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.     

Mechanical properties in the human gastric antrum using B-mode ultrasonography and antral distension

The aims of this study were to investigate gastric antral geometry and stress-strain properties by using transabdominal ultrasound scanning during volume-controlled distensions in the human gastric antrum. Seven healthy volunteers underwent stepwise inflation of a bag located in the antrum with volumes up to 60 ml. The stretch ratio and Cauchy stress and strain were calculated from measurements of pressure, diameter, and wall thickness. A second distension series was conducted in three volunteers during administration of the anticholinergic drug butylscopolamine. Analysis of stretch ratios demonstrated positive strain in the circumferential direction, negative strain in the radial direction, and no strain in the longitudinal direction. The stress-strain relation was exponential and did not differ without or with the administration of butylscopolamine. The wall stress was decomposed into its active and passive components. The well-known length-tension diagram from in vitro studies of smooth muscle strips was reproduced. The maximum active tension appeared at a volume of 50 ml, corresponding to a stretch ratio of 1.5. We conclude that the method provides measures of antral biomechanical wall properties and can be used to reproduce the muscle length-tension diagram in humans.     

A new method for measuring passive length-tension properties of human gastrocnemius muscle in vivo

The study of muscle growth and muscle length adaptations requires measurement of passive length-tension properties of individual muscles, but until now such measurements have only been made in animal muscles. We describe a new method for measuring passive length-tension properties of human gastrocnemius muscles in vivo. Passive ankle torque and ankle angle data were obtained as the ankle was rotated through its full range with the knee in a range of positions. To extract gastrocnemius passive length-tension curves from passive torque-angle data it was assumed that passive ankle torque was the sum of torque due to structures which crossed only the ankle joint (this torque was a 6-parameter function of ankle joint angle) and a torque due to the gastrocnemius muscle (a 3-parameter function of knee and ankle angle). Parameter values were estimated with non-linear regression and used to reconstruct passive length-tension curves of the gastrocnemius. The reliability of the method was examined in 11 subjects by comparing three sets of measurements: two on the same day and the other at least a week later. Length-tension curves were reproducible: the average root mean square error was 5.1+/-1.1 N for pairs of measurements taken within a day and 7.3+/-1.2 N for pairs of measurements taken at least a week apart (about 3% and 6% of maximal passive tension, respectively). Length-tension curves were sensitive to mis-specification of moment arms, but changes in length-tension curves were not. The new method enables reliable measurement of passive length-tension properties of human gastrocnemius in vivo, and is likely to be useful for investigation of changes in length-tension curves over time.     

Is the spring quality of muscle plastic?

During locomotion, major muscle groups are often activated cyclically. This alternate stretch-shorten pattern of activity could enable muscle to function as a spring, storing and recovering elastic recoil potential energy. Because the ability to store and recover elastic recoil energy could profoundly affect the energetics of locomotion, one might expect this to be an adaptable feature of skeletal muscle. This study tests the hypothesis that chronic eccentric (Ecc) training results in a change in the spring properties of skeletal muscle. Nine female Sprague-Dawley rats underwent chronic Ecc training for 8 wk on a motorized treadmill. The spring properties of muscle were characterized by both active and passive lengthening force productions. A single "spring constant (Deltaforce/Deltalength) from the passive length-tension curves was calculated for each muscle. Results from measurements on long heads of triceps brachii muscle indicate that the trained group produced significantly more passive lengthening force (P = 0.0001) as well as more active lengthening force (P = 0.0001) at all lengths of muscle stretch. In addition, the spring constants were significantly different between the Ecc (1.71 N/mm) and the control (1.31 N/mm) groups. A stiffer spring is capable of storing more energy per unit length stretched, which is of functional importance during locomotion.     

Genetic Models in Applied Physiology. Merosin deficiency leads to alterations in passive and active skeletal muscle mechanics.

The role of extracellular elements on the mechanical properties of skeletal muscles is unknown. Merosin is an essential extracellular matrix protein that forms a mechanical junction between the sarcolemma and collagen. Therefore, it is possible that merosin plays a role in force transmission between muscle fibers and collagen. We hypothesized that deficiency in merosin may alter passive muscle stiffness, viscoelastic properties, and contractile muscle force in skeletal muscles. We used the dy/dy mouse, a merosin-deficient mouse model, to examine changes in passive and active muscle mechanics. After mice were anesthetized and the diaphragm or the biceps femoris hindlimb muscle was excised, passive length-tension relationships, stress-relaxation curves, or isometric contractile properties were determined with an in vitro biaxial mechanical testing apparatus. Compared with controls, extensibility was smaller in the muscle fiber direction and the transverse fiber direction of the mutant mice. The relaxed elastic modulus was smaller in merosin-deficient diaphragms compared with controls. Interestingly, maximal muscle tetanic stress was depressed in muscles from the mutant mice during uniaxial loading but not during biaxial loading. However, presence of transverse passive stretch increases maximal contractile stress in both the mutant and normal mice. Our data suggest that merosin contributes to muscle passive stiffness, viscoelasticity, and contractility and that the mechanism by which force is transmitted between adjacent myofibers via merosin possibly in shear.     

Relaxation-induced contraction of smooth muscle surrounding hamster ovarian follicles

Changes in intrafollicular pressure and follicular diameter resulting from injecting or withdrawing fluid from the antrum were measured in preovulatory follicles and used as an assay for changes in tension in the follicular wall by applying the Laplace relationship for thin-walled spheres. Passive length-tension curves were constructed from pressure-volume measurements to establish baseline wall stiffness. Any subsequent change in pressure could then be compared to the length-tension curves to evaluate whether it arose from active tension development or from passive stretch. When intact follicles (1-2h before ovulation) were subjected to release of passive stretch, they exhibited a contractile response that lasted 15 sec-2 min and was characterized by cyclic increases and decreases in tension, with a period of 1 cycle every 2-3 sec. The probability of activating a response in the tissue was most strongly correlated with the rate of release of passive stretch. Intrafollicular pressures generated during active contractile responses sometimes reached 80 mmHg (10.64 mPa), corresponding to a wall tension of 5332 dynes/cm (5.332 N/m) (for a 1 mm follicle) and were clearly well above the passive length-tension curves. Passive stretching of the follicular wall during a contractile response to 5-hydroxytryptamine stimulation resulted in large reductions in active wall tension for the duration of the stretch. These results are consistent with a stretch-activated inhibition of contractile events.     

Whole muscle length-tension relationships are accurately modeled as scaled sarcomeres in rabbit hindlimb muscles

An a priori model of the whole active muscle length-tension relationship was constructed utilizing only myofilament length and serial sarcomere number for rabbit tibialis anterior (TA), extensor digitorum longus (EDL), and extensor digitorum II (EDII) muscles. Passive tension was modeled with a two-element Hill-type model. Experimental length-tension relations were then measured for each of these muscles and compared to predictions. The model was able to accurately capture the active-tension characteristics of experimentally-measured data for all muscles (ICC=0.88 ± 0.03). Despite their varied architecture, no differences in predicted versus experimental correlations were observed among muscles. In addition, the model demonstrated that excursion, quantified by full-width-at-half-maximum (FWHM) of the active length-tension relationship, scaled linearly (slope=0.68) with normalized muscle fiber length. Experimental and theoretical FWHM values agreed well with an intraclass correlation coefficient of 0.99 (p<0.001). In contrast to active tension, the passive tension model deviated from experimentally-measured values and thus, was not an accurate predictor of passive tension (ICC=0.70 ± 0.07). These data demonstrate that modeling muscle as a scaled sarcomere provides accurate active functional but not passive functional predictions for rabbit TA, EDL, and EDII muscles and call into question the need for more complex modeling assumptions often proposed.     

Active length-tension relation and the effect of muscle pinnation on fiber lengthening

The active length-tension relation was determined for the left digastric muscle of seven New Zealand White rabbits anesthetized with pentobarbital. Measurements of muscle length and fiber architecture were made from photographs of resting and actively contracting muscle. There was a marked difference between length-tension curves based upon resting as compared to active muscle length. The active length-tension relation had a longer descending limb than ascending limb, whereas the length-tension relation based on passive muscle length tended to be symmetrical around optimum length. On the average, muscle fibers lengthened 0.77 mm for each 1 mm of extension of the muscle belly. Since the rabbit digastric muscle is unipinnate, this suggests that pinnation serves to enhance the range of muscle excursion in this muscle.     

Unit activity in the superior colliculus of the cat following passive eye movements.

Unit response in the superior colliculus and underlying structures has been examined in the choralose-anaesthetized cat following passive movement of an occluded eye. One group of units was sensitive to small saccadic movements, responded regardless of the initial postion of the eye, and in most instances responded to movements in opposit directions. A second numerically smaller group also responded when they eye was moved at saccadic velocity but only when the eye passed a fixed point. Such units with fixed positional thresholds were found following movements in both nasal and temporal directions as well as to both upward and downward movement. Both types of unit response were found after transection of the optic nerve and were also recorded when individual extraocular muscles were subjected to controlled stretch. It is assumed that most unit activity seen after passive movement of the occluded eye is due to activity in extraocular muscle receptors. In the deep layers of the superior colliculus responses to small eye movements were found to be due to the activation of very low threshold receptors sensitive to vibration in the facial area.     

Myometrial mechanoadaptation during pregnancy: implications for smooth muscle plasticity and remodelling

The smooth muscle of the uterus during pregnancy presents a unique circumstance of physiological mechanotransduction as the tissue remodels in response to stretches imposed by the growing foetus(es), yet the nature of the molecular and functional adaptations remain unresolved. We studied, in myometrium isolated from non-pregnant (NP) and pregnant mice, the active and passive length-tension curves by myography and the expression and activation by immunoblotting of focal adhesion-related proteins known in other systems to participate in mechanosensing and mechanotransduction. In situ uterine mass correlated with pup number and weight throughout pregnancy. In vitro myometrial active, and passive, length-tension curves shifted significantly to the right during pregnancy indicative of altered mechanosensitivity; at term, maximum active tension was generated following 3.94 +/- 0.33-fold stretch beyond slack length compared to 1.91 +/- 0.12-fold for NP mice. Moreover, mechanotransduction was altered during pregnancy as evidenced by the progressive increase in absolute force production at each optimal stretch. Pregnancy was concomitantly associated with an increased expression of the dense plaque-associated proteins FAK and paxillin, and elevated activation of FAK, paxillin, c-Src and extracellular signal-regulated kinase (ERK1/2) which reversed 1 day post-partum. Electron microscopy revealed close appositioning of neighbouring myometrial cells across a narrow extracellular cleft adjoining plasmalemmal dense plaques. Collectively, these results suggest a physiological basis of myometrial length adaptation, long known to be a property of many smooth muscles, whereupon plasmalemmal dense plaque proteins serve as molecular signalling and structural platforms contributing to functional (contractile) remodelling in response to chronic stretch.     

Rises in whole muscle passive tension of mammalian muscle after eccentric contractions at different lengths.

This is a report of experiments carried out on the medial gastrocnemius muscle of the anesthetized cat, investigating the effects of eccentric contractions carried out at different muscle lengths on the passive and active length-tension relationships. In one series of experiments, the motor supply to the muscle was divided into three approximately equal parts; in the other, whole muscles were used. Fifty eccentric contractions were carried out over different regions of the active length-tension curve for each partial or whole muscle. Active and passive length-tension curves were measured before and after the eccentric contractions. When eccentric contractions were carried out at longer lengths, there was a larger shift of the optimum length for active tension in the direction of longer muscle lengths and a larger fall in peak isometric tension. Passive tension was higher immediately after the eccentric contractions, and if the muscle was left undisturbed for 40 min, it increased further to higher values, particularly after contractions at longer lengths. A series of 20 passive stretches of the same speed and amplitude and covering the same length range as the active stretches, reduced the passive tension which redeveloped over a subsequent 40-min period. It is hypothesized that there are two factors influencing the level of passive tension in a muscle after a series of eccentric contractions. One is injury contractures in damaged muscle fibers tending to raise passive tension; the other is the presence of disrupted sarcomeres in series with still-functioning sarcomeres tending to reduce it.     

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.     

A comparison of two Hill-type skeletal muscle models on the construction of medial gastrocnemius length-tension curves in humans in vivo

Human length-tension curves are traditionally constructed using a model that assumes passive tension does not change during contraction (model A) even though the animal literature suggests that passive tension can decrease (model B). The study's aims were threefold: 1) measure differences in human medial gastrocnemius length-tension curves using model A vs. model B, 2) test the reliability of ultrasound constructed length-tension curves, and 3) test the robustness of fascicle length-generated length-tension curves to variations between the angle and fascicle length relationship. An isokinetic dynamometer manipulated and measured ankle angle while ultrasound was used to measure medial gastrocnemius fascicle length. Supramaximal tibial nerve stimulation was used to evoke resting muscle twitches. Length-tension curves were constructed using model A {angle-torque [A-T((A))], length-torque [L-T((A))]} or model B {length-torque [L-T((B))]} in three conditions: baseline, heel-lift (where the muscle was shortened at each angle), and baseline repeated 2 h later (+2 h). Length-tension curves constructed from model B differed from those produced via model A, indicated by a significant increase in maximum torque (≈23%) when using L-T((B)) vs. L-T((A)). No parameter measured was different between baseline and +2 h for any method, indicating good reliability when using ultrasound. Length-tension curves were unaffected by the heel-lift condition when using L-T((A)) or L-T((B)) but were affected when using A-T((A)). Since the muscle model used significantly alters human length-tension curves, and given animal data indicate model B to be more accurate when passive tension is present, we recommend that model B should be used when constructing medial gastrocnemius length-tension curves in humans in vivo.     

Correlation between active and passive isometric force and intramuscular pressure in the isolated rabbit tibialis anterior muscle

The purpose of this study was to quantify the relationship between intramuscular pressure (IMP) and muscle force during isometric muscle contraction of the rabbit tibialis anterior (TA) absent the effect of either bone or fascia. To quantify this relationship, length-tension experiments were performed on the isolated TA of the New Zealand White rabbit (mass=2.5+/-0.5kg, n=12). The knee was fixed in a custom jig, the distal tendon of the TA was attached to a servomotor, and a 360 microm fiber optic pressure transducer was inserted into the TA. The peroneal nerve was stimulated to define optimal length (L(0)). The length-tension curve was created using 40Hz isometric contractions with 2-min rest intervals between each contraction. Measurements began at L(0)-50%L(f) and progressed to L(0)+50%L(f), changing the length-tension in 5% L(f) increments after each contraction. Qualitatively, the length-tension curve for isometric contractions was mimicked by the length-pressure curve for both active and passive conditions. Linear regression was performed individually for each animal for the ascending and descending limb of the length-tension curve and for active and passive conditions. Pressure-force coefficients of determination ranged from 0.138-0.963 for the active ascending limb and 0.343-0.947 for the active descending limb. Passive pressure coefficients of determination ranged from 0.045-0.842 for the ascending limb and 0.672-0.982 for the descending limb. These data indicate that IMP measurement provide a fairly accurate index of relative muscle force, especially at muscle lengths longer than optimal.     

Changes in shear wave propagation within skeletal muscle during active and passive force generation

Muscle force can be generated actively through changes in neural excitation, and passively through externally imposed changes in muscle length. Disease and injury can disrupt force generation, but it can be challenging to separate passive from active contributions to these changes. Ultrasound elastography is a promising tool for characterizing the mechanical properties of muscles and the forces that they generate. Most prior work using ultrasound elastography in muscle has focused on the group velocity of shear waves, which increases with increasing muscle force. Few studies have quantified the phase velocity, which depends on the viscoelastic properties of muscle. Since passive and active forces within muscle involve different structures for force transmission, we hypothesized that measures of phase velocity could detect changes in shear wave propagation during active and passive conditions that cannot be detected when considering only group velocity. We measured phase and group velocity in the human biceps brachii during active and passive force generation and quantified the differences in estimates of shear elasticity obtained from each of these measurements. We found that measures of group velocity consistently overestimate the shear elasticity of muscle. We used a Voigt model to characterize the phase velocity and found that the estimated time constant for the Voigt model provided a way to distinguish between passive and active force generation. Our results demonstrate that shear wave elastography can be used to distinguish between passive and active force generation when it is used to characterize the phase velocity of shear waves propagating in muscle.     

A method to characterize the passive elasticity in contracting muscle bundles

There is concern among researchers whether the passive muscle properties, characterized by purely passive material testing procedures, are an appropriate representation of the actual passive component of the muscle. This aspect is of particular importance in the biomechanical analysis of heart muscle response where it is generally agreed that the so-called parallel elasticity cannot be ignored as is done justifiably in the analysis of skeletal muscle response. In the present article, a method of quantifying the passive elasticity in contracting muscle bundles is presented. The method consists of imposing isometric transients (such as the quick-stretch or quick release) on a muscle bundle during the contraction phase and observing the differences in decayed force levels between a normal twitch and that of a perturbed twitch. The proposed method provides a means of obtaining useful passive properties from contracting muscle bundles and circumvents the difficulty of having to characterize muscle properties from separate experiments on quiescent muscle bundles.     

Viscous elements have little impact on measured passive length-tension properties of human gastrocnemius muscle-tendon units in vivo

Several studies have measured the elastic properties of a single human muscle-tendon unit in vivo. However the viscoelastic behavior of single human muscles has not been characterized. In this study, we adapted QLV theory to model the viscoelastic behavior of human gastrocnemius muscle-tendon units in vivo. We also determined the influence of viscoelasticity on passive length-tension properties of human gastrocnemius muscle-tendon units. Eight subjects participated in the experiment, which consisted of two parts. First, the stress relaxation response of human gastrocnemius muscle-tendon units was determined at a range of knee and ankle angles. Subsequently, passive ankle torque and ankle angle were collected during cyclic dorsiflexion and plantarflexion at a range of knee angles. Viscous parameters were determined by fitting the stress relaxation experiment data with a two-term exponential function, and elastic parameters were estimated by fitting the QLV model and viscous parameters to the cyclic experiment data. The model fitted the experimental data well at slow speeds (RMSE: 1.7 ± 0.5N) and at fast speeds (RMSE: 1.9 ± 0.2N). Muscle-tendon units demonstrated a large amount of stress relaxation. Nonetheless, viscoelastic passive length-tension curves estimated with the QLV model were similar to elastic passive length-tension curves obtained using a model that ignored viscosity. There was little difference in the elastic passive length-tension curves at different loading rates. We conclude that (a) the QLV model can be used to quantify viscoelastic behaviors of relaxed human gastrocnemius muscle-tendon units in vivo, and (b) over the range of velocities we examined, the velocity of loading has little effect on the passive length-tension properties of human gastrocnemius muscle-tendon units.     

A mathematical model for estimating muscle tension in vivo during esophageal bolus transport

We present a model of esophageal wall muscle mechanics during bolus transport with which the active and "passive" components of circular muscle tension are separately extracted from concurrent manometric and videofluoroscopic data. Local differential equations of motion are integrated across the esophageal wall to yield global equations of equilibrium which relate total tension within the esophageal wall to intraluminal pressure and wall geometry. To quantify the "passive" (i.e. inactive) length-tension relationships, the model equations are applied to a region of the esophagus in which active muscle contraction is physiologically inhibited. Combining the global equations with space-time-resolved intraluminal pressure measured manometrically and videofluoroscopic geometry data, the passive model is used to separate active and "passive" components of esophageal muscle tension during bolus transport. The model is of general applicability to probe basic muscle mechanics including the space-time stimulation of circular muscle, the relationship between longitudinal muscle tension and longitudinal muscle shortening, and the contribution of the collagen matrix surrounding muscle fibers to passive tension during normal human esophageal bolus transport and in pathology. Example calculations of normal esophageal function are given where active tone is found to extend only over a short intrabolus segment near the bolus tail and segmental regions of active muscle squeeze are demonstrated.     

A quantitative model of intersarcomere dynamics during fixed-end contractions of single frog muscle fibers.

A numerical model of a muscle fiber as 400 sarcomeres, identical except for their initial lengths, was used to simulate fixed-end tetanic contractions of frog single fibers at sarcomere lengths above the optimum. The sarcomeres were represented by a lumped model, constructed from the passive and active sarcomere length-tension curves, the force-velocity curve, and the observed active elasticity of a single frog muscle fiber. An intersarcomere force was included to prevent large disparities in lengths of neighboring sarcomeres. The model duplicated the fast rise, slow creep rise, peak, and slow decline of tension seen in tetanic contractions of stretched living fibers. Decreasing the initial non-uniformity of sarcomere length reduced the rate of rise of tension during the creep phase, but did not decrease the peak tension reached. Limitations of the model, and other processes that might contribute to the shape of the fixed end tetanic tension record are discussed. Taking account of model and experimental results, it is concluded that the distinctive features of the tension records of fixed end tetanic contraction at lengths beyond optimum can be explained by internal motion within the fiber.     

Support for a linear length-tension relation of the torso extensor muscles: An investigation of the length and velocity EMG-force relationships

This study investigated the hypothesis that the length-tension relation of the torso erectors would be linear, mirroring the observed linear increase in extension strength capability toward full flexion. The effect of torso extension velocity on the tension capability of these muscles was also investigated for common motion speeds. A myoelectric-based approach was used wherein a dynamic biomechanical model incorporating active and passive tissue characteristics provided muscle kinematic estimates during controlled sagittal plane extension motions. A double linear optimization formulation from the literature provided muscle tension estimates. The data of five male subjects supported the hypothesis of a linear length-tension relation toward full flexion for both the erector spinae and latissimus muscles. Velocity trends agreed with that predicted by Hill's exponential relation, although linear trends were found to fit the data almost as well. The results have implications for muscle tension estimation in biomechanical torso modeling, and suggest a possible low back pain injury mechanism through tissue strain while lifting in fully flexed postures.