despite the step-induced changes in muscle contractility. Both sets of findings were analyzed in the context of a quasi-structural model describing the shortening-dependent stiffness of lightly loaded tracheal muscle strips.     

Interaction of viscoelastic tissue compliance with lumbar muscles during passive cyclic flexion–extension

Human and animal models using electromyography (EMG) based methods have hypothesized that viscoelastic tissue properties becomes compromised by prolonged repetitive cyclic trunk flexion–extension which in turn influences muscular activation including the flexion–relaxation phenomenon. Empirical evidence to support this hypothesis, especially the development of viscoelastic tension–relaxation and its associated muscular response in passive cyclic activity in humans, is incomplete. The objective of this study was to examine the response of lumbar muscles to tension–relaxation development of the viscoelastic tissue during prolonged passive cyclic trunk flexion–extension. Activity of the lumbar muscles remained low and steady during the passive exercise session. Tension supplied by the posterior viscoelastic tissues decreased over time without corresponding changes in muscular activity. Active flexion, following the passive flexion session, elicited significant increase in paraspinal muscles EMG together with increase in the median frequency. It was concluded that reduction of tension in the lumbar viscoelastic tissues of humans occurs during cyclic flexion–extension and is compensated by increased activity of the musculature in order to maintain stability. It was also concluded that the ligamento-muscular reflex is inhibited during passive activities but becomes hyperactive following active cyclic flexion, indicating that moment requirements are the controlling variable. It is conceived that prolonged routine exposure to cyclic flexion minimizes the function of the viscoelastic tissues and places increasing demands on the neuromuscular system which over time may lead to a disorder and possible exposure to injury.