Site of allergic airway narrowing and the influence of exogenous surfactant in the Brown Norway rat.

BACKGROUND: The parameters R(N) (newtonian resistance), G (tissue damping), and H (tissue elastance) of the constant phase model of respiratory mechanics provide information concerning the site of altered mechanical properties of the lung. The aims of this study were to compare the site of allergic airway narrowing implied from respiratory mechanics to a direct assessment by morphometry and to evaluate the effects of exogenous surfactant administration on the site and magnitude of airway narrowing. METHODS: We induced airway narrowing by ovalbumin sensitization and challenge and we tested the effects of a natural surfactant lacking surfactant proteins A and D (Infasurf®) on airway responses. Sensitized, mechanically ventilated Brown Norway rats underwent an aerosol challenge with 5% ovalbumin or vehicle. Other animals received nebulized surfactant prior to challenge. Three or 20 minutes after ovalbumin challenge, airway luminal areas were assessed on snap-frozen lungs by morphometry. RESULTS: At 3 minutes, R(N) and G detected large airway narrowing whereas at 20 minutes G and H detected small airway narrowing. Surfactant inhibited R(N) at the peak of the early allergic response and ovalbumin-induced increase in bronchoalveolar lavage fluid cysteinyl leukotrienes and amphiregulin but not IgE-induced mast cell activation in vitro. CONCLUSION: Allergen challenge triggers the rapid onset of large airway narrowing, detected by R(N) and G, and subsequent peripheral airway narrowing detected by G and H. Surfactant inhibits airway narrowing and reduces mast cell-derived mediators.

Could an increase in airway smooth muscle shortening velocity cause airway hyperresponsiveness?

Airway hyperresponsiveness (AHR) is a characteristic feature of asthma. It has been proposed that an increase in the shortening velocity of airway smooth muscle (ASM) could contribute to AHR. To address this possibility, we tested whether an increase in the isotonic shortening velocity of ASM is associated with an increase in the rate and total amount of shortening when ASM is subjected to an oscillating load, as occurs during breathing. Experiments were performed in vitro using 27 rat tracheal ASM strips supramaximally stimulated with methacholine. Isotonic velocity at 20% isometric force (Fiso) was measured, and then the load on the muscle was varied sinusoidally (0.33 ± 0.25 Fiso, 1.2 Hz) for 20 min, while muscle length was measured. A large amplitude oscillation was applied every 4 min to simulate a deep breath. We found that: 1) ASM strips with a higher isotonic velocity shortened more quickly during the force oscillations, both initially (P < 0.001) and after the simulated deep breaths (P = 0.002); 2) ASM strips with a higher isotonic velocity exhibited a greater total shortening during the force oscillation protocol (P < 0.005); and 3) the effect of an increase in isotonic velocity was at least comparable in magnitude to the effect of a proportional increase in ASM force-generating capacity. A cross-bridge model showed that an increase in the total amount of shortening with increased isotonic velocity could be explained by a change in either the cycling rate of phosphorylated cross bridges or the rate of myosin light chain phosphorylation. We conclude that, if asthma involves an increase in ASM velocity, this could be an important factor in the associated AHR.

A continuous-binding cross-linker model for passive airway smooth muscle.

Although the active properties of airway smooth muscle (ASM) have garnered much modeling attention, the passive mechanical properties are not as well studied. In particular, there are important dynamic effects observed in passive ASM, particularly strain-induced fluidization, which have been observed both experimentally and in models; however, to date these models have left an incomplete picture of the biophysical, mechanistic basis for these behaviors. The well-known Huxley cross-bridge model has for many years successfully described many of the active behaviors of smooth muscle using sliding filament theory; here, we propose to extend this theory to passive biological soft tissue, particularly ASM, using as a basis the attachment and detachment of cross-linker proteins at a continuum of cross-linker binding sites. The resulting mathematical model exhibits strain-induced fluidization, as well as several types of force recovery, at the same time suggesting a new mechanistic basis for the behavior. The model is validated by comparison to new data from experimental preparations of rat tracheal airway smooth muscle. Furthermore, experiments in noncontractile tissue show qualitatively similar behavior, suggesting support for the protein-filament theory as a biomechanical basis for the behavior.

Calculation of muscle maximal shortening velocity by extrapolation of the force-velocity relationship: afterloaded versus isotonic release contractions.

The maximal shortening velocity of a muscle (V(max)) provides a link between its macroscopic properties and the underlying biochemical reactions and is altered in some diseases. Two methods that are widely used for determining V(max) are afterloaded and isotonic release contractions. To determine whether these two methods give equivalent results, we calculated V(max) in 9 intact single fibres from the lumbrical muscles of the frog Xenopus laevis (9.5-15.5 °C, stimulation frequency 35-70 Hz). The data were modelled using a 3-state cross-bridge model in which the states were inactive, detached, and attached. Afterloaded contractions gave lower predictions of Vmax than did isotonic release contractions in all 9 fibres (3.20 ± 0.84 versus 4.11 ± 1.08 lengths per second, respectively; means ± SD, p = 0.001) and underestimated unloaded shortening velocity measured with the slack test by an average of 29% (p = 0.001, n = 6). Excellent model predictions could be obtained by assuming that activation is inhibited by shortening. We conclude that under the experimental conditions used in this study, afterloaded and isotonic release contractions do not give equivalent results. When a change in the V(max) measured with afterloaded contractions is observed in diseased muscle, it is important to consider that this may reflect differences in either activation kinetics or cross-bridge cycling rates.

Criteria for dynamic similarity in bouncing gaits.

Animals of different sizes tend to move in a dynamically similar manner when travelling at speeds corresponding to equal values of a dimensionless parameter (DP) called the Froude number. Consequently, the Froude number has been widely used for defining equivalent speeds and predicting speeds of locomotion by extinct species and on other planets. However, experiments using simulated reduced gravity have demonstrated that equality of the Froude number does not guarantee dynamic similarity. This has cast doubt upon the usefulness of the Froude number in locomotion research. Here we use dimensional analysis of the planar spring-mass model, combined with Buckingham's Pi-Theorem, to demonstrate that four DPs must be equal for dynamic similarity in bouncing gaits such as trotting, hopping and bipedal running. This can be reduced to three DPs by applying the constraint of maintaining a constant average speed of locomotion. Sensitivity analysis indicates that all of these DPs are important for predicting dynamic similarity. We show that the reason humans do not run in a dynamically similar manner at equal Froude number in different levels of simulated reduced gravity is that dimensionless leg stiffness decreases as gravity increases. The reason that the Froude number can predict dynamic similarity in Earth gravity is that dimensionless leg stiffness and dimensionless vertical landing speed are both independent of size. In conclusion, although equal Froude number is not sufficient for dynamic similarity, it is a necessary condition. Therefore, to detect fundamental differences in locomotion, animals of different sizes should be compared at equal Froude number, so that they can be as close to dynamic similarity as possible. More generally, the concept of dynamic similarity provides a powerful framework within which similarities and differences in locomotion can be interpreted.

Ability of the planar spring-mass model to predict mechanical parameters in running humans.

The planar spring-mass model is a simple mathematical model of bouncing gaits, such as running, trotting and hopping. Although this model has been widely used in the study of locomotion, its accuracy in predicting locomotor mechanics has not been systematically quantified. We determined the percent error of the model in predicting 10 locomotor parameters in running humans by comparing the model predictions to experimental data from humans running in normal gravity and simulated reduced gravity. We tested the hypotheses that the model would overestimate horizontal impulse and the change in mechanical energy of the centre of mass (COM) during stance. The model provided good predictions of stance time, vertical impulse, contact length, duty factor, relative stride length and relative peak force. All predictions of these parameters were within 20% of measured values and at least 90% of predictions of each parameter were within 10% of measured values (median absolute errors: <7%). This suggests that the model incorporates all features of running humans that have a significant influence upon these six parameters. As simulated gravity level decreased, the magnitude of the errors in predicting each of these parameters either decreased or stayed constant, indicating that this is a good model of running in simulated reduced gravity. As hypothesised, horizontal impulse and change in mechanical energy of the COM during stance were overestimated (median absolute errors: 43.6% and 26.2%, respectively). Aerial time and peak vertical COM displacement during stance were also systematically overestimated (median absolute errors: 17.7% and 22.9%, respectively). Care should be taken to ensure that the model is used only to investigate parameters which it can predict accurately. It would be useful to extend this analysis to other species and gaits.

History-dependence of isometric muscle force: effect of prior stretch or shortening amplitude.

It is well-recognised that steady-state isometric muscle force is decreased following active shortening (force depression, FD) and increased following active stretch (force enhancement, FE). It has also been demonstrated that passive muscle force is increased following active stretch (passive FE). Several studies have reported that FD increases with shortening amplitude and that FE and passive FE increase with stretch amplitude. Here, we investigate whether these trends continue with further increases in shortening or stretch amplitude. Experiments were performed using in situ cat soleus muscles (n=8 for FD; n=7 for FE and passive FE). FD, FE and passive FE were measured after shortening or stretch contractions that covered as wide a range of amplitudes as practically possible without damaging the muscles. FD increased approximately linearly with shortening amplitude, over the full range of amplitudes investigated. This is consistent with the hypothesis that FD arises from a stress-induced inhibition of crossbridges. FE increased with stretch amplitude only up to a point, and then levelled off. Passive FE, and the transient increase in force at the end of stretch, showed relationships to stretch amplitude that were qualitatively very similar to the relationship for FE, increasing only until the same critical stretch amplitude had been reached. We conclude that FE and passive FE do not increase with stretch amplitude under all circumstances. This finding has important consequences for determining the mechanisms underlying FE and passive FE because any mechanism that is proposed to explain them must be able to predict it.

Dynamically similar locomotion in horses.

It is possible for animals of very different sizes to use the same patterns of locomotion, i.e. to move in a ;dynamically similar fashion'. This will only occur, however, if relevant biomechanical parameters scale with size in such a way that they compensate for the effects of size differences. Here we apply this principle to understanding the effects of size on locomotion within a species: the domestic horse. We predict that, without any factor to compensate for size differences, detectable deviations from dynamically similar locomotion would occur over the size range present in adult horses. We measured relative stride length (RSL) and duty factor (DF) in 21 trotting horses (body mass: 86-714 kg), and interpolated the data to predict RSL and DF at equivalent speeds (Froude numbers: 0.5, 0.75, 1.0). RSL and DF at equal Froude number were not significantly related to body mass. This is consistent with the hypothesis that horses trot in a dynamically similar fashion at equal Froude number. We show that the nonlinear stress-strain relationship of tendon can contribute to reducing deviations from dynamic similarity, ;buffering' the effects of variation in body mass, but conclude that this effect is unlikely to explain fully our results. This suggests that a ;compensatory distortion' may occur in horses, counteracting the effects of size differences. The approach used here is also applicable to understanding the consequences of size changes within an individual during growth.

Consequences of forward translation of the point of force application for the mechanics of running.

In running humans, the point of force application between the foot and the ground moves forwards during the stance phase. Our aim was to determine the mechanical consequences of this 'point of force translation' (POFT). We modified the planar spring-mass model of locomotion to incorporate POFT, and then compared spring-mass simulations with and without POFT. We found that, if leg stiffness is adjusted appropriately, it is possible to maintain very similar values of peak vertical ground reaction force (GRF), stance time, contact length and vertical centre of mass displacement, whether or not POFT occurs. The leg stiffness required to achieve this increased as the distance of POFT increased. Peak horizontal GRF and mechanical work per step were lower when POFT occurred. The results indicate that the lack of POFT in the traditional spring-mass model should not prevent it from providing good predictions of peak vertical GRF, stance time, contact length and vertical centre of mass displacement in running humans, if an appropriate spring stiffness is used. However, the model can be expected to overestimate peak horizontal GRF and mechanical work per step. When POFT occurs, the spring stiffness in the traditional spring-mass model is not equivalent to leg stiffness. Therefore, caution should be exercised when using spring stiffness to understand how the musculoskeletal system adapts to different running conditions. This can explain the contradictory results in the literature regarding the effect of running speed on leg stiffness.

Scaling of elastic energy storage in mammalian limb tendons: do small mammals really lose out?

It is widely believed that elastic energy storage is more important in the locomotion of larger mammals. This is based on: (a) comparison of kangaroos with the smaller kangaroo rat; and (b) calculations that predict that the capacity for elastic energy storage relative to body mass increases with size. Here we argue that: (i) data from kangaroos and kangaroo rats cannot be generalized to other mammals; (ii) the elastic energy storage capacity relative to body mass is not indicative of the importance of elastic energy to an animal; and (iii) the contribution of elastic energy to the mechanical work of locomotion will not increase as rapidly with size as the mass-specific energy storage capacity, because larger mammals must do relatively more mechanical work per stride. We predict how the ratio of elastic energy storage to mechanical work will change with size in quadrupedal mammals by combining empirical scaling relationships from the literature. The results suggest that the percentage contribution of elastic energy to the mechanical work of locomotion decreases with size, so that elastic energy is more important in the locomotion of smaller mammals. This now needs to be tested experimentally.

Distorting limb design for dynamically similar locomotion.

Terrestrial mammals of different sizes tend to move in a dynamically similar manner when travelling at speeds corresponding to equal values of the Froude number. This means that certain dimensionless locomotor parameters, including peak vertical ground reaction force relative to body weight, stride length relative to leg length and duty factor, are independent of animal size. The Froude number is consequently used to define equivalent speeds for mammals of different sizes. However, most musculoskeletal-tissue properties, including tendon elastic modulus, do not scale in a dynamically similar manner. Therefore, mammals could not be completely dynamically similar, even if perfectly geometrically similar. We argue that, for mammals to move in a dynamically similar manner, they must exhibit systematic 'distortions' of limb structure with size that compensate for the size independence of the tendon elastic modulus. An implication of this is that comparing mammals at equal Froude numbers cannot remove all size-dependent effects. We show that the previously published allometry of limb moment arms is sufficient to compensate for size-independent tendon properties. This suggests that it is an important factor in allowing mammals of different sizes to move in a dynamically similar manner.