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`Human Movement Science 3 (1984) 119-153 North-Holland 119 EMG AND MUSCLE FORCE: AN INTRODUCTION * A.L. HOF Hof, A.L., 1984. EMG and muscle force: an introduction. Human Movement Science 3, 119-153. This paper is intended as an introduction to those methods of processing and presentation of the electromyogram (EMG) that give information about the muscle force or work in human move- ment. The physiological origin of the EMG is treated briefly, followed by a discussion of EMG recording and preprocessing: electrodes, preamplifier, rectifier, smoothing filter. Special attention is given to the prevention and suppression of interferences. The relation between EMG, muscle length and
`force is explained on the basis of a three-component Hill muscle model. With this background, some possibilities on how to obtain quantitative information about muscle force, work and energy consumption in various categories of movement are summed up and discussed. Some possible applications in human movement studies are suggested. Introduction Electromyography (EMG) is becoming more and more a standard tool in the study of human movement. Many researchers, nevertheless, seem to feel some reserve towards this technique. This is quite understanda- ble; at first sight the EMG signal seems erratic, badly reproducible and bearing little direct relation to the muscle force. It is therefore most of all used as a timing signal of the muscle activation; to determine whether the muscle is ‘on’ or ‘off’, or - at most - whether the activity is ‘small’ or ‘large’. The main purpose of this paper is to show that this approach does not do justice to the quantitative information that can be gained from the EMG. In fact there is a very close relationship * The kinetic analysis reported under Application A was performed in a joint project with C.N.A. Prank and J.A. van Best (Departments of Rehabilitation and Neurology, Erasmus University, Rotterdam). We thank Prof. dr. Jw. van den Berg, Prof. dr. ir. L. de Pater and L.N.H. Goeken MD for helpful comments. Author’s address: A.L. Hof, Laboratory of Medical Physics, Rijksuniversiteit Groningen. Bloemsingel 10. 9712 KZ Groningen. The Netherlands. 0167-9457/84/$3.00 0 1984, Elsevier Science Publishers B.V. (North-Holland)
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`between EMG and muscle force. That this relationship is somewhat complicated, is due to the complexities of the muscle contraction mechanics and not to deficiencies in the EMG. This paper is intended as an introduction to those methods of processing and presentation of the EMG that give quantitative informa- tion about the mechanical output of the muscle: force and work. It does not pretend the completeness of a review: this purpose is much better served by the recent paper of Perry and Bekey (1981) and the earlier review of Bouisset (1973). However, relevant papers since 1981 are included. There are more reviews that are of interest. As general introductions to EMG the book chapter by Grieve (1975) and the book of Basmajian et al. (1975) are recommended. Related review papers are the discussion on mathematical modelling of the EMG signal by De Luca (1979) and the extensive review on the neural control of muscular activity by Freund (1983). Indispensable for anyone working in the field of EMG is the ISEK report on units, terms and standards (Winter et al. 1980). After a brief account of the origin of the EMG, a description is given of the way in which it may be picked up, amplified and preprocessed. A few technical points are treated in some detail; they are rather trivial from an engineer’s point of view and therefore seldom mentioned in papers. For this reason they may easily be overlooked by investigators from other disciplines. The next section deals with the relation between EMG and muscle force. It can be seen as a summary and a generaliza- tion of the work of van den Berg and the present author (Hof and van den Berg 1981a, b, c, d). The final section sums up and discusses some possibilities on how to obtain quantitative information from the EMG about muscle force, work and energy consumption in various categories of movement. It concludes with some suggestions for applications.
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`The EMG
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`Introduction The EMG is the signal that can be recorded by electrodes from an active muscle. Branches of a nerve fibre each activate the motor endplate of a muscle fibre (fig. 1). This induces two depolarization waves which travel at a speed of 3-6 m/set to either end of the muscle fibre. The tissue between and around the active fibre is electrically
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`conductive. Electrical signals related to the fibre depolarization can therefore be recorded by electrodes at some distance from the fibre: the EMG. The depolarization wave is also led into the interior of the fibre by very fine transverse tubuli where it releases calcium ions which initiate the mechanical contraction process. The latter process is much slower than the electrical depolarization, which lasts only 2 msec. After a single depolarization the maximum force is not reached before 20-150 msec and the gradual decline of the force, due to reabsorption of the released calcium ions, takes at least twice as long. The mechani- cal processes as such are not accompanied by electrical phenomena. The course of events in a muscle contraction may to a certain extent be compared to that in an automobile engine. Here too, the electrical impulses cause the ‘ignition’ in each cylinder. When the electrical signals from the cylinders are recorded, it can be deduced whether the engine is active and - after more computation - what are the number of revolutions per minute. The power developed by the engine cannot be found from these ignition signals alone, however. Additional infor- mation about the mechanical load and about the properties of the engine is needed for this. The motor unit A skeletal muscle is composed of muscle fibres, groups of which are innervated by a single alpha-motor neuron. The motor neuron, which is 2 1 4 P motorneurones - actlon potential < > endplate zone Fig. 1. Schematic diagram of two motorunits. Unit no. 1 has just fired.
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`122 A. L. Hof/EMG und muscle force situated in the spinal cord, has a long axon which goes, combined with other axons in a nerve, to the muscle. There each axon splits up into a number of branches each of which ends on a motor endplate on a muscle fibre. The ensemble of a motor neuron and the muscle fibres it innervates is called the motor unit. As the firing of a motor neuron leads to a contraction of all muscle fibres of the unit, the motor unit can be called the basic functional unit in muscular contraction. The muscle fibres of one motor unit are scattered over a considerable area of the muscle cross section, intermingled with the fibres of some hundred other units. The motor units may have very different sizes, from a few fibres up to several thousands in large muscles. The mechanical and chemical properties are different among motor units. The small units are usually of the ‘slow unfatiguable’ type. The larger units can be ‘slow unfatiguable’, ‘fast unfatiguable’ or ‘fast fatiguable’. The composition varies between muscles, postural muscles are predomi- nantly slow, while muscles mainly involved in short and snappy con- tractions contain as a rule more fast fibres. There are differences between individuals as well, making some people apparently more fit for sprinting and others more for long-term activities. There are two ways of controlling muscle force: changing the number of active motor units (‘recruitment’) and changing the firing frequency of the active units (‘rate coding’). When a subject increases the force of a muscle the motor units are recruited one by one in order of magni- tude (‘size principle’). After recruitment the firing rate of each motor unit increases steadily with the exerted force. As a rule the units fire asynchronously. This course of events is reflected in the EMG (fig. 2). At very slight contraction (fig. 2a) only a few motor units are firing. At higher levels of activity so many units are active that at any instant the action potentials of several motor units overlap and a noise-like signal results, fig. 2b. This effect is analogous to what happens when one listens to the applause of an audience, at various levels of participation (‘ recruitment’) and enthusiasm (‘ firing rate’). Electrodes The main properties to be demanded from electrodes in quantitative EMG are a proper degree of selectivity and freedom from interferences, especially motion artefacts. The required amount of selectivity implies a compromise: the electrodes should record from the largest possible
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`force 125 smallest non-disposable types, which stick with double-sided adhesive rings [2]. These electrodes fulfil the rather strict requirements regarding freedom of motion artefacts. In recordings of ‘raw’ EMG, namely, interference is easily noticed and can be interpreted as such, but when the EMG has to be processed in some way the high peaks of the motion artefacts are very disturbing and it is difficult to get rid of them afterwards. One of the recommended countermeasures is high-pass filtering (Halbertsma and de Boer 1981), but it remains necessary to combat the evil at the root, by a good electrode. For muscles that are not accessible from the skin surface, for very small muscles and when regional differences within one muscle are to be studied, recording with fine-wire electrodes may be necessary. These electrodes consist of one (monopolar) or two (bipolar) very fine, iso- lated wires, 50 pm diameter, hooked and bare at the tips. They are inserted into the muscle with an injection needle, which is withdrawn afterwards. They are very selective, sometimes too much so, recording only from muscle fibres within some 0.3 mm from the bare ends of the wires (Gath and Stalberg 1979). This may include a sizeable number of motor units, for that matter, because of the scattered positions of the motor unit fibres. Drawbacks are motion artefacts, changes in sensitiv- ity, wire fractures due to movements within the muscle and above all their invasiveness, which makes them less acceptable to subjects. Check- ing their location in non-superficial muscles, moreover, is very difficult (Rozendal and Meijer 1982). Needle electrodes, finally, have all the drawbacks of wire electrodes to an even higher degree, which makes them plainly unsuitable for EMG that is to be processed. The amplifier The elements of the EMG preprocessing are given in fig. 3 and their required characteristics in table 1. It should be noted that these specifi- cations are guidelines for the types of EMG processing as discussed in this paper. A practical elaboration has been given by Halbertsma and de Boer (1981). Other methods - spectral analysis, single fibre record- ings - and special circumstances - high interference, telemetry - will make other demands. Not really a link in the preprocessing chain, but very practical, is monitoring the preamplified EMG by means of a [2] e.g. Beckmann Mini.
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`126 A. L. Hof/EMG and muscle force Table 1 EMG preprocessing. Component Property Minimum specification Remarks Electrodes Preamplifier Impedance Input impedance CMRR Noise Band-pass Lower limiting filter frequency Upper limiting frequency Rectifier Full-wave, range Low-pass filter Time constant (Whole unit) Total gain < 30 kQ at 50 Hz > 10 MQ at 50 Hz 1100 Ma at 50 Hz > 10.000 ( = 80 dB) < 5!J”& 30 Hz 600 Hz Up to 10 kHz 1:lOOO lo-25 msec Up to 1 set 0-20.000 Reduce by skin cleaning. abrasion Electrode cables up to 2 m Very short cables ( < 20 cm) 100 k.Q source resistance Reduces electrode artifacts Reduces noise. surface electrodes Wire electrodes Dynamic, fast/slow muscles Static Continuously variable loudspeaker. Movement artefacts and other sources of interference are easily recognized when listening. The specifications of the input preamplifier deserve some comment. A very important requirement for the first amplifier stage is a sufficient suppression of mains interference (‘hum’), which manifests itself as a 50/60 Hz common mode voltage on both input electrodes. In a preamplifier with a high Common Mode Rejection Ratio (CMRR) such a common mode signal is highly suppressed compared to the differen- tial EMG signal. The overall CMRR, however, is degraded when both electrode impedances Z, and Z, are not perfectly equal at 50/60 Hz, due to a voltage division with the preamplifier input impedance Z, (Huhta and Webster 1973). This degradation amounts to CMRR (inbalance) = Z,/( Z, - Z,) Differences Z, - Z, of 5 - 10 k!J can hardly electrodes. In order to achieve a CMRR over electrodes (4 be avoided with surface 10.000 a very high input band pass filter full-wove rectifier smoothing filter P ~ ground el e(t) Fig. 3. Block diagram of the EMG pre-processing. See text.
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`EMG and muscle force 127 impedance (more than 100 MQ) is therefore desirable, but this makes only sense if the preamplifier can be placed within a few cm of the electrodes. A shielded electrode cable of 1 metre, namely, has a capaci- tance of about 100 pF and therefore an impedance of only 30 ML? at 50/60 Hz. In such a case it is of little use to have an input impedance over 10 Ma, and one has to be satisfied with an effective CMRR of about 1000. This story may explain why a bad electrode contact manifests itself first of all by an increased hum and why long electrode cables can introduce hum, even if they are perfectly shielded. Rectifying and smoothing The third and fourth stages of the preprocessing scheme as proposed in fig. 3 are full-wave rectifying and low-pass filtering (‘smoothing’). Many investigators use this approach, but not all (see Perry and Bekey (1981) and the ISEK report (Winter et al. 1980)). A justification, based on a description of the EMG signal, (cf. fig. 2) is therefore needed. e(t) = I(t).t?(t) Here y1( t) is a stationary stochastic process with zero mean and unit variance. In more common terms this means that n(t) is a noise signal with unit intensity and with the characteristics of the EMG signal at constant contraction. I(t) is, in this formulation, the time-varying EMG intensity (in mV r.m.s.). The validity of the representation (3) is based on the fact that the characteristics of g(t), like the normalized ampli- tude distribution or the power spectrum, are not (or hardly) dependent on the EMG intensity I(t) or on the magnitude of the muscle force (Shwedyk et al. 1977; Hogan and Mann 1980b). Because of this and because of the experimental evidence to be discussed below, it will be assumed in what follows that the intensity I(t) of the EMG contains all necessary information to determine the muscle force. The only reserva- tion to be made is that no fatigue occurs. The restriction to the intensity of the EMG only is a consequence of the subject matter of this paper: the relation between EMG and force. It does not imply that the EMG power spectrum and related variables, like correlation functions and zero-crossing counts, do not contain interesting information. Only the extraction of the average motor unit firing frequency (Blinowska et al. 1979, van Boxtel and Schomaker
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`A. L. Hof/EMG and muscle force 1983) and the effects of fatigue, which deserve a review of their own, are here mentioned. All that can be done on the latter subject is to give some openings to the vast literature: Bigland-Ritchie et al. 1980; Porter and Whelan 1981; and Petrofsky et al. 1982. The simplest way to obtain an estimate of I(t) is to rectify the EMG and to smooth it subsequently by means of a low-pass filter. E(t) is then obtained, which is the smoothed version of I(t). Some smoothing is necessary because of the random character of e(r) which means that E(t) contains random fluctuations as well. Expressed as a fraction E of E(t) itself this amounts to (Kadefors 1973): & = 1/(2BT)“2 (r.m.s) (4) where
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`is the statistically equivalent bandwidth of the unprocessed EMG, which is usually between 100 and 300 Hz for surface electrodes. It can be seen that the smoothing filter must satisfy two conflicting requirements: it should smooth I(t) as little as possible and, on the other hand, it should have a long effective averaging time
`gives the fastest response (Kreifeldt 1971; Garland et al. 1972), but there may be valid reasons to choose some other type of filter. The simple first-order RC filter that is often used, is far from optimal, however. For studies of EMG in fast movements the smoothing time constant should be short and the random error must be accepted. For the human calf muscles, which have twitch contraction times around 100 msec, an averaging filter with 7r = 25 msec is used giving rise to (with
`280 Hz) an E of 27%. When the contractions only change slowly in strength, as in many isometric experiments, the filter time constant can be taken much longer, up to one second (with E around 5%). A reduction in the random fluctuations below the limit of eq. (4) seems possible but requires considerable effort:
`can be enlarged somewhat by intricate filtering techniques or the signals of several pairs of electrodes can be pooled (Hogan and Mann 1980a, b; Harba and Lynn 1981). When the EMG patterns are repeatable (but how to determine that?) the rectified EMGs can be averaged over some hundred contractions to obtain reasonably low E values, with hardly any pre- smoothing (Wadman et al. 1980; Erkelens and Bosman 1983).
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`is the effective averaging time of the smoothing filter and
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`130 A. L. HoJ/EMG and muscle force To determine g, it is obviously necessary that the muscle force be measurable. This is not always easy. The best way is to use a dynamo- meter, fixed rigidly to the limb, which can measure the moment of the force that the muscle exerts around a joint. Often it will be sufficient to use the EMG-joint moment relation thus obtained. When the muscle force is to be calculated, the musculo-skeletal geometry should be known. When no measuring device is available - not even a set of weights ~ or when calculation of the absolute muscle force is not possible, the smoothed rectified EMG can be expressed as a fraction of the EMG at a short maximum voluntary contraction (MVC), i.e., a contraction a motivated subject can hold for a few seconds. It will be clear that this is not a very rigid standard. For several muscles, e.g. the small finger muscles, the MVC seems to be quite reproducible. Our own experience with leg muscles is, however, that a slight discomfort in the limb fixation can prevent the subject - quite unaware ~ from exerting his real maximum force. Another complication is that there can be more muscle groups in a kinematic chain, and only one group forms the weakest link. When the load is held in the hand, for example, are the elbow flexors then determining the MVC, or the wrist flexors, or the shoulder muscles? This depends very much on the mechanical set-up. It may be remarked that in dynamical contractions the EMG can be higher than the level corresponding to 100% isometric MVC. Dynamic contractions The remarkably simple result (5) of the preceding paragraph holds only for a muscle that remains isometric, constant in length. In the general case with non-isometric contractions, however, the EMG alone is not sufficient to predict muscle force but the time course of the muscle length should be known as well. Contractions will be considered here in the widest sense, in which the time course of the muscle length and of the activation may have an arbitrary form. In the section to follow some special cases will be covered. In what follows, mathematical formulas could not be completely avoided, because they are at times the only way to express things briefly and unambiguously. Readers not familiar with this practice may be advised to skip them on first reading and to try to follow the argument by inspecting the figures. The basic idea of EMG-to-force-processing is (a) that it be assumed that the preprocessed EMG E(t) is an adequate measure of muscle
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`A. L. HoJ/EMG and nzuscle force 131 PEC load Fig. 4. Schematic diagram of the Hill muscle model. For symbols see Appendix. activation; (b) that the muscle length is determined in some way; and (c) that the muscle force from these two signals be calculated on the basis of a physiological model of the muscle. In the author’s laboratory it has been shown that this approach results in a reasonably accurate prediction of the muscle force for the human triceps surae (Hof and van den Berg 1981b, c, d). This in turn indicates that the assumption (a) is valid and that the muscle model (c) as used is suitable for the purpose. A short description of this model will be given. Details, discussion and references can be found in Hof and van den Berg (1981a). The Hill muscle model (fig. 4) consists of three components. The parallel elastic component (PEC) represents the elasticity of the passive muscle and the ligaments. The behaviour of the active muscle is determined by the contractile component (CC) and the series elastic component (SEC), which are connected in series. These model compo- nents should not too readily be interpreted as muscle structures. The tendon and the aponeuroses seem, indeed, to share the greater part of the SEC extension, but the muscle crossbridges are, also, somewhat compliant. The lengths of the elements are expressed as normalized lengths x = l/1,, in which
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`is the instantaneous muscle length and I, the length at a standardized position. Length changes of limb muscles can be calculated from joint angle changes [3]. From the arrangement [3] In order to obtain more generally applicable formulae and figures, the calf muscle data of Hof and van den Berg (1981a-d) are in the following expressed in forces and lengths: F= M/d and x = d/1,(71/2- 4)+1, with I, = shank length = 40 cm and d = lever arm of the calf muscles with respect to the ankle = 5 cm.
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`of the components in the diagram of fig. 4 it can be seen that x = x,. + x, (64 F= F,.+- F,, (6’4 further, that the PEC length is equal to the total muscle length x, and that the forces in CC and SEC are equal (= F). A different arrange- ment, with PEC parallel to CC, is also in use, but the differences with the author’s model are in practice very small. The parallel elastic component represents the properties of muscle, tendons and joint ligaments when the muscle is not active and is characterized by a load-extension F,(x)-diagram (fig. 5a). This relation can be modelled by an exponential function FP (x) = FP,,ep(x-‘) (7) or, where necessary, by a sum of more exponentials (Yoon and Mansour 1982), in which case F,(x) can become negative for a certain range of x. Usually the passive force will have a significant value only near the longest and shortest muscle lengths allowed in vivo. Force-length relation In an active muscle which is kept isometric, the muscle force depends on the muscle length, in fact on the length of the CC because the effect is due to a changing degree of overlap of the thick and thin filaments. Fig. 5b gives an example. This relation can be expressed as F,. =fb,.)F, (x, constant) (8) where the function f(x,.) has a value between 0 and 1. This function can be approximated by a broken line (as in fig. 5b), but also by a parabola (Woittiez et al. 1983) or by a Gaussian curve (Hatze 1981). The variable F, has a value equal to the isometric force at the maximum of the force-length relation. F, will be called the active state of the muscle and will be returned to later. Force-velocity relation As soon as the CC is no longer isometric, the muscle force is
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`influenced by the muscle’s shortening speed u,. = - dx,./dt. This is described by the Hill equation, which, in the form used here, is in fact a force-length-velocity relation: F, = F f ( x,. > - nu,./b c
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`1 + u/b with F,, I (1 + c)&f(x,.). The latter inequality sets an upper bound to F,, at negative (i.e., lengthening) velocities. In fig. 5c the Hill eq. (9) is shown for some values of f( xc). It can be seen that the force decreases with increasing rate of shortening, below the isometric value, which is determined by the force-length relation. The rate of decrease with velocity depends on the parameter b, while parameter n determines the concave form of the curves. When the muscle is lengthened the force is some 10-20s (depending on the parameter c) higher than when isometric. The series elastic component has a load-extension characteristic simi- lar to the PEC, but now the SEC length x, is the dependent variable, fig. 5d. In the same way as the PEC, and in fact as most soft biological tissues, the SEC is initially compliant and becomes stiffer at higher forces. A knitted stocking is an everyday example of the same phenom- enon. A useful model is a combination of a logarithmic and a linear function:
`x,=-ln (Y in which (Y, k and F, are parameters; this function has been drawn in fig. 5d. It should be noted that even in a so-called isometric contraction (with x constant) the CC may shorten very considerably, while stretch- ing the SEC. E.g. at F,. = 2000 N, x, amounts to 7% of the muscle length and the CC may shorten from 1.00 to 0.93, cf. figs. 5d and 5b. The active state F, in the Hill model is assumed not to be influenced by the mechanical events: force, length or velocity. This assumption, together with the experimental finding (5) and with (8) suggests for situations where F, and the smoothed EMG E can be considered stationary, that there is a linear relation between both quantities F,=gE (quasi-static) (II)
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`FN)
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`135 This relation, with FO obtained from (9) was already confirmed in 1954 by Bigland and Lippold in experiments with isotonic (4, constant) contractions. In general, however, F, may change rapidly in time and a more complicated processing than the simple proportionality of (11) is neces- sary to obtain the active state F,(t) from the smoothed rectified EMG E(t). The temporal characteristics and the summation properties of the active state, as they are known in physiology, should here be taken into account as much as possible. Fig. 6 shows how this can be done. As long as E(t) rises, F,(t) is made equal to gE(t), as in (11). When a relative maximum of gE(t) occurs, this maximum is held for a time r2 and followed by an exponential decay with time constant r3, fig. 6a. This time course of F,(t)
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`on until gE( t), or the plateau resulting from a later peak of gE( t), becomes larger than F,(t). In that case F,(t) follows the rise of gE(t) again, see fig. 6b. The time course of
`fig. 6a gives the isometric twitch as an example. This is mainly due to the CC-SEC interaction: at the onset of a contraction the SEC will be stretched first, the CC therefore has to shorten initially at a high speed and at a low force (fig. 5~). In a twitch the turning point in this process, where the shortening speed U, is zero and
`is already declining again (fig. 6a). After this the SEC recoils and the CC is stretched (u, is negative). In non-isometric contractions the course of things is much more complicated: at any instant the CC length x, is determined by the difference between the muscle length x, which is measured, and the SEC stretch x,, which is determined by the CC force
`(eq. 6a). The influence of the changing Fig. 5. Components of the Hill muscle model. Curves are characteristic for the human calf muscles. For orientation: in a 70 kg subject walking at moderate speed the peak force can be 2500 N and & is between 0.95 and 1.02. (a) Parallel elastic component, passive force Fp as a function of whole muscle length x. Thin lines: measured data, note hysteresis. Thick line: exponential model (7) with F,a = 50 N and p = 60. (b) Contractile component, force-length relation f (x,). Points are measured data, the dashed line gives the approximation. It may be expected that
`will decrease above x, = 1.00 (Gordon et al. 1966). (c) Contractile component, Hill relation: CC force F, as a function of CC shortening speed U, at /(xc) = 1.0, 0.7 and 0.3 according to eq. (9). Parameter values h = 0.15 SK’, c = 0.2, n = 0.12. (d) Series elastic component. SEC extension x, as a function of the applied force F,. Parameter values: a = 80, k = 1.6.105 N, F, = 20 N.
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`F, =f( xc) F,
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`Fig. 6. Active state F, as processed from the smoothed rectified EMG E(I), see text. Parameters: 72 = 30 msec, 7, = 60 msec. (a) One short burst of EMG activity gives a F,(t) response resembling that of a single twaitch. The contractile force response for an isometric contraction has been added: F,. (b) A more complicated EMG pattern. Note the effects of the peak holding. The ‘silent period’ in the EMG. e.g., results only in a gradual and delayed decrease of F,. SEC stretch on CC speed, force and contractile efficiency should certainly not be underestimated. In human walking, for example, it often occurs that the CC shortens while the muscle as a whole is stretched. When this happens, work done on the muscle is stored as elastic energy in the SEC (Hof et al. 1983a). Applications Assuming the EMG-force relation as sketched above to be valid, several relations between EMG and mechanical variables that have been pro- posed in literature can be evaluated. These relations apply to the force (A-D), the mechanical work (E) and the energy consumption (F). Following these, some methods of presentation of the EMG will be discussed and consideration given to what they can say about muscle activity and function (G-K). (A) The complete model gives the possibility to calculate the force of a single muscle from the EMG and the muscle length for arbitrary contractions. Several things are needed for this. A representative and artefact-free EMG should be recorded. The muscle length is to be determined, e.g., from limb angle measurements by a geometrical conversion, for which anatomical data on the muscle leverage are needed (cf. Frigo and Pedotti 1978). A computational facility is neces- sary to solve the set of (differential) eqs. (6-10) and to perform the
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`active state processing that together make up the muscle model. In our (1981a) set-up an electronic analogue processor was used, this has several advantages, but, today, an implementation on a digital com- puter would be more practical for most users. Finally the parameters of the muscle model are to be determined. Some of these can be consid- ered constant for one muscle for various subjects, but others need to be assessed for every subject, the gain factor g even changes for every new electrode placement. Every experimental session is therefore to be preceded by a calibration procedure, in which the model output is compared to the muscle force, measured by a dynamometer, for a standardized set of contractions. For calf muscle experiments of the author, to give an example, the calibration takes about two hours, including the application of the electrodes and the necessary calcula- tions. The EMG to force processing itself, on the other hand, is done in real time. This is in contrast with kinetic analysis, where the prepara- tion time may be shorter, but where the digitizing and the computing can usually not be done in real-time. In addition to previous results (Hof and van den Berg 1981b, c, d; Hof et al. 198