A generalization of hooke's law in muscle elasticity

Experimental data concerning stress-strain relations of biological substances, including single muscle fibers, are reviewed in the literature. A reconsideration of the conclusions reached from these data is made. Thus, the experiments indicate that prima facie a linear theory of elasticity such as Hooke's law does not obtain because of the complicated form of the stress-strain curves. It is then shown that from a consideration oftrue stress at a point, where true stress is the force per unitactual area at the point, Hooke's law may be so generalized as to predict qualitatively and semi-quantitatively the complicated experimental curves. This complication arises from the long range “elasticity” of biological substances in general and muscle fibers in particular. Thus, substitutingtrue stress for stress, the stress-strain relation of muscle fibers remains linear. In the case of “small” strains, the true stress reduces to the usual stress concept in which the force is considered per unitinitial area at the point.     

A model for steady isometric muscle activation

The present model of the motoneuronal (MN) pool – muscle complex (MNPMC) is deterministic and designed for steady isometric muscle activation. Time-dependent quantities are treated as time-averages. The character of the model is continuous in the sense that the motor unit (MU) population is described by a continuous density function. In contrast to most already published models, the wiring (synaptic weight) between the input fibers to the MNPMC and the MNs (about which no detailed data are known) is deduced, whereas the input–force relation is given. As suggested by experimental data, this relation is assumed to be linear during MU recruitment, but the model allows other, nonlinear relations. The input to the MN pool is defined as the number of action potentials per second in all input fibers, and the excitatory postsynaptic potential (EPSP) conductance in MNs evoked by the input is assumed to be proportional to the input. A single compartment model with a homogeneous membrane is used for a MN. The MNs start firing after passing a constant voltage threshold. The synaptic current–frequency relation is described by a linear function and the frequency–force transformation of a MU by an exponential function. The sum of the MU contraction forces is the muscle force, and the activation of the MUs obeys the size principle. The model parameters were determined a priori, i.e., the model was not used for their estimation. The analysis of the model reveals special features of the activation curve which we define as the relation between the input normalized by the threshold input of the MN pool and the force normalized by the maximal muscle force. This curve for any muscle turned out to be completely determined by the activation factor, the slope of the linear part of the activation curve (during MU recruitment). This factor determines quantitatively the relation between MU recruitment and rate modulation. This property of the model (the only known model with this property) allows a quantification of the recruitment gain (Kernell and Hultborn 1990). The interest of the activation factor is illustrated using two human muscles, namely the first dorsal interosseus muscle, a small muscle with a relatively small force at the end of recruitment, and the medial gastrocnemius muscle, a strong muscle with a relatively large force at the end of recruitment. It is concluded that the present model allows us to reproduce the main features of muscle activation in the steady state. Its analytical character facilitates a deeper understanding of these features. Received: 24 November 1997 / Accepted in revised form: 30 November 1998     

Response time and threshold of a random net

The response time of a random net is defined as the expected time (measured in the number of synaptic delays) required for the excitation in the net (measured by the fraction of neurons firing per unit time) to reach a certain level. The response time is calculated in terms of the net parameters as a function of the intensity of the outside stimulation. Two principal types of cases are studied, 1) an instantaneous initial stimulation, and 2) continuously applied stimulation. It is shown that for a certain type of net where the required level of excitation is small, the response time-intensity equation reduces to the one derived on the basis of the “one-factor” theory applied to a neural connection. More general assumptions, however, give different types of equations. The concept of the “net threshold” is defined, and its calculation indicated. The net threshold for instantaneous stimulation is, in general, greater than that for continuous stimulation. The results are discussed with reference to existing theories of reaction times.     

Muscles within muscles: the neuromotor control of intra-muscular segments

The aim of this investigation was to anatomically identify, and then determine the function of, individual segments within the human deltoid muscle. The anatomical structure of the deltoid was determined through dissection and/or observation of the shoulder girdles of 11 male cadavers (aged 65–84 years). These results indicate that the deltoid consists of seven anatomical segments (D1–D7) based upon the distinctive arrangement of each segment's origin and insertion. Radiographic analysis of a cadaveric shoulder joint suggested that only the postero-medial segment D7 has a line of action directed below the shoulder joint's axis of rotation. The functional role of each individual segment was then determined utilising an electromyographic (EMG) technique. Seven miniature (1 mm active plate; 7 mm interelectrode distance) bipolar surface electrodes were positioned over the proximal portion of each segment's muscle belly in 18 male and female subjects (18–30 years). EMG waveforms were then recorded during the production of rapid isometric shoulder abduction and adduction force impulses with the shoulder joint in 40 degrees of abduction in the plane of the scapula. Each subject randomly performed 15 abduction and 15 adduction isometric force impulses following a short familiarisation period. All subjects received visual feed back on the duration and amplitude of each isometric force impulse produced via a visual force-time display which compared subject performance to a criterion force-time curve. Movement time was 400 ms (time-to-peak isometric force) at an intensity level of 50% maximal voluntary contraction. Temporal and intensity analyses of the EMG waveforms, as well as temporal analysis of the isometric force impulses, revealed the neuromotor control strategies utilised by the CNS to control the activity of each muscle segment. The results showed that segmental neuromotor control strategies differ across the breadth of the muscle and that individual segments of the deltoid can be identified as having either “prime mover”, “synergist”, “stabiliser” or “antagonist” functions; functional classifications normally associated with whole muscle function. Therefore, it was concluded that the CNS can “fine tune” the activity of at least six discrete segments within the human deltoid muscle to efficiently meet the demands of the imposed motor task. Accepted: 15 December 1997     

The inverse dynamics problem of neuromuscular control

The myoskeletal inverse dynamics problem and the myocybernetic control inverse problem were investigated with respect to their ill-posedness. The first problem consists of finding from observed experimental motion and reaction force data the resultant muscle moments that generated the observed motion, while the second aims at finding the corresponding neural controls. It is shown that both problems belong to the class of incorrectly posed (ill-posed) problems that, by definition, do not possess unique solutions. To illustrate this point, results of a forward dynamics simulation of a comprehensive neuromusculoskeletal model of the human body are presented. These results demonstrate that fairly chaotic neural control perturbations have very little influence on the resulting motion trajectory, at least in the present example. While a regularization procedure may be applied to solve successfully the myoskeletal inverse dynamics problem, the myocybernetic control inverse problem is unsolvable. The latter fact has the important implication that, based on the somatosensory inputs it receives, the pars intermedia in the cerebellum is not able to control individual motor unit stimulation rates and recruitment patterns but only whole muscles by means of a single compound signal. The latter signal is identified as the “common drive.” Presumably at the spinal level, special neural circuits are used to decompose the common drive signal into motor unit recruitment patterns and stimulation rates that are specific for a given mode of contraction and probably obey certain optimality principles. Received: 26 February 1999 / Accepted in revised form: 11 June 1999     

Motor unit recruitment for dynamic tasks: current understanding and future directions

Skeletal muscle contains many muscle fibres that are functionally grouped into motor units. For any motor task there are many possible combinations of motor units that could be recruited and it has been proposed that a simple rule, the ‘size principle’, governs the selection of motor units recruited for different contractions. Motor units can be characterised by their different contractile, energetic and fatigue properties and it is important that the selection of motor units recruited for given movements allows units with the appropriate properties to be activated. Here we review what is currently understood about motor unit recruitment patterns, and assess how different recruitment patterns are more or less appropriate for different movement tasks. During natural movements the motor unit recruitment patterns vary (not always holding to the size principle) and it is proposed that motor unit recruitment is likely related to the mechanical function of the muscles. Many factors such as mechanics, sensory feedback, and central control influence recruitment patterns and consequently an integrative approach (rather than reductionist) is required to understand how recruitment is controlled during different movement tasks. Currently, the best way to achieve this is through in vivo studies that relate recruitment to mechanics and behaviour. Various methods for determining motor unit recruitment patterns are discussed, in particular the recent wavelet-analysis approaches that have allowed motor unit recruitment to be assessed during natural movements. Directions for future studies into motor recruitment within and between functional task groups and muscle compartments are suggested.     

Steady states in random nets: I

A neural net is taken to consist of a semi-infinite chain of neurons with connections distributed according to a certain probability frequency of the lengths of the axones. If an input of excitation is “fed” into the net from an outside source, the statistical properties of the net determine a certain steady state output. The general functional relation between the input and the output is derived as an integral equation. For a certain type of probability distribution of connections, this equation is reducible to a differential equation. The latter can be solved by elementary methods for the output in terms of the input in general and for the input in terms of the output in special cases.     

Recognition of sex in the acoustic communication of the grasshopper Chorthippus biguttulus (Orthoptera, Acrididae)

Many gomphocerine grasshoppers communicate acoustically: a male's calling song is answered by a female which is approached phonotactically by the male. Signals and recognition mechanisms were investigated in Chorthippus biguttulus with regard to the cues which allow sex discrimination. (1) The stridulatory files on the hindfemur of both sexes are homologous in that they are derived from the same row of bristles, but convergent with respect to the “pegs”. In males the pegs are derived from the bristles, and in females from the wall of the bristle's cup. (2) Male and female songs are generated by similar, probably homologous motor programs, but differ in the duration, intensity, “gappyness” of syllables, risetime of pulses, and the frequency spectra. The hindleg co-ordination during stridulation and the resulting temporal song patterns are less variable in males than in females. (3) For both sexes, recognition of a mate's signal depends on species-specific syllable structure. For males it is essential that the female syllables consist of distinct short pulses, whereas females reject “gappy” syllables. Males strongly prefer “ramped” pulses, females respond to syllables irrespective of steeply or slowly rising ramps. Males react only to the low-frequency component, whereas females prefer spectra containing both, low and high frequency components. Accepted: 20 November 1996     

Motor unit recruitment during prolonged isometric contractions

Motor unit recruitment patterns were studied during prolonged isometric contraction using fine wire electrodes. Single motor unit potentials were recorded from the brachial biceps muscle of eight male subjects, during isometric endurance experiments conducted at relative workloads corresponding to 10% and 40% of maximal voluntary contraction (MVC), respectively. The recordings from the 10% MVC experiment demonstrated a characteristic time-dependent recruitment. As the contraction progressed both the mean number of motor unit spikes counted and the mean amplitude of the spikes increased significantly (P<0.01). This progressive increase in spike activity was the result of a discontinuous process with periods of increasing and decreasing activity. The phenomenon in which newly recruited motor units replace previously active units is termed motor unit rotation and appeared to be an important characteristic of motor control during a prolonged low level contraction. In contrast to the 10% MVC experiment, there was no indication of de novo recruitment in the 40% MVC experiment. Near the point of exhaustion a marked change in action potential shape and duration dominated the recordings. These findings demonstrate a conspicuous difference in the patterns of motor unit recruitment during a 10% and a 40% MVC sustained contraction. It is suggested that there is a close relationship between intrinsic muscle properties and central nervous system recruitment strategies which is entirely different in fatiguing high and low level isometric contractions.     

Recruitment patterns in Antarctic Peninsula shelf sediments: evidence of decoupling from seasonal phytodetritus pulses

Summer phytoplankton blooms on the West Antarctic Peninsula (WAP) shelf result in episodic deposition of labile food material for benthic detritivores. This summer deposition is thought to enhance benthic recruitment of macro- and megafauna. To explore seasonality in benthic recruitment, juvenile invertebrates (>100 μm) were collected in a seasonal time series at three stations on the WAP continental shelf. 4,098 juveniles were collected (average densities 2,000–7,000 m⁻²), with polychaetes dominant (2,581 individuals). The majority of polychaetes showed evidence of enhanced recruitment prior to the summer bloom, although patterns varied across stations. Additional taxa showed recruitment peaks in summer, but again, patterns varied among stations. Based on observed patterns, polychaete taxa are classified as “seasonal”, “marginally seasonal”, and “non-seasonal” recruiters, with the latter two patterns predominating. The year-round presence of small juveniles in most taxa suggests that recruitment occurs continuously, with periodic enhancement. Year-round recruitment is consistent with the presence of a persistent “food bank” of labile organic material in WAP shelf sediments, allowing recruitment to be largely decoupled from seasonal bloom dynamics.     

Relative amounts of sialic acid and fucose of amniotic fluid glycoconjugates in relation to pregnancy age

The present knowledge concerning the glycan structures and role of glycoconjugates derived from amniotic fluid is fragmentary and mainly focuses on the individual glycoproteins. The question has arisen as whether the general glycosylation pattern of amniotic fluid glycoconjugates can change with the progression of a normal pregnancy. In the present work we have described the dynamic, quantitative alterations in relative amounts of sialic acid and fucose linked by a variety of anomeric linkages to subterminal oligosaccharide structures of amniotic fluid glycoconjugates in relation to pregnancy age. The analysis was performed in the following groups of amniotic fluids derived from normal pregnancy by lectin dotting method: “2nd trimester” (14–19 weeks), “3rd trimester” (29–37 weeks), “perinatal period” (38–40 weeks) , “delivery at term” (39–41 weeks) and “post date pregnancy” (41–43 weeks). In the “3rd trimester” the amniotic fluid glycoconjugates contained higher relative amounts of glycans terminated by α2-6-linked sialic acid (p < 0.00002) and by α1-6 innermost fucose (p < 0.000001) than those in the 2nd trimester. In contrast, they showed the lower relative amount of fucose linked α1-3 (p < 0.02). At the perinatal period the relative amount of α2-6-linked sialic acid increased (p < 0.03), and it then decreased during delivery (p < 0.02) to the level found in the “3rd trimester” group. In the post date pregnancy all parameters studied increased. The sialyl- and fucosyl-glycotopes of the amniotic fluid glycoconjugates may play an critical role in growth and tissue remodeling of the foetus, as well as may might reflect maturation of a foetus. Additionally, a determination of the glycotope expressions might be helpful in prenatal diagnosis as predictor factors for well being of mother and child.     

Self-reproduction and serial message transfer: Two related problems

For a certain class of physical machines, termed “structure-determined,” the problem of self-reproduction can be reduced to the problem of serial message reproduction. Serial message reproduction however presupposes a sort of “open system” constraint. This leads to the principle of pseudo, or exogenously standardized, respectively, self-reproduction. It seems to be consistent with both chemical and biological self-reproduction. It thus may reflect a general principle of biological design. The proposed principle is a physico chemical analog to Robert Rosen's abstract relational self-reproduction constraint.     

Ultra-fastChara myosin: A test case for the swinging lever arm model for force production by myosin

Recent breakthroughs and technological improvements are rapidly generating evidence supporting the “swinging lever arm model” for force production by myosin. Unlike previous models, this model posits that the globular domain of the myosin motor binds to actin with a constant orientation during force generation. Movement of the neck domain of the motor is hypothesized to occur relative to the globular domain much like a lever arm. This intramolecular conformational change drives the movement of the bound actin. The swinging lever arm model is supported by or consistent with a large number of experimental data obtained with skeletal muscle or slime mold myosins, all of which move actin filaments at rates between 1 and 10 μm/sin vitro. Recently myosin was purified, fromChara internodal cells.In vitro the purifiedChara myosin moves actin filaments at rates one order of magnitude faster than the “fast” skeletal muscle myosin. While this ultra fast movement is not necessarily inconsistent with the swinging lever arm model, one or more specific facets of the motor must be altered in theChara motor in order to accommodate such rapid movement. These characteristics are experimentally testable, thus the ultra fast movement byChara myosin represents a powerful and compelling test of the swinging lever arm model.     

Field-induced forces at dielectric interfaces as a possible mechanism of RF hearing effects

A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.     

The effect of fast and slow motor unit activation on whole-muscle mechanical performance: the size principle may not pose a mechanical paradox

The output of skeletal muscle can be varied by selectively recruiting different motor units. However, our knowledge of muscle function is largely derived from muscle in which all motor units are activated. This discrepancy may limit our understanding of in vivo muscle function. Hence, this study aimed to characterize the mechanical properties of muscle with different motor unit activation. We determined the isometric properties and isotonic force–velocity relationship of rat plantaris muscles in situ with all of the muscle active, 30% of the muscle containing predominately slower motor units active or 20% of the muscle containing predominately faster motor units active. There was a significant effect of active motor unit type on isometric force rise time (p < 0.001) and the force–velocity relationship (p < 0.001). Surprisingly, force rise time was longer and maximum shortening velocity higher when all motor units were active than when either fast or slow motor units were selectively activated. We propose this is due to the greater relative effects of factors such as series compliance and muscle resistance to shortening during sub-maximal contractions. The findings presented here suggest that recruitment according to the size principle, where slow motor units are activated first and faster ones recruited as demand increases, may not pose a mechanical paradox, as has been previously suggested.     

Input output curves of aggregates of “simple counter” neurons

The refractory periods of an aggregate of simple “counter” neurons are assumed distributed according to some probability frequency. The output of the aggregate is computed for rectangular and triangular distributions. In particular, it is shown that the maximum output of an aggregate with any triangular distribution cannot exceed the maximum output of its average neuron by a factor greater than 2 ln 2. This puts an upper bound on the amount of departure from the behavior of the average neuron which an aggregate characterized by a certain type of distribution can show. Next, the aggregate is supposed to be subjected to regularly spaced stimuli. Under these conditions, a single neuron will give a discontinuous output curve. If, however, the refractory periods are distributed according to some frequency, the output curve may be “smoothed out.” A general condition on the distribution is derived which makes the output monotone increasing with the input. The condition is applied to some special cases.     

Energy-optimal controls in the mammalian neuromuscular system

The hypothesis is advanced that the specific patterns of motor unit recruitment and stimulation frequencies observed in mammalian skeletal muscle under static isometric contractions are determined by a minimum-energy principle. By performing a constrained energy optimization based on a control model of skeletal muscle comprising three different fibre types, and appropriate expressions for the energy rates, it is indeed possible to obtain detailed predictions of recruitment and stimulation frequency patterns which agree well with the experimentally observed functions, thereby providing strong support for the minimum-energy hypothesis. Since the orderly recruitment sequence determined by the size principle is also, independently, predicted by the minimum-energy principle, it is concluded that there exists a relationship between motor unit size and the myoenergetic properties of the recruited unit. It is suggested that this relationship, together with the possibility of adjusting the relative proportions of the fibre types present in a muscle, constitutes an optimal adaptation of the neuromuscular system for practically all types of muscular performances normally encountered. For various types of muscles, the energy rates as functions of the force output are also discussed.     

Contribution to the probabilistic theory of neural nets: I. Randomization of refractory periods and of stimulus intervals

Aggregates of neurons are considered in which the frequency of occurrence of neurons with a specified value of the refractory period follows certain probability distributions. Input-output functions are derived for such aggregates. In particular, if input and output intensities are defined in terms of stimulus frequencies and firing frequencies per neuron respectively, it is shown that a rectangular distribution of refractory periods leads to a logarithmic input-output curve. If input and output are defined in terms of the total number of stimuli and firings in the aggregate, it is shown how the “mobilization” picture leads to the logarithmic input-output curve. By randomizing the intervals between stimuli received by a single neuron and by introducing an inhibitory neuron a very simple “filter net” can be constructed whose output will be sensitive to a particular range of the input, and this range can be made arbitrarily small.     

Biosemiosis and the Cellular Basis of Mind

The human brain is a complex organ made up of neurons and several other cell types, and whose role is processing information for use in elicitation of behaviors. To accomplish this, the brain requires large amounts of energy, and this energy is obtained by the oxidation of glucose (Glc). However, the question of how the oxidation of Glc by individual neurons in brain results in their collective ability to rapidly generate feats of cognition that allow them to recognize the nature of the universe in which they live and to communicate this information remains unclear. In this article, insights into this process are provided by first considering the brain’ s homeostatic “operating system” for supply of energy to stimulated neurons, and how this system defines the basic unit of brain “structure”. This is followed by consideration of the brain’s “two-cell” neuronal communication mechanism which defines the basic unit of brain “function”. Finally, an analysis of the nature of frequency-encoded “neuronal languages” that enable ensembles of neurons to translate energy derived from the oxidation of Glc into a collective “mind”, the aggregate of all brain processes including those involving perception, thought, insight, foresight, imagination and behavior.