Muscle Models - Hill Type Model Quiz

Muscle Models

• Muscle parameters include area, length, dynamic parameters, and pennation angle.
• Hill's equation: (Force+a)*(speed+b) = b(Isometric tetanic force+a) describes muscle dynamics.

Force-Velocity Relationship vs Force-Length Relationship

• Muscle models can be classified into two types: Hill type model and Huxley's Cross-Bridge Model.
• Hill type model:
  • Sarcomere (CE) force is in series and in parallel with elastic structures (fascia's, PE and SE) depending on tendon length.
  • Critical notes:
    • Large number of unknown parameters for each muscle.
    • Negative stiffness in F-L characteristic.
    • Assumes F-L and F-v characteristics are independent.
    • Parameters are assumed constant, no history dependence.
    • Short Range Stiffness does not emerge!
    • No link to microscopic mechanisms.
• Huxley's Cross-Bridge Model:
  • Attachment and detachment rate functions f and g describe probabilities → fraction of attached cross-bridges n(x,t) per length x.
  • Includes Short Range Stiffness and historical dependence.
  • Explains F-V curve and predicts ATP consumption from CB detachment.

Optimization of Muscle Forces

• More muscles present than Degrees of Freedom (600 -200), resulting in many combinations of muscle force producing the same joint moment.
• Muscle fiber dynamics are modeled as their moment arms around the joints, cross-area, and pennation angles.

Muscle Morphology and Physiology

• Skeletal muscles:
  • Each muscle is an organ.
  • Each fiber has its own nuclei.
  • Adaptation to load.
  • Cell Regeneration.
  • Striated Microscopic pattern.
  • Voluntary / Involuntary controlled.
  • Attaches to bone, fascia, and skin.
  • ~40% of body mass.
• Force build-up:
  • First type I, then type II.
  • Force increases with number of motor units and frequency of stimulation.
  • Force buildup evolves in three distinct phases:
    • Excitation: Action potential from nerve system along muscle fiber.
    • Activation: Fast release of Ca2+ (20ms) from voltage difference.
    • Contraction: Action-Myosin interaction by means of the Cross-Bridge Cycle.
• Sarcomere Force-Length relationship:
  • Constant length = isometric.
  • Sarcomeres have a minimal length from which force increases quickly to the maximum, where there is a total overlap of actin and Myosin, after which the force will decrease until 0 where no overlap is anymore.

Muscle Form & Function

• Constraints on muscles:
  • Mobility and size → muscle force (m2) vs mass (m3).
  • Body development and age form a constraint.
  • Training and more usage will give better blood circulation and muscle growth.
• General Aspects of the muscle organ:
  • Motor/actuator for mobility.
  • Circulation of the blood, lymph, or digestion.
  • Heating of the body (mechanical).
  • Protein buffer to protect vital organs.
  • Blood sugar homeostasis.
  • Cell motility (spontaneous movement of a cell from one location to another by consumption of energy) is the driving force.
  • Same proteins are involved in non-muscles as in muscle cells.
• Hierarchy in form and function:
  • Myosin: Molecular motor which is the ‘grabbing’ head in a Cross-Bridge with actin.