Figure 1.​8 shows many of the main skeletal muscles in the body.

Skeletal muscles account for of the typical body mass, or 30 kg of a 70 kg person. At rest, they use 18% of the body energy consumption rate (which is called the basal metabolic rate or BMR); they use much more during activities, such as motion. Of the total energy “burned” by skeletal muscle, only 25% is used for work, and this is the muscular efficiency. The other 75% is released as heat. (This inefficiency of the body does have a positive purpose—it is a consistent and very important source of body heat.)

The maximum muscle force or tension T that a muscle can develop is PCA, where PCA is the physiological cross-sectional area of the muscle. The range of the maximum values of is 20–100 N/cm during isometric (constant length) conditions; the larger values are for muscles with the pinnate fiber structure that is described below. (See Fig. 5.46 below and Problem 5.2.) In the quadriceps, the forces are up to 70 N/cm during running and jumping and 100 N/cm under isometric conditions. We will discuss this more later.

Countermovements before sudden motion are known to increase athletic performance [63]. Quickly squatting before squat jumps leads to higher jumps. It is not known whether this pre-stretching allows more time for muscles to become active, optimizes sarcomere lengths and forces (see below), induces the activation of other muscles, or stores elastic energy in tendons, ligaments or the elastic components of muscles. This countermovement may be the reason why balls can be thrown faster with a windup during baseball pitching, and this might be due to the storage and subsequent release of elastic energy.

Sometimes the estimate that a maximum of 250–500 W are generated per kg of active muscle for isotonic conditions (constant tension) is used in calculations of motion (and this with pre-stretching) [13, 25, 78, 79]. Because this is averaged over the areas, lengths and speeds of the muscles that cause motion, we will usually use the muscle force per unit area in analysis.

Many muscles that cross the hip, knee, and ankle joints are important in locomotion. The relative significance of these leg muscles depends on the locations of their points of origin and insertion, lengths, and their PCAs. Quite a few of these muscles are depicted in Figs. 3.​3, 3.​4, 3.​5. (Analogous sets of musclesare involved in controlling our arms and hands, as seen below in Figs. 5.22 and 5.23.) The relative PCAs are given in Tables 5.1, 5.2, 5.3. In general, longer muscles enable larger angles of rotation about joints. The larger the muscle PCA, the more the muscle strength. Muscles with smaller PCAs can be important in providing stability.

As is clear from Figs. 1.​8 and 3.​2 and from Tables 5.1, 5.2, 5.3, many of these leg muscles pass over more than one joint. Figure 5.2 shows the three such major biarticulate (two joint) muscles in the leg. The forces exerted by the muscles on the bones at the points of origin and insertion are the same (Newton’s Third Law), but the torques are different at the proximal and distal joints because the moment arms are different. As seen in Fig. 5.2, the gastrocnemius is a knee flexor and ankle plantarflexor (extensor), with the torque about the latter joint greater because of its larger moment arm (5 cm vs. 3.5 cm). During stance the net effect of this muscle is to cause the leg to rotate posteriorly and to prevent the knee from collapsing. The hamstrings are extensors of the hip and flexors of the knee, with hip extension having twice the moment of knee flexion. During stance, this causes the thigh to rotate posteriorly and prevents the knee from collapsing. The rectus femoris of the quadriceps is a hip flexor and knee extensor, with a slightly larger moment about the hip. However, the major action of the quadriceps is knee extension because 84% of the quadriceps PCA is from other muscles, the uniarticulate knee extensors (and all of these muscles fire simultaneously). The net effect of these three major biarticulate muscles is the extension of all three leg joints, and they help prevent against collapse due to gravity. Coordinated motion of these muscles, such as the lengthening of one of these muscles and shortening of another, is needed to achieve the full range of rotation of these joints because of the limited change of muscle length of any one of them [81].

Muscles have a fiber structure with successive levels of fiber-like substructures called fasciculi (fuh-sik’-you-lie). (A single one is a fasciculus (fuh-sik’-you-lus).) On a macroscopic basis, these fibers are arranged in one of several ways. This is illustrated in Fig. 5.3. It appears that the forces generated by individual muscle fibers and muscles can be added independently [65, 66].

In fusiform muscles the muscle fibers are parallel and they narrow and blend into tendons that attach to the skeleton. In parallel muscles the fibers are also parallel. They tend to be long, such as the sartorius—the longest muscle in the body, which spans from the hip to the tibia (Figs. 1.​8 and 5.4). (The fibers are also parallel in the rectus abdominis (the “abs”).) We will usually not differentiate between fusiform and parallel muscles because of their similar arrangement of muscle fibers. These muscles consist of many sarcomere components in series (see below), and as such they can become much shorter to produce much movement of bones for motion about joints, and they can do so quickly. In unipinnate muscles, parallel muscle fibers attach to tendons at an angle, such as with the flexor policis longus (poe-lee’-cis) in the lower hand/thumb and the extensor digitorium longus (di-gi-tor’-ee-um) in the lower leg/foot. In bipinnate muscles, such parallel muscle fibers attach to a tendon in two different directions, such as with the rectus femoris (fe-more’-is) in the thigh. These pinnate (or pennate or pinnation) structures resemble the structure of feathers and of some leaves on branches. The fibers attach on the central tendon at several angles in the multipinnate deltoid (shoulder) muscles. Many short muscle fibers can attach to such short tendons in pinnate muscles, leading to larger forces than for parallel muscles and more movement, but with less efficient use of the muscles forces (see below and Problem 5.17). The orbicularis oculi (or-bee-queue-lar’-is ok’-you-lie) about the eye are circular muscles, in which the muscle fibers are in a circle about the object. The pectoralis major (pec-tor-al’-is) in the upper chest (the “pects”) is a convergent muscle; such muscles are broad at their origin and narrow at insertion, leading to large forces near the insertion point. Examples of each of these muscle types in the body are shown in Fig. 5.4.

The way the forces from muscle fibers add to give the total force on the attaching tendon differs for these different muscle structures. In parallel, fusiform muscles, all the force of the fibers is transmitted to the tendon. In pinnate muscles, the fibers are attached to the tendon at an angle , and only of the force of each fiber is effectively transmitted. While this is a distinct disadvantage of the pinnate design, it has other relative advantages. Because the geometry allows fibers to attach along part of the length of the tendon (Fig. 5.5), many more fibers can be attached to the tendon. Also, this geometry allows the central tendon to move a longer distance than in the fusiform scheme, so the bones attached to the tendon can move more. This overcomes the limited change in length in the muscles that can limit the range of angular motion of bones about joints. These and related issues are addressed in Problem 5.17. The mass, fiber length, PCA, and pinnation angle for several muscles are given in Table 5.4.

The microscopic components of the fibers are illustrated in Figs. 5.6 and 5.7, where the muscle belly of a fusiform muscle is seen to be composed of many parallel fasciculi. Each fasiculus is composed of many parallel muscle fibers (or muscle cells). Each muscle fiber is composed of many parallel myofibrils. Each myofibril is composed of myofilaments arranged into 2–3 m long units called sarcomeres (sar’-koe-meres). There are thick myofilaments with a serial arrangement of many myosin (my’-oh-sin) molecules and thin myofilaments with globules of F-actin (or actin) molecules that form twisting strands, which are surrounded by two other proteins: tropomyosin—which forms strands that twist about the actin strands—and troponin-T—which attaches at regular intervals to the actin and tropomyosin strands. Theinteraction between the myosin and actin proteins on adjacent myofilaments is the fundamental, chemical-induced, force-producing interaction in the muscle, which involves the hydrolysis of ATP and the change in conformation of the myosin.

In the large limb of an adult the muscle fibers are 50m in diameter. This diameter can double with weight training. Depending on the type of muscle, there are – muscle fibers per muscle (Table 5.5). There are – sarcomeres per muscle fiber, depending on the type of muscle (Table 5.6).

The electron micrograph in Fig. 5.7 shows the banded myofilament structure that is also sketched in the figure. The A band is a wide dark, anisotropic region, while the I band is a wide light, isotropic region. There is a lighter H zone or band in the middle of the dark A band, and a darker M line in the middle of the H zone. The dark Z lines run through the light I bands.

Each sarcomere is bound between the adjacent Z lines. The dark A band in the center of each sarcomere consists of thick (myosin) myofilaments (or thick filaments), which are connected to each other in the central M line within the H zone. They are overlapped to some degree by the thin (actin) myofilaments (or thin filaments). There are thick filaments but no thin filaments in the central H zone. The light I band regions next tox the Z lines are the thin myofilaments in regions where they do not overlap the thick myofilaments; they are bound to each other at the Z line. This is shown schematically in Fig. 5.7.

Electrical stimuli lead to twitches in the muscles that temporarily increase the force exerted by them. These twitches are delayed by about 15 ms after the electrical stimulus. They peak 40 ms later, and then decay to zero 50 ms later (Fig. 5.8a, Table 5.7). The shape of a twitch can be modeled as
with twitch time T.

By increasing the frequency of these stimuli and consequently of the twitches, there is an increase in the force exerted by the muscle (Fig. 5.8b, c). At a large enough frequency the twitches overlap to produce an almost steady level of force called unfused tetanus, and at an even higher frequency they produce a force that is constant in time called tetanus (Fig. 5.9). Roughly 50–60 electrical shocks per second are required to fully tetanize mammalian muscles at room temperature. This varies from about 30/s for the soleus muscle to s for eye muscles. (Also see Fig. 5.11 below.)

There are three different types of muscle fibers, which differ in how fast they contract and their resistance to fatigue. They appear in different types of muscles in varying proportions (Fig. 5.10). For a given muscle type, their relative concentrations can be different in different people. Slow-twitch (ST) red fibers (Type I) have a long contraction time (110 ms) and are very resistant to fatigue because they are aerobic, i.e., they use oxygen to produce ATP. These fibers are red because they have blood to supply oxygen. Fast-twitch (FT) fibers generally can create more force than ST fibers, and reach a peak tension in less time (50 ms). FT red intermediate fibers (Type IIA) have a relatively short contraction time, an intermediate fatiguing rate, and aerobic generation of ATP. FT white fibers (Type IIB) have a short contraction time and fatigue quickly because they use anaerobic (i.e., no oxygen) processes to produce ATP. One of the reasons for the faster response of the fast twitch muscle is the larger neuron exciting it.

The “average” muscle has roughly 50% ST fibers and 25% red and white FT fibers. The contraction time of a muscle depends on the proportion of FT and ST fibers. Figure 5.11 shows the twitch response for three types of muscles. The ocular muscles in the eye have mostly FT muscles and a response time of  s. The gastrocnemius (gas-trok-nee’-mee-us) muscle has many FT muscles and a response time of  s. The soleus (soh’-lee-us) muscle has many ST muscles and a response time of  s.

All of this makes sense in terms of the body’s needs. The eye muscles must be fast for our needed rapid eye reflex. The gastrocnemius and soleus muscles in the upper calf are both connected to the Achilles (calcaneal) tendon in the foot, which is connected to the calcaneus bone in the heel. The soleus muscle is a broad calf muscle that is deep relative to the medial and lateral heads of the gastrocnemius muscle (see Figs. 1.​8b and 3.​5). The soleus muscle is used more for standing and stability, for which endurance and resistance to fatigue are important and a fast response is not very important. The gastrocnemius muscle is used mostly for jumping and running, for which a fast response is necessary, even at the expense of endurance. The relative fraction of ST and FT muscles in the knee for trained athletes is depicted in Fig. 5.12 and Table 5.8. Clearly, athletes in sports that require endurance—such as marathon runners—have a higher fraction of ST muscle fibers in muscles used in running, while those in sports that require speed and strength—such as sprint runners and weightlifters—have a higher fraction of FT muscles in those muscles heavily used in these activities. There is a similar correlation for the cross-sectional areas of these different muscle fibers.