Muscle Anthropometry & Function

Muscle Anthropometry & Function

Effects of Muscle Force on Joints

• Muscle force can create several effects on joints:

  • Approximation: Compression of joint surfaces.

  • Distraction: Traction or separation of joint surfaces.

  • Shear: Forces parallel to the joint surfaces.

  • Moment / Torque: Rotational force that causes joint rotation.

Measuring Muscle Performance: Torque

• When measuring muscle performance, we are primarily interested in TORQUE, not just direct force.

• Torque is defined as the product of force and the perpendicular distance from the axis of rotation to the line of action of the force:

  • $Torque = Force \times distance_{\perp}$

• Most muscles in the body act as an effort force in a 3rd class lever system.

  • Consequence: The muscle's lever arm is typically much shorter than the resistance lever arm (the distance to the external load).

  • Advantage: This lever arrangement allows for a large range of motion at the joint for a relatively small amount of muscle shortening, enabling greater speed and range of movement, which is beneficial for daily activities.

Muscle Strength vs. Force

• Muscle Strength often refers to the torque generation capacity of the muscle-joint system.

• Torque or Moment = Force * Lever Arm.

• Factors that affect the lever arm of a muscle include joint angle and the anatomical attachment points of the muscle-tendon unit.

• Several factors determine how much force a muscle-tendon unit can generate (discussed in detail below).

Factors Affecting Muscle Force Production

1. Angle of Pennation (PA)

2. Physiological Cross-sectional Area (PCSA)

3. Specific Tension (ST)

4. Length-Tension relationship

5. Force-Velocity relationship

6. History of Contraction

7. Excitation/activation level

The combined effect on overall muscle force can be generally expressed as:
$Muscle \, Force = PCSA \times ST \times f(l) \times f(v) \times a$
Where:

• $PCSA$ = Physiological Cross-sectional Area

• $ST$ = Specific Tension

• $f(l)$ = Function of muscle length (Length-Tension relationship)

• $f(v)$ = Function of muscle velocity (Force-Velocity relationship)

• $a$ = Excitation/activation level

• History of Contraction is often not explicitly included in this basic formula but is a significant factor.

1. Angle of Pennation ($\Theta$)

• Definition: The acute angle between the direction of the muscle fiber and the central tendon to which it attaches.

• Effect on Force: If a force $F$ is generated by a muscle fiber at an angle $\Theta$ to the tendon, the effective force transmitted along the tendon is $F \times \cos(\Theta )$.

  • Example: For an angle of $\Theta = 30^\circ$ , the effective force along the tendon is $F \times \cos(30^\circ )$.

• Why Pennated Muscles?

  • Pennation allows for a greater packing of sarcomeres (and thus muscle fibers) in parallel within a given muscle volume compared to non-pennated muscles.

  • Sarcomeres arranged in parallel are primarily designed for producing large forces.

  • While individual fibers in pennated muscles lose a partial amount of force along the central tendon due to the angle (e.g., a $\text{45}^\circ$ pennation angle results in a $\text{cos(45}^\circ) \approx 0.707$, representing approximately a \text{29.3%} loss in the direct-line force contribution of each fiber), the significant increase in the total number of fibers packed into the muscle (e.g., a \text{50%} increase) results in an overall net gain in force production capacity.

  • Overall: The gain in total fiber number (e.g., \text{50%} more fibers) often outweighs the loss per fiber due to angle (e.g., \text{30%} loss on individual fiber projection), leading to stronger muscles.

  • Muscle Strengthening Effects: After strengthening exercises, pennation angles can change, and muscle volume (and thus PCSA) increases, contributing to greater force production.

2. Muscle Size: Physiological Cross-sectional Area (PCSA)

• Principle: Generally,