Active Stress of Muscles

The stress–strain curves described so far apply to passive tissue: stress appears only when the tissue is stretched. Muscle is different. A contracting muscle generates stress internally, whether or not it is being stretched, and it can change that stress in a few tens of milliseconds. This active stress is what lets the larynx adjust vocal fold tension, and therefore pitch, faster than any passive mechanism could.

Passive Plus Active Stress

The total longitudinal stress in a muscle is the sum of two parts:

σ = σ_p(ε) + σ_a

σ_p(ε), the passive stress, comes from the connective tissue in and around the fibers (endomysium, perimysium, epimysium) and from the elastic protein titin inside the sarcomeres. It behaves like the nonlinear elastic tissue described earlier: near zero at rest length and rising steeply with elongation.
σ_a, the active stress, comes from cross-bridge cycling between actin and myosin. It depends on how strongly the muscle is activated by its nerve and on the current length and shortening velocity of the fibers.

Because the two add, a stretched and contracting muscle can carry a much larger stress than either mechanism alone would give. This is exactly the situation of the thyroarytenoid muscle when the cricothyroid stretches it during a rise in pitch.

Dependence on Activation

Active stress scales with the level of neural activation. If a is a normalized activation (0 = relaxed, 1 = maximal contraction) and σ_am is the maximum active stress the muscle can produce, then to a first approximation:

σ_a ≈ a · σ_am · g(ε)

where g(ε) is the length–tension factor described below (g = 1 at the optimal length). Activation is graded in two ways: by recruiting more motor units and by increasing the firing rate of the units already recruited. A single stimulus produces a brief twitch; repeated stimulation lets twitches fuse into a sustained tetanus, at which σ_am is reached.

The Length–Tension Relation

Active stress is greatest at an intermediate sarcomere length, where the overlap between thick and thin filaments allows the largest number of cross-bridges to form. If the muscle is shortened, the thin filaments begin to collide and overlap one another and the stress falls; if it is stretched too far, the filaments pull apart and fewer cross-bridges can attach, so the stress again falls.

The result is a roughly parabolic curve of active stress against length, peaking near the rest length of the muscle in the body. Superimposed on the passive curve, which rises steeply with elongation, the total stress of an activated muscle keeps rising with length even past the active peak. For the vocal folds this means:

At short lengths (low pitch, thyroarytenoid dominant) the active contribution can dominate the total stress.
At long lengths (high pitch, cricothyroid dominant) the passive stress in the ligament and cover dominates, and further thyroarytenoid activation adds relatively little.

This balance is the physical basis of the body–cover model of pitch control developed in Chapter 8.

The Force–Velocity Relation

Active stress also depends on how fast the muscle is changing length. A muscle shortening quickly can generate far less stress than one contracting isometrically (at constant length), and a muscle being stretched while it contracts (an eccentric contraction) can briefly sustain more than its isometric maximum. This is described by Hill’s force–velocity relation, which is why maximum active stress is measured under isometric conditions.

For phonation the practical consequence is that the intrinsic laryngeal muscles usually work close to isometric conditions: they hold a configuration against the pull of their antagonists and against aerodynamic forces, adjusting stress rather than length by large amounts.

How Much Stress? Values for Laryngeal Muscle

Maximal isometric stress in mammalian skeletal muscle is typically on the order of 200–300 kPa. The small intrinsic laryngeal muscles appear to develop somewhat less. Measurements on excised canine thyroarytenoid muscle with direct electrical stimulation give a maximum active stress of roughly 100 kPa (Alipour-Haghighi, Titze & Perlman, 1989), a value used in later chapters to estimate the upper limit of chest-register fundamental frequency. Values obtained in living humans are almost certainly lower, because voluntary activation never recruits every fiber synchronously.

Two other quantities matter for voice:

Speed. The adductor muscles of the larynx are among the fastest skeletal muscles in the body, with twitch contraction times of the order of 10–15 ms in the canine thyroarytenoid; the cricothyroid is noticeably slower. This speed underlies rapid airway protection, quick voice onsets and pitch changes lasting only tens of milliseconds.
Fatigue resistance. Because these muscles are also active in breathing, they must sustain low-level activation for long periods. The mixture of fiber types that makes this possible is the subject of the next section.

Why Active Stress Matters for Pitch

Chapter 8 will show that the fundamental frequency of a vibrating vocal fold rises with the square root of its longitudinal stress. Two mechanisms are available for raising that stress:

Lengthen the fold with the cricothyroid, exploiting the steep passive stress–strain curve of the ligament and cover.
Contract the thyroarytenoid, adding active stress to the body of the fold—even while the fold is being shortened.

The second route is only possible because muscle can generate stress internally. It allows stiffness to change with little or no change of length (an isometric adjustment), and it is what makes the thyroarytenoid both a pitch-lowering muscle (through shortening) and, under the right conditions, a pitch-raising one (through active stiffening).

Summary

Muscle tissue carries passive stress from stretch plus active stress from contraction. Active stress rises with neural activation, peaks at an intermediate length, and falls as the muscle shortens rapidly. Canine thyroarytenoid muscle can develop about 100 kPa of active stress under maximal stimulation, and laryngeal adductors contract exceptionally fast. These properties allow the larynx to change vocal fold stiffness—and therefore pitch—quickly and, when needed, without changing fold length.

Key Takeaways

✅ Total muscle stress is the sum of passive stress (from stretch) and active stress (from cross-bridge cycling)
✅ Active stress scales with neural activation and is greatest at an intermediate, near-resting length
✅ Rapid shortening reduces active stress; isometric conditions give the maximum
✅ Canine thyroarytenoid develops roughly 100 kPa of maximum active stress, less than typical limb muscle
✅ Laryngeal adductors are among the fastest skeletal muscles, with twitch times of tens of milliseconds
✅ Active stiffening lets the thyroarytenoid raise stress without lengthening—the basis of body–cover pitch control

Active Stress of Muscles

Active Stress of Muscles

Passive Plus Active Stress

Dependence on Activation

The Length–Tension Relation

The Force–Velocity Relation

How Much Stress? Values for Laryngeal Muscle

Why Active Stress Matters for Pitch

Summary

Key Takeaways

Related Topics

Further Reading