Section modulus calculation

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I have a data set in which cross-sectional properties on bones were derived from CTs in BoneJ and that includes section moduli around A-P and M-L anatomical planes. This dataset is complemented with data from literature which include only moments of area (inertia) and external dimensions (AP and ML diameters). I need to calculate section moduli for this subset as well. Is the general formula, e.g. Ix/(APdiameter/2) for such calculations adequate? When I tried to compare section moduli calculated by boneJ and by this general formula on my CT derived sample, the values were significantly different. Is there any other way? I work with human femora, specifically subtrochanteric level which is not very circular.

Thanks for any help


Not really, bones are usually not circular / rectangular in cross-section, which is assumed by this relation. It’s also not necessary if you have the CT images because BoneJ calculates section modulus (Zmax and Zmin), without need for assuming annular geometry.

That seems likely. Bear in mind that that the chord length that you divide I by to get Z is measured as the perpendicular distance from the principal axis to the most distant point from the principal axis. This is because this point is the one that will experience greatest strain under an applied bending moment, and so is where failure is most likely to occur. If you have included something in your ROI, as small as a single pixel of noise, that is a long way from the principal axis in comparison to the perimeter of your bone, you will get wrong results for Z.


Ok, thanks much Michael. From you reply, I thus assume that calculating Zx and Zy only from Ix, Iy and their respective external dimensions in the other dataset is not possible (or rather reliable).


It is possible to calculate Z, provided that:

  • the direction that the diameter (d) was measured in is perpendicular to the principal axis (d/2 would give you the chord length)
  • I values consider the bone only and the medullary cavity as hollow (some approximations treat the bone as not having a medullary cavity
  • if assuming annular or circular cross-sections for approximating I, that the bone actually is approximately circular
  • the principal axes pass through the centre of the bone (i.e. d/2 chord length on both sides)

Also consider whether Z tells you something important for your study that I does not, which might make you question whether to calculate it at all.