The stress

Stress (physics)

In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

–strain index

Strain (materials science)

In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...

(SSI), of a bone

Bone

Bones are rigid organs that constitute part of the endoskeleton of vertebrates. They support, and protect the various organs of the body, produce red and white blood cells and store minerals. Bone tissue is a type of dense connective tissue...

, is a surrogate measure of bone strength

Strength of materials

In materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear. Strength of materials is a subject which deals with loads, deformations and the forces acting on a material. A load applied to a...

 determined from a cross-sectional scan by QCT or pQCT (radiological scan

Radiology

Radiology is a medical specialty that employs the use of imaging to both diagnose and treat disease visualized within the human body. Radiologists use an array of imaging technologies to diagnose or treat diseases...

). The stress–strain index is used to compare the structural parameters determined by analysis of QCT/pQCT cross-sectional scans to the results of three point bending test

Three point flexural test

The three point bending flexural test provides values for the modulus of elasticityin bending E_f, flexural stress \sigma_f, flexural strain \epsilon_f and the flexural stress-strain response of the material. The main advantage of a three point flexural test is the ease of the specimen preparation...

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Definition

It is calculated using the following formula:



Where:

• r_max is the distance of voxel from centre
• CD is the apparent cortical (bone)
  Cortical bone
  Cortical bone, synonymous with compact bone, is one of the two types of osseous tissue that form bones. Cortical bone facilitates bone's main functions: to support the whole body, protect organs, provide levers for movement, and store and release chemical elements, mainly calcium. As its name...
  
   density
  Density
  The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
  
  
• ND is the normal (cortical bone) density
  Density
  The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
  
  
• r_i is the pixel position from the centre
• a is the area
  Area
  Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
  
   of a pixel
  Pixel
  In digital imaging, a pixel, or pel, is a single point in a raster image, or the smallest addressable screen element in a display device; it is the smallest unit of picture that can be represented or controlled....
  
  

History and relation to moments of inertia

It was developed by the manufacturer of a peripheral quantitative CT

Peripheral quantitative computed tomography

In medicine, peripheral quantitative computed tomography, commonly abbreviated pQCT, is a type of quantitative computed tomography , used for making measurements of the bone mineral density in a peripheral part of the body...

 (pQCT) scanner, and is considered to be by some an improvement over the information provided by calculating the area moments of inertia and polar moments of inertia

Polar moment of inertia

Polar moment of inertia is a quantity used to predict an object's ability to resist torsion, in objects with an invariant circular cross section and no significant warping or out-of-plane deformation. It is used to calculate the angular displacement of an object subjected to a torque...

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