Calculating Muscle Forces

Objectives

  • Understand skeletal muscle architecture.

  • Read Chapter 8.

  • Review statics concepts.

  • Note: Quiz 1 in class.

    • Closed book/notes.

    • 1 page of notes allowed.

    • 45-minute time limit.

Muscle Force Calculations

  • Objectives for quiz: Calculate PCSA, Fo, and Vo for the following two hamstring muscles under the assumption of 100% fast twitch fibers.

Given Parameters

  • Muscle density: 1.056 g/cm³

Hamstring Muscles Information

  1. Semimembranosus

    • Fiber Length: 172 cm

    • Pennation Angle: 17°

    • Muscle Mass: 6.5 g

    • PCSA Calculation:
      PCSA=172 g⋅cos⁡(17°)1.056 g/cm³⋅6.5 cm=24 cm²\text{PCSA} = \frac{172 \text{ g} \cdot \cos(17°)}{1.056 \text{ g/cm³} \cdot 6.5 \text{ cm}} = 24 \text{ cm²}

    • Force Output (Fo):
      Fo=(40 N/cm²)(24 cm²)=960 NF_o = (40 \text{ N/cm²})(24 \text{ cm²}) = 960 \text{ N}

    • Velocity Output (Vo):
      Vo=(16 s−1)(6.5 cm)=104 cm/secV_o = (16 \text{ s}^{-1})(6.5 \text{ cm}) = 104 \text{ cm/sec}

  2. Biceps Femoris Long Head

    • Fiber Length: 152 cm

    • Pennation Angle: 7°

    • Muscle Mass: 9.8 g

    • PCSA Calculation:
      PCSA=152 g⋅cos⁡(7°)1.056 g/cm³⋅9.8 cm=14.6 cm²\text{PCSA} = \frac{152 \text{ g} \cdot \cos(7°)}{1.056 \text{ g/cm³} \cdot 9.8 \text{ cm}} = 14.6 \text{ cm²}

    • Force Output (Fo):
      Fo=(40 N/cm²)(14.6 cm²)=584 NF_o = (40 \text{ N/cm²})(14.6 \text{ cm²}) = 584 \text{ N}

    • Velocity Output (Vo):
      Vo=(16 s−1)(9.8 cm)=157 cm/secV_o = (16 \text{ s}^{-1})(9.8 \text{ cm}) = 157 \text{ cm/sec}

Calculating Muscle Forces

  • Muscle forces are derived from both experimental data and theoretical models:

Force Equation

  • General equation:
    F=PCSA⋅ST⋅FL⋅FV⋅ACF = \text{PCSA} \cdot \text{ST} \cdot \text{FL} \cdot \text{FV} \cdot \text{AC}

Normalized Terms in the Equation

  • FL: A parabolic model for force-length relationship.

    • FL=y=FFoFL = y = \frac{F}{F_o}

  • FV: Described by Hill's equation.

    • FV=FFoFV = \frac{F}{F_o}

  • AC: Represents the activation coefficient defined as:
    AC=IEMGaIEMGmAC = \frac{\text{IEMGa}}{\text{IEMGm}}

Relationships of Variables

  • Modified equation incorporating activation:
    F=Fob−avb+vF = \frac{F_o b - a v}{b + v}

  • Force-Length Relationship:

    • Parabolic relationship illustrated by:

    • y=ax2+bx+cy = ax² + bx + c

    • x=LLox = \frac{L}{L_o}

Muscle Activation

  • The whole muscle force-velocity curves (F-V curves) are a function of the activation level with these considerations:

    • Force-Activation Relation: Varies with level:

      • 100% activation

      • 50% activation

  • Whole muscle force-length curves (F-L curves) also depend on activation levels.

    • Relation between F-L and F-V constructs a system of surfaces for activation coefficient (AC) that ranges from 0 to 1.

Mindfulness Exercise

  • Considerations to aid focus and relaxation:

    • Consciously focus on your breath.

    • Inhale deeply and exhale slowly.

    • Aim to relax your mind and body throughout the calculations.