THE POTASSIUM EQUILIBRIUM IN MUSCLE

1. Analyses were made of the K and HCO₃ content, the irritability, and weight change of isolated frog sartorius muscles after immersion for 5 hours in Ringer''s solutions modified as to pH and potassium content. 2. At each pH a concentration of potassium in the solution was found which was in diffusion equilibrium with the potassium in the muscle. In greater concentrations potassium moved into the muscle against the concentration gradient and vice versa. 3. The greater the alkalinity of the solution the smaller the concentration of the potassium at equilibrium so that the product of the concentrations of OH and K in the solution at equilibrium tends to remain approximately constant. 4. The pH inside the muscle is approximately equal to that outside when first dissected but it tends to change during immersion so as to follow the changes in the pH of the solution. This finding is in direct conflict with the theory according to which the high potassium concentration inside should be accompanied by an equally high hydrogen ion concentration in relation to that outside. 5. The diffusion of potassium into the muscle makes its contents more alkaline but the increase in alkalinity is not always, nor usually, equivalent to the amount of potassium which has diffused and conversely, the pH inside can change in either direction according to the pH outside without there being any diffusion of potassium. Hence potassium is not the only penetrating ion. 6. The irritability of the muscles is at a maximum in concentrations of potassium which are greater than that in normal Ringer''s solution, or about 20 mg. per cent potassium. This optimum does not seem to be a function of pH and is therefore not dependent upon the direction of movement of the potassium but probably on the ratio of potassium outside to that inside. 7. Swelling of the muscles occurs in solutions which injure the muscle so as to permit both cations and anions to enter without permitting the organic protein anions to escape. Anion impermeability is necessary to prevent this same osmotic swelling under normal conditions. 8. An increase in the CO₂ tension in muscle and solution causes a greater increase in acidity in the solution than in the muscle and leads to a loss of potassium. One expects therefore a potassium shift from tissues to blood comparable to the chlorine shift from plasma to corpuscles.     

Morphological and Functional Questions on the Growth and Plasticity of Mammalian and Avian Jaw Muscles

SYNOPSIS: Growth studies of mammalian jaw muscles and studiesdetermining the degree of plasticity of these muscles are few.There are questions concerning the degrees and types of morphologicaland physiological change occurring in these muscles during normalgrowth and the ability of external forces to modify this growthprocess. There are also questions on the effects of sensoryloss on muscle growth and on changes in the motor system asthese muscles change. In this report, questions are proposedand hypotheses presented that deal with these areas relativeto the jaw muscles. It is suggested that (1) changes in themorphology and function of jaw muscles during growth vary regionallyand are related to the action of the muscle and the loadingforces imposed; (2) the degree of muscle plasticity varies regionallyand varies depending on the type of loading forces and age ofthe animal; (3) loss of sensory input during the growth of thejaw muscles would produce marked changes in the histochemicalprofile, the distribution of motor neurons, and the activitypattern of these muscles; and (4) organization of the trigeminalmotor nucleus changes as the jaw muscles grow and may also changein response to sensory loss or application of different typesof loading forces. In addition, possible approaches to thesequestions are discussed.     

Effects of lumbo-pelvic rhythm on trunk muscle forces and disc loads during forward flexion: A combined musculoskeletal and finite element simulation study

Previous in-vivo studies suggest that the ratio of total lumbar rotation over pelvic rotation (lumbo-pelvic rhythm) during trunk sagittal movement is essential to evaluate spinal loads and discriminate between low back pain and asymptomatic population. Similarly, there is also evidence that the lumbo-pelvic rhythm is key for evaluation of realistic muscle and joint reaction forces and moments predicted by various computational musculoskeletal models. This study investigated the effects of three lumbo-pelvic rhythms defined based on in-vivo measurements on the spinal response during moderate forward flexion (60°) using a combined approach of musculoskeletal modeling of the upper body and finite element model of the lumbosacral spine. The muscle forces and joint loads predicted by the musculoskeletal model, together with the gravitational forces, were applied to the finite element model to compute the disc force and moment, intradiscal pressure, annular fibers strain, and load-sharing. The results revealed that a rhythm with high pelvic rotation and low lumbar flexion involves more global muscles and increases the role of the disc in resisting spinal loads, while its counterpart, with low pelvic rotation, recruits more local muscles and engages the ligaments to lower the disc loads. On the other hand, a normal rhythm that has balanced pelvic and lumbar rotations yields almost equal disc and ligament load-sharing and results in more balanced synergy between global and local muscles. The lumbo-pelvic rhythm has less effect on the intradiscal pressure and annular fibers strain. This work demonstrated that the spinal response during forward flexion is highly dependent on the lumbo-pelvic rhythm. It is therefore, essential to adapt this parameter instead of using the default values in musculoskeletal models for accurate prediction of muscle forces and joint reaction forces and moments. The findings provided by this work are expected to improve knowledge of spinal response during forward flexion, and are clinically relevant towards low back pain treatment and disc injury prevention.     

Mechanically simulated muscle forces strongly stabilize intact and injured upper cervical spine specimens

Although muscles are assumed to be capable of stabilizing the spinal column in vivo, they have only rarely been simulated in vitro. Their effect might be of particular importance in unstable segments. The present study therefore tests the hypothesis that mechanically simulated muscle forces stabilize intact and injured cervical spine specimens. In the first step, six human occipito-cervical spine specimens were loaded intact in a spine tester with pure moments in lateral bending (+/- 1.5 N m), flexion-extension (+/- 1.5 N m) and axial rotation (+/- 0.5 N m). In the second step, identical flexibility tests were carried out during constant traction of three mechanically simulated muscle pairs: splenius capitits (5 N), semispinalis capitis (5 N) and longus colli (15 N). Both steps were repeated after unilateral and bilateral transection of the alar ligaments. The muscle forces strongly stabilized C0-C2 in all loading and injury states. This was most obvious in axial rotation, where a reduction of range of motion (ROM) and neutral zone to <50% (without muscles=100%) was observed. With increasing injury the normalized ROM (intact condition=100%) increased with and without muscles approximately to the same extend. With bilateral injury this increase was 125-132% in lateral bending, 112%-119% in flexion-extension and 103-116% in axial rotation. Mechanically simulated cervical spine muscles strongly stabilized intact and injured cervical spine specimens. Nevertheless, it could be shown that in vitro flexibility tests without muscle force simulation do not necessarily lead to an overestimation of spinal instability if the results are normalized to the intact state.     

Velocity-dependent cost function for the prediction of force sharing among synergistic muscles in a one degree of freedom model

Prediction of accurate and meaningful force sharing among synergistic muscles is a major problem in biomechanics research. Given a resultant joint moment, a unique set of muscle forces can be obtained from this mathematically redundant system using nonlinear optimization. The classical cost functions for optimization involve a normalization of the muscle forces to the absolute force capacity of the target muscles, usually by the cross-sectional area or the maximal isometric force. In a one degree of freedom model this leads to a functional relationship between moment arms and the predicted muscle forces, such that for constant moment arms, or constant ratios of moment arms, agonistic muscle forces increase or decrease in unison. Experimental studies have shown however that the relationship between muscle forces is highly task-dependent often causing forces to increase in one muscle while decreasing in a functional agonist, likely because of the contractile conditions and contractile properties of the involved muscles. We therefore, suggest a modified cost function that accounts for the instantaneous contraction velocity of the muscles and its effect on the instantaneous maximal force. With this novel objective function, a task-dependent prediction of muscle force distribution is obtained that allows, even in a one degree of freedom system, the prediction of force sharing loops, and simultaneously increasing and decreasing forces for agonist pairs of muscles.     

Jaw-muscle activity in ferrets, Mustela putorius furo.

Electromyographical (EMG) activity was recorded bilaterally from the masseter and temporalis muscles of alert ferrets (Mustela putorius furo) during mastication and crushing. Electromyographic activity was also recorded during biting while a bite-force transducer placed between the carnassial teeth registered forces ranging from 1.5 to 48.8 N. Linear regression analysis demonstrates that temporalis and masseter EMG activity are linearly related to bite force. Electromyographic activity from the balancing-side muscles is nearly equal to EMG activity of the working-side muscles during bone crushing with the carnassial teeth. It is hypothesized that a high percentage of balancing-side muscle activity in ferrets can be recruited during carnassial biting because the postglenoid process prevents ventral displacement of the working-side mandibular condyle.     

Myofascial force transmission: muscle relative position and length determine agonist and synergist muscle force.

Equal proximal and distal lengthening of rat extensor digitorum longus (EDL) were studied. Tibialis anterior, extensor hallucis longus, and EDL were active maximally. The connective tissues around these muscle bellies were left intact. Proximal EDL forces differed from distal forces, indicating myofascial force transmission to structures other than the tendons. Higher EDL distal force was exerted (ratio approximately 118%) after distal than after equal proximal lengthening. For proximal force, the reverse occurred (ratio approximately 157%). Passive EDL force exerted at the lengthened end was 7-10 times the force exerted at the nonlengthened end. While kept at constant length, synergists (tibialis anterior + extensor hallucis longus: active muscle force difference approximately -10%) significantly decreased in force by distal EDL lengthening, but not by proximal EDL lengthening. We conclude that force exerted at the tendon at the lengthened end of a muscle is higher because of the extra load imposed by myofascial force transmission on parts of the muscle belly. This is mediated by changes of the relative position of most parts of the lengthened muscle with respect to neighboring muscles and to compartment connective tissues. As a consequence, muscle relative position is a major codeterminant of muscle force for muscle with connectivity of its belly close to in vivo conditions.     

Development of a mathematical model that predicts optimal muscle activation patterns by using brief trains.

Because muscles must be repetitively activated during functional electrical stimulation, it is desirable to identify the stimulation pattern that produces the most force. Previous experimental work has shown that the optimal pattern contains an initial high-frequency burst of pulses (i.e., an initial doublet or triplet) followed by a low, constant-frequency portion. Pattern optimization is particularly challenging, because a muscle's contractile characteristics and, therefore, the optimal pattern change under different physiological conditions and are different for each person. This work describes the continued development and testing of a mathematical model that predicts isometric forces from fresh and fatigued muscles in response to brief trains of electrical pulses. By use of this model and an optimization algorithm, stimulation patterns that produced maximum forces from each subject were identified.     

Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses

There are different opinions in the literature on whether the cost functions: the sum of muscle stresses squared and the sum of muscle stresses cubed, can reasonably predict muscle forces in humans. One potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization-based models. In this study, the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees-of-freedom (DOF) model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function. Analytical results revealed that, generally, the non-zero optimal force of each muscle depends in a very complex non-linear way on moments at all three joints and moment arms and physiological cross-sectional areas (PCSAs) of all muscles. Deviations of the model parameters (moment arms and PCSAs) from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria, but also the number of non-zero forces in the optimal solution and the combination of muscles with non-zero predicted forces. Muscle force magnitudes calculated by both criteria were similar. They could change several times as model parameters changed, whereas patterns of muscle forces were typically not as sensitive. It is concluded that different opinions in the literature about the behavior of optimization-based models can be potentially explained by differences in employed model parameters.     

Electromyography and mechanics of mastication in the albino rat.

The masticatory apparatus in the albino rat was studied by means of electromyography and subsequent estimation of muscular forces. The activity patterns of the trigeminal and suprahyoid musculature and the mandibular movements were recorded simultaneously during feeding. The relative forces of the individual muscles in the different stages of chewing cycles and biting were estimated on the basis of their physiological cross sections and their activity levels, as measured from integrated electromyograms. Workinglines and moment arms of these muscles were determined for different jaw positions. In the anteriorly directed masticatory grinding stroke the resultants of the muscle forces at each side are identical; they direct anteriorly, dorsally and slightly lingually and pass along the lateral side of the second molar. Almost the entire muscular resultant force is transmitted to the molars while the temporo-mandibular joint remains unloaded. A small transverse force, produced by the tense symphyseal cruciate ligaments balances the couple of muscle resultant and molar reaction force in the transverse plane. After each grinding stroke the mandible is repositioned for the next stroke by the overlapping actions of three muscle groups: the pterygoids and suprahyoids produce depression and forward shift, the suprahyoids and temporal backward shift and elevation of the mandible while the subsequent co-operation of the temporal and masseter causes final closure of the mouth and starting of the forward grinding movement. All muscles act in a bilaterally symmetrical fashion. The pterygoids contract more strongly, the masseter more weakly during biting than during chewing. The wide gape shifts the resultant of the muscle forces more vertically and moreposteriorly. The joint then becomes strongly loaded because the reaction forces are applied far anteriorly on the incisors. The charateristic angle between the almost horizontal biting force and the surface of the food pellet indicates that the lower incisors produce a chisel-like action. Tooth structure reflects chewing and biting forces. The transverse molar lamellae lie about parallel to the chewing forces whereas perpendicular loading of the occlusal surfaces is achieved by their inclination in the transverse plane. The incisors are loaded approximately parallel to their longitudinal axis, placement that avoids bending forces during biting. It is suggested that a predominantly protrusive musculature favors the effective force transmission to the lower incisors, required for gnawing. By grinding food across transversely oriented molar ridges the protrusive components of the muscles would be utilized best. From the relative weights of the masticatory muscles in their topographical relations with joints, molars and incisors it may be concluded that the masticatory apparatus is a construction adapted to optimal transmission of force from muscles to teeth.     

Simulating the response of a standing operator to vibration stress by means of a biomechanical model

Under vibration stress the compressive forces transmitted in the joints of a standing operator are composed of nearly static and oscillating force parts. Because these forces can hardly be measured they were assessed by means of a biomechanical model. In the model, 27 rigid bodies with 103 degrees of freedom represent the segments of the human body. 106 force elements imitate the muscles of the trunk and the legs. At first, the model parameter were varied so that for the simulated sitting posture the model fits the seat-to-head transmissibility given in the literature and in ISO/CD 5982. For the standing posture, the transfer functions between the ground acceleration and the oscillating forces in the ankle, the knee, the hip, and the motion segment L3-L4 were computed. According to the moduli of these functions the forces in the ankles are higher than those in the knees or the hips and they nearly come up to the forces in the lumbar spine. Further the results of the simulation indicate that under equal vibration stress in the standing and the sitting posture the differences between the compressive forces in the lumbar spine are small.     

Oxidation of myosin heavy chain and reduction in force production in hyperthyroid rat soleus.

We tested the hypothesis that a force reduction in hyperthyroid rat soleus muscle would be associated with oxidative modification in myosin heavy chain (MHC). Daily injection of thyroid hormone [3,5,3'-triiodo-L-thyronine (T3)] for 21 days depressed isometric forces of whole soleus muscle across a range of stimulus frequencies (P < 0.01). In fiber bundles, hyperthyroidism also led to pronounced reductions (P < 0.01) in both K+ - and 4-chloro-m-cresol-induced contracture forces. The degrees of the reductions were similar between these two contractures that were induced by distinct reagents. Treatment with T3 elicited a significant decrease ( approximately 14%; P < 0.05) in the relative content of MHC contained in myofibrillar proteins. The content of carbonyl groups in myofibrillar protein extracts was elevated (P < 0.05) by approximately 50% in T3-treated muscles. Immunoblot analyses on T3-treated muscles showed a greater increase (106%; P < 0.05) of the carbonyl content in MHC than in myofibrillar protein extracts. These data suggest that in hyperthyroidism the decrease in force production of skeletal muscles may stem primarily from failure in myofibrillar protein function resulting from oxidative modification of MHC.     

Glenohumeral contact forces in reversed anatomy shoulder replacement

A major requirement to design an implant is to develop our understanding of the applied internal forces during everyday activities. In the absence of any basic apparatus for measuring forces directly, it is essential to rely on modelling. The major aim of this study was therefore to understand the biomechanical function of subjects with the reversed anatomy Bayley?Walker prosthesis, using an inverse dynamic shoulder model. In this context, the muscle and joint forces of 12 Bayley–Walker subjects were compared to those of 12 normal subjects during 12 activities of daily living.Maximum glenohumeral contact forces for normal and Bayley–Walker subjects were found to be 77% (±15) and 137% (±21) body weight for lifting a 2 kg shopping bag, and the least forces 29% (±4) and 67% (±8) body weight for reaching to opposite axilla, respectively. For normal subjects, middle deltoid, supraspinatus and infraspinatus were found to be the most active muscles across the subjects and tasks. On the other hand, for implanted subjects with a lack of rotator cuff muscles, the middle deltoid and coracobrachialis muscles were found to be the most active. The biomechanical model can therefore be used in order to gain knowledge about the pathology as well as possible post surgical rehab for subjects with reversed shoulder replacement.     

The functional significance of morphological variation of the human mandible and masticatory muscles

A review is given of what is known about the functional significance of variation of the morphology of the human mandible and jaw muscles. First, the mandible is a lever transferring muscular forces to the teeth. The angle between corpus and ramus and the width of the ramus are particularly relevant in this respect as they determine the mechanical advantage of the lever system and the capacity for sagittal (open-close) movement. The stability of the mandible in asymmetric bites is especially affected by the ratio between the intermolar and intercondylar distances. The repertoire of bite forces that can be generated at any tooth and the loading pattern of the temporomandibular joint are strongly dependent on the relative size of the masseter, temporalis and medial pterygoid muscles. Second, executing its function as a lever, the mandible is subjected to shearing, bending and torsional forces. The bony parts harbouring the teeth, joints and muscle attachments serve to counter these forces; additional strength is needed in three areas i.e. in the symphysis, the condylar neck and in the transition area between corpus and ramus. In human populations there are clear-cut patterns of correlation between some facial skeletal traits, jaw joint morphology and strength and line of action of the jaw muscles. As a result, facial morphologies can be distinguished with marked differences in mechanical performance of their masticatory apparatus. It is suggested that they emerge as a result of diverging environmental influences during postnatal growth.     

Individual muscle contributions to the axial knee joint contact force during normal walking

Muscles are significant contributors to the high joint forces developed in the knee during human walking. Not only do muscles contribute to the knee joint forces by acting to compress the joint, but they also develop joint forces indirectly through their contributions to the ground reaction forces via dynamic coupling. Thus, muscles can have significant contributions to forces at joints they do not span. However, few studies have investigated how the major lower-limb muscles contribute to the knee joint contact forces during walking. The goal of this study was to use a muscle-actuated forward dynamics simulation of walking to identify how individual muscles contribute to the axial tibio-femoral joint force. The simulation results showed that the vastii muscles are the primary contributors to the axial joint force in early stance while the gastrocnemius is the primary contributor in late stance. The tibio-femoral joint force generated by these muscles was at times greater than the muscle forces themselves. Muscles that do not cross the knee joint (e.g., the gluteus maximus and soleus) also have significant contributions to the tibio-femoral joint force through their contributions to the ground reaction forces. Further, small changes in walking kinematics (e.g., knee flexion angle) can have a significant effect on the magnitude of the knee joint forces. Thus, altering walking mechanics and muscle coordination patterns to utilize muscle groups that perform the same biomechanical function, yet contribute less to the knee joint forces may be an effective way to reduce knee joint loading during walking.     

The sensitivity of muscle force predictions to changes in physiologic cross-sectional area

The mechanical effects of a muscle are related in part to the size of the muscle and to its location relative to the joint it crosses. For more than a century, researchers have expressed muscle size by its 'physiological cross-sectional area' (PCSA). Researchers mathematically calculating muscle and joint forces typically use some expression of a muscle's PCSA to constrain the solution to one which is reasonable (i.e. a solution in which small muscles may not have large forces, and large muscles have large forces when expected or when there is significant electromyographic activity). It is obvious that muscle mass (and therefore any expression of PCSA) varies significantly from person to person, even in individuals of similar weight and height. Since it is not practical to predict the PCSA of each muscle in a living subject's limb or trunk, it is important to generally understand the sensitivity of muscle force solutions to possible variations in PCSA. We used nonlinear optimization techniques to predict 47 muscle forces and hip contact forces in a living subject. The PCSA (volume/muscle fiber length) of each of 47 lower limb muscle elements from two cadaver specimens and the 47 PCSA's reported by pierrynowski were input into an optimization algorithm to create three solution sets. The three solutions were qualitatively similar but at times a predicted muscle force could vary as much as two to eight times. In contrast, the joint force solutions were within 11% of each other and, therefore, much less variable.(ABSTRACT TRUNCATED AT 250 WORDS)     

Cardiac minute volume and its pattern in Rana ridibunda frogs

In frogs with an average body mass 56 g, the minute volume of the heart is equal to 4.5 ml/min X 100 g, which is approximately an order lower than in mammals with the same body mass. Pulmonary fraction constitutes 52% of the minute volume of the heart. The main bulk of systemic fraction of the minute volume of the heart (78%) passes to locomotor system and skin, whereas 19% of this volume are adressed to vegetative organs. This pattern of distribution significantly differs from that in mammals with a similar body mass, in which the vegetative and locomotor fractions are approximately equal. Differentiation in muscular blood supply was noted--there is a threefold difference in the volume of blood flow between gastrocnemius and submandibular muscles.     

Estimation of the forces generated by the thigh muscles for transtibial amputee gait

The forces generated by the muscles with origin on the human femur play a major role in transtibial amputee gait, as they are the most effective of the means that the body can use for propulsion. By estimating the forces generated by the thigh muscles of transtibial amputees, and comparing them to the forces generated by the thigh muscles of normal subjects, it is possible to better estimate the energy output needed from prosthetic devices. The purpose of this paper is to obtain the forces generated by the thigh muscles of transtibial amputees and compare these with forces obtained from the same muscles in the case of normal subjects. Two transtibial amputees and four normal subjects similar in size to the amputees were investigated. Level ground walking was chosen as the movement to be studied, since it is a common activity that most amputees engage in. Inverse dynamics and a muscle recruitment algorithm (developed by AnyBody Technology^®) were used for generating the muscle activation patterns and for computing the muscle forces. The muscle forces were estimated as two sums: one for all posterior muscles and one for the anterior muscles, based on the position of the muscles of the thigh relative to the frontal plane of the human body. The results showed that a significantly higher force is generated by the posterior muscles of the amputees during walking, leading to a general increase of the metabolic cost necessary for one step.     

Effect of aging on the recovery following contraction-induced injury in muscles of female mice.

By the age of 80 yr, the skeletal muscles of men and women decrease in mass and maximum force by approximately 30%. Severe contraction-induced injury may contribute to these age-related declines. One to two months after a 225 lengthening contraction protocol (LCP), muscles of young/adult male mice recovered completely, whereas those of old male mice sustained deficits of approximately 15% in mass and approximately 25% in maximum force. Although gender-related differences in the early events of contraction-induced injury have been reported, the recovery phase of muscles in old female animals has not been investigated. The hypothesis tested was that 2 mo after a severe LCP to the plantar flexor muscle group, the magnitude of recovery of mass and force for old female mice is less than that for adult female mice. The LCP was administered to muscles of adult and old, female C57BL/6 mice. At 3 days, 1 mo, and 2 mo following the LCP, maximum isometric force was measured, and muscles were removed and weighed. Two months following the LCP, the muscles of adult female mice recovered mass and force. In contrast, for old female mice, even after 2 mo, muscle masses were decreased by 11% and maximum forces by 38%. We conclude that, as reported previously for old male mice, a severe contraction-induced injury to muscles of old female mice results in prolonged deficits in mass and force.     

Analysis of human mandibular mechanics based on screw theory and in vivo data

In this paper the mechanics of human mandibular function is described in terms of the associated screws. The two distinct, yet related features of jaw mechanics, involving the motion itself as well as the forces, are both functions of the anatomical constraints, namely the contact areas that exist within the temporomandibular joint, and the forces of the muscles and tendons that allow motion to occur. The relationships that exist between these two aspects of jaw-motion are identified in this paper showing that muscle forces can be uniquely represented in terms of the action screw. This new approach to analyzing the mechanics of jaw-motion also incorporates the previously studied motion screw or helical axis. A consistent dynamic model is formulated where the action screw is used to represent the action of the closing muscle forces while the moment arms of the muscle forces are determined about the motion screw representing mandibular kinematics. The action screw formulation is verified using in vivo motion data and MR image information for a single asymptomatic subject. The results confirm the feasibility of the method and its application in dental research. A general increase in the mechanical advantage of most muscles, in the distance between action and motion screws as well as in the expended energy towards the end of the jaw-closing phase was observed. Asymmetries in the distribution of muscle force magnitudes appeared to influence the resultant force and moment of the action screw but had little effect on its spatial location. The method presented is intended to facilitate understanding of mandibular function and dysfunction.