Lumbar Spine Biomechanics

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Movements

Bones can undergo translation and rotation

Movement	Description	Movement occurs when	Force
Translation	Every point on a bone moving in the same direction and to the same extent	Single force or net single force acts on a bone	Shear force
Rotation	All the points on a bone move in parallel around a curved path that is centred on a fixed point, but to different extents depending on their distance from the centre of rotation. May be due to two opposed muscular actions, or muscular action and ligamentous resistance, or gravity opposed by either muscular action or ligamentous resistance.	Two unaligned forces acting in opposing directions on different parts of the bone forming a force couple	Torque

• Axis of rotation
  • Formal definition = that region that does not move when two or more opposing, unaligned forces act on a bone.
  • With rotation of a bone, all the points on the bone can be grouped into individual planes that lie parallel to the direction of movement.
  • In each plane, the points move about a centre located in that plane
  • When all the centres of all the planes line up they depict a straight line forming the axis of rotation of the bone.
  • It is a region where all opposing forces cancel out, and there is no net force acting, and so it stays stationary.
  • Different forces create different axes of rotation.

Stress-Strain

• With stretching of a collagen fibre, the fibre resists elongation due to a resistance force from the chemical bonds between the collagen fibrils, between tropocollagen molecules, between collagen fibres, and between collagen fibres and proteoglycans.
• Stress = the applied elongating force, measured in units of force (newtons)
• Strain = the extent to which a fibre is elongated, measured as the fractional or percentage increase in length relative to the initial length.
• A fibre of length L₀ when stretched to a new length L₁ undergoes a strain of L₁/L₂ x 100%
• Tension strain = this occurs with a deforming force causing a structure to be stretched longitudinally
• Compression strain = this occurs with a deforming force causing a structure to be squashed
  • Measured as the fractional or percentage decrease in height of a structure
• Shear force = forces that cause two vertebrae to slides with respect to one another
• Shear strain = the strain that occurs in the intervening intervertebral disc
• Shear vs tension: tension conventionally applies to forces that are exerted along the long axis of a structure. Shear forces are applied across the axis.
• Torsion = when an object twists, the force is a torque, and the resultant strain is a torsion strain.