Glossary of Spinal Deformity Biomechanical Terms

(Selected and adapted from Panjabi MM and White AA: Appendix: Glossary, in:
Clinical Biomechanics of the Spine. (2nd Edition)
by White AA and Panjabi MM, Philadelphia: J.B. Lippincott, 1990)
Proposed by the SRS Terminology Committee, 1999

This short guide to terms in spinal biomechanics is divided into five sections:

AXES SYSTEMS, ETC.

local, regional, spinal and global axis systems (see figure 1)

Vector - a quantity that possesses both a magnitude and a direction (e.g. force; velocity; displacement).

 Figure 1 click to enlarge
Figure 1: Local, regional, spinal and global axis systems. Note: these are Cartesian systems, defined by three mutually perpendicular axes.

LOADING

Force - an action that causes a body to displace or deform. (SI Unit of measure = Newton, i.e. N)

Tension force - a force that tends to elongate a structure or material.

Compression force - a force that tends to shorten a structure or material.

Moment or Torque - The sum of the forces applied to a structure multiplied by their perpendicular distance from a reference point or axis. (SI Unit of measure = Newton-metre, i.e. Nm)

Bending Moment at a point within a structure. (See Figure 2). The moment that tends to bend a structure. It is usually the sum of the moments due to several forces.

Couple - Two equal an opposite parallel forces separated by a distance, producing a torque.

3-Point bending (See Figure 3) - a structure is loaded in 3-point bending when a single force is applied on one side and two forces are applied on the other side acting in opposite directions.

4-Point bending (See Figure 3) - a structure is loaded in 4-point bending when two forces are applied on one side and two forces are applied on the other side acting in opposite directions.

Stress - the force per unit area of a structure and a measurement of the intensity of the force (SI Units are Newtons/m2 = Pascals. Hence 1 N/m2 = 106 N/mm2 = 1 mega Pascal = 1 MPa).

Normal stress - the intensity of force perpendicular to the surface on which it acts.

Shear stress - the intensity of force parallel to the surface on which it acts.

Compressive stress - a normal stress that tends to shorten material.

Tensile stress - a normal stress that tends to elongate material.

Principal stresses - the stresses normal to the principal planes of a material are called principal stresses. The principal planes are those where the stresses are maximum and minimum.

Stress concentration - A site of stress that is high compared to that of nearby sites in a structure or material. It is often caused by a sharp change in shape.

Center of gravity - the point in a body in which the body mass is centered.

 

 Figure 2 - Click to enlarge
Figure 2: Bending moment (produced here by the force in a Harrington rod) at a point in a structure is the force multiplied by the perpendicular (shortest) distance from that point to the force.

Figure 3 - Click to enlarge
Figure 3:  3 and 4 point bending. For 3 point bending, the maximum bending moment is at point B. For 4-point bending with four equal forces, the bending moment between forces B and C is uniform (constant).

DISPLACEMENT/DEFORMATION

Absolute motion - Motion of a rigid body relative to the global axis system.

Relative motion - motion of a rigid body relative to the local axis system of an adjacent body.

Translation (Figure 4) - motion of a rigid body in which a straight line in the body always remains parallel to itself.

Rotation (Figure 4) - motion of a rigid body in which a certain straight line within or adjacent to the body remains motionless. (That straight line is the axis of rotation)

Plane motion - a motion of a rigid body in which the body moves in a single plane.

Degrees of freedom(Figure 5) - the number of independent translations and rotations that can occur in a mechanism (e.g. the spine and its instrumentation).

Instantaneous Axis of Rotation (IAR) (Figure 5) - when a rigid body moves at every instant there is a line in the body or some hypothetical extension of it that does not move. For plane motion the axis of rotation becomes the center of rotation. Note: The IAR can describe the absolute motion of a body, or its relative motion with respect to an adjacent moving body (e.g. an adjacent vertebra).

Bending - angular deformation of a structure, caused by a bending moment.

Neutral axis - line or axis within a beam or other structure about which bending occurs.

Strain - (Figure 6) Deformation (change in length) divided by the original length.

Normal strain is defined as the change in length divided by the original length. Normal strain can be tensile or compressive.

Shear strain - shear deformation divided by the thickness perpendicular to the shear.

Plastic Deformation(Figure 7) - Deformation that remains after the deforming load is removed.Strain - (Figure 6) Deformation (change in length) divided by the original length.

Normal strain is defined as the change in length divided by the original length. Normal strain can be tensile or compressive.

Shear strain - shear deformation divided by the thickness perpendicular to the shear.

Plastic Deformation (Figure 7) - Deformation that remains after the deforming load is removed. 
 
 
 

 Figure 4 - Click to enlarge
Figure 4: Rotation and translation motion. The motion from A to B is a pure rotation, with an axis of rotation lying outside the vertebra. The motion from A to C is a pure translation.
 
 
 
 

Figure 5 - Click to enlarge
Figure 5: A motion segment has six degrees of freedom (i.e. six possible relative displacements of one vertebrae relative to its neighbor). The motion at any instant can be described as a translation along and a rotation about an instantaneous axis of rotation.
 
 
 

Figure 6 - Click to enlarge
Figure 6: Stress is the standardized measure of loading (force divided by the original area) and strain is the standardized measure of deformation (deformation divided by original length).
(a) Normal stress and strain. (b) Shear stress and strain. 

LOAD-DEFORMATION, AND STRESS-STRAIN RELATIONSHIPS

Elastic Behavior:

Stiffness - force divided by the deformation it produces (i.e. the slope of the force-deformation relationship).

Modulus of elasticity- Stress divided by the strain it produces (i.e. the slope of the stress-strain relationship). (e.g. Young's Modulus = normal stress divided by normal strain)

Torsional rigidity - Torque divided by the rotation that it produces.

 

Time Dependent Behavior:

Creep - Deformation produced over time by a constant load.

Viscoelasticity - Material behavior in which the resistance to deformation depends on the amount of deformation (elastic) and the rate of deformation (viscous).

Stress Relaxation - Loss of stress over time in a material while the strain is held constant.

FAILURE

Yield Stress - (Figure 7) magnitude of stress on the stress-strain curve at which appreciable deformation takes place without any appreciable increase in the stress.

Ductility- property of a material in which there is a large amount of deformation possible after the yield point. This implies that a large amount of deformation energy is absorbed by the material before failure. (opposite of brittle)

Fatigue - Eventual failure after repeated cycles of sub-yield loading. This usually occurs as a result of the process of the growth of cracks in structures subjected to repetitive load cycles.  

 Figure 7 - Click to enlarge
Figure 7: Stress-strain graph of a typical material. A sample was loaded past its elastic limit, unloaded to demonstrate plastic deformation, then loaded again to failure.

EQUILIBRIUM

State of a structure in which all forces and moments are balanced, hence it does not move.

Free body analysis(Figure 8) - A technique for determining the internal forces in a structure subjected to external loads. It involves an equilibrium analysis in which a system is split into real or imagined component parts (free bodies), in order to check that each part is in equilibrium.

Statics - the branch of mechanics that deals with the equilibrium of bodies at rest or in motion with zero acceleration.

Dynamics - The branch of mechanics that deals with motion of systems in which the accelerations of masses have significant effect.

Kinematics The branch of mechanics that deals with motion alone.

Figure 8 click to enlarge
Figure 8: Simple static analysis (no motion occurring) of lifting mechanics to determine forces at the thoracolumbar junction. Here a free-body analysis is used. All forces acting on the upper part of the body must be in equilibrium (i.e. no net force or moment acting on the upper body) - otherwise it would be forced to accelerate.

STABILITY:

Behavior of a system whereby it returns to its equilibrium position after being disturbed. The stable equilibrium position is a position of minimum potential energy - any displacement of the structure requires a net input of energy. Although stiffness or rigidity of a structure can contribute to its stability, stiffness and stability are not the same thing. When referring to the rigidity of, for example an instrumentation construct, use the term stiffness or rigidity, not stability.

Buckling - A kind of instability in which a structure suddenly bends and collapses when a certain critical load is applied


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