Potential distribution and single-fibre action potentials in a radially bounded muscle model

In modelling the electrical behaviour of muscle tissue, we used to employ a frequency-dependent volume conductor network model, which was infinitely extended in all directions. Equations in this model could be solved using a finite-difference approach. The most important restriction of this model was the fact that no boundary effects could be incorporated. Analytical models of muscle tissue normally do not have this disadvantage, but in those models the microscopic structure of muscle tissue cannot be taken into account. In the paper, we present a combined numerical/analytical approach, which enables the study of potential distributions and SFAPs in simulated microscopic muscle tissue in which the influence of the muscle boundary has been considered. We considered muscle models with radii of 1.5 mm and 10 mm. Both models were compared with an unbounded network model. In the model with a radius of 1.5 mm we varied the position of the active fibre relative to the muscle surface. It appeared that in most cases the presence of a boundary had a considerable effect on the potential distribution. An increase in the peak-to-peak value of the SFAP amplitude up to 300 per cent was noticed when the active fibre was positioned 500 microns beneath the muscle surface in a model with a radius of 1.5 mm.     

Simulation of single muscle fibre action potentials

Using the volume conductor model, a single muscle fibre action potential can be expressed as a convolution of the transmembrane current and a weighting function. By simplifying the weighting function, the line source model is derived. We have developed similar expressions to compute the single muscle fibre action potential using simple models and physical considerations without any mathematical complexity. The relationship between the conduction velocity and amplitude is analysed and it is concluded that, for a given fibre, the amplitude is inversely proportional to the conduction velocity. This agrees with the experimental data reported in the literature. The relation between amplitude and fibre diameter is studied. The amplitude increases with diameter owing to the increase in membrane current, but it is counteracted by the increase in conduction velocity. Because of the opposing effects, a point of inflection in the amplitude/diameter relationship is observed. Squareroot, square and linear dependencies of conduction velocity on fibre diameter were used. The difference in the peak-to-peak amplitude with these relationships is small and a linear relation between amplitude and fibre diameter seems reasonable irrespective of the conduction velocity/fibre diameter relationship. The effect of lumping the transmembrane current at the axis of the fibre is discussed. This approximation results in an underestimation of the peak-to-peak amplitude near the surface, and the error is close to 50% for very large fibres. This error is accounted for in the model. The recording distance at which the peak-to-peak amplitude of the signal is 100 μV is found to be 400 μm in the model. This is in good agreement with values obtained from a single-fibre electrode recording. The model is computationally fast and precise. It can easily be used with few modifications to simulate single fibre action potentials recorded using different electrodes.     

Growth induced by incremental static stretch in adult rabbit latissimus dorsi muscle

Incrementally applied static stretch over 3 weeks resulted in a 72 % increase in the weight of the in situ latissimus dorsi muscle in rabbits. True growth rather than tissue oedema was confirmed by increases in the protein content (130 %), the cross-sectional area of the type I fibres (30 %) and the muscle length (i.e. number of sarcomeres in series increased 25 %). Despite an increase in the proportion of fibres staining positive for the enzyme succinate dehydrogenase (SDH), the myosin ATPase stain showed no appreciable fibre type transformation. While total power output in the stretched muscle was unchanged, its maximum mass specific power output, as determined by oscillatory work loops, was decreased by 50 %. The cross-sectional area that was occupied by connective tissue increased from 15 to 19 % in the stretched muscles, with a concomitant increase in passive energy dissipation. Some incrementally stretched muscles were then allowed an additional 3 weeks of maintained stretch to determine whether the adaptive changes would be preserved or reversed. Previous gains in muscle weight, length and area of type I fibres all remained. In contrast, the connective tissue content and the passive properties returned to control values during this period.     

Microfluorometric analyses of glycogen in freshly dissected, single skeletal muscle fibres of the cane toad using a mechanically skinned fibre preparation

The main objective of this study was to analyse glycogen in single muscle fibres, using a recently developed microfluorometric method which detects subpicomol amounts of NADPH, glucose and glycogen (as glucosyl units) (detection limit 0.16–0.17pmol in a 25nl sample) without fluorochrome amplification. The fibres were freshly dissected from the twitch region of the iliofibularis muscle of the cane toad (Bufo marinus), and were mechanically skinned under paraffin oil to gain access to the intracellular compartments. The results show that: (1) glycogen concentrations in toad skeletal muscle fibres range between 25.8 and 369mmol glucosyl units/litre fibre volume; (2) there is a large variation in glycogen content between individual fibres from the iliofibularis muscle of one animal; (3) there are seasonal differences in the glycogen content of toad single muscle fibres; (4) the total amount of glycogen in single muscle fibres of the toad does not decrease significantly when storing the tissue, under paraffin oil, at 20–25°C for up to 6h or at 4°C for up to 24h; and (5) 15–26% of fibre glycogen can be washed in an aqueous solution at pH 5–7, within 5min, while 74–85% of fibre glycogen remains associated with the washed skinned fibre, even after 40min exposure of the skinned fibre preparation to the aqueous environment. The retention of most glycogen in the fibre preparation after mechanical removal of the plasma membrane and extensive washing indicates that in toad skeletal muscle fibres the largest proportion of glycogen is tightly bound to intracellular structures. The results also show that the skinned muscle fibre preparation is well suited for microfluorometric glycogen determination, since low molecular weight non-glycogen contributors to the fluorescence signal can be removed from the myoplasmic space prior to the glycogen hydrolysis step.This revised version was published online in September 2005 with corrections to the Cover Date.     

Effect of spatial filtering on crosstalk reduction in surface EMG recordings

Increasing the selectivity of the detection system in surface electromyography (EMG) is beneficial in the collection of information of a specific portion of the investigated muscle and to reduce the contribution of undesired components, such as non-propagating components (due to generation or end-of-fibre effects) or crosstalk from nearby muscles. A comparison of the ability of different spatial filters to reduce the amount of crosstalk in surface EMG measurements was conducted in this paper using simulated signals. It focused on the influence of different properties of the muscle anatomy (changing subcutaneous layer thickness, skin conductivity, fibre length) and detection system (single, double and normal double differential, with two inter-electrode distances - IED) on the amount of crosstalk present in the measurements. A cylindrical multilayer (skin, subcutaneous tissue, muscle, bone) analytical model was used to simulate single fibre action potentials (SFAPs). Fibres were grouped together in motor units (MUs) and motor unit action potentials (MUAPs) were obtained by adding the SFAPs of the corresponding fibres. Interference surface EMG signals were obtained, modelling the recruitment of MUs and rate coding. The average rectified value (ARV) and mean frequency (MNF) content of the EMG signals were studied and used as a basis for determining the selectivity of each spatial filter. From these results it was found that the selectivity of each spatial filter varies depending on the transversal location of the measurement electrodes and on the anatomy. An increase in skin conductivity favourably affects the selectivity of normal double differential filters as does an increase in subcutaneous layer thickness. An increase in IED decreases the selectivity of all the analysed filters.     

Distributions of adipocyte, blood vessel, and muscle fiber in human lateral petrygoid muscle during ageing.

The composition of adipocyte, blood vessel, and muscle fiber during ageing from 30 to 90 years of age was examined by a computer analyzing system in human lateral petrygoid muscle. The human lateral petrygoid muscle, the intramuscular connective tissue with adipocyte and blood vessel, displayed a specific change in morphology during ageing. Numerous adipocyte appeared around the blood vessel in the perimysium of the human petrygoid muscle from 60 years of age. The percentage and size of adipocyte and vein per 10,000 micron 2 of the cross sectional area in the muscle increased as well. However, the cross sectional area of muscle fiber was almost constant. The increase of adipocyte was related with changes of blood vessel and connective tissue in the perimysium.     

Membrane properties underlying spontaneous activity of denervated muscle fibres

We have examined the events underlying the initiation of spontaneous action potentials (fibrillation) in fibres of previously denervated rat diaphragm maintained in organ culture for up to 10 days.1. Based on discharge pattern, two classes of spontaneously active fibres were found: rhythmically discharging fibres, and fibres in which action potentials occur at irregular intervals.2. Sites of action potentials initiation were located by exploration along the fibre length with two independent extracellular recording electrodes. The majority of sites of origin in both regular and irregular fibres were at the former end-plate zone; however, there was no region along the length that could not, at least in some fibres, be a site of origin.3. Intracellular recording at or near sites of origin of action potential discharge showed two types of initiating events. Irregularly discharging fibres were brought to threshold by discrete depolarizations of up to 15 mV in amplitude, while regularly occurring action potentials were associated with oscillations of the membrane potential.4. Discrete depolarizations (called fibrillatory origin potentials or f.o.p.s) at sites of origin in irregularly discharging fibres have the following properties: (a) random occurrence and nearly constant amplitude outside a refractory period during which both amplitude and probability of a second f.o.p. are reduced; (b) associated inward current flow which is localized to about 100 mum or less along the fibre length, and (c) dependence of amplitude and frequency on membrane potential.5. Oscillation of membrane potential found at sites of origin of action potential discharge in regular fibres also occurred locally along the fibre length and was sensitive to changes in membrane potential.6. Both f.o.p.s and oscillations of membrane potential were reversibly abolished by low Na(+)-Ringer fluid or tetrodotoxin.7. Neither type of initiating event was appreciably affected by concentrations of D-tubocurarine which blocked extrajunctional sensitivity to acetylcholine.8. We conclude that spontaneous action potentials under these conditions arise from a localized Na(+)-conductance change in the membrane of the active fibre; this conductance change is distinct from the increased Na(+)-conductance which follows the interaction of acetylcholine with its receptor. Spontaneous activity in single, denervated muscle fibres is cyclical and self-inhibiting (Purves & Sakmann, 1974); thus the Na(+)-conductance change underlying the initiation of spontaneous action potentials is affected by muscle fibre activity.     

Structural alterations in oedematous and apparently normal skeletal muscle of domestic Turkey

The morphology and histochemistry of oedematous and apparently normal turkey muscle were compared. Alterations in structural morphology were observed in the majority of the oedematous muscles and in about half the control muscles. Both the pectoralis thoracicus and biceps femoris were affected, with the former to a slightly greater extent. Histological features included proliferated endomysial and peri-mysial connective tissue, fatty replacement of necrotic areas of muscular tissue, evidence of fibre hypercontraction, necrosis of isolated fibres, shrunk and pyknotic nuclei and infiltration of the walls of blood vessels by mononuclear cells. In affected muscle, the histochemical reactions were weak and/or uniform amongst fibre types. There was no apparent association between the observed structural alterations and the oedematous condition.     

The complex Young's modulus of skeletal muscle fibre segments in the high frequency range determined from tension transients

Summary Stiffness measurements of muscle fibres are often based on application of a length change at one end of the muscle fibre and recording of the following tension change at the other end. In this study a method is developed to determine in the high frequency range (up to 40 kHz) the complex Young's modulus of skeletal muscle fibre as a function of frequency from the tension transient, following a rapid stepwise length change completed within 40 s. For this purpose both a new mechanical moving part of the displacement generating system and a force transducer with a high natural frequency (70 kHz) had to be developed. In addition to stiffness measurements of a silk fibre to test the displacement generating system and the method of analysis, stiffness of skeletal muscle fibres in relaxed and rigor state have been measured. The complex Young's moduli of relaxed muscle fibres as well as muscle fibres in rigor state are frequency dependent. In both cases the complex Young's modulus increases smoothly with increasing frequency over a range of 250 Hz up to 40 kHz. The phase angles of the responses remained almost constant at a value of 0.3 radians for a fibre in rigor and 0.6 radians for a relaxed fibre. This leads to the conclusion that for muscle fibres in rigor state the recovery in the tension response to a step length change shows a continuous distribution of relaxation times rather than a few discrete ones. Results of our stiffness measurements are compared with results obtained from current viscoelastic models used to describe stiffness of muscle fibre in this frequency range. The frequency dependence of stiffness of muscle fibres in rigor state suggests that the frequency used has to be taken into account while determining the elastic range of a crossbridge.     

Histochemical and ultrastructural characteristics of leg muscle fibres in patients with repairative abdominal aortic aneurysm (AAA)

Tibialis anterior (ta) muscle biopsies before and after elective abdominal aortic aneurysm (AAA) repair operation were obtained, in order to observe possible changes after the aortic declamping reperfusion. Open muscle biopsies were taken from each of eight patients (60-75 years old) which were processed for enzyme histochemistry, and for transmission electron microscopy (EM). Morphometric analysis was applied to estimate the number and the area of muscle fibres of each fibre type. Rectus abdominis muscle biopsies were served as controls. Before the operation the predominant elements found were the presence of atrophic muscle fibres, fibre size diversity, localised cellular reactions, increased extent of connective tissue, disappearance, in many cases, of the mosaic pattern, predominance of type I and oxidative fibres, and existence of fibres with core-like structures in the sarcoplasm. Type I fibres consisted of 66.95 +/- 9% of all muscle fibres, the mean cross sectional area of which was 3,372.8 +/- 1,016 microm(2) and of type II fibres was 3,786.5 +/- 6,046 microm(2). After the aortic clamping was performed mitochondrial swelling was found, as well as disorganisation of sarcomeres. After declamping of the aorta, there were also severe edema, local fibre necrosis, and adhesion of leucocytes, whereas muscle fibre areas became 3,935.18 micro 531 microm(2) for type I and 5,804 +/- 1,075 microm(2) for type II. The short ischemic period during aortic clamping and the subsequent reperfusion resulted mainly in ultrastructural changes.     

Some probability models for diagnosing neurogenic disorders

Healthy human skeletal muscles are composed of two distinguishable types of fibre, apparently randomly arranged within fascicles (bundles of fibres surrounded by connective tissue). Large groups of fibres of the same type indicate a neurogenic muscle disorder. An objective method for detecting nonrandom arrangements of fibres could improve the diagnosis of such disorders, particularly at an early stage. The number of enclosed fibres (NEF)--fibres surrounded by others of the same type--is considered here as a measure of nonrandomness. The distribution of NEF is shown to be approximately negative binomial for a non-free-sampling model, which is then compared with a free-sampling model studied previously. A modification for a known boundary effect is also investigated. The models are applied to data from m. vastus lateralis obtained post mortem from 24 previously healthy men. Finally, the relationship between size of biopsy and the accuracy of predictions is discussed.     

Changes in the distribution of synapses during growth: a quantitative morphological study of the neuromuscular system of fishes

The distribution of synaptic sites on multiply innervated muscle fibres was analysed in four teleost fish species (zebrafish, trout, goldfish and stickleback), using acetylcholinesterase histochemistry. Fishes were chosen for this study rather than other vertebrates because of their long period of growth and continuous increase of muscle fibre size. We found that length and diameter of the fibres increase linearly with fish length but that the distance between synaptic sites increases only as the square root of the fish length and of muscle fibre size. This is explained functionally in connection with the increase of the space constant of a muscle fibre that is expected to accompany the increase of its diameter. We suggest that the change in the synaptic distribution is caused by factors associated with the increasingly wider spread of postsynaptic potentials along the growing fibres, as the intersynaptic distance was found to correlate more strongly with fibre size than with other factors, such as age, speed of growth and genetical background.     

Characterisation of connective tissue from the hypertrophic skeletal muscle of myostatin null mice

Myostatin is a potent inhibitor of muscle development. Genetic deletion of myostatin in mice results in muscle mass increase, with muscles often weighing three times their normal values. Contracting muscle transfers tension to skeletal elements through an elaborate connective tissue network. Therefore, the connective tissue of skeletal muscle is an integral component of the contractile apparatus. Here we examine the connective tissue architecture in myostatin null muscle. We show that the hypertrophic muscle has decreased connective tissue content compared with wild-type muscle. Secondly, we show that the hypertrophic muscle fails to show the normal increase in muscle connective tissue content during ageing. Therefore, genetic deletion of myostatin results in an increase in contractile elements but a decrease in connective tissue content. We propose a model based on the contractile profile of muscle fibres that reconciles this apparent incompatible tissue composition phenotype.     

Classification of myositis. Correlations between morphological and clinical classifications of inflammatory muscle disease

Insufficient clinical data given to pathologists often hamper the differentiation of inflammatory muscle diseases. Thus we proved the value of a classification based only upon morphological criteria. Among 160 biopsies with myositic pattern (4.9% of a series of 3264 muscle biopsies) we could distinguish the following groups: Interstitial inflammation with only few fibre necroses (17.6%), predominance of fibre necroses with few inflammatory infiltrates (38.1%), small vessel vasculitis (20.0%), arteritis (13.1%), granulomatous myositis (8.8%) and polymorphonuclear leukocytic infiltrates (2.6%). This classification is compared with the used clinical diagnoses. Some special morphological aspects (histometric and immunocytologic examinations, tissue calcification, inclusion bodies, neurogenic atrophies) are analysed and so are some clinical peculiarities (e.g. malignoma-association, differentiation of mixed connective tissue syndrome, drug-induced reactions). The diagnostic value of purely morphologic criteria is restricted. For better diagnostic work a great number of clinical informations is required. Nevertheless, certain morphological patterns give important directions, e.g. to occult malignoma.     

Mechanical properties of passive rat muscle during sinusoidal stretching

The dynamic passive response of the left gastrocnemius medialis muscle of thirty male Wistar rats was studied as a function of muscle dimensions and absolute and relative amount of connective tissue. Values of the absolute active and passive length-force curves (active force, passive force, active working range) correlated well (coefficients of correlation in a range of 0.62–0.92) with morphological variables (such as muscle optimum length, mean muscle fibre optimum length, physiological cross section, muscle weight and amount of intramuscular connective tissue). To eliminate dimensional effects the active and passive length-force curves were normalized taking maximal active twitch force and muscle optimum length as reference values (100%). The width of the normalized active length-force curve (relative active working range) was correlated negatively with muscle weight, muscle optimum length and physiological cross section. Relative amount of connective tissue and passive tension at optimum length (both independent of muscle dimensions) were positively correlated, indicating that passive muscles are stiffer when relative amount of intramuscular connective tissue is higher. Sinusoidal movements with several amplitudes and frequencies of movement were imposed on the passive gastrocnemius medialis muscle over a range of muscle lengths. In accordance with the approximately exponential increase of static passive muscle force with length, muscle length has a large influence on the shape and magnitude of the hysteresis diagrams resulting from sinusoidal movements: the value of all variables selected increases approximately exponentially with muscle length with the exception of the value of loss tangent, a factor indicating the amount of energy dissipated during each cycle relative to the amount of energy stored and released elastically. Velocity of movement has only minor influence on variables of the hysteresis diagrams as is shown by changing the frequency of movement. As loss tangent and relative amount of connective tissue did not vary with muscle dimensions in the muscles studied, it is likely that material properties of the components causing passive resistance were similar in these muscles.     

A biomechanical model of agonist-initiated contraction in the asthmatic airway

This paper presents a modelling framework in which the local stress environment of airway smooth muscle (ASM) cells may be predicted and cellular responses to local stress may be investigated. We consider an elastic axisymmetric model of a layer of connective tissue and circumferential ASM fibres embedded in parenchymal tissue and model the active contractile force generated by ASM via a stress acting along the fibres. A constitutive law is proposed that accounts for active and passive material properties as well as the proportion of muscle to connective tissue. The model predicts significantly different contractile responses depending on the proportion of muscle to connective tissue in the remodelled airway. We find that radial and hoop-stress distributions in remodelled muscle layers are highly heterogenous with distinct regions of compression and tension. Such patterns of stress are likely to have important implications, from a mechano-transduction perspective, on contractility, short-term cytoskeletal adaptation and long-term airway remodelling in asthma.     

Some Probability Models for Diagnosing Neurogenic Disorders

Healthy human skeletal muscles are composed of two distinguishabletypes of fibre, apparently randomly arranged within fascicles(bundles of fibres surrounded by connective tissue). Large groupsof fibres of the same type indicate a neurogenic muscle disorder.An objective method for detecting nonrandom arrangements offibres could improve the diagnosis of such disorders, particularlyat an early stage. The number of enclosed fibres (NEF)—fibressurrounded by others of the same type—is considered hereas a measure of nonrandomness. The distribution of NEF is shownto be approximately negative binomial for a non-free-samplingmodel, which is then compared with a free-sampling model studiedpreviously. A modification for a known boundary effect is alsoinvestigated. The models are applied to data from m. vastuslateralis obtained post mortem from 24 previously healthy men.Finally, the relationship between size of biopsy and the accuracyof predictions is discussed.     

Muscle fibre damage and regeneration resulting from surgical limb distraction

Using an animal model of limb distraction, the extent of muscle fibre damage and atrophy resulting from distraction at two different rates (1.3 or 3.0 mm day(-1)) was investigated. It was found that at the high rate of distraction there was a significantly greater loss of range of joint movement and more muscle fibre atrophy and fibre damage than at the low rate. Muscle fibre damage is usually followed by regeneration. This involves the expression of the neonatal form of myosin heavy chain, which can therefore be used as an indicator of regeneration. It was found that whilst many more fibres showed evidence of damage at the high compared to the low rate, the number of fibres expressing neonatal myosin was significantly reduced, indicating the presence of a population of fibres which was undergoing degeneration without subsequent regeneration. Thus it would appear that beyond a certain rate of distraction, regeneration may be insufficient to replace contractile material damaged by overstretching. It is suggested that these fibres are replaced with connective tissue. This process may contribute to the muscle weakness and loss of range of joint movement which sometimes accompanies limb distraction procedures.     

Blood flow occlusion,maximal force production and EMG in two rat gastrocnemius muscle compartments

 The proximal and distal compartments of rat medial gastrocnemius muscle are dominated, respectively by, fast-twitch oxidative and fast twitch glycolytic fibres. In the present study it was hypothesized that repetitive in situ activation with an intact blood supply would cause greater declines in maximal tetanic force, compound action potential (CAP) amplitude and CAP area in the distal compared to the proximal compartment. Furthermore, it was hypothesized that these differences would be eliminated after occlusion of the blood supply to the muscle. A twitch followed by a tetanus (120 Hz, 200 ms duration) was given every 3 s for 2 min. This exercise protocol was applied once with, and once without, blood supply. During the first minute of the exercise, as expected, occlusion enhanced the decline of proximal force to 77.4 ± 0.8%, a level comparable (P>0.05) to the decline of distal force (79.7 ± 1.2%). In contrast with the hypothesis, CAP amplitude was not significantly affected by occlusion and it changed significantly less in the proximal (to 102.9 ± 4.5%) compared to the distal (to 69.0 ± 6.7%) compartment. During the second minute of activation without blood flow, sudden declines of distal CAP amplitude (to 18.4 ± 3.4%) coupled with parallel declines in force (to 17.6 ± 2.8%) were observed to occur in the distal but not in the proximal compartment. Proximal final force and CAP amplitude were 54.2 ± 2.6% and 80.6 ± 5.9% respectively. Thus, in contrast with the hypothesis, occlusion enhanced the differences between compartments. These results are discussed in relation to fibre type composition and metabolic changes. It is suggested that a loss of force caused by a decreased muscle fibre excitability upon repetitive activation depends not only on fibre type, but also on the intramuscular location of the fibres. Received: 20 March 1996 / Received after revision: 18 June 1996 / Accepted: 6 September 1996     

Tools for flash-photolysis experiments on voltage-clamped muscle fibre segments

An experimental set-up is described that allows the combination of rapid transmembrane voltage changes and photometric calcium recording with the fast photochemical turnover of substances applied externally or intracellularly to cut skeletal muscle fibres. It consists of a double-vaseline-gap system, designed for use with a xenon-flash-lamp device and a dual-wavelength microscope photometer. The pools of the vaseline gap chamber that contain the solutions surrounding the cut ends and the voltage-clamped segment of the muscle fibre are closed and have volumes of 20-50 microl. Thin tubes allow rapid solution change or continuous perfusion in the chamber compartments. Accessory tools were constructed to simplify focussing and measuring the flash-light intensity. A pilot light delivered from a red laser diode is used as a guide beam to target the ultraviolet (UV) flash to the preparation. The light distribution in the focal region and the relative changes in flash intensity with increasing numbers of flashes were quantified with an instrument that integrates the photo-current of a UV-sensitive silicon diode. The function of the set-up was demonstrated by measuring the efficiency of Ca2+ release from DM-nitrophen in quartz capillaries using the Ca(2+)-sensitive dye antipyrylazo III and by recording the flash-induced recovery of L-type calcium currents in muscle fibres blocked by the light-sensitive dihydropyridine drug nifedipine.