Comprehensive Physiology Wiley Online Library

Muscle, the Motor

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Abstract

The sections in this article are:

1 Representation of Muscle Properties
1.1 Dimensions Used
1.2 Models
1.3 Real Motor Systems
1.4 Summary
2 Properties of the Contractile Unit
2.1 Passive Mechanical Contributions
2.2 Response to Neural Signals
2.3 Interaction Between Neural and Other Inputs
2.4 Functional Variations
2.5 Summary
3 Multiple Units of Muscle
3.1 The Unit of Muscle Function
3.2 Relationships in Multiunit Function
3.3 Summary
4 Some Measures of Muscle Function
4.1 Summary
5 Motor Functions of Muscles
6 Final Summary
7 Epilogue
8 Appendix
8.1 Units for Measure of Motor Function
Figure 1. Figure 1.

Examples of physiological actions of various muscles. A: twitch response to excitation of a few motor nerve fibers of human muscle obtained as ensemble average of output force from whole arm. Upper record, response during weak contraction of whole muscle; lower record, response from same motor units stimulated when remainder of muscle was strongly contracted. In the twitch during strong contractions, averaged force contribution rose to an appreciably lower peak than in the other series; then the average decreased to a value less than background level. In this measure both the primary or direct effect of excitation of the test unit and any consistent secondary effects that modify the activity of other units are combined in the total recorded response. B: two voluntary movements of human arm. Thickness of horizontal bars, periods of high, low, and no electromyograph (EMG) activity in agonist and antagonist muscles. First record made during a relaxed movement, second with a stiff arm. Periods of agonist and antagonist activities in first record show alternation with complete separation. In 2nd record the periods are completely overlapping with a rapid cycling of intensity of EMG. In spite of differences in electrical activity, however, the two movements follow similar time courses of position. C: sound produced by vibration of locust tympanum by tymbale muscle when artificially stimulated at 22.5 pulses/s. Stimulus points shown on lower record. Compare Fig. 7B, which shows isometric response of a similar muscle stimulated at 22 pulses/s. D: measures of triceps sura muscle action in 2 steps of a uniformly walking cat 399. All of the data originated in measurements (*) of length, force, and EMG by Yager 563. Continuous approximations of length, velocity, and acceleration were derived by applying spline functions 408,559 to 128 photographically determined point values of length. Power calculated as product of velocity and force (measured by transducer on tendon). EMG is shown as rectified and filtered interpretation of direct record. Ratio of force to acceleration does not represent changing inertia of load, in part because system is not free of external forces and also because acceleration is not measured in an inertial reference frame. For 1st step (ending at arrowheads) force, velocity, and length are plotted also in a pseudo‐3‐dimensional form, starting in swing phase and progressing continuously in direction of time arrow; pickets mark 10‐ms intervals and eliminate ambiguity of 4‐dimensional points as graphed on a plane. This trajectory over the phase plane (length vs. velocity) shows that in swing phase large velocities and displacements are associated with small forces, while largest forces occur at midlengths and lengthening velocities during stance phase of step. Rest length, l = 1, is near long end of lengths involved in walking, as also described in ref. 483. The EMG trajectory for this same step can be seen in ref. 393. For separated soleus and gastrocnemius records of force in walking cat, see refs. 285,286and 531. Note that 2 steps shown in this figure to have similar length patterns have appreciably more variation in acceleration, velocity, and EMG 278. As is most apparent on phase plane graph, when muscle returns to the starting length for 1st step, 2nd step is initiated at a different velocity and therefore cannot follow a course identical to the first.

A: from Milner‐Brown et al. 373, with permission of Cambridge Univ. Press. B: from Wacholder 521. C: from Pringle 411, with permission of Cambridge Univ. Press. D: from Partridge 399, with permission of Raven Press
Figure 2. Figure 2.

Conventional nomenclature of successive structural subdivisions of vertebrate skeletal muscle down to sarcomere level. Functional motor unit does not correspond to any of these divisions. (For examples of diffuse distribution of a motor unit within a muscle, see Fig. 13 in the chapter by Burke in this Handbook and refs. 90,94,148,155,313,319. It also should be noted that individual fibers may cross from one fasciculus to another 267,268 or end within a fasciculus 6,32,33,127,255. Furthermore, the densely packed organization of fibers seen in histological section and in this schematic diagram of a fasciculus may represent a shift of extracellular fluid after loss of blood pressure 64,123,312. Normally, adjacent fibers may float separately within the muscle.

Adapted from Bloom and Fawcett 55
Figure 3. Figure 3.

Details of structure in gross muscles. A: primitive vertebrate muscle arrangement as seen in a single myomere in cartilagenous fish. Longitudinal and cross‐sectional views show pattern that may be approximated as alternating concentric cones made up of these segmentally innervated muscle units. B: regional organization of major innervation divisions (arbitrarily numbered) as projected on two surface views of anterior tibial muscle of dog, showing mixtures of series and parallel relationships. C: conformation change in simple pennate frog muscle as result of total contraction 47. Table summarizes measured length and angle changes associated with A' fasciculus produced by contraction of whole muscle. The 40% shortening contribution by muscle fasciculus exceeded the 32% shortening of that fasciculus itself and includes effect of increase in angle of these active fibers. An added 13% decrease of total length resulted from the changing angle of connective tissue. Due to changing angles, as well as fiber shortening, total shortening of 7.7 mm is greater, not less, than 5.5‐mm shortening of involved fibers in spite of angled orientation of fibers. D: organization of fasciculi (dashed lines) in the frequently studied frog gastrocnemius, as seen from superficial and deep surfaces and from a longitudinal section. Solid lines and locations Ap, Z, D, and P all mark major connective tissue structures. Sample fasciculus lengths, overall length and width, and a few pennation angles are marked.

A: from Alexander 10. B: from Wilder et al. 548. C and D: from Beritoff 47
Figure 4. Figure 4.

Effects of load modify muscle responses. A: twitches of muscle from different initial lengths in frog gastrocnemius muscle operating on nearly isometric load (left), compliant spring load (middle), and isotonic load (right). These loads determine force‐length slope through course of any contraction and thereby influence the pattern of maxima reached in the twitches. Passive length‐force relationship (right border, each record) also differs slightly between stretching sequence (upper passive curve, each record) and release sequence. Load‐dependent length‐tension curves for twitch maxima are joined by dashed lines. B: cat triceps sura muscle responses to modulated stimulus. Cyclic modulation of rate of stimulus used for both tests is shown as middle graph. Upper graph, isometric force, measured in newtons. Lower graph, force from the identical muscle, subjected to the same stimulus sequence, but attached to an inertial load. Response was measured with an accelerometer in gravity units g from which the newton scale N was calculated. Mean force and length were similar in both cases, and isometric force changed smoothly with period of stimulus. Inertial load was moved against gravity with the same period, but change in force producing that load movement does not have a simple period. Actually only a small fraction of maximum isometric force (and that delivered intermittently) is required to move physiological‐sized loads at moderate frequencies. C: calculated stretch of “series elastic component” with changes of the load on rat gracilis anticus muscles. Compliance (slope of curve) decreases as force increases. Bars, standard deviation of values measured from 5 muscles. This stretch represents the part of an overall length change that is considered not to occur in the contractile components. D: energy exchanges occurring with complex load on a 2‐joint muscle (human hamstrings) through part of a running step. The 2‐joint load allows separation of muscle length change (right graph) from that due to individual joint movement (two curves on left graph). Contributions to muscle length deviations, produced separately by hip movement and by knee movement, are plotted against force, as is total resulting change in muscle length. Numbered points identify correspondence of time on the 3 lines. Energy exchange at individual joint need not represent just energy produced or absorbed by the muscle. Area under curves is work done (integral of force with respect to distance). From 1–10 at knee, work is done on muscle by the load, whereas work is done by muscle at hip. Right: combined effect or net exchange in muscle energy for same points in time. Area under right curve from 1st to 6th point shows energy actually absorbed by muscle, and area under curve from 6th to 10th point shows mechanical energy delivered by muscle (part of delivered energy probably was from series elastic structures that shortened as tensile force was decreasing; if lengthening parallel elastic elements were under tension in this period they would have been absorbing energy). Comparison of areas under 3 curves shows that energy is conserved by transfer through muscle from knee to hip joint.

A: from Blix 54. B: from Partridge 394. C: from Bahler 24. D: from Elftman 158
Figure 5. Figure 5.

Static and dynamic properties of unstimulated muscles. A: variations in relationships between muscle length and measured force in unstimulated muscles of several species. Abscissa lengths are normalized at maximum body lengths. In some muscles no force is generated passively within lengths attainable in situ, but for other muscles passive tension in normal operating range of lengths exceeds active contribution (see also Fig. 16B). Curve A, bumblebee flight muscle; curve B, locust flight muscle; curve C, frog sartorius; curve D, clam (mytilus) anterior byssal retractor; curve E, snail (Helix) pharynx retractor muscle. Other muscle curves can also be seen in part B and Figs. 4A; 11C and D; and 16B. B: length‐tension relationship in an unstimulated frog gastrocnemius muscle measured at different rates of loading and unloading, using mercury to produce smooth force changes. Less stretch occurred with force increase, and particularly with fast increase, than with unloading. Force vs. displacement graphs were recorded directly using a special mechanical linkage. Dynamic aspect of passive response of muscle represented by difference between stretch and shortening curves commonly is ignored in dealing with muscle properties (compare Fig. 13.). C: “stress relaxation” after a step change in length of an unstimulated ileotibialis muscle of tortoise. Unbroken curve, force change in period immediately after stretch; dashed line, level at which force finally stabilized. D: three different time expansions of a record of “creep” of length after a step change in load on a single unstimulated frog fiber. Time marks in curve III, 10 s; time marks in curves II and I, 0.1 s and 0.01 s, also show initial oscillatory transient details as well as creep. Stretch scaled in percentage of equilibrium length (just taut).

A: from Hanson and Lowy 229. B: from Blix 54. C: from Hill 254. D: from Buchthal and Kaiser 82
Figure 6. Figure 6.

Various responses of muscles to single stimulus pulses. A: first published record of muscle twitch 238. Frog gastrocnemius was attached to a complex inertial and elastic load, and record was made by a steel point scratching on a lightly smoked, moving glass plate. Oscillatory detail is characteristic of the particular combination of load and muscle and is avoided in most modern muscle experiments by reducing both inertia and elastic compliance of loads. B: Simultaneous force and length records through a series of twitches with different isotonic loads. Frog gastrocnemius muscle was afterloaded; that is, load was mechanically supported at a fixed position before and after muscle tension exceeded force required to lift the load. Characteristically the latent period for load movement increased with load size (weight marked in g), and movement period decreased. The shorter latent period for force development was unchanged. (The same 1893–1895 ref. 54 contains a large number of other records of twitches made with different types of load and load transients; both time‐based records and force vs. length records are included.) C: effect of preload on muscle twitch (weight in g marked on lines). Weights were hung near the fulcrum to minimize effect of inertia, thus approximating an isotonic load. Stretch of loaded muscle before stimulus as well as changes in response can be seen. D: volume change in frog sartorius during isometric twitch. Major divisions on abscissa, 10 ms. Detail of volume change is highly sensitive to load conditions 34. Peak volume decrease is about 5 × 10–3% of total muscle volume.

A: from Helmholtz 238. B and C: from Blix 54. D: from Baskin 34
Figure 7. Figure 7.

Time graphs of muscle response to 2 or more stimuli in succession. A: traditional student laboratory demonstration (1905) of wave summation for 2 stimuli in nearly isotonic contractions of frog gastrocnemius. Stationary ordinates mark stimulus points. Lower line, time at 50 periods/s. Upper 2 records, response to 2 stimuli superimposed on record produced following a single stimulus. B: typical isometric response of striated muscle to trains of stimulus pulses delivered at 0.9, 22, 46, and 100 pulses/s. At 100 pulses/s response approaches a fused tetanus. The muscle used for this record was tymbal muscle of locust. Compare to physiological response of a similar muscle when attached to its normal load in Fig. 1C. C: isometric records of wave summation. Lower records, from cat soleus with 2 stimuli delivered at a 70 ms‐interval at 37°C. Area added to record (mechanical impulse) by second stimulus is greater than that produced by 1st stimulus. Upper record, from frog sartorius with stimulus interval of 120 ms. (Time scale of frog muscle record is 77% as fast as that shown for cat record.) Impulse added by 2nd stimulus in this case is less than that contributed by 1st. In both records time from stimulus to peak of contributed force is longer for 2nd twitch than for 1st. D: successive contributions of individual stimuli in a sequence. Upper graphs, superimposed records of responses with different total number of stimuli in trains. Lower graphs, contribution of individual stimuli calculated by subtracting responses to trains differing by one pulse. Left graphs: theoretical linear summation, each impulse producing same contribution. Right graphs: actual frog sartorius responses, 5 pulses/s. Contribution and rate of rise of successive pulses decreased markedly, especially at higher rate. See Fig. 8C for a measure of isotonic contribution in displacement time product resulting from a pulse as a function of stimulus rate at which it is added.

A: from Beddard et al. 42. B: from Pringle 411, with permission of Cambridge Univ. Press. C: from Ranatunga 425. D: from Gilson et al. 191
Figure 8. Figure 8.

Effects of stimulus rate on muscle response. A: several different ways of representing the same results. For these graphs a single fiber from frog semitendinosis was used, and isometric response was measured from periods of steady stimulus. Curve a, force differences in individual responses; curve b, contraction remainder at low point in response between stimuli; curve c, ratio of contraction remainder to stimulus rate; curve d, force peak (a + b); curve e, mean tension over time. All curves are plotted as functions of stimulus rate. B: rate of rise of tension (right ordinate and × values) at beginning of a stimulus train continues to increase through appreciably higher stimulus rates than does contractile tension (left ordinate and • values). This is an additional example of measures of muscle response that are not equally sensitive to stimulus rate. C: family of nearly isotonic responses of cat triceps sura muscle to slowly increasing stimulus rate (1 pulse/s2). Separate lines are made with different loads. At low stimulus rates and with small loads the responses to individual stimuli are particularly apparent (compare twitches in Fig. 6C). Lower graphs show derivative of average (negative) length with respect to stimulus rate (–d//dR), which was calculated using spline functions 408,559 on mean (smoothed) values of the upper graphs. These superimposed curves indicate that the principal sensitivity to stimulus rate for this muscle falls in the range of 8–25 pulses/s over a variety of loads. Separate peaks could represent populations of fast and slow muscle units within this muscle.

A: from Buchthal 76. B: from Machin and Pringle 352. C: from Partridge 395
Figure 9. Figure 9.

Dynamic effects of modulated stimulation. A: time graphs of response of load moving by cat triceps sura muscle driven with a sinusoidally modulated stimulus rate, 5–25 pulses/s, and at modulation frequencies marked on graphs. Amplitude of modulation was constant, but response amplitude changed with frequency of modulation. B: change in movement amplitude with frequency of modulation cycle. All stimulus cycles ranged from 5 to 35 pulses/s. Although the gravity part of loads was constant, each line represents a different load inertia, spanning a 28‐fold variation within the physiological range 394. Periodic force required for sinusoidally moving an inertial load increases proportional to inertia and proportional to the square of the frequency or, for this range 28 × (6.3/0.04)2 = 7 × 105, which is the ratio of force cycles for a constant amplitude movement. Considering the proportionality of force cycle to movement amplitude, this graph represents an actual 8 × 103 range of amplitudes of response cycles of force produced by a constant amplitude of modulation of stimulus rate. C: temporal displacement between stimulus cycle and response cycle in isometric records of cat triceps sura force as a function of cyclic frequency. Upper graph, lag of response in ms; lower graph, same data in fractions of a 360° cycle. D: representation of muscle properties combining both nonlinear and dynamic aspects. Each set of 3 coefficients (G0, fn, and ζ) define one 2nd‐order differential equation approximating data similar to that shown in parts in C and B. These coefficients when inserted in the equation specify dynamic properties of the muscle in one operating range of stimulus rates. Changes of coefficients with firing rate range represent some of the nonlinearities. •, ○, Values obtained from different muscles.

A and B: from Partridge 394. C: from Partridge 393. D: from Mannard and Stein 354, with permission of Cambridge Univ. Press
Figure 10. Figure 10.

Relations between muscle actions and temperature. A: twitch variations in frog muscle at 3 different temperatures. Time reference, 100 Hz. B: effect of temperature on tortoise muscle stiffness. Lower lines, static stiffness; upper lines, dynamic stiffness. Pairs of points are measured from one sequence of increasing and one sequence of decreasing temperature. C: height of frog muscle twitches at a sequence of temperatures between 0°C and 36°C. D: effect of temperature on duration of twitch. Temperature ranges between 5°C and 41°C, at which point response failed completely. E: change in temperature of body core, rt, and of muscle, mt, as a result of muscle activity in human. Crossing of the two curves shows a reversal of direction of heat transfer between muscle and relatively constant body core. Externally observable motor performance also changed in speed with temperature in this study, which may be related to “warm up” before athletic activity.

A: from Handbook of Physiology, by W. D. Halliburton, © 1911, used with permission of McGraw‐Hill Book Co. B: from Fowler and Crowe 180. C and D: from Howell 263. E: from Asmussen and Bøje 18
Figure 11. Figure 11.

Muscle contraction as modified by length. A: relationship between stress and strain in 12 tetanically stimulated glossopharyngeal muscles of frog. Data are from tables made by Weber in 1847 537. Eleven muscles, •, were loaded before stimulus. One muscle, ▽, was stimulated before loading. Normalization to stress and strain from length and tension, as described by Weber, allows comparison of muscles of quite different sizes. (We have crudely confirmed Weber's description of the very long range of lengths over which this muscle can respond.) B: comparison of active contribution to length‐tension effect in several different muscles. (For passive contributions of the same muscles, see Fig. 5A.) A, bee flight muscle; B, locust flight muscle; C, frog sartorius; D, anterior byssal retractor of clam. Ordinates are not normalized to compensate for muscle size differences. C: conventional measurement of active contribution to length‐tension effect. Passive response and maximal voluntary force were measured directly in human forearm flexor muscle with cineplastic tunnel prepared to allow external action of the tendon. Developed tension is calculated as difference between passive and maximal forces with no correction for result of local stresses within muscle and tendon. See Fig. 4A for similar data from twitches. D: family of length‐tension curves for single fiber of frog semimembranous muscle. Parameter distinguishing individual curves is stimulus rate. Note nonuniform increments of stimulus rate and compare Fig. 8. Values were calculated as mean of 2 values measured with increasing and with decreasing stimulus rate.

B: from Hanson and Lowry 229. C: from Ralston et al. 423. D: from Buchthal 76
Figure 12. Figure 12.

Effect of velocity on muscle response, measured at constant velocities while passing through a test length. All sets of curves are drawn on same abscissa. A: Force‐velocity effect at several different stimulus rates in cat soleus muscle using rotation of stimulus among 5 nerve branches. (Also see ref. 296 for differences introduced by slightly different test conditions.) B: rate of exchange of energy between muscle and load, or power, is equal to product of force F and velocity V. Negative power indicates output of energy by the muscle. (Energy delivered by each impulse, i.e., power ÷ pulse rate, varies with stimulus rate but is nearly independent of velocity over an appreciable range.) C: slope ∂F/∂V calculated from force‐velocity curves in A, a measure of sensitivity of force to velocity, or mechanical impedance (as in ref. 397). Negative values are proportional to a viscosity‐like measure. The value of this measure is greatest at low shortening velocities with high stimulus rates. Graphs B and C were calculated for this review from data points on force‐velocity graph (A) using spline interpolation 408,559. Spline fit lines pass through same data points, but they differ slightly from lines joining points in A.

A: from Joyce and Rack 294, with permission of Cambridge Univ. Press
Figure 13. Figure 13.

Expected 3‐dimensional mechanical relationship in response of muscle. Muscle force as related to length, velocity, and excitation drawn by combining usual descriptions (for related experimental data, see Figs. 8C, 9B, 10, 11D, 12A). Arrows on velocity axes show relationship between velocity sign and change of length (angle). Arrows on torque axis in F relate torque to corresponding direction of change of velocity. A: one 3‐dimensional description of response properties of a single muscle at a particular moment. Excitation of the muscle defines length‐tension‐velocity relationships in that muscle. At a single length this relationship is described as a force‐velocity curve, and at a single velocity it is a length‐tension curve. For length and velocity at some moment, instantaneous force falls at intersection of 2 such curves in length‐velocity‐force space. Red and green lines might correspond to 2 curves from a stimulus rate family, such as shown in Fig. 11D for length axis and Fig. 12A along velocity axis. At any other moment force output could be defined in terms of intersection of an appropriate stimulus‐determined pair of intersecting length‐tension and force‐velocity curves, at least a 4‐dimensional relationship. (Note: No dynamic component is represented in the passive response, although one is known to exist; see Fig. 5BD.) B: the 26 different red graphs of active length‐tension curves intersect in this diagram with each of the 26 red force‐velocity curves to define 676 of the points to which a particular excitation level might bring a muscle. Same number of intersections in green represent passive muscle. (The different individual curves were derived from assumption that at any length the nonlinear velocity effect is proportional to isometric active force at that length.) Inclusion of all possible points between samples drawn here would produce a “response surface”. If red surface designates the possible responses of maximally active muscle, then neural control would operate in space between red and green surfaces. (see ref. 25 for an experimentally derived half‐surface drawn with a different orientation of the axes.) C: another variation of a response surface differing from B by a simple shift in relationship between passive and active length effects. Different muscles have properties that range between and beyond these types. D: representation of a sinusoidal movement as a trajectory over a response surface. A sinusoidal change in length, l = A sin ωt, defines a cyclic velocity, V = A ω cos ωt, that varies in amplitude with frequency. Such pairs of curves trace eliptic paths on phase (base) plane and define complex closed loop trajectories over response surface. Time‐varying force traced by such trajectories is periodic but not sinusoidal. This transformation from movement into force is inferred by the accepted length and velocity properties of maximally and constantly activated muscle. Response cycle has a phase‐shift based on shape of response surface; it changes with movement frequency, amplitude, and bias. (Nonsinusoidal patterns of movement similarly can be graphed over this theoretical surface. As illustrated in Figs. 15 and 16, more complex stimulus and movement patterns tend to produce deviations from response surface predicted by the usual muscle description and represented by these graphs.) E: time graphs for one movement over response surface of D. Two cycles of sinusoidal length change centered around rest length, Lo, are shown by black curve at top of figure. Corresponding but phase‐shifted force cycle for a maximally activated muscle is shown by the periodic, nonsinusoidal, red curve marked Fmax. In some stretching parts of the cycle that force exceeds maximum isometric force, 100% Fi. At the specified lengths passive forces are all near 0 (0% Fi), as shown by line marked Fmin. Any constant force (e.g., 40% of Fi) falls at different relative positions with respect to minimum and maximum force for velocity‐length combinations as values change through the movement. If such a constant force can be produced through a movement, then a variation of activation of the muscle would be required. Here activation A is defined for any particular force as the relative position of that force between Fmax and the passive force for existing physical conditions at the moment. In this example in order to maintain the constant 40% Fi force through the described movement, the neural drive would have to provide a time‐varying activation (from 33% to 80% of maximal), as plotted on line marked % A. F: theoretical response surfaces for a pair of matched antagonist muscles. Green lines represent surface expected while both muscles are unexcited. Red lines represent the response surface expected when both muscles are maximally active. This surface does not show a simple cancellation of force; i.e., coactive surface is not a horizontal plane equal to passive surface. For the slopes, ∂T/∂θ relates to stiffnesslike properties, and ∂T/∂V relates to a viscosity‐like property. Lengths, velocities, and forces that describe linear action of a single muscle are replaced here by angles, angular velocities, and torques, which describe combined action of antagonist muscles on a hinge joint.

Adapted from Partridge 399
Figure 14. Figure 14.

Effects of excitation history on dynamics of muscle response. A: sequence of afterload frog muscle twitches recorded as fatigue develops. Increased height over first few trials (treppe) is followed by decreased amplitude (fatigue) as well as by increased latent period, increased time to peak, and slowed relaxation. This latter effect is known as contracture. B: change of response in 2 cat limb muscles as a result of surgically crossed innervation. Upper two graphs, normal muscle twitches in crureus and gracilis muscles. Lower records, altered response under influence of reinnervation by crossed nerves—slow muscle becoming faster and fast muscle becoming slower. Line below twitch record shows a digital measure of contraction time in ms arranged in series of dots, each column with a maximum of 10 1‐ms points. C: adaptation of response of anterior tibial muscle of rabbit to long‐term activity pattern. Two isometric responses to stimulus trains of 25 pulses/s. Lower record, response of normal muscle; upper record, muscle modified by stimulation at 10 pulses/s over a 5‐month period.

A: from Handbook of Physiology by W. D. Halliburton, © 1911. Used with permission of McGraw‐Hill Book Co. B: from Buller et al. 87, with permission of Cambridge Univ. Press. C: from Salmon 447
Figure 15. Figure 15.

Deviations of muscle response to stimulus from that of a simple, response surface model with lag. Examples show that muscle responses vary with stimulus history and past activity in other units and that mechanical effects are variable with stimulus level. A: hysteresis in cat triceps sura muscle response to rate modulation of stimulus. Insert, time sequence of stimulus. In graph of length vs. stimulus rate, time progresses in a counterclockwise direction. After a high stimulus rate, contraction is sustained even at appreciably lower stimulus rate. Similar hysteresis patterns are also found in isometric responses. Hysteresis did not occur in cycle with lowest maximum rate. B: difference in relationships between stimulus rate and force in lengthening and in isometric muscle. At high stimulus rates lengthening muscle, •, produced more force than isometric muscle, ×, a relationship represented in the response surface diagrams of Fig. 13. At low stimulus rates, however, the relationship is reversed, suggesting a locally reversed slope for the force‐velocity curve at such stimulus rates. C: hysteresis in muscle response to recruiting type of stimulus modulation in human peroneus muscle at constant rate of 50 pulses/s. Ust, time graphs of stimulus intensity; Miso, isometric responses to stimulus. Lowest graph, force vs. stimulus, derived by combining data of type shown in the 2 time graphs and as labeled for point A and point B.

A: from Partridge 396. B: from Joyce et al. 296, with permission of Cambridge Univ. Press. C: from Trnkoczy 508
Figure 16. Figure 16.

Responses to mechanical inputs that deviate from response prediction implied by a simple version of the type of model illustrated in Fig. 13. A: response of stimulated triceps sura muscle to stretch showing mechanical hysteresis. In both lines stimulus was 120 pulses/s and velocity 0 at the same final lengths. In response marked by stimulus was started with muscle at a shorter length followed by a quick stretch to test length, producing a persistent increase of force over that in other response, with test length used throughout stimulus period. (See also Fig. 11A.) B: length‐tension relationship in flight muscle of water beetle. Lower curve, passive muscle; upper curve, active muscle; loop, trajectory plotted on work plane with tetanized muscle subjected to cyclic stretch. Response travels around loop in an energy‐delivering, counterclockwise direction, in contrast to energy‐absorbing, clockwise loops ordinarily described with other muscles. In this case, unlike the diagramed force surfaces, force at shortening velocities is greater than those at the same length and lengthening velocities. This relationship allows these muscles to drive an oscillatory movement without a corresponding oscillating excitation pattern. C: length of a tetanically stimulated muscle before, during, and after a transition from one force to a larger force. In each line, muscle shortened at beginning of stimulus, stretched as load increased, then lengthened again at the end of stimulus. Initial and final forces were the same for each load increase, but rate of change of force varied, increasing from line 1 to line 4. Effect of different rates of loading persisted in terminal periods of constant and equal load. Greatest stretch occurred with fastest loading. D: disruption of fusion of tetanus during mechanical movement. Left part of record shows a stretch; right part shows a subsequent release of cat soleus while stimulated at 8.5 pulses/s. Upper lines, force; lower lines, muscle length.

A: from Walker 528. B: from Machin and Pringle 352. C: from Katz 304, with permission of Cambridge Univ. Press. D: from Joyce et al. 296, with permission of Cambridge Univ. Press
Figure 17. Figure 17.

Combinations of independent units of muscle. (See also Figs. 1B, 13F, and 15C.) A: recruitment of 3 separate respiratory motor units and accompanying increase of firing in individual units (measured from unit electromyogram (EMG) records) as total response intensity increases. Measured motor response is tidal air moved as it increased with rebreathing. B: smoothing of soleus isometric response by alternation of excitation among groups of motor units. Muscle nerve was divided into 5 branches, and each was provided with separate stimulus electrodes. Responses to individual stimuli can be distinguished in record made with synchronous stimulus to all branches. Rotating of branch stimulus (with each division stimulated in turn at same rate) produced response that was not only smoother but greater in magnitude than average of synchronous response. (Normal recruitment produces asynchronous instead of rotating excitation, presumably a less effective means of smoothing.) C: combination of activity of several muscles during bicycling. Weak and strong EMG activity are shown by single and broad lines, respectively. Note variable overlap between muscle activity periods, as well as two separated phases of strong activity in gracilis, Gr. D: recruitment of 3 types of motor units in 2 muscles of lion as speed of locomotion increases. Discontinuities in graphs represent change in type of gait. As seen in histochemical evidence, relative intensity of activity of different types of units does not change in the same order through all gaits and muscles.

A: from Gesell et al. 188. B: from Rack and Westbury 421, with permission of Cambridge Univ. Press. C: from Houtz and Fischer 262. D: from Armstrong et al. 17
Figure 18. Figure 18.

Relationships between several measures of muscle action. Broad arrows represents the multiple signals carried in the signal pathway within the biological system. Mechanical and electrical impedances through which biological signals are coupled to recorder system are marked Z. Electromyogram (EMG) signal may be further processed to some form of pulse signal or to an averaged EMG. Functional output may be measured as any of a variety of motor actions, as well as in form of direct muscle responses. A: nerve activity (ENG) and motor action as measured from phrenic nerve and as tracheal pressure show examples of entry of nerve signal into a muscle system and a motor consequence. B: direct EMG, averaged EMG (AEMG), muscle force, and length—measured during one step of walking, from cat triceps sura muscle. Non‐phase‐shifting digital filter was used to average EMG signal. Force was sampled from tendon in situ and length measured from slow motion movie films. These signals differ as a result of transformations that have occurred in instrumentation as well as in biological components. C: muscle sound pulses recorded from auricularis superior muscle. Myosonogram (MSG) pulses are related one to one to EMG pulses of same unit. Little systematic information is available about how effects of length, velocity, and temperature are represented in the sonogram. D: 3 pulse‐based measures from a unit of respiratory muscle. Bottom line, time of visually identified unit pulses; points on graph, pulse‐by‐pulse calculation of firing rates (inverse interval); solid line, smoothed pattern of firing rate. Accepted methods include variations in derivation of each of these measures of muscle activity, and these variations introduce noticeable differences in the way a particular action is displayed.

A: from Gesell 187. B: from Yager 563. C: from Gordon and Holbourn 203, with permission of Cambridge Univ. Press. D: from Gesell et al. 189
Figure 19. Figure 19.

Variation of relations between measures of physiological muscle activity with type of measurement and mechanical conditions. A: relationship between muscle force and integrated electromyogram (EMG). Each measurement on upper line made from the muscle while shortening; measurements on lower line made during lengthening of same muscle, showing velocity effect on force‐EMG relationship. B: effect of muscle length on force‐EMG relation in human soleus. Separate lines, lengths determined by ankle position in 0.5‐in. increments of muscle length. Mechanical action of gastrocnemius was avoided by bending the knee. C: different nonlinear functions relating force to integrated EMG and to action potential count from same EMG (scaled to match at high and low ends of samples). D: effect of different electrode arrangements on relationship between force and EMG recorded in same tests. Monopolar and bipolar electrodes were used, and spike count was measured. Electrode placements also affects voltage and frequency distributions of EMG 337.

A: from Bigland and Lippold 49, with permission of Cambridge Univ. Press. B: from Close et al. 110. C and D: from Close 109


Figure 1.

Examples of physiological actions of various muscles. A: twitch response to excitation of a few motor nerve fibers of human muscle obtained as ensemble average of output force from whole arm. Upper record, response during weak contraction of whole muscle; lower record, response from same motor units stimulated when remainder of muscle was strongly contracted. In the twitch during strong contractions, averaged force contribution rose to an appreciably lower peak than in the other series; then the average decreased to a value less than background level. In this measure both the primary or direct effect of excitation of the test unit and any consistent secondary effects that modify the activity of other units are combined in the total recorded response. B: two voluntary movements of human arm. Thickness of horizontal bars, periods of high, low, and no electromyograph (EMG) activity in agonist and antagonist muscles. First record made during a relaxed movement, second with a stiff arm. Periods of agonist and antagonist activities in first record show alternation with complete separation. In 2nd record the periods are completely overlapping with a rapid cycling of intensity of EMG. In spite of differences in electrical activity, however, the two movements follow similar time courses of position. C: sound produced by vibration of locust tympanum by tymbale muscle when artificially stimulated at 22.5 pulses/s. Stimulus points shown on lower record. Compare Fig. 7B, which shows isometric response of a similar muscle stimulated at 22 pulses/s. D: measures of triceps sura muscle action in 2 steps of a uniformly walking cat 399. All of the data originated in measurements (*) of length, force, and EMG by Yager 563. Continuous approximations of length, velocity, and acceleration were derived by applying spline functions 408,559 to 128 photographically determined point values of length. Power calculated as product of velocity and force (measured by transducer on tendon). EMG is shown as rectified and filtered interpretation of direct record. Ratio of force to acceleration does not represent changing inertia of load, in part because system is not free of external forces and also because acceleration is not measured in an inertial reference frame. For 1st step (ending at arrowheads) force, velocity, and length are plotted also in a pseudo‐3‐dimensional form, starting in swing phase and progressing continuously in direction of time arrow; pickets mark 10‐ms intervals and eliminate ambiguity of 4‐dimensional points as graphed on a plane. This trajectory over the phase plane (length vs. velocity) shows that in swing phase large velocities and displacements are associated with small forces, while largest forces occur at midlengths and lengthening velocities during stance phase of step. Rest length, l = 1, is near long end of lengths involved in walking, as also described in ref. 483. The EMG trajectory for this same step can be seen in ref. 393. For separated soleus and gastrocnemius records of force in walking cat, see refs. 285,286and 531. Note that 2 steps shown in this figure to have similar length patterns have appreciably more variation in acceleration, velocity, and EMG 278. As is most apparent on phase plane graph, when muscle returns to the starting length for 1st step, 2nd step is initiated at a different velocity and therefore cannot follow a course identical to the first.

A: from Milner‐Brown et al. 373, with permission of Cambridge Univ. Press. B: from Wacholder 521. C: from Pringle 411, with permission of Cambridge Univ. Press. D: from Partridge 399, with permission of Raven Press


Figure 2.

Conventional nomenclature of successive structural subdivisions of vertebrate skeletal muscle down to sarcomere level. Functional motor unit does not correspond to any of these divisions. (For examples of diffuse distribution of a motor unit within a muscle, see Fig. 13 in the chapter by Burke in this Handbook and refs. 90,94,148,155,313,319. It also should be noted that individual fibers may cross from one fasciculus to another 267,268 or end within a fasciculus 6,32,33,127,255. Furthermore, the densely packed organization of fibers seen in histological section and in this schematic diagram of a fasciculus may represent a shift of extracellular fluid after loss of blood pressure 64,123,312. Normally, adjacent fibers may float separately within the muscle.

Adapted from Bloom and Fawcett 55


Figure 3.

Details of structure in gross muscles. A: primitive vertebrate muscle arrangement as seen in a single myomere in cartilagenous fish. Longitudinal and cross‐sectional views show pattern that may be approximated as alternating concentric cones made up of these segmentally innervated muscle units. B: regional organization of major innervation divisions (arbitrarily numbered) as projected on two surface views of anterior tibial muscle of dog, showing mixtures of series and parallel relationships. C: conformation change in simple pennate frog muscle as result of total contraction 47. Table summarizes measured length and angle changes associated with A' fasciculus produced by contraction of whole muscle. The 40% shortening contribution by muscle fasciculus exceeded the 32% shortening of that fasciculus itself and includes effect of increase in angle of these active fibers. An added 13% decrease of total length resulted from the changing angle of connective tissue. Due to changing angles, as well as fiber shortening, total shortening of 7.7 mm is greater, not less, than 5.5‐mm shortening of involved fibers in spite of angled orientation of fibers. D: organization of fasciculi (dashed lines) in the frequently studied frog gastrocnemius, as seen from superficial and deep surfaces and from a longitudinal section. Solid lines and locations Ap, Z, D, and P all mark major connective tissue structures. Sample fasciculus lengths, overall length and width, and a few pennation angles are marked.

A: from Alexander 10. B: from Wilder et al. 548. C and D: from Beritoff 47


Figure 4.

Effects of load modify muscle responses. A: twitches of muscle from different initial lengths in frog gastrocnemius muscle operating on nearly isometric load (left), compliant spring load (middle), and isotonic load (right). These loads determine force‐length slope through course of any contraction and thereby influence the pattern of maxima reached in the twitches. Passive length‐force relationship (right border, each record) also differs slightly between stretching sequence (upper passive curve, each record) and release sequence. Load‐dependent length‐tension curves for twitch maxima are joined by dashed lines. B: cat triceps sura muscle responses to modulated stimulus. Cyclic modulation of rate of stimulus used for both tests is shown as middle graph. Upper graph, isometric force, measured in newtons. Lower graph, force from the identical muscle, subjected to the same stimulus sequence, but attached to an inertial load. Response was measured with an accelerometer in gravity units g from which the newton scale N was calculated. Mean force and length were similar in both cases, and isometric force changed smoothly with period of stimulus. Inertial load was moved against gravity with the same period, but change in force producing that load movement does not have a simple period. Actually only a small fraction of maximum isometric force (and that delivered intermittently) is required to move physiological‐sized loads at moderate frequencies. C: calculated stretch of “series elastic component” with changes of the load on rat gracilis anticus muscles. Compliance (slope of curve) decreases as force increases. Bars, standard deviation of values measured from 5 muscles. This stretch represents the part of an overall length change that is considered not to occur in the contractile components. D: energy exchanges occurring with complex load on a 2‐joint muscle (human hamstrings) through part of a running step. The 2‐joint load allows separation of muscle length change (right graph) from that due to individual joint movement (two curves on left graph). Contributions to muscle length deviations, produced separately by hip movement and by knee movement, are plotted against force, as is total resulting change in muscle length. Numbered points identify correspondence of time on the 3 lines. Energy exchange at individual joint need not represent just energy produced or absorbed by the muscle. Area under curves is work done (integral of force with respect to distance). From 1–10 at knee, work is done on muscle by the load, whereas work is done by muscle at hip. Right: combined effect or net exchange in muscle energy for same points in time. Area under right curve from 1st to 6th point shows energy actually absorbed by muscle, and area under curve from 6th to 10th point shows mechanical energy delivered by muscle (part of delivered energy probably was from series elastic structures that shortened as tensile force was decreasing; if lengthening parallel elastic elements were under tension in this period they would have been absorbing energy). Comparison of areas under 3 curves shows that energy is conserved by transfer through muscle from knee to hip joint.

A: from Blix 54. B: from Partridge 394. C: from Bahler 24. D: from Elftman 158


Figure 5.

Static and dynamic properties of unstimulated muscles. A: variations in relationships between muscle length and measured force in unstimulated muscles of several species. Abscissa lengths are normalized at maximum body lengths. In some muscles no force is generated passively within lengths attainable in situ, but for other muscles passive tension in normal operating range of lengths exceeds active contribution (see also Fig. 16B). Curve A, bumblebee flight muscle; curve B, locust flight muscle; curve C, frog sartorius; curve D, clam (mytilus) anterior byssal retractor; curve E, snail (Helix) pharynx retractor muscle. Other muscle curves can also be seen in part B and Figs. 4A; 11C and D; and 16B. B: length‐tension relationship in an unstimulated frog gastrocnemius muscle measured at different rates of loading and unloading, using mercury to produce smooth force changes. Less stretch occurred with force increase, and particularly with fast increase, than with unloading. Force vs. displacement graphs were recorded directly using a special mechanical linkage. Dynamic aspect of passive response of muscle represented by difference between stretch and shortening curves commonly is ignored in dealing with muscle properties (compare Fig. 13.). C: “stress relaxation” after a step change in length of an unstimulated ileotibialis muscle of tortoise. Unbroken curve, force change in period immediately after stretch; dashed line, level at which force finally stabilized. D: three different time expansions of a record of “creep” of length after a step change in load on a single unstimulated frog fiber. Time marks in curve III, 10 s; time marks in curves II and I, 0.1 s and 0.01 s, also show initial oscillatory transient details as well as creep. Stretch scaled in percentage of equilibrium length (just taut).

A: from Hanson and Lowy 229. B: from Blix 54. C: from Hill 254. D: from Buchthal and Kaiser 82


Figure 6.

Various responses of muscles to single stimulus pulses. A: first published record of muscle twitch 238. Frog gastrocnemius was attached to a complex inertial and elastic load, and record was made by a steel point scratching on a lightly smoked, moving glass plate. Oscillatory detail is characteristic of the particular combination of load and muscle and is avoided in most modern muscle experiments by reducing both inertia and elastic compliance of loads. B: Simultaneous force and length records through a series of twitches with different isotonic loads. Frog gastrocnemius muscle was afterloaded; that is, load was mechanically supported at a fixed position before and after muscle tension exceeded force required to lift the load. Characteristically the latent period for load movement increased with load size (weight marked in g), and movement period decreased. The shorter latent period for force development was unchanged. (The same 1893–1895 ref. 54 contains a large number of other records of twitches made with different types of load and load transients; both time‐based records and force vs. length records are included.) C: effect of preload on muscle twitch (weight in g marked on lines). Weights were hung near the fulcrum to minimize effect of inertia, thus approximating an isotonic load. Stretch of loaded muscle before stimulus as well as changes in response can be seen. D: volume change in frog sartorius during isometric twitch. Major divisions on abscissa, 10 ms. Detail of volume change is highly sensitive to load conditions 34. Peak volume decrease is about 5 × 10–3% of total muscle volume.

A: from Helmholtz 238. B and C: from Blix 54. D: from Baskin 34


Figure 7.

Time graphs of muscle response to 2 or more stimuli in succession. A: traditional student laboratory demonstration (1905) of wave summation for 2 stimuli in nearly isotonic contractions of frog gastrocnemius. Stationary ordinates mark stimulus points. Lower line, time at 50 periods/s. Upper 2 records, response to 2 stimuli superimposed on record produced following a single stimulus. B: typical isometric response of striated muscle to trains of stimulus pulses delivered at 0.9, 22, 46, and 100 pulses/s. At 100 pulses/s response approaches a fused tetanus. The muscle used for this record was tymbal muscle of locust. Compare to physiological response of a similar muscle when attached to its normal load in Fig. 1C. C: isometric records of wave summation. Lower records, from cat soleus with 2 stimuli delivered at a 70 ms‐interval at 37°C. Area added to record (mechanical impulse) by second stimulus is greater than that produced by 1st stimulus. Upper record, from frog sartorius with stimulus interval of 120 ms. (Time scale of frog muscle record is 77% as fast as that shown for cat record.) Impulse added by 2nd stimulus in this case is less than that contributed by 1st. In both records time from stimulus to peak of contributed force is longer for 2nd twitch than for 1st. D: successive contributions of individual stimuli in a sequence. Upper graphs, superimposed records of responses with different total number of stimuli in trains. Lower graphs, contribution of individual stimuli calculated by subtracting responses to trains differing by one pulse. Left graphs: theoretical linear summation, each impulse producing same contribution. Right graphs: actual frog sartorius responses, 5 pulses/s. Contribution and rate of rise of successive pulses decreased markedly, especially at higher rate. See Fig. 8C for a measure of isotonic contribution in displacement time product resulting from a pulse as a function of stimulus rate at which it is added.

A: from Beddard et al. 42. B: from Pringle 411, with permission of Cambridge Univ. Press. C: from Ranatunga 425. D: from Gilson et al. 191


Figure 8.

Effects of stimulus rate on muscle response. A: several different ways of representing the same results. For these graphs a single fiber from frog semitendinosis was used, and isometric response was measured from periods of steady stimulus. Curve a, force differences in individual responses; curve b, contraction remainder at low point in response between stimuli; curve c, ratio of contraction remainder to stimulus rate; curve d, force peak (a + b); curve e, mean tension over time. All curves are plotted as functions of stimulus rate. B: rate of rise of tension (right ordinate and × values) at beginning of a stimulus train continues to increase through appreciably higher stimulus rates than does contractile tension (left ordinate and • values). This is an additional example of measures of muscle response that are not equally sensitive to stimulus rate. C: family of nearly isotonic responses of cat triceps sura muscle to slowly increasing stimulus rate (1 pulse/s2). Separate lines are made with different loads. At low stimulus rates and with small loads the responses to individual stimuli are particularly apparent (compare twitches in Fig. 6C). Lower graphs show derivative of average (negative) length with respect to stimulus rate (–d//dR), which was calculated using spline functions 408,559 on mean (smoothed) values of the upper graphs. These superimposed curves indicate that the principal sensitivity to stimulus rate for this muscle falls in the range of 8–25 pulses/s over a variety of loads. Separate peaks could represent populations of fast and slow muscle units within this muscle.

A: from Buchthal 76. B: from Machin and Pringle 352. C: from Partridge 395


Figure 9.

Dynamic effects of modulated stimulation. A: time graphs of response of load moving by cat triceps sura muscle driven with a sinusoidally modulated stimulus rate, 5–25 pulses/s, and at modulation frequencies marked on graphs. Amplitude of modulation was constant, but response amplitude changed with frequency of modulation. B: change in movement amplitude with frequency of modulation cycle. All stimulus cycles ranged from 5 to 35 pulses/s. Although the gravity part of loads was constant, each line represents a different load inertia, spanning a 28‐fold variation within the physiological range 394. Periodic force required for sinusoidally moving an inertial load increases proportional to inertia and proportional to the square of the frequency or, for this range 28 × (6.3/0.04)2 = 7 × 105, which is the ratio of force cycles for a constant amplitude movement. Considering the proportionality of force cycle to movement amplitude, this graph represents an actual 8 × 103 range of amplitudes of response cycles of force produced by a constant amplitude of modulation of stimulus rate. C: temporal displacement between stimulus cycle and response cycle in isometric records of cat triceps sura force as a function of cyclic frequency. Upper graph, lag of response in ms; lower graph, same data in fractions of a 360° cycle. D: representation of muscle properties combining both nonlinear and dynamic aspects. Each set of 3 coefficients (G0, fn, and ζ) define one 2nd‐order differential equation approximating data similar to that shown in parts in C and B. These coefficients when inserted in the equation specify dynamic properties of the muscle in one operating range of stimulus rates. Changes of coefficients with firing rate range represent some of the nonlinearities. •, ○, Values obtained from different muscles.

A and B: from Partridge 394. C: from Partridge 393. D: from Mannard and Stein 354, with permission of Cambridge Univ. Press


Figure 10.

Relations between muscle actions and temperature. A: twitch variations in frog muscle at 3 different temperatures. Time reference, 100 Hz. B: effect of temperature on tortoise muscle stiffness. Lower lines, static stiffness; upper lines, dynamic stiffness. Pairs of points are measured from one sequence of increasing and one sequence of decreasing temperature. C: height of frog muscle twitches at a sequence of temperatures between 0°C and 36°C. D: effect of temperature on duration of twitch. Temperature ranges between 5°C and 41°C, at which point response failed completely. E: change in temperature of body core, rt, and of muscle, mt, as a result of muscle activity in human. Crossing of the two curves shows a reversal of direction of heat transfer between muscle and relatively constant body core. Externally observable motor performance also changed in speed with temperature in this study, which may be related to “warm up” before athletic activity.

A: from Handbook of Physiology, by W. D. Halliburton, © 1911, used with permission of McGraw‐Hill Book Co. B: from Fowler and Crowe 180. C and D: from Howell 263. E: from Asmussen and Bøje 18


Figure 11.

Muscle contraction as modified by length. A: relationship between stress and strain in 12 tetanically stimulated glossopharyngeal muscles of frog. Data are from tables made by Weber in 1847 537. Eleven muscles, •, were loaded before stimulus. One muscle, ▽, was stimulated before loading. Normalization to stress and strain from length and tension, as described by Weber, allows comparison of muscles of quite different sizes. (We have crudely confirmed Weber's description of the very long range of lengths over which this muscle can respond.) B: comparison of active contribution to length‐tension effect in several different muscles. (For passive contributions of the same muscles, see Fig. 5A.) A, bee flight muscle; B, locust flight muscle; C, frog sartorius; D, anterior byssal retractor of clam. Ordinates are not normalized to compensate for muscle size differences. C: conventional measurement of active contribution to length‐tension effect. Passive response and maximal voluntary force were measured directly in human forearm flexor muscle with cineplastic tunnel prepared to allow external action of the tendon. Developed tension is calculated as difference between passive and maximal forces with no correction for result of local stresses within muscle and tendon. See Fig. 4A for similar data from twitches. D: family of length‐tension curves for single fiber of frog semimembranous muscle. Parameter distinguishing individual curves is stimulus rate. Note nonuniform increments of stimulus rate and compare Fig. 8. Values were calculated as mean of 2 values measured with increasing and with decreasing stimulus rate.

B: from Hanson and Lowry 229. C: from Ralston et al. 423. D: from Buchthal 76


Figure 12.

Effect of velocity on muscle response, measured at constant velocities while passing through a test length. All sets of curves are drawn on same abscissa. A: Force‐velocity effect at several different stimulus rates in cat soleus muscle using rotation of stimulus among 5 nerve branches. (Also see ref. 296 for differences introduced by slightly different test conditions.) B: rate of exchange of energy between muscle and load, or power, is equal to product of force F and velocity V. Negative power indicates output of energy by the muscle. (Energy delivered by each impulse, i.e., power ÷ pulse rate, varies with stimulus rate but is nearly independent of velocity over an appreciable range.) C: slope ∂F/∂V calculated from force‐velocity curves in A, a measure of sensitivity of force to velocity, or mechanical impedance (as in ref. 397). Negative values are proportional to a viscosity‐like measure. The value of this measure is greatest at low shortening velocities with high stimulus rates. Graphs B and C were calculated for this review from data points on force‐velocity graph (A) using spline interpolation 408,559. Spline fit lines pass through same data points, but they differ slightly from lines joining points in A.

A: from Joyce and Rack 294, with permission of Cambridge Univ. Press


Figure 13.

Expected 3‐dimensional mechanical relationship in response of muscle. Muscle force as related to length, velocity, and excitation drawn by combining usual descriptions (for related experimental data, see Figs. 8C, 9B, 10, 11D, 12A). Arrows on velocity axes show relationship between velocity sign and change of length (angle). Arrows on torque axis in F relate torque to corresponding direction of change of velocity. A: one 3‐dimensional description of response properties of a single muscle at a particular moment. Excitation of the muscle defines length‐tension‐velocity relationships in that muscle. At a single length this relationship is described as a force‐velocity curve, and at a single velocity it is a length‐tension curve. For length and velocity at some moment, instantaneous force falls at intersection of 2 such curves in length‐velocity‐force space. Red and green lines might correspond to 2 curves from a stimulus rate family, such as shown in Fig. 11D for length axis and Fig. 12A along velocity axis. At any other moment force output could be defined in terms of intersection of an appropriate stimulus‐determined pair of intersecting length‐tension and force‐velocity curves, at least a 4‐dimensional relationship. (Note: No dynamic component is represented in the passive response, although one is known to exist; see Fig. 5BD.) B: the 26 different red graphs of active length‐tension curves intersect in this diagram with each of the 26 red force‐velocity curves to define 676 of the points to which a particular excitation level might bring a muscle. Same number of intersections in green represent passive muscle. (The different individual curves were derived from assumption that at any length the nonlinear velocity effect is proportional to isometric active force at that length.) Inclusion of all possible points between samples drawn here would produce a “response surface”. If red surface designates the possible responses of maximally active muscle, then neural control would operate in space between red and green surfaces. (see ref. 25 for an experimentally derived half‐surface drawn with a different orientation of the axes.) C: another variation of a response surface differing from B by a simple shift in relationship between passive and active length effects. Different muscles have properties that range between and beyond these types. D: representation of a sinusoidal movement as a trajectory over a response surface. A sinusoidal change in length, l = A sin ωt, defines a cyclic velocity, V = A ω cos ωt, that varies in amplitude with frequency. Such pairs of curves trace eliptic paths on phase (base) plane and define complex closed loop trajectories over response surface. Time‐varying force traced by such trajectories is periodic but not sinusoidal. This transformation from movement into force is inferred by the accepted length and velocity properties of maximally and constantly activated muscle. Response cycle has a phase‐shift based on shape of response surface; it changes with movement frequency, amplitude, and bias. (Nonsinusoidal patterns of movement similarly can be graphed over this theoretical surface. As illustrated in Figs. 15 and 16, more complex stimulus and movement patterns tend to produce deviations from response surface predicted by the usual muscle description and represented by these graphs.) E: time graphs for one movement over response surface of D. Two cycles of sinusoidal length change centered around rest length, Lo, are shown by black curve at top of figure. Corresponding but phase‐shifted force cycle for a maximally activated muscle is shown by the periodic, nonsinusoidal, red curve marked Fmax. In some stretching parts of the cycle that force exceeds maximum isometric force, 100% Fi. At the specified lengths passive forces are all near 0 (0% Fi), as shown by line marked Fmin. Any constant force (e.g., 40% of Fi) falls at different relative positions with respect to minimum and maximum force for velocity‐length combinations as values change through the movement. If such a constant force can be produced through a movement, then a variation of activation of the muscle would be required. Here activation A is defined for any particular force as the relative position of that force between Fmax and the passive force for existing physical conditions at the moment. In this example in order to maintain the constant 40% Fi force through the described movement, the neural drive would have to provide a time‐varying activation (from 33% to 80% of maximal), as plotted on line marked % A. F: theoretical response surfaces for a pair of matched antagonist muscles. Green lines represent surface expected while both muscles are unexcited. Red lines represent the response surface expected when both muscles are maximally active. This surface does not show a simple cancellation of force; i.e., coactive surface is not a horizontal plane equal to passive surface. For the slopes, ∂T/∂θ relates to stiffnesslike properties, and ∂T/∂V relates to a viscosity‐like property. Lengths, velocities, and forces that describe linear action of a single muscle are replaced here by angles, angular velocities, and torques, which describe combined action of antagonist muscles on a hinge joint.

Adapted from Partridge 399


Figure 14.

Effects of excitation history on dynamics of muscle response. A: sequence of afterload frog muscle twitches recorded as fatigue develops. Increased height over first few trials (treppe) is followed by decreased amplitude (fatigue) as well as by increased latent period, increased time to peak, and slowed relaxation. This latter effect is known as contracture. B: change of response in 2 cat limb muscles as a result of surgically crossed innervation. Upper two graphs, normal muscle twitches in crureus and gracilis muscles. Lower records, altered response under influence of reinnervation by crossed nerves—slow muscle becoming faster and fast muscle becoming slower. Line below twitch record shows a digital measure of contraction time in ms arranged in series of dots, each column with a maximum of 10 1‐ms points. C: adaptation of response of anterior tibial muscle of rabbit to long‐term activity pattern. Two isometric responses to stimulus trains of 25 pulses/s. Lower record, response of normal muscle; upper record, muscle modified by stimulation at 10 pulses/s over a 5‐month period.

A: from Handbook of Physiology by W. D. Halliburton, © 1911. Used with permission of McGraw‐Hill Book Co. B: from Buller et al. 87, with permission of Cambridge Univ. Press. C: from Salmon 447


Figure 15.

Deviations of muscle response to stimulus from that of a simple, response surface model with lag. Examples show that muscle responses vary with stimulus history and past activity in other units and that mechanical effects are variable with stimulus level. A: hysteresis in cat triceps sura muscle response to rate modulation of stimulus. Insert, time sequence of stimulus. In graph of length vs. stimulus rate, time progresses in a counterclockwise direction. After a high stimulus rate, contraction is sustained even at appreciably lower stimulus rate. Similar hysteresis patterns are also found in isometric responses. Hysteresis did not occur in cycle with lowest maximum rate. B: difference in relationships between stimulus rate and force in lengthening and in isometric muscle. At high stimulus rates lengthening muscle, •, produced more force than isometric muscle, ×, a relationship represented in the response surface diagrams of Fig. 13. At low stimulus rates, however, the relationship is reversed, suggesting a locally reversed slope for the force‐velocity curve at such stimulus rates. C: hysteresis in muscle response to recruiting type of stimulus modulation in human peroneus muscle at constant rate of 50 pulses/s. Ust, time graphs of stimulus intensity; Miso, isometric responses to stimulus. Lowest graph, force vs. stimulus, derived by combining data of type shown in the 2 time graphs and as labeled for point A and point B.

A: from Partridge 396. B: from Joyce et al. 296, with permission of Cambridge Univ. Press. C: from Trnkoczy 508


Figure 16.

Responses to mechanical inputs that deviate from response prediction implied by a simple version of the type of model illustrated in Fig. 13. A: response of stimulated triceps sura muscle to stretch showing mechanical hysteresis. In both lines stimulus was 120 pulses/s and velocity 0 at the same final lengths. In response marked by stimulus was started with muscle at a shorter length followed by a quick stretch to test length, producing a persistent increase of force over that in other response, with test length used throughout stimulus period. (See also Fig. 11A.) B: length‐tension relationship in flight muscle of water beetle. Lower curve, passive muscle; upper curve, active muscle; loop, trajectory plotted on work plane with tetanized muscle subjected to cyclic stretch. Response travels around loop in an energy‐delivering, counterclockwise direction, in contrast to energy‐absorbing, clockwise loops ordinarily described with other muscles. In this case, unlike the diagramed force surfaces, force at shortening velocities is greater than those at the same length and lengthening velocities. This relationship allows these muscles to drive an oscillatory movement without a corresponding oscillating excitation pattern. C: length of a tetanically stimulated muscle before, during, and after a transition from one force to a larger force. In each line, muscle shortened at beginning of stimulus, stretched as load increased, then lengthened again at the end of stimulus. Initial and final forces were the same for each load increase, but rate of change of force varied, increasing from line 1 to line 4. Effect of different rates of loading persisted in terminal periods of constant and equal load. Greatest stretch occurred with fastest loading. D: disruption of fusion of tetanus during mechanical movement. Left part of record shows a stretch; right part shows a subsequent release of cat soleus while stimulated at 8.5 pulses/s. Upper lines, force; lower lines, muscle length.

A: from Walker 528. B: from Machin and Pringle 352. C: from Katz 304, with permission of Cambridge Univ. Press. D: from Joyce et al. 296, with permission of Cambridge Univ. Press


Figure 17.

Combinations of independent units of muscle. (See also Figs. 1B, 13F, and 15C.) A: recruitment of 3 separate respiratory motor units and accompanying increase of firing in individual units (measured from unit electromyogram (EMG) records) as total response intensity increases. Measured motor response is tidal air moved as it increased with rebreathing. B: smoothing of soleus isometric response by alternation of excitation among groups of motor units. Muscle nerve was divided into 5 branches, and each was provided with separate stimulus electrodes. Responses to individual stimuli can be distinguished in record made with synchronous stimulus to all branches. Rotating of branch stimulus (with each division stimulated in turn at same rate) produced response that was not only smoother but greater in magnitude than average of synchronous response. (Normal recruitment produces asynchronous instead of rotating excitation, presumably a less effective means of smoothing.) C: combination of activity of several muscles during bicycling. Weak and strong EMG activity are shown by single and broad lines, respectively. Note variable overlap between muscle activity periods, as well as two separated phases of strong activity in gracilis, Gr. D: recruitment of 3 types of motor units in 2 muscles of lion as speed of locomotion increases. Discontinuities in graphs represent change in type of gait. As seen in histochemical evidence, relative intensity of activity of different types of units does not change in the same order through all gaits and muscles.

A: from Gesell et al. 188. B: from Rack and Westbury 421, with permission of Cambridge Univ. Press. C: from Houtz and Fischer 262. D: from Armstrong et al. 17


Figure 18.

Relationships between several measures of muscle action. Broad arrows represents the multiple signals carried in the signal pathway within the biological system. Mechanical and electrical impedances through which biological signals are coupled to recorder system are marked Z. Electromyogram (EMG) signal may be further processed to some form of pulse signal or to an averaged EMG. Functional output may be measured as any of a variety of motor actions, as well as in form of direct muscle responses. A: nerve activity (ENG) and motor action as measured from phrenic nerve and as tracheal pressure show examples of entry of nerve signal into a muscle system and a motor consequence. B: direct EMG, averaged EMG (AEMG), muscle force, and length—measured during one step of walking, from cat triceps sura muscle. Non‐phase‐shifting digital filter was used to average EMG signal. Force was sampled from tendon in situ and length measured from slow motion movie films. These signals differ as a result of transformations that have occurred in instrumentation as well as in biological components. C: muscle sound pulses recorded from auricularis superior muscle. Myosonogram (MSG) pulses are related one to one to EMG pulses of same unit. Little systematic information is available about how effects of length, velocity, and temperature are represented in the sonogram. D: 3 pulse‐based measures from a unit of respiratory muscle. Bottom line, time of visually identified unit pulses; points on graph, pulse‐by‐pulse calculation of firing rates (inverse interval); solid line, smoothed pattern of firing rate. Accepted methods include variations in derivation of each of these measures of muscle activity, and these variations introduce noticeable differences in the way a particular action is displayed.

A: from Gesell 187. B: from Yager 563. C: from Gordon and Holbourn 203, with permission of Cambridge Univ. Press. D: from Gesell et al. 189


Figure 19.

Variation of relations between measures of physiological muscle activity with type of measurement and mechanical conditions. A: relationship between muscle force and integrated electromyogram (EMG). Each measurement on upper line made from the muscle while shortening; measurements on lower line made during lengthening of same muscle, showing velocity effect on force‐EMG relationship. B: effect of muscle length on force‐EMG relation in human soleus. Separate lines, lengths determined by ankle position in 0.5‐in. increments of muscle length. Mechanical action of gastrocnemius was avoided by bending the knee. C: different nonlinear functions relating force to integrated EMG and to action potential count from same EMG (scaled to match at high and low ends of samples). D: effect of different electrode arrangements on relationship between force and EMG recorded in same tests. Monopolar and bipolar electrodes were used, and spike count was measured. Electrode placements also affects voltage and frequency distributions of EMG 337.

A: from Bigland and Lippold 49, with permission of Cambridge Univ. Press. B: from Close et al. 110. C and D: from Close 109
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L. D. Partridge, L. A. Benton. Muscle, the Motor. Compr Physiol 2011, Supplement 2: Handbook of Physiology, The Nervous System, Motor Control: 43-106. First published in print 1981. doi: 10.1002/cphy.cp010203