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Recent experiments involving muscle force measurements over a range of muscle lengths show that effects of botulinum toxin (BTX) are complex e.g., force reduction varies as a function of muscle length. We hypothesized that altered conditions of sarcomeres within active parts of partially paralyzed muscle is responsible for this effect. Using finite element modeling, the aim was to test this hypothesis and to study principles of how partial activation as a consequence of BTX affects muscle mechanics. In order to model the paralyzing effect of BTX, only 50% of the fascicles (most proximal, or middle, or most distal) of the modeled muscle were activated. For all muscle lengths, a vast majority of sarcomeres of these BTX-cases were at higher lengths than identical sarcomeres of the BTX-free muscle. Due to such "longer sarcomere effect", activated muscle parts show an enhanced potential of active force exertion (up to 14.5%). Therefore, a muscle force reduction originating exclusively from the paralyzed muscle fiber populations, is compromised by the changes of active sarcomeres leading to a smaller net force reduction. Moreover, such "compromise to force reduction" varies as a function of muscle length and is a key determinant of muscle length dependence of force reduction caused by BTX. Due to longer sarcomere effect, muscle optimum length tends to shift to a lower muscle length. Muscle fiber-extracellular matrix interactions occurring via their mutual connections along full peripheral fiber lengths (i.e., myofascial force transmission) are central to these effects. Our results may help improving our understanding of mechanisms of how the toxin secondarily affects the muscle mechanically., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Effects of extramuscular myofascial force transmission on the acute effects of aponeurotomy were studied using finite element modeling and implications of such effects on surgery were discussed. Aponeurotomized EDL muscle of the rat was modeled in two conditions: (1) fully isolated (2) with intact extramuscular connections. The specific goal was to assess the alterations in muscle length-force characteristics in relation to sarcomere length distributions and to investigate how the mechanical mechanism of the intervention is affected if the muscle is not isolated. Major effects of extramuscular myofascial force transmission were shown on muscle length-force characteristics. In contrast to the identical proximal and distal forces of the aponeurotomized isolated muscle, substantial proximo-distal force differences were shown for aponeurotomized muscle with extramuscular connections (for all muscle lengths F (dist) > F (prox) after distal muscle lengthening). Proximal optimal length did not change whereas distal optimal length was lower (by 0.5 mm). The optimal forces of the aponeurotomized muscle with extramuscular connections exerted at both proximal and distal tendons were lower than that of isolated muscle (by 15 and 7%, respectively). The length of the gap separating the two cut ends of the intervened aponeurosis decreases substantially due to extramuscular myofascial force transmission. The amplitude of the difference in gap length was muscle length dependent (maximally 11.6% of the gap length of the extramuscularly connected muscle). Extramuscular myofascial force transmission has substantial effects on distributions of lengths of sarcomeres within the muscle fiber populations distal and proximal to the location of intervention: (a) Within the distal population, the substantial sarcomere shortening at the proximal ends of muscle fibers due to the intervention remained unaffected however, extramuscular myofascial force transmission caused a more pronounced serial distribution towards the distal ends of muscle fibers. (b) In contrast, extramuscular myofascial force transmission limits the serial distribution of sarcomere lengths shown for the aponeurotomized isolated muscle in the proximal population. Fiber stress distributions showed that extramuscular myofascial force transmission causes most sarcomeres within the aponeurotomized muscle to attain lengths favorable for higher force exertion. It is concluded that acute effects of aponeurotomy on muscular mechanics are affected greatly by extramuscular myofascial force transmission. Such effects have important implications for the outcome of surgery performed to improve impeded function since muscle in vivo is not isolated both anatomically and mechanically.

Finite element modeling of aponeurotomized rat extensor digitorium longus muscle was performed to investigate the acute effects of proximal aponeurotomy. The specific goal was to assess the changes in lengths of sarcomeres within aponeurotomized muscle and to explain how the intervention leads to alterations in muscle length-force characteristics. Major changes in muscle length-active force characteristics were shown for the aponeurotomized muscle modeled with (1) only a discontinuity in the proximal aponeurosis and (2) with additional discontinuities of the muscles' extracellular matrix (i.e., when both myotendinous and myofascial force transmission mechanisms are interfered with). After muscle lengthening, two cut ends of the aponeurosis were separated by a gap. After intervention (1), only active slack length increased (by approximately 0.9 mm) and limited reductions in muscle active force were found (e.g., muscle optimum force decreased by only 1%) After intervention (2) active slack increased further (by 1.2 mm) and optimum length as well (by 2.0 mm) shifted and the range between these lengths increased. In addition, muscle active force was reduced substantially (e.g., muscle optimum force decreased by 21%). The modeled tearing of the intramuscular connective tissue divides the muscle into a proximal and a distal population of muscle fibers. The altered force transmission was shown to lead to major sarcomere length distributions [not encountered in the intact muscle and after intervention (1)], with contrasting effects for the two muscle fiber populations: (a) Within the distal population (i.e. fibers with no myotendinous connection to the muscles' origin), sarcomeres were much shorter than within the proximal population (fibers with intact myotendinous junction at both ends). (b) Within the distal population, from proximal ends of muscle fibers to distal ends, the serial distribution of sarcomere lengths ranged from the lowest length to high lengths. In contrast within the proximal population, the direction of the distribution was reversed. Such differences in distribution of sarcomere lengths between the proximal and distal fiber populations explain the shifts in muscle active slack and optimal lengths. Muscle force reduction after intervention (2) is explained primarily by the short sarcomeres within the distal population. However, fiber stress distributions showed contribution of the majority of the sarcomeres to muscle force: myofascial force transmission prevents the sarcomeres from shortening to nonphysiological lengths. It is concluded that interfering with the intramuscular myofascial force transmission due to rupturing of the intramuscular connective tissue leads to a complex distribution of sarcomere lengths within the aponeurotomized muscle and this determines the acute effects of the intervention on muscle length-force characteristics rather than the intervention with the myotendinous force transmission after which the intervention was named. These results suggest that during surgery, but also postoperatively, major attention should be focused on the length and activity of aponeurotomized muscle, as changes in connective tissue tear depth will affect the acute effects of the intervention.

Certain recent studies showed that extra-muscular myofascial force transmission affects the length-force characteristics of rat extensor digitorium longus (EDL) muscle significantly after distal or proximal lengthening. This suggested that the relative position of a muscle with respect to its surrounding connective tissues is a co-determinant of muscle force in addition to muscle length, and indicated major effects on muscular mechanics. The specific goal of the present study is to investigate such effects by studying: (1) distributions of lengths of sarcomeres within muscle fibres and (2) the relative contributions of muscle fibres and the extra-cellular matrix to muscle total force, using a finite element model. The length of the muscle modelled was kept constant at a high and at a low muscle length whereas the relative position of the muscle was altered exclusively. For both muscle lengths, the forces exerted at distal and proximal tendons were unequal at almost all muscle relative positions. The proximo-distal force difference was enhanced as the muscle was repositioned away from its reference position. This confirmed the role of relative position of a muscle as a co-determinant of muscle force. At higher muscle lengths, distributions of lengths of sarcomeres arranged in series within muscle fibres were substantial. The force transmitted by the muscles' extra-cellular matrix comprised a sizable part of muscle total force. At lower muscle lengths distribution of sarcomere lengths was relatively limited indicating that the extra-cellular matrix is bearing the extra-muscular force. However, minor sarcomere length changes were shown to accumulate to sizable effects on the summed forces exerted by the muscle fibres. In addition, the extra-muscular load was shown to manipulate the force exerted by the extra-cellular matrix. We conclude that the relative position of a muscle has substantial effects on intra-muscular mechanics and the importance of the role of the extra-cellular matrix in determining the proximo-distal force differences is comparable to that of the intra-cellular domain.

Background: Myofascial force transmission occurs between muscles (intermuscular myofascial force transmission) and from muscles to surrounding nonmuscular structures such as neurovascular tracts and bone (extramuscular myofascial force transmission). The purpose was to investigate the mechanical role of the epimuscular connections (the integral system of inter- and extramuscular connections) as well as the isolated role of extramuscular connections on myofascial force transmission and to test the hypothesis, if such connections are prestrained., Method of Approach: Length-force characteristics of extensor hallucis longus (EHL) muscle of the rat were measured in two conditions: (I) with the neighboring EDL muscle and epimuscular connections of the muscles intact: EDL was kept at a constant muscle tendon complex length. (II) After removing EDL, leaving EHL with intact extramuscular connections exclusively., Results: (I) Epimuscular connections of the tested muscles proved to be prestrained significantly. (1) Passive EHL force was nonzero for all isometric EHL lengths including very low lengths, increasing with length to approximately 13% of optimum force at high length. (2) Significant proximodistal EDL force differences were found at all EHL lengths: Initially, proximal EDL force = 1.18 +/- 0.11 N, where as distal EDL force = 1.50 +/- 0.08 N (mean +/- SE). EHL lengthening decreased the proximo-distal EDL force difference significantly (by 18.4%) but the dominance of EDL distal force remained. This shows that EHL lengthening reduces the prestrain on epimuscular connections via intermuscular connections; however; the prestrain on the extramuscular connections of EDL remains effective. (II) Removing EDL muscle affected EHL forces significantly. (1) Passive EHL forces decreased at all muscle lengths by approximately 17%. However, EHL passive force was still non-zero for the entire isometric EHL length range, indicating pre-strain of extramuscular connections of EHL. This indicates that a substantial part of the effects originates solely from the extramuscular connections of EHL. However, a role for intermuscular connections between EHL and EDL, when present, cannot be excluded. (2) Total EHL forces included significant shape changes in the length-force curve (e.g., optimal EHL force decreased significantly by 6%) showing that due to myofascial force transmission muscle length-force characteristics are not specific properties of individual muscles., Conclusions: The pre-strain in the epimuscular connections of EDL and EHL indicate that these myofascial pathways are sufficiently stiff to transmit force even after small changes in relative position of a muscle with respect to its neighboring muscular and nonmuscular tissues. This suggests the likelihood of such effects also in vivo.

The effects of inter- and extramuscular myofascial force transmission on muscle length force characteristics were studied in rat. Connective tissues at the bellies of the experimental synergistic muscles of the anterior crural compartment were left intact. Extensor digitorium longus (EDL) muscle was lengthened distally whereas tibialis anterior (TA) and extensor hallucis longus (EHL) were kept at constant muscle-tendon complex length. Substantial differences were found in EDL force measured at the proximal and distal tendons (maximally 46% of the proximal force). EDL with intact inter- as well as extramuscular connections had an increased length range between active slack and optimum length compared to EDL with extramuscular connections exclusively: optimum muscle length was shifted by more than 2 mm. Distal EDL lengthening caused the distal force exerted by TA+EHL complex to decrease (approximately 17% of the initial force). This indicates increased intermuscular myofascial force transmission from TA+EHL muscle complex to EDL muscle. Finite-element modeling showed that: (1) Inter- and extramuscular myofascial force transmission leads to a substantial distribution of the lengths of the sarcomeres arranged in series within muscle fibers. Distribution of stress within the muscle fibers showed that the muscle fiber cannot be considered as a unit exerting equal forces at both ends. (2) Increased heterogeneity of mean fiber sarcomere lengths (i.e., a "parallel" distribution of length of sarcomeres among different muscle fibers) is found, particularly at high muscle lengths. This also explains the shift in muscle optimum length to higher lengths. It is concluded that inter- and extramuscular myofascial force transmission has substantial effects on muscle length-force characteristics.

Background: Effects of extramuscular connective tissues on muscle force (experimentally measured) and lengths of sarcomeres (modeled) were investigated in rat. It was hypothesized that changes of muscle-relative position affect the distribution of lengths of sarcomeres within muscle fibers., Method of Approach: The position of extensor digitorum longus muscle (EDL) relative to intact extramuscular connective tissues of the anterior crural compartment was manipulated without changing its muscle-tendon complex length., Results: Significant effects of EDL muscle relative position on proximal and distal EDL forces were found, indicating changes of extramuscular myofascial force transmission. EDL isometric force exerted at its proximal and distal tendons differed significantly. Finite-element modeling showed that the distribution of lengths of sarcomeres is altered by changes of muscle-relative position., Conclusions: It is concluded that forces exerted on a muscle via extramuscular myofascial pathways augment distributions of lengths of sarcomeres within that muscle.

In previous applications of the finite element method in modeling mechanical behavior of skeletal muscle, the passive and active properties of muscle tissue were lumped in one finite element. Although this approach yields increased understanding of effects of force transmission, it does not support an assessment of the interaction between the intracellular structures and extracellular matrix. In the present study, skeletal muscle is considered in two domains: (1) the intracellular domain and (2) extracellular matrix domain. The two domains are represented by two separate meshes that are linked elastically to account for the trans-sarcolemmal attachments of the muscle fibers' cytoskeleton and extracellular matrix. With this approach a finite element skeletal muscle model is developed, which allows force transmission between these domains with the possibility of investigating their interaction as well as the role of the trans-sarcolemmal systems. The model is applied to show the significance of myofascial force transmission by investigating possible mechanical consequences due to any missing link within the trans-sarcolemmal connections such as found in muscular dystrophies. This is realized by making the links between the two meshes highly compliant at selected intramuscular locations. The results indicate the role of extracellular matrix for a muscle in sustaining its physiological condition. It is shown that if there is an inadequate linking to the extracellular matrix, the myofibers become deformed beyond physiological limits due to the lacking of mechanical support and impairment of a pathway of force transmission by the extracellular matrix. This leads to calculation of a drop of muscle force and if the impairment is located more towards the center of the muscle model, its effects are more pronounced. These results indicate the significance of non-myotendinous force transmission pathways.

The aim of the present study was to develop a Hill type muscle model that accounts for the effects of shortening history. For this purpose, a function was derived that relates force depression to starting length, shortening amplitude and contraction velocity. History parameters were determined from short-range isokinetic experiments on rat medial gastrocnemius muscle (GM). Simulations of isokinetic as well as isotonic experiments were performed with the new model and a standard Hill type model. The simulation results were compared with experimental results of rat GM to evaluate if incorporation of history effects leads to improvements in model predictions. In agreement with the experimental results, the new model qualitatively described force reduction during and after isokinetic shortening as well as the experimental observation that isometric endpoints of isotonic contractions are attained at higher muscle lengths than is expected from the fully isometric length-force curve. Consequently, the new model gave a better quantitative prediction of the experimental results compared to the standard model. It was concluded that incorporation of history effects can improve the predictive power of a Hill type model considerably. The applicability of the model to conditions other than those described in the present paper is discussed.

Muscle architecture is an important aspect of muscle functioning. Hence, geometry and material properties of muscle have great influence on the force-length characteristics of muscle. We compared experimental results for the gastrocnemius medialis muscle (GM) of the rat to model results of simple geometric models such as a planimetric model and three-dimensional versions of this model. The capabilities of such models to adequately calculate muscle geometry and force-length characteristics were investigated. The planimetric model with elastic aponeurosis predicted GM muscle geometry well: maximal differences are 6, 1, 4 and 6% for fiber length, aponeurosis length, fiber angle and aponeurosis angle respectively. A slanted cylinder model with circular fiber cross-section did not predict muscle geometry as well as the planimetric model, whereas the geometry results of a second slanted cylinder model were identical to the planimetric model. It is concluded that the planimetric model is capable of adequately calculating the muscle geometry over the muscle length range studied. However, for modelling of force-length characteristics more complex models are needed, as none of the models yielded results sufficiently close to experimental data. Modelled force-length characteristics showed an overestimation of muscle optimum length by 2 mm with respect to experimental data, and the force at the ascending limb of the length force curve was underestimated. The models presented neglect important aspects such as non-linear geometry of muscle, certain passive material properties and mechanical interactions of fibers. These aspects may be responsible for short-comings in the modelling. It is argued that, considering the inability to adequately model muscle length-force characteristics for an isolated maximally activated (in situ) muscle, it is to be expected that prediction will fail for muscle properties in conditions of complex movement with many interacting factors. Therefore, modelling goals should be limited to the heuristic domain rather than expect to be able to predict or even approach medical or biological reality. However, the increased understanding about muscular mechanisms obtained from heuristic use of such simple models may very well be used in creating progress in, for example, clinical applications.

In models of the excitation of muscles it is often assumed that excitation during a tetanic contraction can be obtained by the linear summation of responses to individual stimuli from which the active state of the muscle is calculated. The purpose of this study was to investigate whether such a model adequately describes the process of excitation of muscle. Parameters describing the contraction dynamics of the muscle model used were derived from physiological and morphological measurements made on the gastrocnemius medialis muscle of three adult Wistar rats. Parameters pertaining to the excitation dynamics were optimized such that the muscle model correctly predicted force histories recorded during an isometric twitch. When a relationship between intracellular calcium and active state from literature on rat muscle was used, the muscle model was capable of generating force histories at stimulation frequencies of 20, 40, 60 and 80 Hz and other muscle-tendon complex lengths which closely matched those measured experimentally - albeit forces were underestimated slightly in all cases. Differences in responses to higher stimulation frequencies between animals could be traced back to differences in twitch dynamics between the animals and adequate predictions of muscle forces were obtained for all animals. These results suggest that the linear summation of responses to individual stimuli indeed gives an adequate description of the excitation of muscle.

In muscle modelling submaximal force exertion is often modelled on the basis of simple scaling of maximal length force characteristics. In such a case it is implicitly assumed that two basic physiological properties of muscle, i.e. length force characteristics and activity of the muscle by recruitment and firing rate coding are factors which independently determine actual muscle force. In this review it is argued that, on the basis of intracellular properties of muscle fibres as well as architectural variables of muscle morphology, muscle length force characteristics are affected in such a drastic way that the assumption of independence of these variables is no longer tenable.

Models are useful when studying how architectural and physiological properties of muscle-tendon complexes are related to function, because they allow for the simulation of the behaviour of such complexes during natural movements. In the construction of these models, evaluation of their accuracy is an important step. In the present study, a model was constructed to calculate the isometric force-length relationship of the rat extensor digitorum longus muscle-tendon complex. The model is based on the assumption that a muscle-tendon complex is a collection of independent units, each consisting of a muscle fibre in series with a tendon fibre. By intention, values for model parameters were derived indirectly, using only the measured maximal isometric tetanic force, the distance between origin and insertion at which it occurred (optimum lOI) and an estimate of muscle fibre optimal length. The accuracy of the calculated force-length relationship was subsequently evaluated by comparing it to the relationship measured in isometric tetanic contractions of a real complex in the rat. When the length of distal muscle fibres, measured during isometric contraction at optimal lOI of the whole complex, was used as an estimate for muscle fibre optimal length of all muscle fibre-tendon fibre units in the model, the calculated relationship was too narrow. That is, both on the ascending limb and on the descending limb the calculated tetanic force was lower than the measured tetanic force.(ABSTRACT TRUNCATED AT 250 WORDS)

A three-dimensional muscle model with complex geometry is described and tested against experimental data. Using this model, several muscles were constructed. These muscles have equal optimum length but differ in architecture. The force exerted by the constructed muscles, in relation to their actual length and velocity of shortening, is discussed. Generally speaking, the constructed muscles with considerable pennation have great fiber angles, a great physiological cross section, a narrow active and steep passive length-force relation, and a low maximal velocity of shortening. The maximal power (force times velocity) delivered by the constructed muscles is shown to be almost independent of the architecture of the muscles. The steepness of the passive length-force relation is determined mainly by the shortest fibers within the group of constructed muscles, whereas maximal velocity of shortening and the width of the active length-force relation are determined mainly by the longest fibers. The validity of the three-dimensional muscle model with respect to some morphological and functional characteristics is tested. Length-force relations of constructed muscles are compared with the actual length-force relations of mm. gastrocnemii mediales and mm. semimembranosi of male Wistar rats. Moreover, actual fiber angle, fiber length, and muscle thickness of three mm. gastrocnemii mediales are compared with values found for constructed muscles. It is concluded that the three-dimensional muscle model closely approximates the actual muscle form and function.

In explosive movements involving the lower extremity elastic recoil and transportation of power from knee to ankle via m. gastrocnemius allow power output about the ankle to reach values over and above the maximum power output of the plantar flexors. The object of this study was to estimate the relative power and work contributions of these two mechanisms for the push-off phase in one-legged jumping. During jumps of ten subjects ground reaction forces and cinematographic data were recorded. The data were used for a kinematic and kinetic analysis of the jumps yielding, among other variables, the velocity with which origins of m. soleus and m. gastrocnemius approach insertion (V OI), and net power output about the ankle (P A). V OI of m. soleus and m. gastrocnemius were imposed upon a model of the muscle-tendon complex of m. triceps surae, and power contributions of muscle fibers (P fibers), tendinous structures (P tendon), and transportation (P transported) were calculated. During the last 150 ms before toe-off, P A was found to increase rapidly and to attain an average peak value of 1790 W. The curve obtained by summation of P fibers, P tendon and P transported closely resembled that of P A. On the instant that the latter peaked (50 ms before toe-off) P fibers and P tendon of m. triceps surae contributed 27 and 53% respectively, and P transported contributed 20%.(ABSTRACT TRUNCATED AT 250 WORDS)

The purpose of this study was to gain more insight into the behavior of the muscle-tendon complex of human m. triceps surae in jumping. During one-legged vertical jumps of ten subjects ground reaction forces as well as cinematographic data were registered, and electromyograms were recorded from m. soleus and m. gastrocnemius. A model was developed of m. triceps surae, incorporating assumptions concerning dimensions, architecture, force-length and force-velocity relationships of muscle fibers, as well as assumptions concerning dimensions and elastic behavior of tendinous tissue in series with the muscle fibers. The velocity with which origin approaches insertion (V OI) was calculated for m. soleus and m. gastrocnemius using cine film data, and served as input of the model. During the last part of the push-off phase EMG-levels were found to be more or less constant, V OI of m. soleus and m. gastrocnemius rapidly increased, and the plantar flexing moment obtained by solving equations concerning a free body diagram of the foot rapidly declined. A similar decline was observed in the plantar flexing moment obtained by multiplying force calculated with help of the model by estimated moment arm at the ankle. As a result of the decline of exerted force tendon length decreases. According to the model the shortening velocity of tendon reaches higher values than that of muscle fibers. The results of a kinetic analysis demonstrate that during the last part of the push-off phase a combination of high angular velocities with relatively large plantar flexing moments is required. It is concluded that without a compliant tendon m. triceps surae would not be able to satisfy this requirement.

Force-velocity and force-length relations were obtained for the edl of four Wistar rats in order to characterise the contractile properties (CE) of these muscle-tendon complexes. Compliances of the undamped part of the series components (SE) were measured in quick length decreases. Force-extension relations of SEs were obtained by integration of compliance to force. A muscle model consisting of CE, SE and a visco-elastic element was used to simulate the force output of the muscle tendon complex in response to a changing muscle length lOI as input. This simulated force was compared with the experimental force of the same muscle measured in response to the same lOI as input. Tetanic contractions were used in all experiments. The results show that this muscle model can predict the experimental force within a mean maximal error not larger than approximately 14% of the force amplitude. However the comparison of simulated force with experimental force and a few additional experiments show that the muscles do not have a unique instantaneous force-velocity characteristic. As shown by several other studies, force seems to be influenced by many other variables (time, history etc.) than CE length and velocity.