9.1 Skeletal Muscle Morphology

Skeletal muscle is the largest organ in the body. It accounts for approximately 40% of total body weight and is organized into hundreds of separate entities, or body muscles, each of which has been assigned a specific task to enable the great variety of movements that are essential to normal life. Each muscle is composed of muscle fibers and connective tissue. The muscle fibers are the active elements, while connective tissues are the passive elements and serve as the connection between the muscle fibers and the skeleton. The muscle fibers are arranged in parallel and normally extend from one tendon to another ( Fig. 9.1 ). A thin layer of connective tissue, the endomysium, surrounds each individual muscle fiber. The individual fibers together with their endomysium are arranged in bundles (fascicles) and each bundle is surrounded by another layer of connective tissue, the perimysium. Muscle fiber bundles have a diameter of approximately 1 to 3 mm. The whole muscle is enclosed by the epimysium. The epimysium is continuous with the fascia, which allows the muscle to slide with respect to surrounding tissues. The connective tissue of the muscle also contains blood vessels and nerves ( Fig. 9.1a ).

Muscle fibers, or muscle cells, are cable-like structures composed of tightly packed subunits, myofibrils, that fill up most of the volume of the fibers ( Fig. 9.1b ). Satellite cells are located between the basal membrane and the cell membrane of the muscle fiber. These cells are the muscle fiber stem cells, also called myogenic progenitor cells. Given that fully differentiated muscle fibers are postmitotic, the only cells that can divide to serve in different repair and regeneration processes are the satellite cells. The satellite cells are not innervated but are influenced by the microenvironment and chemical signal substances produced in the muscle fibers.

In humans, the length of the muscle fibers may vary between a few millimeters and many centimeters. It is generally assumed that the length of a muscle fiber can be about 60% of the total muscle length. The mean diameter of a muscle cell is approximately 50 μm, especially in untrained individuals. The relationship between the muscle cell diameter and muscle fiber length is called the aspect ratio; a muscle cell with a diameter of 50 μm and a length of 15 cm is 3000 times longer than it is thick; that is, it has an aspect ratio of 3000.

The myofibrils are made up of filaments, called myofilaments. The myofilaments are arranged in sarcomeres, which are the contractile units of the muscle fibers. Sarcomeres are arranged in series and in parallel and are responsible for force generation and shortening of the muscle fiber. The sarcomere is defined as the part of the myofibril enclosed between the so-called Z-disks or Z-lines ( Fig. 9.1b ). From the Z-disk, (thin) actin myofilaments project towards the middle of each sarcomere and in the central region of each sarcomere they interdigitate with (thick) myosin filaments. Each (thick) myosin filament is surrounded by a hexagonal array of (thin) actin filaments. When a muscle is in a relaxed state there is some overlap between the myosin and the actin filaments.

Force is generated in the sarcomere through interaction between the actin and myosin filaments ( Fig. 9.1c ). 1– 4 Structures called cross-bridges form part of the (thick) myosin filaments. They attach to the backbone of these filaments in such a way as to enable them to attach to sites on the (thin) actin filaments that are close by. The cross-bridges are functionally identical and act independently. The probability of a cross-bridge attaching to an actin filament is influenced by local biochemical conditions such as the calcium ion concentration. At any given time during activity of a muscle, some cross-bridges are attached to the actin filaments but others are detached or moving towards new attachment sites ( Fig. 9.2 ).

When attachment occurs, the cross-bridges undergo structural deformation. Force is generated and the thin filament (actin) is pulled along the thick filament (myosin). The myofilaments slide in relation to each other and the overlap between the filaments increases; at the same time, the sarcomere shortens ( Fig. 9.3 ). According to the theory of contraction, the length of the myosin filaments is assumed to be constant and not to contribute to the shortening of the sarcomere. Therefore, the shortening of a sarcomere is assumed to occur only via the sliding of the filaments relative to each other. The total shortening of the myofibril is the sum of the length changes occurring in the sarcomeres arranged in series in that myofibril. Supposing we have two myofibrils, one consisting of ten sarcomeres and the other of five sarcomeres arranged in series. The amount of shortening of the former will be twice that of the latter.

It is assumed that active muscle force originates exclusively from cross-bridges. As a consequence, active force generated at any given time is dependent on the number of parallel cross-bridges attached to the thin (actin) filaments. Because of the sarcomeres within a myofibril are arranged in series, the force generated by one unit has to be maintained and transmitted to the next unit, and thus the force of the whole structure is equal to the force of a single unit, that is, the force of one sarcomere. The force being transmitted from one half of the sarcomere, that is, from the Z-disk to the myosin filament via the actin filament, must be equal to the force transmitted to the actin filament via the myosin filament in the other half of the sarcomere ( Fig. 9.4 ). 5 It follows that an equal number of active cross-bridges should be attached in both parts of the sarcomere. If the number of active cross-bridges is small, the force developed is low. If the number of active cross-bridges increases, the force developed will also increase.

In general it is believed that forces developed in the sarcomeres are propagated to the tendon through musculotendinous junctions. This model is true for muscle fibers ending close to the tendon or fascia of the muscle. Some muscle fibers, however, end within the muscle belly. In these cases it is generally believed that the force generated in the sarcomere is transmitted via shear forces to the endomysium of the muscle cell. It follows that forces developed in a muscle fiber are transmitted not only in the longitudinal direction but also perpendicularly. Forces can therefore be transmitted perpendicularly between sarcomeres and neighboring myofibrils and between myofibrils and the muscle cell membrane. The transmitted forces perpendicular to the direction of the muscle fiber occur through the interaction of intermediate filaments, for example desmin filaments, and through the muscle fiber’s connections to costameres located in the muscle cell membrane (see Fig. 9.1d ). In addition, muscle fibers also contain dystrophin and dystrophin-associated proteins. This protein complex connects the cytoskeleton of the muscle fiber to the extracellular matrix. The main functions of this complex are to transmit forces generated in the sarcomeres to the extracellular matrix and to stabilize the cell membrane during muscular contractions ( Fig. 9.5 ).

Titin is an important molecule within the sarcomere and creates a continuous filament system throughout the length of the myofibril. It is suggested that titin serves as a stretch sensor at the cellular level and may act in protein up- and down-regulation as well as influencing various gene activities.

9.2 The Force–Length Relationship

Sarcomeres arranged in series are called myofibrils. Muscle fibers are a collection of myofibrils arranged in parallel. Thus, muscle fibers are a collection of sarcomeres arranged both in series and in parallel. The maximum force developed in a muscle fiber will increase in proportion to the quantity of myofibrils arranged in parallel; in other words, the force is proportional to the cross-sectional area of the muscle fiber ( Fig. 9.4 ). Experiments have shown that the amount of force developed in a muscle fiber depends on the length of the muscle fibers at the time of activation and the contraction velocity. These dependencies are understood to be determined by the filament system and by the parallel and serial arrangement of sarcomeres within the muscle fibers. 6– 10

Since the late nineteenth century, it has been known that the force developed by a muscle of constant length (that is, during isometric contraction) varies with its length at the start of the contraction. The muscle generates less force when it is in a very much shortened or lengthened state than it does at a mid-range length. The isometric force–length relationship can be measured directly when a muscle is maximally stimulated at a variety of discrete lengths and the resulting force is recorded. When the maximum force at each length is plotted against the length, a relationship like that shown in Fig. 9.6 is obtained. The force–length curve represents the results of many experiments plotted on the same graph, which is an artificial connection of individual data points from isometric experiments. Therefore, the force–length relationship is strictly valid only for isometric contractions. The structural basis for the force–length relationship was elucidated in the early 1960s. Basically, the force–length relationship in skeletal muscle is understood as a direct function of the overlap between actin and myosin filaments.1, 9

9.3 The Force–Velocity Relationship

Skeletal muscle has an inherent capacity to adjust its active force to precisely match the load exerted on it during shortening, or to regulate the resistive force during muscle elongation. This property distinguishes muscle from a simple elastic structure and is based on the fact that active force generation is continuously adjusted to the speed of the contractile system. The maximum force that a muscle can develop depends not just on its length but also on the velocity of the contraction. It can be observed that the active force developed by a skeletal muscle is higher when the contraction velocity is low and decreases as the contraction velocity increases. Thus, when the load is high, the active muscle force is increased to the required level by reducing the speed of contraction. Conversely, when the load is low, the active force can be made correspondingly small by increasing the speed of shortening.

Fig. 9.7 shows the relationship between force and velocity of an isolated whole sartorius muscle of the frog, published by Hill. 8 Like the force–length relationship, the force–velocity relationship is a curve that represents the results of several experiments plotted together on the same graph. A muscle is stimulated maximally and allowed to shorten or to lengthen against a constant load. The contraction velocity during shortening or lengthening is measured and then plotted as a function of the load.

According to Hill, the relationship between the magnitude of force F and the contraction velocity v during a concentric (shortening) contraction may be described by the equation

In this equation, a and b are experimentally derived constants. The values of a and b are estimated at approximately 0.25. F_max is the maximum tetanic force developed at a given muscle length. The maximum force development is achieved at a contraction velocity v equal to zero. The maximum contraction velocity v_max is observed at force F equal to zero ( Fig. 9.7 ). The Hill equation can be used to predict the relative change in muscle force occurring as a muscle is allowed to contract.

The reason why muscle force is related to contraction velocity is because a certain amount of time is required for the cross-bridges between actin and myosin to attach and detach—the rate at which they cycle through attachment/detachment is therefore a constant. 3, 7, 16 At any point in time, the force generated by a muscle depends on the number of cross-bridges attached. When the contraction velocity increases, the filaments slide past one another faster and faster, fewer cross-bridges can be attached, and therefore force decreases. Conversely, as the relative filament velocity decreases, more cross-bridges have time to attach and generate force, so that force increases. This account does not aim to give a full description of the foundation of the force–velocity relationship, but only to provide some insight into how cross-bridge rate constants can affect force generation as a function of velocity.

9.4 Theoretical Modeling of Skeletal Muscle Behavior

The purpose of skeletal muscle modeling is to predict static and dynamic behavior in different situations. The model of a muscle is constructed from single elements with known mechanical properties. Elements may be combined to represent properties of the whole muscle. Hill6 developed a muscle model consisting of two basic elements: a contractile element and an elastic element ( Fig. 9.8a ). The contractile element models the myofilaments responsible for active force development. The elastic element describes the passive elastic properties of the structure. The mechanical property of the elastic element equals the elastic property of a spring (see Chapter 2 ). Like a spring, the elastic elements store energy during elongation and release virtually all the energy as they return to their original length.

In its simplest form, the Hill6 model is constructed from a contractile element connected in series with a passive elastic element. In this model, the contractile elements are considered to have force–length as well as force–velocity characteristics similar to those described for muscle fibers. As the two elements are connected in series, both are subject to the identical tensile force. The change in length of the combined model is the sum of the length changes occurring in each element of the model. The velocity of shortening and lengthening of the model is the sum of the velocities of both elements of the model.

The combined function of the elastic and contractile elements connected in series seems to be important for producing fine, coordinated movements. 17, 18 It follows from the model that, during contraction of a muscle, force will increase slowly. This is assumed to be due to the simultaneous shortening of the contractile and lengthening of the elastic elements. The length changes of the contractile and elastic elements counteract each other, allowing a smooth movement to occur without any jerking. In other words, the elastic elements dampen rapid increases in muscle force. 19

If a muscle fiber is shorter than its optimum length, further shortening of the fiber leads to a decrease in force development accompanied by simultaneous shortening of the series elastic element (in series to the contractile element). When the contraction velocity of a muscle fiber increases, the force is reduced (because of the force–velocity relationship) and the series elastic element is again allowed to shorten. As a consequence, the overall length change in the model that combines contractile and elastic elements is greater than the length change that would be possible with an isolated contractile element.

To explain the mechanical behavior of passive muscles, a third element is introduced: the parallel elastic element ( Fig. 9.8b ). The parallel elastic element is arranged in parallel to the contractile element. As the stiffness and the tensile strength of the contractile element are assumed to be negligibly small, the parallel elastic element is the source of the force preventing rupture of contractile elements during passive elongation of a muscle. On the other hand, the force of the parallel elastic element is negligibly small compared with the maximum force of the contractile element, so when maximum active force is generated, the parallel elastic element will resist only a small fraction of the external force and will consequently shorten.

9.5 Mechanical Properties of Tendons

Tendinous tissue behaves like a nonlinear elastic structure. Fig. 9.9 shows an example of a force–length characteristic of tendon, based on data published by Woo et al. 20 A specimen consisting of a tendon and its insertion into bone (tendon–bone complex) was investigated. Starting from its resting length, the tendon– bone complex was elongated up to rupture or failure at the site of insertion, and the opposing (resistive) force was measured. The stiffness of the complex at each point of the curve is defined as the ratio of force increase and length increase, that is, ΔF/ΔL [N/m]. The figure shows that the stiffness of the tendon is a function of elongation. With minor elongation of the tendon, stiffness is low, so, for example, small changes in force have relatively large effects on tendon length. As elongation increases, stiffness increases as well. In the linear portion of the curve, stiffness is virtually constant. The stress σ_max (force divided by crosssectional area) of a tendon at the point of rupture amounts to approximately 100 MPa; the strain ε_max at rupture is in the region of 10% of the starting length.

The series elastic elements located in tendinous tissue are important for optimum function of active muscles. When a muscle develops force, the length of the tendon increases and the muscle is allowed to shorten. Because of the change in tendon length, a muscle–tendon unit will have an increased operating range relative to the range of muscle fibers alone. If the muscle–tendon unit is strained by small forces during a movement, the length change in the unit will occur at the tendon because of its lower stiffness. The result is that a fraction of the length change that would have to be accommodated by muscle fibers is actually taken up by tendons. Thus, by attaching muscles to bones via compliant (elastically elongating) tendons, the length changes of the muscle fibers are reduced. Length changes of muscles and their tendons may also have opposite signs. When the force of a muscle–tendon unit with constant length is reduced, the tendon is allowed to shorten, while muscle length will increase. Length changes of tendons also dampen sharp increases in muscle force, so the time elapsing until the muscle force reaches its maximum value is, in fact, increased.18

Plastic deformation of tendons is negligible; after release, a stretched tendon will return to its original length. The energy expended on stretching the tendon is stored as potential energy and released almost completely as the force exerted on the tendon decreases to zero. The loss of energy is less than 10%. The force–length characteristics of tendons are dependent only to a minor extent upon the velocity of stretching. Therefore, the deformation energy stored in a tendon during stretching is given by the area below the force–length curve.20– 22

In this formula E denotes the energy, F the magnitude of the resistive force, and dL the change in length. The integral extends from the resting length of the tendon (with zero force F) up to the length reached under the force applied. The amount of stored energy increases as stretching increases (see Chapter 3 ). At higher forces the tendon is rather stiff and the change in length relative to the change in force will be small. Therefore, in this situation the increase in stored energy will be small as well. A greater amount of energy could be stored if the length change in the tendon were increased. In real life these increased ranges of elongation are obtained during stretch–shortening cycles occurring in a variety of movements. During a stretch–shortening cycle the initial stretching of the muscle–tendon unit is followed by active shortening of the complex. During the stretching phase energy is stored in the unit.

The potential energy stored in a muscle–tendon unit is released by decreasing the force exerted on the structure. If this is done slowly, the energy will become available slowly; if it is done at a rapid rate, the energy will be released rapidly as well. The amount of energy released per unit of time, the power P, is given by

where F is the force and v the shortening velocity of the muscle–tendon unit.

It is of practical importance that tendons can store energy during a stretch–shortening cycle at a relatively low rate. Upon lengthening, the tendon then acts as an energy reservoir that can be emptied at a high rate to effect movements with high speed and power.5 This situation may be compared with shooting an arrow with a bow. The potential energy of the bow is increased when the active muscles pull on the string, thereby deforming the bow. When the string is suddenly released, the deformation energy is set free and the arrow will be launched with high power, resulting in a high velocity.

9.6 Force Regulation in Skeletal Muscles

An excitatory impulse generated naturally in the central nervous system or artificially by an electrical signal generator creates a so-called action potential (specific electrical field) at the relevant muscle fibers. The tensile force developed by a single fiber in response to a single action potential invading the axon terminals is called a twitch. As the frequency of the stimulating impulses increases, twitches begin to overlap. At frequencies above a certain limit, single twitches can no longer be discriminated and tetanic contraction develops. The frequency limit, where tetanic contraction or tetanic force generation occurs, varies among different fibers and individual motor units. This limit is normally observed in the range between 10 and 100 Hz ( Fig. 9.10 ). The higher the frequency of stimulation of the muscle fibers, the greater is the force produced in the muscle as a whole. percent of the maximum force

Skeletal muscle fibers possess a wide spectrum of morphologic, contractile, and metabolic properties. Muscle fibers are classified as fast or slow, oxidative or nonoxidative, and glycolytic or nonglycolytic. 23, 24 Often, only three different types are described; for details see Table 9.1 . The three types differ characteristically with respect to speed of shortening, force generation, and endurance. Fast-contracting fiber types (type IIb) shorten approximately two to three times faster than slow-contracting fibers (type I). The specific tensile stress (force divided by cross-sectional area) of fast muscle fiber types is higher than that of slow muscle fibers. In general, slow muscle fibers (type I) have the greatest endurance, followed by type IIa and type IIb fibers.

The functional unit of force generation in a muscle is the sarcomere (in fact, the half-sarcomere, due to sarcomere symmetry). The functional unit of force generation of the muscle is the motor unit. A motor unit comprises an α-motoneuron and the muscle fibers innervated by it. This unit is the smallest part of the muscle that can be made to contract independently. Motoneurons have their cell bodies in the ventral root of the spinal cord. The axons of the neurons terminate at the motor endplate of the fibers. When stimulated, all the fibers of a motor unit respond simultaneously. The fibers of a motor unit are said to show an “all-or-nothing response” to stimulation: they contract either maximally or not at all.

Motor units are usually classified according to the physiological properties of their muscle fibers.24 These properties are the motor unit twitch tension, the tetanic tension recorded at an intermediate stimulation frequency, and the fatigability of the unit in response to a specific stimulation protocol ( Fig. 9.11 ). In general, motor units belong to three different groups. Those that have a fast contraction time and a low fatigue index are known as fast fatigable (FF) units. Those that have a fast contraction time and a high fatigue index are designated fast fatigue-resistant (FR) units. Those that have slow contraction times, and which are most resistant to fatigue, are classified as slow (S) units.

A whole muscle is subdivided into many motor units, each of which comprises a single motoneuron and its related muscle fibers. The muscle fibers belonging to one motoneuron have the same physiological, biochemical, and ultrastructural properties. The number of muscle fibers belonging to a motor unit, and the number of motor units within a whole muscle, vary widely. This is closely related to the degree of control required of the muscle. The muscle fibers within a motor unit are interspersed among fibers of other motor units. The functional consequence of this dispersion is that the forces generated by a unit will spread over a larger tissue area. This may minimize mechanical stress in focal regions within the muscle.

The nervous system can vary muscle force output by two mechanisms. By varying the stimulation frequency, the force will be changed: when the frequency of stimulation is increased, the force output will increase as well. Thus, the force output is positively related to the discharge rate of a motor unit. This phenomenon is termed temporal summation. Alternatively, muscle force can be varied by changing the number of motor units that are active at a given time. For relatively low-force contractions, few motor units are activated, while for higher force generation, more units are activated. 26 The process by which motor units are added as muscle force increases is termed recruitment.

In their classical study, Henneman et al 27 showed that, at very low forces, low-amplitude voltage signals of short duration (“spikes”) were observed at the nerve. As muscle force increased, the size of the spikes also increased in a very orderly fashion: as force continued to increase, the units recruited exhibited larger and larger spikes. The entire process was reversed as force decreased. From these observations it was concluded that, at low muscle force levels, motor units with the smallest axons and the lowest threshold and depolarization frequency were recruited first. As force increased, larger and larger axons with higher activation thresholds and higher excitation amplitudes were recruited. This is known as the “size principle” and provides an anatomical basis for the orderly recruitment of motor units to produce a smooth contraction. In later studies (for example, that by Binder and Mendell 28) it was determined that, in general, small motor axons innervate slow motor units (type I) and larger motor axons innervate fast motor units (types IIa and IIb). These findings were confirmed in studies on human motor units. 29, 30

Based on the above findings, the following scheme was proposed for the voluntary recruitment of motor units ( Fig. 9.12 ). At very low excitation levels, the smallest axons with the lowest threshold to activation are activated first. As voluntary effort increases, most of the next-largest axons are recruited, activating the type IIa fibers. During maximal effort, the largest axons innervating type IIb fibers are activated. This activation pattern seems reasonable, since the most frequently activated S units are those with the greatest endurance. The FF units, which are rarely activated, have the lowest endurance. In addition, the S units (type I), which are activated first, develop the lowest tension, so that low tension is generated as contraction begins. This provides a mechanism for smoothly increasing tension as first S units, then FR units, and finally FF units are recruited.