A 3D skeletal muscle model coupled with active contraction of muscle fibres and hyperelastic behaviour

This paper presents a three-dimensional finite element model of skeletal muscle which was developed to simulate active and passive non-linear mechanical behaviours of the muscle during lengthening or shortening under either quasi-static or dynamic condition. Constitutive relation of the muscle was determined by using a strain energy approach, while active contraction behaviour of the muscle fibre was simulated by establishing a numerical algorithm based on the concept of the Hill's three-element muscle model. The proposed numerical algorithm could be used to predict concentric, eccentric, isometric and isotonic contraction behaviours of the muscle. The proposed numerical algorithm and constitutive model for the muscle were derived and implemented into a non-linear large deformation finite element programme ABAQUS by using user-defined material subroutines. A number of scenarios have been used to demonstrate capability of the model for simulating both quasi-static and dynamic response of the muscle. Validation of the proposed model has been performed by comparing the simulated results with the experimental ones of frog gastrocenemius muscle deformation. The effects of the fusiform muscle geometry and fibre orientation on the stress and fibre stretch distributions of frog muscle during isotonic contraction have also been investigated by using the proposed model. The predictability of the present model for dynamic response of the muscle has been demonstrated by simulating the extension of a squid tentacle during a strike to catch prey.     

A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii

Biomechanical models generally assume that muscle fascicles shorten uniformly. However, dynamic magnetic resonance (MR) images of the biceps brachii have recently shown nonuniform shortening along some muscle fascicles during low-load elbow flexion (J. Appl. Physiol. 92 (2002) 2381). The purpose of this study was to uncover the features of the biceps brachii architecture and material properties that could lead to nonuniform shortening. We created a three-dimensional finite-element model of the biceps brachii and compared the tissue strains predicted by the model with experimentally measured tissue strains. The finite-element model predicted strains that were within one standard deviation of the experimentally measured strains. Analysis of the model revealed that the variation in fascicle lengths within the muscle and the curvature of the fascicles were the primary factors contributing to nonuniform strains. Continuum representations of muscle, combined with in vivo image data, are needed to deepen our understanding of how complex geometric arrangements of muscle fibers affect muscle contraction mechanics.     

Stress relaxation of heterogeneous myocardial tissue. Numerical experiments with 3D model

We present here the simple block model of a heterogeneous system describing the processes of stress relaxation in spatial and mechanically heterogeneous myocardial tissue. In numerical experiments by the model it is established that to obtain the same level of tension as in the case of a uniform model, less stiff and less viscous heterogeneous blocks are required. It is shown that in the model of heterogeneous myocardial tissue one observes not only stress relaxation but also strain relaxation—creep. Notably, step-by-step adjustment of the neighbor structural blocks in response to the whole model deformation takes place. Furthermore, stationary deformation properties of separated blocks become nonlinear.     

A method to quantify glucose utilization in vivo in skeletal muscle and white adipose tissue of the anaesthetized rat.

A quantitative method allowing determination of glucose metabolism in vivo in muscles and white adipose tissue of the anaesthetized rat is presented. A tracer dose of 2-deoxy[3H]glucose was injected intravenously in an anaesthetized rat and the concentration of 2-deoxy[3H]glucose was monitored in arterial blood. After 30-80 min, three muscles, the soleus, the extensor digitorum longus and the epitrochlearis, periovarian white adipose tissue and brain were sampled and analysed for their content of 2-deoxy[3H]glucose 6-phosphate. This content could be related to glucose utilization during the same time period, since (1) the integral of the decrease of 2-deoxy[3H]glucose in arterial blood was known and (2) correction factors for the analogue effect of 2-deoxyglucose compared with glucose in the transport and phosphorylation steps were determined from experiments in vitro. Glucose utilization was then measured by this technique in the tissues of post-absorptive rats in the basal state (0.1 munit of insulin/ml of plasma) or during euglycaemic-hyperinsulinaemic glucose clamp (8 munits of insulin/ml of plasma) and of 48 h-starved rats. Results corresponded qualitatively and quantitatively to the known physiological characteristics of the tissues studied.     

Intermuscular interaction via myofascial force transmission: effects of tibialis anterior and extensor hallucis longus length on force transmission from rat extensor digitorum longus muscle.

Force transmission in rat anterior crural compartment, containing tibialis anterior (TA), extensor hallucis longus (EHL) and extensor digitorum longus (EDL) muscles, was investigated. These muscles together with the muscles of the peroneal compartment were excited maximally. Force was measured at both proximal and distal tendons of EDL muscle as well as at the tied distal tendons of TA and EHL muscles (the TA + EHL complex). Effects of TA + EHL complex length and force on proximally and distally measured forces of EDL muscle kept at constant muscle-tendon complex length were assessed. Length changes of EDL muscle were imposed by movement of the proximal force transducer to different positions.Proximal EDL force was unequal to distal EDL force (active as well as passive) over a wide range of EDL muscle-tendon complex lengths. This is an indication that force is also transmitted out of EDL muscle via pathways other than the tendons (i.e. inter- and/or extramuscular myofascial force transmission). At constant low EDL length, distal lengthening of the TA + EHL complex increased proximal EDL force and decreased distal EDL force. At optimum EDL length, TA+EHL active force was linearly related to the difference between proximal and distal EDL active force. These results indicate intermuscular myofascial force transmission between EDL muscle and the TA + EHL complex. The most likely pathway for this transmission is via connections of the intact intermuscular connective tissue network. The length effects of the TA + EHL complex can be understood on the basis of changes in the configuration, and consequently the stiffness, of these connections. Damage to connective tissue of the compartment decreased the proximo-distal EDL force difference, which indicates the importance of an intact connective tissue network for force transmission from muscle fibers to bone.     

A novel 3D shape context method based strain analysis on a rat stomach model

The stomach has the ability to change its geometry and volume during digestion. Thus, the stomach shape changes dynamically due to changes in contents and due to pressure from adjacent organs. Full-field strain analysis is therefore important for accurate estimation of the true deformation in this highly non-homogeneous, anisotropic organ. The aim of this study is to introduce a modified non-rigid image registration based 3D shape context method combined with a full-field strain analysis method to describe a distension-induced 3D gastric deformation. The geometry of a normal rat stomach at distension pressures from 0.05 kPa to 0.8 kPa were obtained by ultrasonic scanning. The full-field strain distribution of the 3D gastric model between the reference state and the distended state were computed on the basis of the improved 3D shape context method and full-field strain analysis method. The registered surface showed a good agreement with the real deformed surface for all distension states. However, the errors increased with the distension pressure due to increasing dissimilarity between the deformed and the reference surface. The strain distributions on the stomach surface were non-uniform with the largest deformation in the non-glandular part and the greater and lesser curvature when the pressure was higher than 0.2 kPa. The wall stiffness of the non-glandular part was softer than that of the glandular part. The modelling analysis method which is closely allied with the non-rigid image registration and strain analysis provides a kinematically possible deformation mode of the gastric wall. This method can be potentially used for clinical data estimating the kinematical properties of the human visceral organs in health and disease.     

Effects of anabolic steroids and high intensity exercise on rat skeletal muscle fibres and capillarization. A morphometric study.

The effects were investigated of high intensity short duration exercise and anabolic steroid treatment on the medial gastrocnemius muscle of female rats. Twelve rats were divided equally into four groups, exercise with and without steroid administration and sedentary with and without steroid administration. Animals were made to swim for 5 weeks, 6 days.week-1. Muscle fibres were classified as slow-twitch (ST), fast-twitch oxidative glycolytic (FOG) and fast-twitch glycolytic (FG). Muscle fibre size was measured as the equivalent circle diameter. Exercise (P less than 0.001) and steroid (P less than 0.05) treatments alone, significantly elevated FOG and decreased FG fibre proportions. Overall proportions of fast-twitch and ST muscle fibres did not vary with any of the treatments. Significant differences in the proportion of muscle fibres were found to exist between different areas within the gastrocnemius muscle (P less than 0.05). Exercise and steroid treatments alone did not alter muscle fibre diameters. Combined exercise and steroid treatments did significantly increase ST fibre diameters (P less than 0.05). Exercise only treatment resulted in significant increases in the number of capillaries surrounding ST fibre (P less than 0.05) and FOG fibre (P less than 0.01) types. In conclusion the main finding of this study indicated that anabolic steroids in conjunction with high intensity swimming instigated ST fibre hypertrophy. Exercise and steroid only treatments significantly elevated FOG fibre proportions while FG fibre proportions diminished. Exercise only treatment resulted in significant increases in the number of capillaries surrounding both ST and FOG fibre types.     

Effect of short-term fasting on [123I] iodohexadecenoic acid metabolism in the isolated perfused rat heart. Validation of mathematical model by comparison with experimental measurements.

In order to study metabolic modifications induced by short term fasting and their consequences on the uptake and intracellular fate of fatty acids iodine labelled in omega position, rats undergo a 36h fasting. Hearts are perfused in a Langendorff system with a glucose (11 mM) perfusion medium; [123I] hexadecenoic acid (IHA) is injected as a bolus. A comparison between time-activity curves p.i. demonstrates a much faster activity decrease for the hearts fasted animals. The intracellular analysis shows that short fasting did not significantly increase the myocardial uptake of fatty acids, but decreased the storage and increased the degradation of the fatty acids taken up. Mathematical analysis of the myocardial time-activity curves obtained by external detection provided results comparable to those of intracellular analysis. The coefficients of correlation between the values of the aqueous phases, organic phases and free fatty acids measured by intracellular analysis and calculated with the compartmental model are consistently higher than 0.97. Consequently, this experimental model combined with mathematical analysis of the time-course of myocardial radioactivity after 123IHA administration appears to be very promising method for studying the effects of drugs or variations of energy substrate availability on myocardial fatty-acid metabolism.     

A comparative study of the myosin light chain kinases from myoblast and muscle sources. Studies on the kinases from proliferative rat myoblasts in culture, rat thigh muscle, and rabbit skeletal muscle.

Myosin light chain kinases have been isolated from rat thigh and rabbit skeletal muscle and cultured rat myoblasts. From these preparations, two types of kinases can be distinguished: calcium-dependent and calcium-independent. Both types of kinases can phosphorylate isolated P-light chains of myosin from several sources (skeletal muscle, cardiac muscle, and platelet). Data are shown which support the phosphorylation of the same site on the non-muscle P-light chains by both types of kinases. The rates of these reactins are, however, different for the two types of kinases. Kinetic analysis of the myoblast kinase shows differing affinities for various P-light chains (non-muscle greater than cardiac greater than skeletal). In the proliferative rat myoblast, phosphorylation of myosin is a prerequisite for actin activation of the myosin ATPase activity.     

Effect of ageing on the expression of protein kinase C and its activation by 1,25(OH)2-vitamin D3 in rat skeletal muscle

To characterize age-induced effects on muscle protein kinase C (PKC) and its regulation by the steroid hormone 1,25(OH)2-vitamin D3 [1,25(OH)2D3], changes in PKC activity and the expression and translocation of the specific PKC conventional isoforms alpha and beta, novel isoforms delta, epsilon, and theta and atypical isoform zeta were studied in homogenates and subcellular fractions from skeletal muscle of young (3 months) and aged (24 months) rats treated in vitro with 1,25(OH)2D3. The hormone (10(-9) M) increased total and membrane PKC activity, within 1 min, and these effects were completely blunted in muscle from aged rats. The presence of PKC isoenzymes was shown by Western blot analysis with the use of specific antibodies. The expression of PKC alpha, beta and delta was greatly diminished in old rats, whereas age-related changes were less pronounced in the isoforms epsilon, theta and zeta. After a short exposure (1 min) of muscle to 1,25(OH)2D3, increased amounts of PKC alpha and beta in muscle membranes and reverse translocation (from membrane to cytosol) of PKC epsilon were observed only in young animals. The data indicate that, in rat muscle, ageing impairs calcium-dependent PKC (alpha and beta) and calcium-independent PKC (delta, epsilon, theta and zeta) signal transduction pathways under selective regulation by 1,25(OH)2D3.     

Pharmacological inhibition of GSK-3 in a guinea pig model of LPS-induced pulmonary inflammation: II. Effects on skeletal muscle atrophy

Background

Chronic obstructive pulmonary disease (COPD) is accompanied by pulmonary inflammation and associated with extra-pulmonary manifestations, including skeletal muscle atrophy. Glycogen synthase kinase-3 (GSK-3) has been implicated in the regulation of muscle protein- and myonuclear turnover; two crucial processes that determine muscle mass. In the present study we investigated the effect of the selective GSK-3 inhibitor SB216763 on muscle mass in a guinea pig model of lipopolysaccharide (LPS)-induced pulmonary inflammation-associated muscle atrophy.

Methods

Guinea pigs were pretreated with either intranasally instilled SB216763 or corresponding vehicle prior to each LPS/saline challenge twice weekly. Pulmonary inflammation was confirmed and indices of muscle mass were determined after 12 weeks. Additionally, cultured skeletal muscle cells were incubated with tumor necrosis factor α (TNF-α) or glucocorticoids (GCs) to model the systemic effects of pulmonary inflammation on myogenesis, in the presence or absence of GSK-3 inhibitors.

Results

Repeated LPS instillation induced muscle atrophy based on muscle weight and muscle fiber cross sectional area. Intriguingly, GSK-3 inhibition using SB216763 prevented the LPS-induced muscle mass decreases and myofiber atrophy. Indices of protein turnover signaling were unaltered in guinea pig muscle. Interestingly, inhibition of myogenesis of cultured muscle cells by TNF-α or synthetic GCs was prevented by GSK-3 inhibitors.

Conclusions

In a guinea pig model of LPS-induced pulmonary inflammation, GSK-3 inhibition prevents skeletal muscle atrophy without affecting pulmonary inflammation. Resistance to inflammation- or GC-induced impairment of myogenic differentiation, imposed by GSK-3 inhibition, suggests that sustained myogenesis may contribute to muscle mass maintenance despite persistent pulmonary inflammation. Collectively, these results warrant further exploration of GSK-3 as a potential novel drug target to prevent or reverse muscle wasting in COPD.     

The effects of CDP-choline on newborn rat pups with experimental alcohol fetopathy. A Golgi study

Generally accepted features of alcoholic fetopathy are delayed maturation and retarded dendritic development of neocortex, hippocampus and cerebellum. The present study investigates the effects of a membrane stabilizing agent (CDP-choline) on Purkinje cells of chronically alcohol intoxicated newborn rat pups, employing a Golgi impregnation technique. Both quantitative and qualitative data indicate that CDP-choline modifies the alcohol induced lesion.     

A variant form of the 1,25-dihydroxyvitamin D3 receptor with low apparent hormone affinity in cultured monkey kidney cells (LLC-MK2). A model for tissue resistance to vitamin D

Chandler et al. (Chandler, J.S., Chandler, S.K., Pike, J.W., and Haussler, M.R. (1984) J. Biol. Chem. 259, 2214-2222) previously demonstrated that 1,25-dihydroxyvitamin D3 (1,25-(OH)2D3) caused the induction of 25-hydroxyvitamin D3-24-hydroxylase (24-hydroxylase) in a rhesus monkey kidney cell line (LLC-MK2) apparently deficient in the high affinity 1,25-(OH)2D3 receptor. We have re-examined this phenomenon and report here that 24-hydroxylase induction is mediated by a receptor variant in LLC-MK2 cells with low hormone affinity. Dose response analysis showed that in contrast to LLC-PK1 (a typical receptor-positive cell line), the LLC-MK2 line was less sensitive to 1,25-(OH)2D3 by 2 orders of magnitude. Employing optimal concentrations of 1,25-(OH)2D3 for 24-hydroxylase induction in each cell type, the early time courses of this bioresponse were identical in LLC-MK2 and LLC-PK1 and were consistent with a nuclear action of hormone-receptor complexes. Moreover, the rank order of potency of vitamin D3 congeners as inducers of 24-hydroxylase activity in LLC-MK2 cells agreed well with their relative affinity for the 1,25-(OH)2D3 receptor. An examination of 1,25-(OH)2D3 receptor content via DNA-cellulose chromatography in LLC-MK2 cells incubated at ligand concentrations 10-25-fold higher than the normal 2 nM revealed a minimum of 1600 receptor-like molecules/LLC-MK2 cell. These results show that LLC-MK2 cells possess a variant receptor form with apparent low affinity for 1,25-(OH)2D3. This system should serve as a model for clinical syndromes characterized by the requirement for massive doses of vitamin D to prevent rickets.     

A computational model for cell/ECM growth on 3D surfaces using the level set method: a bone tissue engineering case study

Three-dimensional open porous scaffolds are commonly used in tissue engineering (TE) applications to provide an initial template for cell attachment and subsequent cell growth and construct development. The macroscopic geometry of the scaffold is key in determining the kinetics of cell growth and thus in vitro ‘tissue’ formation. In this study, we developed a computational framework based on the level set methodology to predict curvature-dependent growth of the cell/extracellular matrix domain within TE constructs. Scaffolds with various geometries (hexagonal, square, triangular) and pore sizes (500 and 1,000  \(\upmu \) m) were produced in-house by additive manufacturing, seeded with human periosteum-derived cells and cultured under static conditions for 14 days. Using the projected tissue area as an output measure, the comparison between the experimental and the numerical results demonstrated a good qualitative and quantitative behavior of the framework. The model in its current form is able to provide important spatio-temporal information on final shape and speed of pore-filling of tissue-engineered constructs by cells and extracellular matrix during static culture.     

Molecular details of the activation of soluble phospholipase A2 on lipid bilayers. Comparison of computer simulations with experimental results.

The initial rate of hydrolysis of large unilamellar vesicles of dipalmitoylphosphatidylcholine by phospholipase A2 from the venom of Agkistrodon piscivorus piscivorus is small and elevates gradually until it suddenly increases by a factor of 10 to 1000 depending on the experimental conditions. This abrupt onset of high enzyme activity appears to be correlated to a specific mole fraction of reaction product at which point a cooperative compositional phase transition in the bilayer occurs. Five models that describe the activation process in terms of its being coupled to the putative product-induced lipid transition are presented. These models include one in which the lipid structure enhances the affinity of enzyme binding to the bilayer surface, two in which the equilibrium position between an active and an inactive form of the enzyme-substrate complex is altered, and two in which the rate of a quasi-irreversible spontaneous activation process is increased. Whether the active form of the enzyme is a monomer or dimer is also considered in the last two pairs of models. Computer simulations of time courses for the different models show how a set of four experimental observables distinguishes qualitatively among them. Comparison of the experimental behavior with the computer-simulated behavior of the observables for each model indicates that activation of phospholipase A2 on the lipid surface involves formation of an enzyme dimer which spontaneously converts to an active form. The active enzyme persists in the active state as it exchanges between vesicles. This model of activation is similar to that proposed previously for activation of porcine pancreatic phospholipase A2.