Capturing data on cross-sectional properties of long-bone shafts
The most direct method of measuring cross-sectional properties of a bone is to physically section the bone at the point of interest and digitise the cross-section thus revealed. However, the damage that this causes to skeletal collections is unacceptable in most instances. Most studies therefore use non-invasive methods.
The technigue of choice is CT scanning. This is non-destructive and produces an accurate two-dimensional, digitised image of the cross-section of a bone. Various computer programmes have been developed for determining second moments of area and other parameters from digital images of cross-sections (Ruff, 2019).
When cost or other practical constraints preclude CT scanning, an alternative is to use radiography. Two radiographs are taken in perpendicular planes (usually antero-posterior and medio-lateral views). Second moments of area and other parameters can be estimated from radiographic measurements of antero-posterior and medio-lateral total bone widths and medullary widths using geometric formulae, provided one makes assumptions about the shape of a cross-section (for example, for humeral cross-sections at the 35% point along the shaft an elliptical shape is assumed). Comparison of results with those from physically cut sections show that for the humerus (Fresia et al„ 1990), femur and tibia (O'Neill & Ruff, 2004) the biplanar radiographic method provides results closely correlated with true values, although there is a slight tendency toward over-estimation of parameters.
The biplanar radiographic method can be refined if the actual contour of the outer surface of the bone is recorded using a latex cast and only the medullary cavity is reconstructed from radiographs. Because bone furthest from the central axis contributes most to shaft rigidity, accurate recording of the subperiosteal contour is more critical than the endosteal contour (O’Neill & Ruff, 2004). Taking this point further, some studies (e.g. Spar- acello et al„ 2015) estimate cross-sectional geometric properties from the external contour of the bone alone. This can be recorded using the cast method or by surface laser or structured light scanning. This approach has the advantage of obviating the need for radio- graphic or CT study. Whilst methods that involve the modelling of both periosteal and endosteal contours must be regarded as preferable, correlations between these and data collected just using the external shape are high (Stock & Shaw, 2007; Sparacello & Pearson, 2010), meaning that this latter method is valuable when imaging techniques to reconstruct the endosteal surface are not available. It has been argued (e.g. Pearson, 2000; Wescott, 2006) that useful inferences regarding biomechanical loadings can even be obtained from simple calliper measurements of external bone shaft widths. In addition to the ease and simplicity of recording calliper measurements, because they have long been taken in osteoarchaeology there are large amounts of published data for comparison. However, comparative study (Stock & Shaw, 2007) seems to confirm that external shaft widths are rather crude substitutes for accurate modelling of subperiosteal contours, so they are likely to be less sensitive indicators of loading environment (Ruff, 2002; Larsen, 2015: 247-249).
For comparative purposes, second moments of area and section moduli need to be standardised for body mass and bone length. Body mass contributes to loading directly via the force of gravity, but body mass is also indirectly related to forces imposed on bones from muscular contraction because of the relationship between total body mass and muscle mass. Bending and torsion involve both a force and a moment (or lever) arm, which can be considered proportional to bone length. The best way of standardising for these parameters has been debated for some time (Pearson, 2000; Ruff & Larsen, 2014). Current consensus appears to be that second moments of area should be standardised by body mass multiplied by the square of bone length, and section moduli by body mass multiplied by bone length (Sparacello et al„ 2011; Davies & Stock, 2014; Ruff, 2019). Using body mass in standardisation presents some problems because it is difficult to estimate from skeletal remains. Various formulae have been devised, relying on measurement of bi-iliac breadth of the pelvis and stature, femoral head breadth, or cortical bone area at various locations in the femur. Evaluation of these methods on modern subjects of known body mass suggests that they work poorly (Lacoste Jeanson et al„ 2017). It has been suggested (Pomeroy et al„ 2018) that they might be more accurate for archaeological skeletons as it is likely that, in ancient populations, people generally lacked the large and somewhat variable amounts of adipose tissue that typify people in modern industrialised populations but, as there are no archaeological skeletal series for which body mass was recorded in life, this remains speculative. For second moments of area, an alternative to estimating body mass is to standardise by bone length raised to the power of 5.33, which provides an approximate standardisation for body mass and bone length. Indices, such as lm|/lap, used to investigate differences between populations in orientation of bone loading, and measures of left-right asymmetry in second moments of area or other parameters, do not need to be standardised for most purposes.
