Prediction of peak forces for a shortening smooth muscle tissue subjected to vibration.

The objective of the present study is to investigate the peak forces for a tracheal smooth muscle tissue subjected to an applied longitudinal vibration following isotonic shortening. A non-linear finite element analysis was carried out to simulate the vibratory response under experimental conditions that corresponds to forced length oscillations at 33 Hz for 1 second. The stiffness change and hysteresis estimated from the experimental data was used in the analysis. The finite element results of peak forces are compared to the experimental data obtained. The comparison of results indicate that the approach and the vibratory response obtained may be useful for describing the cross-bridge de-attachments within the cells as well as connective tissue connections characteristic of tracheal smooth muscle tissue.

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.

Mechanical state of airway smooth muscle at very short lengths.

Although the shortening of smooth muscle at physiological lengths is dominated by an interaction between external forces (loads) and internal forces, at very short lengths, internal forces appear to dominate the mechanical behavior of the active tissue. We tested the hypothesis that, under conditions of extreme shortening and low external force, the mechanical behavior of isolated canine tracheal smooth muscle tissue can be understood as a structure in which the force borne and exerted by the cross bridge and myofilament array is opposed by radially disposed connective tissue in the presence of an incompressible fluid matrix (cellular and extracellular). Strips of electrically stimulated tracheal muscle were allowed to shorten maximally under very low afterload, and large longitudinal sinusoidal vibrations (34 Hz, 1 s in duration, and up to 50% of the muscle length before vibration) were applied to highly shortened (active) tissue strips to produce reversible cross-bridge detachment. During the vibration, peak muscle force fell exponentially with successive forced elongations. After the episode, the muscle either extended itself or exerted a force against the tension transducer, depending on external conditions. The magnitude of this effect was proportional to the prior muscle stiffness and the amplitude of the vibration, indicating a recoil of strained connective tissue elements no longer opposed by cross-bridge forces. This behavior suggests that mechanical behavior at short lengths is dominated by tissue forces within a tensegrity-like structure made up of connective tissue, other extracellular matrix components, and active contractile elements.

On the terminology for describing the length-force relationship and its changes in airway smooth muscle.

The observation that the length-force relationship in airway smooth muscle can be shifted along the length axis by accommodating the muscle at different lengths has stimulated great interest. In light of the recent understanding of the dynamic nature of length-force relationship, many of our concepts regarding smooth muscle mechanical properties, including the notion that the muscle possesses a unique optimal length that correlates to maximal force generation, are likely to be incorrect. To facilitate accurate and efficient communication among scientists interested in the function of airway smooth muscle, a revised and collectively accepted nomenclature describing the adaptive and dynamic nature of the length-force relationship will be invaluable. Setting aside the issue of underlying mechanism, the purpose of this article is to define terminology that will aid investigators in describing observed phenomena. In particular, we recommend that the term "optimal length" (or any other term implying a unique length that correlates with maximal force generation) for airway smooth muscle be avoided. Instead, the in situ length or an arbitrary but clearly defined reference length should be used. We propose the usage of "length adaptation" to describe the phenomenon whereby the length-force curve of a muscle shifts along the length axis due to accommodation of the muscle at different lengths. We also discuss frequently used terms that do not have commonly accepted definitions that should be used cautiously.

Tissue elastance influences airway smooth muscle shortening: comparison of mechanical properties among different species.

We have observed striking differences in the mechanical properties of airway smooth muscle preparations among different species. In this study, we provide a novel analysis on the influence of tissue elastance on smooth muscle shortening using previously published data from our laboratory. We have found that isolated human airways exhibit substantial passive tension in contrast to airways from the dog and pig, which exhibit little passive tension (<5% of maximal active force versus approximately 60% for human bronchi). In the dog and pig, airway preparations shorten up to 70% from Lmax (the length at which maximal active force occurs), whereas human airways shorten by only approximately 12% from Lmax. Isolated airways from the rabbit exhibit relatively low passive tension (approximately 22% Fmax) and shorten by 60% from Lmax. Morphologic evaluation of airway cross sections revealed that 25-35% of the airway wall is muscle in canine, porcine, and rabbit airways in contrast to approximately 9% in human airway preparations. We postulate that the large passive tension needed to stretch the muscle to Lmax reflects the high connective tissue content surrounding the smooth muscle, which limits shortening during smooth muscle contraction by imposing an elastic load, as well as by causing radial constraint.