A model of the mechanics of airway narrowing

To examine the interaction between airway smooth muscle shortening and airway wall thickening on changes in pulmonary resistance, we have developed a model of the tracheobronchial tree that allows simulation of the mechanisms involved in airway narrowing. The model is based on the symmetrical dichotomous branching tracheobronchial tree as described by Weibel and uses fluid dynamic equations proposed by Pedley et al. to calculate inspiratory resistance during quiet tidal breathing. To allow for changes in lung volume, we used the airway pressure-area curves developed by Lambert et al. The model is easily implemented with a spreadsheet and personal computer that allows calculation of total and regional pulmonary resistance. At each airway generation in the model, provision is made for airway wall thickness, the maximal airway smooth muscle shortening achievable, and an S-shaped dose-response relationship to describe smooth muscle shortening. To test the validity of the model, we compared pressure-flow curves generated with the model with measurements of pulmonary resistance while normal subjects breathed air and 20% O2-80% He at a variety of lung volumes. By simulating progressive airway smooth muscle shortening, realistic pulmonary resistance vs. dose-response curves were produced. We conclude that this model provides realistic estimates of pulmonary resistance and shows potential for examining the various mechanisms that could produce excessive airway narrowing in disease.     

Historical perspective on airway smooth muscle: the saga of a frustrated cell.

Despite the lack of a clearly defined physiological function, airway smooth muscle receives substantial attention because of its involvement in the pathogenesis of asthma. Recent investigations have turned to the ways in which the muscle is influenced by its dynamic microenvironment. Ordinarily, airway smooth muscle presents little problem, even when maximally activated, because unending mechanical perturbations provided by spontaneous tidal breathing put airway smooth muscle in a perpetual state of "limbo," keeping its contractile machinery off balance and unable to achieve its force-generating potential. The dynamic microenvironment affects airway smooth muscle in at least two ways: by acute changes associated with disruption of myosin binding and by chronic changes associated with plastic restructuring of contractile and cytoskeletal filament organization. Plastic restructuring can occur when dynamic length changes occur between sequential contractile events or within a single contractile event. Impairment of these normal responses of airway smooth muscle to its dynamic environment may be implicated in airway hyperresponsiveness in asthma.     

Residual force enhancement and force depression in human single muscle fibres

Residual force depression (rFD) and residual force enhancement (rFE) are intrinsic contractile properties of muscle. rFD is characterized as a decrease in steady-state isometric force following active shortening compared with a purely isometric contraction at the same muscle length and level of activation. By contrast, isometric force is increased following active lengthening compared to a reference isometric contraction at the same muscle length and level of activation; this is termed rFE. To date, there have been no investigations of rFD and rFE in human muscle fibres, therefore the purpose of this study was to determine whether rFD and rFE occur at the single muscle fibre level in humans. rFD and rFE were investigated in maximally activated single muscle fibres biopsied from the vastus lateralis of healthy adults. To induce rFD, fibres were activated and shortened from an average sarcomere length (SL) of 3.2–2.6 μm. Reference isometric contractions were performed at an average SL of 2.6 μm. To induce rFE, fibres were actively lengthened from an average SL of 2.6–3.2 μm and a reference isometric contraction was performed at an average SL of 3.2 μm. Isometric steady-state force was lower following active shortening (p < 0.05), and higher following active lengthening (p < 0.05), as compared to the reference isometric contractions. We demonstrated rFD and rFE in human single fibres which is consistent with previous animal models. The non-responder phenomenon often reported in rFE studies involving voluntary contractions at the whole human level was not observed at the single fibre level.     

Effects of smooth muscle activation on axial mechanical properties of excised canine bronchi.

This study tested the hypothesis that airway smooth muscle (ASM) activation produces an airway active axial force (AAAF). Bronchi (n = 10) immersed in a tissue bath containing 95% O2-5% CO2-equilibrated Krebs solution were subjected to passive axial lengthening and shortening at 0-20 cmH2O of transmural pressure. ASM was relaxed with isoproterenol and activated with methacholine. Axial tensile (epsilonx), transverse compressive (epsilony), and shear strains (epsilonxy) were computed from the displacements of four markers placed onto the specimen's surface. The AAAF was estimated by subtracting the control axial force (AF) values at a given epsilonx from those obtained after methacholine. epsilonx-AF relationships were curvilinear, with maximum epsilonx being approached at approximately 15 g of AF. The epsilony decreased during bronchial lengthening. Cholinergic stimulation produced 1) a decrease of both epsilonx and epsilony at a given AF relative to control, indicating ASM shortening, and 2) an AAAF that increased with increasing epsilonx and transmural pressure. A portion of the work of expanding the lungs is required to lengthen the airways; therefore, an AAAF would increase lung elastance and recoil.     

Inhibition of the p38 MAP kinase pathway destabilizes smooth muscle length during physiological loading

We tested the hypothesis that mechanical plasticity of airway smooth muscle may be mediated in part by the p38 mitogen-activated protein (MAP) kinase pathway. Bovine tracheal smooth muscle (TSM) strips were mounted in a muscle bath and set to their optimal length, where the active force was maximal (F(o)). Each strip was then contracted isotonically (at 0.32 F(o)) with ACh (maintained at 10(-4) M) and allowed to shorten for 180 min, by which time shortening was completed and the static equilibrium length was established. To simulate the action of breathing, we then superimposed on this steady distending force a sinusoidal force fluctuation with zero mean, at a frequency of 0.2 Hz, and measured incremental changes in muscle length. We found that TSM strips incubated in 10 microM SB-203580-HCl, an inhibitor of the p38 MAP kinase pathway, demonstrated a greater degree of fluctuation-driven lengthening than did control strips, and upon removal of the force fluctuations they remained at a greater length. We also found that the force fluctuations themselves activated the p38 MAP kinase pathway. These findings are consistent with the hypothesis that inhibition of the p38 MAP kinase pathway destabilizes muscle length during physiological loading.     

Airway stability and heterogeneity in the constricted lung.

The effect of bronchoconstriction on airway resistance is known to be spatially heterogeneous and dependent on tidal volume. We present a model of a single terminal airway that explains these features. The model describes a feedback between flow and airway resistance mediated by parenchymal interdependence and the mechanics of activated smooth muscle. The pressure-tidal volume relationship for a constricted terminal airway is computed and shown to be sigmoidal. Constricted terminal airways are predicted to have two stable states: one effectively open and one nearly closed. We argue that the heterogeneity of whole lung constriction is a consequence of this behavior. Airways are partitioned between the two states to accommodate total flow, and changes in tidal volume and end-expiratory pressure affect the number of airways in each state. Quantitative predictions for whole lung resistance and elastance agree with data from previously published studies on lung impedance.     

Longer moment arm results in smaller joint moment development, power and work outputs in fast motions

Effects of moment arm length on kinetic outputs of a musculoskeletal system (muscle force development, joint moment development, joint power output and joint work output) were evaluated using computer simulation. A skeletal system of the human ankle joint was constructed: a lower leg segment and a foot segment were connected with a hinge joint. A Hill-type model of the musculus soleus (m. soleus), consisting of a contractile element and a series elastic element, was attached to the skeletal system. The model of the m. soleus was maximally activated, while the ankle joint was plantarflexed/dorsiflexed at a variation of constant angular velocities, simulating isokinetic exercises on a muscle testing machine. Profiles of the kinetic outputs (muscle force development, joint moment development, joint power output and joint work output) were obtained. Thereafter, the location of the insertion of the m. soleus was shifted toward the dorsal/ventral direction by 1cm, which had an effect of lengthening/shortening the moment arm length, respectively. The kinetic outputs of the musculoskeletal system during the simulated isokinetic exercises were evaluated with these longer/shorter moment arm lengths. It was found that longer moment arm resulted in smaller joint moment development, smaller joint power output and smaller joint work output in the larger plantarflexion angular velocity region (>120 degrees/s). This is because larger muscle shortening velocity was required with longer moment arm to achieve a certain joint angular velocity. Larger muscle shortening velocity resulted in smaller muscle force development because of the force-velocity relation of the muscle. It was suggested that this phenomenon should be taken into consideration when investigating the joint moment-joint angle and/or joint moment-joint angular velocity characteristics of experimental data.     

Terminology for contractions of muscles during shortening, while isometric, and during lengthening.

Communication among scientists must be clear and concise to avoid ambiguity and misinterpretations. The selection of words must be based on accepted definitions. The fields of biomechanics, muscle physiology, and exercise science have had a particularly difficult time with terminology, arising from the complexity of muscle contractions and by the use of inappropriate terminology by scientists. The dictionary definition of the verb "contract," specifically for the case of muscle, is "to undergo an increase in tension, or force, and become shorter." Under all circumstances, an activated muscle generates force, but an activated muscle generating force does not invariably shorten! During the 1920s and 1930s, investigators recognized that the interaction between the force generated by the muscle and the load on the muscle results in either shortening, no length change (isometric), or lengthening of the muscle. The recognition that muscles perform three different types of "contractions" required that contraction be redefined as "to undergo activation and generate force." Modifiers of contraction are then needed to clarify the lack of movement or the directionality of movement. Despite the contradiction, for 75 years the lack of movement has been termed an "isometric contraction." The directionality of the movement is then best described by the adjectives "shortening" and "lengthening." The definitions of "concentric" as "having the same center" and of "eccentric" as "not having the same center" are consistent with hypertrophy, or remodeling of the heart muscle, but are inappropriate to describe the contractions of skeletal muscles.     

Electrical and mechanical activity of respiratory muscles during hypercapnia

In nine anesthetized supine spontaneously breathing dogs, we compared moving average electromyograms (EMGs) of the costal diaphragm and the third parasternal intercostal muscles with their respective respiratory changes in length (measured by sonomicrometry). During resting O2 breathing the pattern of diaphragm and intercostal muscle inspiratory shortening paralleled the gradually incrementing pattern of their moving average EMGs. Progressive hypercapnia caused progressive increases in the amount and velocity of respiratory muscle inspiratory shortening. For both muscles there were linear relationships during the course of CO2 rebreathing between their peak moving average EMGs and total inspiratory shortening and between tidal volume and total inspiratory shortening. During single-breath airway occlusions, the electrical activity of both the diaphragm and intercostal muscles increased, but there were decreases in their tidal shortening. The extent of muscle shortening during occluded breaths was increased by hypercapnia, so that both muscles shortened more during occluded breaths under hypercapnic conditions (PCO2 up to 90 Torr) than during unoccluded breaths under normocapnic conditions. These results suggest that for the costal diaphragm and parasternal intercostal muscles there is a close relationship between their electrical and mechanical behavior during CO2 rebreathing, this relationship is substantially altered by occluding the airway for a single breath, and thoracic respiratory muscles do not contract quasi-isometrically during occluded breaths.     

The passive properties of muscle fibers are velocity dependent

The passive properties of skeletal muscle play an important role in muscle function. While the passive quasi-static elastic properties of muscle fibers have been well characterized, the dynamic visco-elastic passive behavior of fibers has garnered less attention. In particular, it is unclear how the visco-elastic properties are influenced by lengthening velocity, in particular for the range of physiologically relevant velocities. The goals of this work were to: (i) measure the effects of lengthening velocity on the peak stresses within single muscle fibers to determine how passive behavior changes over a range of physiologically relevant lengthening rates (0.1–10L_o/s), and (ii) develop a mathematical model of fiber viscoelasticity based on these measurements. We found that passive properties depend on strain rate, in particular at the low loading rates (0.1–3L_o/s), and that the measured behavior can be predicted across a range of loading rates and time histories with a quasi-linear viscoelastic model. In the future, these results can be used to determine the impact of viscoelastic behavior on intramuscular stresses and forces during a variety of dynamic movements.     

A phenomenological model for estimating metabolic energy consumption in muscle contraction

A phenomenological model for muscle energy consumption was developed and used in conjunction with a simple Hill-type model for muscle contraction. The model was used to address two questions. First, can an empirical model of muscle energetics accurately represent the total energetic behavior of frog muscle in isometric, isotonic, and isokinetic contractions? And second, how does such a model perform in a large-scale, multiple-muscle model of human walking? Four simulations were conducted with frog sartorius muscle under full excitation: an isometric contraction, a set of isotonic contractions with the muscle shortening a constant distance under various applied loads, a set of isotonic contractions with the muscle shortening over various distances under a constant load, and an isokinetic contraction in lengthening. The model calculations were evaluated against results of similar thermal in vitro experiments performed on frog sartorius muscle. The energetics model was then incorporated into a large-scale, multiple-muscle model of the human body for the purpose of predicting energy consumption during normal walking. The total energy estimated by the model accurately reflected the observed experimental behavior of frog muscle for an isometric contraction. The model also accurately reproduced the experimental behavior of frog muscle heat production under isotonic shortening and isokinetic lengthening conditions. The estimated rate of metabolic energy consumption for walking was 29% higher than the value typically obtained from gait measurements.     

Modeling the oscillation dynamics of activated airway smooth muscle strips

When strips of activated airway smooth muscle are stretched cyclically, they exhibit force-length loops that vary substantially in both position and shape with the amplitude and frequency of the stretch. This behavior has recently been ascribed to a dynamic interaction between the imposed stretch and the number of actin-myosin interactions in the muscle. However, it is well known that the passive rheological properties of smooth muscle have a major influence on its mechanical properties. We therefore hypothesized that these rheological properties play a significant role in the force-length dynamics of activated smooth muscle. To test the plausibility of this hypothesis, we developed a model of the smooth muscle strip consisting of a force generator in series with an elastic component. Realistic steady-state force-length loops are predicted by the model when the force generator obeys a hyperbolic force-velocity relationship, the series elastic component is highly nonlinear, and both elastic stiffness and force generation are adjusted so that peak loop force equals isometric force. We conclude that the dynamic behavior of airway smooth muscle can be ascribed in large part to an interaction between connective tissue rheology and the force-velocity behavior of contractile proteins.     

History dependence of force production in submaximal stimulated rat medial gastrocnemius muscle

Studies on maximal stimulated muscle have shown that history dependence is an integral part of muscle force production. The purpose of this study was to evaluate the history dependent effects in submaximal stimulated muscle. For this purpose, lengthening and shortening experiments were performed on the medial gastrocnemius muscle of the rat. The length dependence of lengthening induced force enhancement and shortening induced force depression was studied in maximal (80 Hz) and submaximal (30 Hz) stimulated muscles. The most important results of this study are (a) submaximal stimulation reduces the maximal amplitude of the history effects and (b) lengthening induced force enhancement and shortening induced force deficit are affected differently by submaximal stimulation. The implication of these results for the underlying mechanism and functional relevance of the history dependent effects is discussed.     

Influence of muscle shortening on the geometry of gastrocnemius medialis muscle of the rat

For static and dynamic conditions muscle geometry of the musculus gastrocnemius medialis of the rat was compared at different muscle lengths. The dynamic conditions differed with respect to isokinetic shortening velocity (25, 50 and 75 mm/s) of the muscle-tendon complex and in constancy of force (isotonic) and velocity (isokinetic) during shortening. Muscle geometry was characterized by fibre length and angle as well as aponeurosis length and angle. At high isokinetic shortening velocities (50 and 75 mm/s) small differences in geometry were found with respect to isometric conditions: aponeurosis lengths differed maximally by -2%, fibre length only showed a significant increase (+3.2%) at the highest shortening velocity. The isotonic condition only yielded significant differences of fibre angle (-4.5%) in comparison with isometric conditions. No significant differences of muscle geometry were found when comparing isotonic with isokinetic conditions of similar shortening velocity. The small differences of geometry between isometric and dynamic conditions are presumably due to the lower muscle force in the dynamic condition and the elastic behaviour of the aponeurosis. It is concluded that, unless very high velocities of shortening are used, the relationship between muscle geometry and muscle length in the isometric condition may be used to describe muscle geometry in the dynamic condition.     

Skeletal muscle hypertrophy in response to isometric, lengthening, and shortening training bouts of equivalent duration.

Movements generated by muscle contraction generally include periods of muscle shortening and lengthening as well as force development in the absence of external length changes (isometric). However, in the specific case of resistance exercise training, exercises are often intentionally designed to emphasize one of these modes. The purpose of the present study was to objectively evaluate the relative effectiveness of each training mode for inducing compensatory hypertrophy. With the use of a rat model with electrically stimulated (sciatic nerve) contractions, groups of rats completed 10 training sessions in 20 days. Within each training session, the duration of the stimulation was equal across the three modes. Although this protocol provided equivalent durations of duty cycle, the torque integral for the individual contractions varied markedly with training mode such that lengthening > isometric > shortening. The results indicate that the hypertrophy response did not track the torque integral with mass increases of isometric by 14%, shortening by 12%, and lengthening by 11%. All three modes of training resulted in similar increases in total muscle DNA and RNA. Isometric and shortening but not lengthening mode training resulted in increased muscle insulin-like growth factor I mRNA levels. These results indicate that relatively pure movement mode exercises result in similar levels of compensatory hypertrophy that do not necessarily track with the total amount of force generated during each contraction.     

Effects of tracheal airway occlusion on hyoid muscle length and upper airway volume

Complex relationships exist among electromyograms (EMGs) of the upper airway muscles, respective changes in muscle length, and upper airway volume. To test the effects of preventing lung inflation on these relationships, recordings were made of EMGs and length changes of the geniohyoid (GH) and sternohyoid (SH) muscles as well as of tidal changes in upper airway volume in eight anesthetized cats. During resting breathing, tracheal airway occlusion tended to increase the inspiratory lengthening of GH and SH. In response to progressive hypercapnia, the GH eventually shortened during inspiration in all animals; the extent of muscle shortening was minimally augmented by airway occlusion despite substantial increases in EMGs. SH lengthened during inspiration in six of eight animals under hypercapnic conditions, and in these cats lengthening was greater during airway occlusion even though EMGs increased. Despite the above effects on SH and GH length, upper airway tidal volume was increased significantly by tracheal occlusion under hypercapnic conditions. These data suggest that the thoracic and upper airway muscle reflex effects of preventing lung inflation during inspiration act antagonistically on hyoid muscle length, but, because of the mechanical arrangement of the hyoid muscles relative to the airway and thorax, they act agonistically to augment tidal changes in upper airway volume. The augmentation of upper airway tidal volume may occur in part as a result of the effects of thoracic movements being passively transmitted through the hyoid muscles.     

Mechanics of the parasternal intercostals during occluded breaths in dogs

The electrical activity and the respiratory changes in length of the third parasternal intercostal muscle were measured during single-breath airway occlusion in 12 anesthetized, spontaneously breathing dogs in the supine posture. During occluded breaths in the intact animal, the parasternal intercostal was electrically active and shortened while pleural pressure fell. In contrast, after section of the third intercostal nerve at the chondrocostal junction and abolition of parasternal electrical activity, the muscle always lengthened. This inspiratory muscle lengthening must be related to the fall in pleural pressure; it was, however, approximately 50% less than the amount of muscle lengthening produced, for the same fall in pleural pressure, by isolated stimulation of the phrenic nerves. These results indicate that 1) the parasternal inspiratory shortening that occurs during occluded breaths in the dog results primarily from the muscle inspiratory contraction per se, and 2) other muscles of the rib cage, however, contribute to this parasternal shortening by acting on the ribs or the sternum. The present studies also demonstrate the important fact that the parasternal inspiratory contraction in the dog is really agonistic in nature.     

Effect of bronchomotor tone on work rate of breathing

We studied the optimal airway caliber for minimizing the work rate of breathing in the lung (W) with different bronchomotor tones in six normal subjects. The inhalation of methacholine contracted airway smooth muscle, and the inhalation of salbutamol relaxed it. To calculate W at a given alveolar ventilation (VA), anatomical dead space (VDanat), pulmonary resistance (RL), and dynamic compliance were measured simultaneously, breath by breath, during various breathing maneuvers. VDanat increased and RL decreased with both increased breathing frequency and tidal volume, even at a given airway tone. This suggests that the airway caliber varied even at a given bronchomotor tone. The minimum W at a given VA increased in constricted airways, but there was no significant difference between control airways after saline inhalation and relaxed airways. It has been suggested that airway smooth muscle tones at both control and relaxed conditions bring W to a minimum and that the airway smooth muscle tone existing in the control state acts to keep the airway caliber optimal in order to minimize the W and stabilize the airway mechanics.     

Ia-afferent input to motoneurons during shortening and lengthening muscle contractions in humans.

The central nervous system employs different strategies to execute specific motor tasks. Because afferent feedback during shortening and lengthening muscle contractions differs, the neural strategy underlying these tasks may be quite distinct. Cortical drive may be adjusted or afferent input regulated. The exact mechanisms are not clear. Here, we examine the control of synaptic transmission across the Ia synapse during shortening and lengthening muscle contractions. Subjects were instructed to maintain isolated activity in a single tibialis anterior (TA) motor unit while muscle length was varied from flexion to extension and back. At a fixed interval after a firing of the active motor unit, a single electrical stimulus was applied to the common peroneal nerve to activate Ia afferents from the TA muscle. We investigated the stimulus-induced change in firing probability of 19 individual low-threshold TA motor units during shortening and lengthening contractions. Any change in firing probability depends on both pre- and postsynaptic mechanisms. In this experiment, motoneuron firing rate was similar during both contraction types. There was no difference in the firing probability between shortening and lengthening contractions (0.23 +/- 0.03 and 0.20 +/- 0.02, respectively). We suggest that there is no contraction type-specific control of Ia input to the motoneurons during shortening and lengthening muscle contractions. Cortical adjustments may have occurred.     

Technique for interpretation of electromyography for concentric and eccentric contractions in gait

We present a technique to combine muscle shortening and lengthening velocity information with electromyographic (EMG) profiles during gait. A biomechanical model was developed so that each muscle's length could be readily calculated over time as a function of angles of the joints it crossed. The velocity of shortening and lengthening of the muscle fiber was then calculated, and with computer graphics this information was overlaid on the EMG profiles. Thus, researchers and clinicians were not only able to interpret the processed EMG signal as level of activity (tension) but also to gain insight as to the muscles' role as generators (muscle shortening) or absorbers (muscle lengthening) of energy. Six common muscles are documented, using database profiles; soleus (SOL), medial gastrocnemius (MG), tibialis anterior (TA), vastus lateralis (VL), rectus femoris (RF), and semitendinosus (ST). The protocol thus demonstrates a relatively simple technique for calculating muscle fiber velocity and for combining that velocity information with EMG activity profiles.