Search

The stomach is a central organ in the gastrointestinal tract that performs a variety of functions, in which the spatio-temporal organisation of active smooth muscle contraction in the stomach wall (SW) is highly regulated. In the present study, a three-dimensional model of the gastric smooth muscle contraction is presented, including the mechanical contribution of the mucosal and muscular layer of the SW. Layer-specific and direction-dependent model parameters for the active and passive stress-stretch characteristics of the SW were determined experimentally using porcine smooth muscle strips. The electrical activation of the smooth muscle cells (SMC) due to the pacemaker activity of the interstitial cells of Cajal (ICC) is modelled by using FitzHugh-Nagumo-type equations, which simulate the typical ICC and SMC slow wave behaviour. The calcium dynamic in the SMC depends on the SMC membrane potential via a gaussian function, while the chemo-mechanical coupling in the SMC is modelled via an extended Hai-Murphy model. This cascade is coupled with an additional mechano-electrical feedback-mechanism, taking into account the mechanical response of the ICC and SMC due to stretch of the SW. In this way the relaxation responses of the fundus to accommodate incoming food, as well as the typical peristaltic contraction waves in the antrum for mixing and transport of the chyme, have been well replicated in simulations performed at the whole organ level. STATEMENT OF SIGNIFICANCE: In this article, a novel three-dimensional electro-chemomechanical model of the gastric smooth muscle contraction is presented. The propagating waves of electrical membrane potential in the network ofinterstitial cells of Cajal (ICC) and smooth muscle cells (SMC) lead to a global pattern of change in the calciumdynamics inside the SMC. Taking additionally into account the mechanical response of the ICC and SMC due to stretch of the stomach wall, also referred to as mechanical feedback-mechanism, the result is a complex spatio-temporal regulation of the active contraction and relaxation of the gastric smooth muscle tissue. Being a firstapproach, in future view such a three-dimensional model can give an insight into the complexload transferring system of the stomach wall, as well as into the electro-chemomechanicalcoupling process underlying smooth muscle contraction in health and disease., (Copyright © 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.)

Muscle architecture parameters change when the muscle changes in length. This has multiple effects on the function of the muscle, e.g. on force production and on contraction velocity. Here we present a versatile geometrical model that predicts changes in muscle architecture as a consequence of length changes of the muscle on the basis of the known architecture at a given muscle length. The model accounts for small changes in aponeuroses' dimensions relative to changes in fascicle length and keeps muscle volume constant. We evaluate the model on the rabbit soleus muscle by comparing model predictions of fascicle lengths and pennation angles with experimental data. For this, we determined the internal architecture of the soleus muscle at different muscle belly lengths (67.8 mm at 35° ankle angle and 59.3 mm at 80° ankle angle). The long and the short soleus muscle exhibited mean fascicle lengths and pennation angles of 20.8 ± 1.3 mm, 4 ± 2° and 13.5 ± 1 mm, 10 ± 4°, respectively. The model predicted reasonable mean fascicle lengths and pennation angles for the long and short soleus that differed only by 1 mm and 1° from the measured data, respectively. Differences between predicted and measured distributions seem to stem from interindividual variability in muscle architecture. Even if the proposed approach has been used for the soleus muscle, which is relatively simple in architecture, it is not restricted to homogeneous unipennate architectures., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

An exceptional property of skeletal muscles that distinguishes them from other soft tissues is their ability to contract by generating active forces, which in turn are initiated by an electrochemical trigger. Some of these so-called active material properties are generally characterised using isometric contraction experiments at various muscle lengths. In this context, experimental observations revealed that unlike the widespread assumption in muscle modelling, reaction forces indeed depend on so-called history effects, which can be classified into force enhancement and force depression. For the experimental settings of force enhancement, two subsequent isometric contractions are interrupted by an isokinetic extension. The isometric reaction force is increased after the isokinetic extension with respect to a reference measurement, while in the case of force depression, isokinetic shortening is responsible for forces below a certain isometric reference measurement. Most theoretical investigations of force enhancement and force depression use one-dimensional models to simulate the force response considering muscle deformation to be homogeneous. In contrast, the aim of the present study is to analyse history effects in skeletal muscle tissue using a three-dimensional geometry model of the whole muscle-tendon unit. Therefore, a purely phenomenological approach is presented. The model is implemented in the finite element framework to analyse history effects for the boundary value problem of the entire three-dimensional muscle-tendon geometry. The constitutive model shows good agreement with the experimental data. Furthermore, the simulations reveal information about the inhomogeneous stretch distributions within the muscle tissues.

Recent studies demonstrated that uniaxial transverse loading (F G ) of a rat gastrocnemius medialis muscle resulted in a considerable reduction of maximum isometric muscle force (ΔF im ). A hill-type muscle model assuming an identical gearing G between both ΔF im and F G as well as lifting height of the load (Δh) and longitudinal muscle shortening (Δl CC ) reproduced experimental data for a single load. Here we tested if this model is able to reproduce experimental changes in ΔF im and Δh for increasing transverse loads (0.64 N, 1.13 N, 1.62 N, 2.11 N, 2.60 N). Three different gearing ratios were tested: (I) constant G c representing the idea of a muscle specific gearing parameter (e.g. predefined by the muscle geometry), (II) G exp determined in experiments with varying transverse load, and (III) G f that reproduced experimental ΔF im for each transverse load. Simulations using G c overestimated ΔF im (up to 59%) and Δh (up to 136%) for increasing load. Although the model assumption (equal G for forces and length changes) held for the three lower loads using G exp and G f , simulations resulted in underestimation of ΔF im by 38% and overestimation of Δh by 58% for the largest load, respectively. To simultaneously reproduce experimental ΔF im and Δh for the two larger loads, it was necessary to reduce F im by 1.9% and 4.6%, respectively. The model seems applicable to account for effects of muscle deformation within a range of transverse loading when using a linear load-dependent function for G., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

The urinary bladder is a central organ of vertebrates and imposes, based on its extreme deformation (volume changes up to several 100%), special requirements on the overall bladder tissue. However, studies focusing on three-dimensional modelling of bladder deformation and bladder function during micturition are rare. Based on three fields, namely, the membrane potential, calcium concentration, and placement, a mechano-electrochemical-coupled, three-dimensional model describing the contractile behaviour of urinary bladder smooth muscle is presented using a strain energy function. The strain energy functions for the different layers of the bladder wall are additively decomposed into a passive part comprising elastin, the extracellular matrix (ECM), and collagen and an active electrochemical-driven part comprising the contraction of smooth muscle cells (SMC). While the two-variable FitzHugh-Nagumo-type membrane model (FitzHugh, 1961; Nagumo et al., 1962) has been used to describe the membrane potential characteristics, the four-state, cross-bridge model of Hai and Murphy (1988) is implemented into the finite element method for the quantification of the calcium phase. Appropriate model parameters were determined experimentally using 40 tissue strips isolated from porcine bladders. Characteristic orientation-dependent passive and active stress-stretch relationships were identified for muscle strips, including the entire bladder wall structure and those featuring the isolated muscle layer only. Active experiments on the smooth muscle layers revealed higher stresses in the longitudinal (28.9kPa) direction than in the transversal (22.7kPa) one. Additionally, three-dimensional deformation characteristics were recorded from single muscle strips to qualitatively confirm the strip simulations. Three-dimensional simulations at the tissue strip level and the organ level were performed to analyse the interaction among the electrical action potential, calcium distribution, chemical degree of activation, and equivalent von Mises stress., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Contractions on the descending limb of the total (active + passive) muscle force-length relationship (i. e. when muscle stiffness is negative) are expected to lead to vast half-sarcomere-length inhomogeneities. This is however not observed in experiments-vast half-sarcomere-length inhomogeneities can be absent in myofibrils contracting in this range, and initial inhomogeneities can even decrease. Here we show that the absence of half-sarcomere-length inhomogeneities can be predicted when considering interactions of the semi-active protein titin with the actin filaments. Including a model of actin-titin interactions within a multi-scale continuum-mechanical model, we demonstrate that stability, accurate forces and nearly homogeneous half-sarcomere lengths can be obtained on the descending limb of the static total force-length relation. This could be a key to durable functioning of the muscle because large local stretches, that might harm, for example, the transverse-tubule system, are avoided.

Although recent research emphasises the possible role of titin in skeletal muscle force enhancement, this property is commonly ignored in current computational models. This work presents the first biophysically based continuum-mechanical model of skeletal muscle that considers, in addition to actin-myosin interactions, force enhancement based on actin-titin interactions. During activation, titin attaches to actin filaments, which results in a significant reduction in titin's free molecular spring length and therefore results in increased titin forces during a subsequent stretch. The mechanical behaviour of titin is included on the microscopic half-sarcomere level of a multi-scale chemo-electro-mechanical muscle model, which is based on the classic sliding-filament and cross-bridge theories. In addition to titin stress contributions in the muscle fibre direction, the continuum-mechanical constitutive relation accounts for geometrically motivated, titin-induced stresses acting in the muscle's cross-fibre directions. Representative simulations of active stretches under maximal and submaximal activation levels predict realistic magnitudes of force enhancement in fibre direction. For example, stretching the model by 20 % from optimal length increased the isometric force at the target length by about 30 %. Predicted titin-induced stresses in the muscle's cross-fibre directions are rather insignificant. Including the presented development in future continuum-mechanical models of muscle function in dynamic situations will lead to more accurate model predictions during and after lengthening contractions.

There exists several numerical approaches to describe the active contractile behaviour of skeletal muscles. These models range from simple one-dimensional to more advanced three-dimensional ones; especially, three-dimensional models take up the cause of describing complex contraction modes in a realistic way. However, the validation of such concepts is challenging, as the combination of geometry, material and force characteristics is so far not available from the same muscle. To this end, we present in this study a comprehensive data set of the rabbit soleus muscle consisting of the muscles' characteristic force responses (active and passive), its three-dimensional shape during isometric, isotonic and isokinetic contraction experiments including the spatial arrangement of muscle tissue and aponeurosis-tendon complex, and the fascicle orientation throughout the whole muscle at its optimal length. In this way, an extensive data set is available giving insight into the three-dimensional geometry of the rabbit soleus muscle and, further, allowing to validate three-dimensional numerical models.

In locomotion, humans have to deal with irregularities in the ground. When they encounter uneven terrain with changes in vertical height, they adjust the geometry of their legs. Recent investigations have shown that the preactivation of the gastrocnemius muscle (GM) correlates with the ankle angle at touchdown, but it is as of yet unclear why these adjustments were achieved by the GM and not by the preactivation of the tibialis anterior (TA). To examine the differences between TA regulation and GM regulation regarding (1) ankle angle adjustment and (2) joint stiffness, we used a three-segment musculoskeletal model with two antagonistic muscles (GM, TA). During the GM regulation, the ankle angle was adjusted from 121° to 109° (dorsiflexion) by a 41% decrease in the GM activation. During the TA regulation, the activation of TA must be increased by about 52%. In addition, we found that the ankle stiffness was most sensitive to changes in activation of the GM and decreased by about 20% while adjusting the angle. In contrast, the ankle stiffness remains similar when using TA regulation. Thus, the GM regulation is more adequate for adjustment in the ankle joint, enabling sufficient regulation of angle and stiffness.

Very recent measurements provided data on the ratio between the change in length of the active fibres and the lifting height of a mass compressing the muscle belly transversally to the direction of fibre contraction. In this study, we present additional data of the change in the third (unloaded) muscle dimension, extracted from the same contraction experiments. Using this data set for validation, we verify whether body models of two different geometries, cylindrical or ellipsoidal, can explain the three-dimensional deformation of a contracting muscle, when volume constancy is required as a constraint. Presetting the contractile length change and using this constraint, an additional equation is needed for model predictions. To that, we minimise the sum of the squared and weighted circumference length changes. With a specific set of the three penalty weights, it turns out that the ellipsoid model can explain the three-dimensional deformation. The set of penalty weights can also be interpreted as an anisotropic stiffness distribution of the connective tissue of the muscle belly. In various loading situations, our ellipsoidal model may help to predict the corresponding deformation scenarios or to calculate the stiffness distribution from measured load and deformation data., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Based on previous experimental results of independence on starting length of the tension gradient in constant-velocity stretches of active skeletal muscle at muscle lengths including the ascending limb and the plateau of the tension-length relation, a possible physiological mechanism determining the tension increase in lengthening active muscle is discussed. Considering the sliding filament theory, it is suggested that the tension-length relation of a half-sarcomere in lengthening contractions is different from that in isometric contractions. The assumed mechanism predicts, among others, that the thick filament retains its shortened length in lengthening contractions starting from a half-sarcomere length where this filament is compressed. An example model is implemented and checked with simulations., (Copyright 2010 Elsevier Ltd. All rights reserved.)

Hunting spiders are well adapted to fast locomotion. Space saving hydraulic leg extension enables leg segments, which consist almost soley of flexor muscles. As a result, the muscle cross sectional area is high despite slender legs. Considering these morphological features in context with the spider's segmented C-shaped legs, these specifics might influence the spider's muscle properties. Moreover, these properties have to be known for modeling of spider locomotion. Cupiennius salei (n = 5) were fixed in a metal frame allowing exclusive flexion of the tibia-metatarsus joint of the second leg (counted from anterior). Its flexing muscles were stimulated supramaximally using needle electrodes. Accounting for the joint geometry, the force-length and the force-velocity relationships were determined. The spider muscles produce 0.07 N cm maximum isometric moment (corresponding to 25 N/cm(2) maximum stress) at 160 degrees tibia-metatarsus joint angle. When overextended to the dorsal limit at approximately 200 degrees , the maximum isometric moments decrease to 72%, and, when flexed to the ventral hinge stop at 85 degrees , they drop to 11%. The force-velocity relation shows the typical hyperbolic shape. The mean maximum shortening velocity is 5.7 optimum muscle lengths per second and the mean curvature (a/F (iso)) of the Hill-function is 0.34. The spider muscle's properties which were determined are similar to those of other species acting as motors during locomotion (working range, curvature of Hill hyperbola, peak power at the preferred speeds), but they are relatively slow. In conjunction with the low mechanical advantage (muscle lever/load arm), the arrangement of three considerably actuated joints in series may nonetheless enable high locomotion velocities.

According to the state of the art model (single inverted pendulum) the regulation of quiet human stance seems to be dominated by ankle joint actions. Recent findings substantiated both in-phase and anti-phase fluctuations of ankle and hip joint kinematics can be identified in quiet human stance. Thus, we explored in an experimental study to what extent all three leg joints actually contribute to the balancing problem of quiet human stance. We also aimed at distinguishing kinematic from torque contributions. Thereto, we directly measured ankle, knee, and hip joint kinematics with high spatial resolution and ground reaction forces. Then, we calculated the six respective joint torques and, additionally, the centre of mass kinematics. We searched for high cross-correlations between all these mechanical variables. Beyond confirming correlated anti-phase kinematics of ankle and hip, the main results are: (i) ankle and knee joint fluctuate tightly (torque) coupled and (ii) the bi-articular muscles of the leg are well suited to fulfil the requirements of fluctuations around static equilibrium. Additionally, we (iii) identified high-frequency oscillations of the shank between about 4 and 8 Hz and (iv) discriminated potentially passive and active joint torque contributions. These results demonstrate that all leg joints contribute actively and concertedly to quiet human stance, even in the undisturbed case. Moreover, they substantiate the single inverted pendulum paradigm to be an invalid model for quiet human stance.

The sliding filament and crossbridge theories do not suffice to explain a number of muscle experiments. For example, from the entire muscle to myofibrils, predictions of these theories were shown to underestimate the force output during and after active tissue stretch. The converse applies to active tissue shortening. In addition to the crossbridge cycle, we propose that another molecular mechanism is effective in sarcomere force generation. We suggest that, when due to activation, myosin binding sites are available on actin, the giant protein titin's PEVK region attaches itself to the actin filament at those sites. As a result, the molecular spring length is dramatically reduced. This leads to increased passive force when the sarcomere is stretched and to decreased or even negative passive force when the sarcomere shortens. Moreover, during shortening, the proposed mechanism interferes with active-force production by inhibiting crossbridges. Incorporation of a simple 'sticky-spring' mechanism model into a Hill-type model of sarcomere dynamics offers explanations for several force-enhancement and force-depression effects. For example, the increase of the sarcomere force compared to the force predicted solely by the sliding filament and crossbridge theories depends on the stretch amplitude and on the working range. The same applies to the decrease of sarcomere force during and after shortening. Using only literature data for its parameterization, the model predicts forces similar to experimental results.

Compared to complex structural Huxley-type models, Hill-type models phenomenologically describe muscle contraction using only few state variables. The Hill-type models dominate in the ever expanding field of musculoskeletal simulations for simplicity and low computational cost. Reasonable parameters are required to gain insight into mechanics of movement. The two most common Hill-type muscle models used contain three components. The series elastic component is connected in series to the contractile component. A parallel elastic component is either connected in parallel to both the contractile and the series elastic component (model [CC+SEC]), or is connected in parallel only with the contractile component (model [CC]). As soon as at least one of the components exhibits substantial nonlinearities, as, e.g., the contractile component by the ability to turn on and off, the two models are mechanically different. We tested which model ([CC+SEC] or [CC]) represents the cat soleus better. Ramp experiments consisting of an isometric and an isokinetic part were performed with an in situ cat soleus preparation using supramaximal nerve stimulation. Hill-type models containing force-length and force-velocity relationship, excitation-contraction coupling and series and parallel elastic force-elongation relations were fitted to the data. To test which model might represent the muscle better, the obtained parameters were compared with experimentally determined parameters. Determined in situations with negligible passive force, the force-velocity relation and the series elastic component relation are independent of the chosen model. In contrast to model [CC+SEC], these relations predicted by model [CC] were in accordance with experimental relations. In conclusion model [CC] seemed to better represent the cat soleus contraction dynamics and should be preferred in the nonlinear regression of muscle parameters and in musculoskeletal modeling.

We evaluate an improved method for individually determining neuromuscular properties in vivo. The method is based on Hill's equation used as a force law combined with Newton's equation of motion. To ensure the range of validity of Hill's equation, we first perform detailed investigations on in vitro single muscles. The force-velocity relation determined with the model coincides well with results obtained by standard methods (r=.99) above 20% of the isometric force. In addition, the model-predicted force curves during work loop contractions very well agree with measurements (mean difference: 2-3%). Subsequently, we deduce theoretically under which conditions it is possible to combine several muscles of the human body to model muscles. This leads to a model equation for human leg extension movements containing parameters for the muscle properties and for the activation. To numerically determine these invariant neuromuscular properties we devise an experimental method based on concentric and isometric leg extensions. With this method we determine individual muscle parameters from experiments such that the simulated curves agree well with experiments (r=.99). A reliability test with 12 participants revealed correlations r=.72-.91 for the neuromuscular parameters (p<.01). Predictions of similar movements under different conditions show mean errors of about 5%. In addition, we present applications in sports practise and theory.

Estimation of muscle parameters specifying force-length and force-velocity behavior requires in general a large number of sophisticated experiments often including a combination of isometric, isokinetic, isotonic, and quick-release experiments. This study validates a simpler method (ISOFIT) to determine muscle properties by fitting a Hill-type muscle model to a set of isovelocity data. Muscle properties resulting from the ISOFIT method agreed well with muscle properties determined separately in in vitro measurements using frog semitendinosus muscles. The force-length curve was described well by the results of the model. The force-velocity curve resulting from the model coincided with the experimentally determined curve above approximately 20% of maximum isometric force (correlation coefficient R>0.99). At lower forces and thus higher velocities the predicted curve underestimated velocity. The stiffness of the series elastic component determined with direct experiments was approximately 10% lower than that determined by the ISOFIT method. Use of the ISOFIT method can decrease experimental time up to 80% and reduce potential changes in muscle parameters due to fatigue.