The effects of cracks on the quantification of the cancellous bone fabric tensor in fossil and archaeological specimens: a simulation study

Abstract

Cancellous bone is very sensitive to its prevailing mechanical environment, and study of its architecture has previously aided interpretations of locomotor biomechanics in extinct animals or archaeological populations. However, quantification of architectural features may be compromised by poor preservation in fossil and archaeological specimens, such as post mortem cracking or fracturing. In this study, the effects of post mortem cracks on the quantification of cancellous bone fabric were investigated through the simulation of cracks in otherwise undamaged modern bone samples. The effect on both scalar (degree of fabric anisotropy, fabric elongation index) and vector (principal fabric directions) variables was assessed through comparing the results of architectural analyses of cracked vs. non-cracked samples. Error was found to decrease as the relative size of the crack decreased, and as the orientation of the crack approached the orientation of the primary fabric direction. However, even in the best-case scenario simulated, error remained substantial, with at least 18% of simulations showing a > 10% error when scalar variables were considered, and at least 6.7% of simulations showing a > 10° error when vector variables were considered. As a 10% (scalar) or 10° (vector) difference is probably too large for reliable interpretation of a fossil or archaeological specimen, these results suggest that cracks should be avoided if possible when analysing cancellous bone architecture in such specimens.

Keywords: cancellous bone; fabric tensor; fossils; simulation; taphonomic crack.

Figure 1

The simulation of cracked specimens in this study. (a) A pristine sample of cancellous bone, from the proximal tibiotarsus of a cassowary, Casuarius casuarius (side length of cube = 14.673 mm). The large vector indicates the orientation of the primary fabric direction calculated for the whole sample, and the inset is the three‐dimensional fabric ellipsoid (geometric expression of the fabric tensor) with associated measures (see text for explanation). (b) Nine standard orientations for the simulated cracks in this particular sample; all pass through the centre of the cube. Four planes are parallel to the primary fabric direction, one plane is perpendicular to it, and four planes are at a 45° angle to it. (c) One particular crack, simulated as a planar prism, here with thickness equal to twice the mean trabecular spacing of the sample. (d) Three spherical VOIs were used in the simulations, of diameter five, nine and 13 times the mean trabecular spacing. (e) The simulated cracked sample, where the cancellous bone in the volume of the crack in (c) has been removed, to simulate how a crack obliterates the structure. The resulting effect on the primary fabric orientation and nature of the fabric ellipsoid (and associated measures) is also illustrated.

Figure 2

The effect of cracks on scalar variables describing the cancellous bone fabric tensor. (a) In terms of the mean percentage difference from the pristine sample. (b) In terms of P(Δ_max), the proportion of instances where the maximum acceptable difference was exceeded. For the mean difference plots, filled circles denote positive differences from the values for the pristine sample, and hollow circles denote negative differences from the values for the pristine sample.

Figure 3

The effect of cracks on vector variables describing the cancellous bone fabric tensor. (a) In terms of the angular differences from the pristine sample. (b) In terms of P(Δ_max), the proportion of instances where the maximum acceptable difference was exceeded.

Figure 4

The effect of crack orientation on the quantification of the cancellous bone fabric tensor, as illustrated with several exemplar cases. These three‐dimensional plots tease apart the general patterns shown in Figs 2 and 3, to illustrate how crack orientation (relative to the primary fabric direction) also influences the results of quantitative analysis. (a) Proportion of excessively erroneous instances for degree of anisotropy in SVD analyses. (b) Mean angular difference for the orientation of the primary fabric direction in SVD analyses. (c) Mean percentage difference for positive error in elongation index in MIL analyses. (d) Proportion of excessively erroneous instances for the orientation of the secondary fabric direction in MIL analyses. By and large, the general pattern was that demonstrated in (a) and (b), where error markedly decreases as the crack becomes more parallel to the orientation of the primary fabric direction, although exceptions did exist, as illustrated in (c) (little decrease with more parallel orientation) and (d) (slight increase with more parallel orientation). For illustrative purposes, planes were fitted to the data (and associated r ² values calculated) assuming a coding of parallel orientation = 1, 45° orientation = 2, perpendicular orientation = 3, using the Curve Fitting Toolbox in MATLAB (version 8.0, MathWorks, Natick, MA, USA).