Mathematical models for mass properties

Muscle and ligament forces

• A critical aspect of modeling muscles and ligaments is to determine appropriate lines of action
• Cadaveric measurements are available
• In-vivo reconstructions are possible with current medical imaging, however, appropriate ethical practices are a must

Lines of action

Muscles cross joints

• Muscles cross joints, thus, we must account for the joint motion on the line of action
  • Example: cam-like action of knee

Efficient use of muscles

• Muscle redundancy suggests that more than one muscle can perform the same task
• It is theorized that efficiency might drive “muscle selection”
  • Size of muscle (force limit) and moment arm both effect which muscle is recruited for a task
• Thus, an accurate estimate of muscle generating area is required
• Length of muscle changes during contraction, however, volume is nearly conserved
• Thus, we can calculate an effective area (and force) on the basis of measured length and volume

Joint stability

• Thus far, we have discussed the resultant forces at joints without considering how those forces are passed
• Joint stability is a critical concept whereby the joint must be structurally sound to the applied loads
• Joint stability requires the joint to maintain functional position throughout its range of motion
  • with “normal” loads
  • with “normal” contact forces
• The relationship between these loads and “normal” motion must be maintained or negative consequences can occur (locally and globally within the body)

Idealized stability in synovial joints

• Small changes in the magnitude or direction of the functional load do not lead to large changes in the position of the joint (or its contact points)
• Joint contact occurs between surfaces covered with articular cartilage
• Peripheral loading doesn’t occur
• Their exists a unique equilibrium position for each set of loads

Mechanisms for maintaining joint stability

• Contact at the articular surfaces (passive)
  • ie hip socket provides significant contact surfaces for stability
  • Healthy joints have near frictionless contact
  • Curvature of the surfaces generally enhances the stability of the joint
    • Opportunity for lateral force components
• Muscle Action (active – voluntary)
  • ie muscle contraction increase the contact forces adding stability
• Stretching of the ligaments and capsules (passive)

• Bicondylar joints provide two effective contact points, thus, they transmit moments
• The position of the joint contact can be another unknown in a problem (under determined system)
  • Muscle force and contact position are often interrelated… ie change the force and the contact position must change

• Muscles have a finite reaction time… thus they may not react quickly enough to counteract an unexpected set of forces
• Ligaments limit the range of motion/contact within a joint
  • May apply limited forces for the normal range of motion
  • A health balance exists between stability and laxity (limited range of motion vs dislocation)
  • Trauma or disease can upset the balance
• Surgeons attempt to maintain a healthy balance of stability and laxity during surgical repair, must consider all three stabilizing mechanisms

Range of healthy joint contact forces