Stress–strain index

The stress–strain index (SSI), of a bone, is a surrogate measure of bone strength^[1] determined from a cross-sectional scan by QCT or pQCT (radiological scan). 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.

Definition

It is calculated using the following formula:^[2]

$SSI = \sum_{i=0}^n {{r_i^2 a ({{CD} \over {ND}})} \over {r_{max}}}$

Where:

• r_max is the distance of voxel from centre
• CD is the apparent cortical (bone) density
• ND is the normal (cortical bone) density
• r_i is the pixel position from the centre
• a is the area of a pixel

History and relation to moments of inertia

It was developed by the manufacturer of a peripheral quantitative CT (pQCT) scanner,^[2] 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.

References

1. Ward K, Roberts S, Adams J, Mughal M (2005). "Bone geometry and density in the skeleton of pre-pubertal gymnasts and school children.". Bone 36 (6): 1012–8. doi:10.1016/j.bone.2005.03.001. PMID 15876561.
2. Hasegawa Y, Schneider P, Reiners C (2001). "Age, sex, and grip strength determine architectural bone parameters assessed by peripheral quantitative computed tomography (pQCT) at the human radius.". J Biomech 34 (4): 497–503. doi:10.1016/S0021-9290(00)00211-6. PMID 11266673.