Physiological cross sectional area

In muscle physiology, physiological cross-sectional area (PCSA) is the area of the cross section of a muscle perpendicular to its fibers, generally at its largest point. It is typically used to describe the contraction properties of pennate muscles. It is not the same as the anatomical cross-sectional area (ACSA), which is the area of the crossection of a muscle perpendicular to its longitudinal axis. In a non-pennate muscle the fibers are parallel to the longitudinal axis, and therefore PCSA and ACSA coincide.

One advantage of pennate muscles is that more muscle fibers can be packed in parallel, thus allowing the muscle to produce more force, although the fiber angle to the direction of action means that the maximum force in that direction is somewhat less than the maximum force in the fiber direction.

The muscle cross-sectional area (blue line in figure 1, also known as anatomical cross-section area, or ACSA) does not accurately represent the number of muscle fibers in the muscle. A better estimate is provided by the total area of the cross-sections perpendicular to the muscle fibers (green lines in figure 1). This measure is known as the physiological cross-sectional area (PCSA), and is commonly calculated and defined by the following formula, developed in 1975 by Alexander and Vernon:

where ρ is the density of the muscle:

PCSA increases with pennation angle, and with muscle length. In a pennate muscle, PCSA is always larger than ACSA. In a non-pennate muscle, it coincides with ACSA.

The total force exerted by the fibers in their oblique direction is proportional to PCSA. If the specific tension of the muscle fibers is known (force exerted by the fibers per unit of PCSA), it can be computed as follows:

However, only a component of that force can be used to pull the tendon in the desired direction. This component, which is the true muscle force (also called tendon force), is exerted along the direction of action of the muscle:

The other component, orthogonal to the direction of action of the muscle (Orthogonal force = Total force × sinΦ) is not exerted on the tendon, but simply squeezes the muscle, by pulling its aponeuroses toward each other.

Notice that, although it is practically convenient to compute PCSA based on volume or mass and fiber length, PCSA (and therefore the total fiber force, which is proportional to PCSA) is not proportional to muscle mass or fiber length alone. Namely, the maximum (tetanic) force of a muscle fiber simply depends on its thickness (cross-section area) and type. By no means it depends on its mass or length alone. For instance, when muscle mass increases due to physical development during childhood, this may be only due to an increase in length of the muscle fibers, with no change in fiber thickness (PCSA) or fiber type. In this case, an increase in mass does not produce an increase in force.

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