The Principal Components of Adult Female Insole Shape Align Closely with Two of Its Classic Indicators

<div><p>The plantar surface of the human foot transmits the weight and dynamic force of the owner’s lower limbs to the ground and the reaction forces back to the musculoskeletal system. Its anatomical variation is intensely studied in such fields as sports medicine and orthopedic dysmorphology. Yet, strangely, the shape of the insole that accommodates this surface and elastically buffers these forces is neither an aspect of the conventional anthropometrics of feet nor an informative label on the packet that markets supplementary insoles. In this paper we pursue an earlier suggestion that insole form in vertical view be quantified in terms of the shape of the foot not at the plane of support (the “footprint”) but some two millimeters above that level. Using such sections extracted from laser scans of 158 feet of adult women from the University of Zagreb, in conjunction with an appropriate modification of today’s standard geometric morphometrics (GMM), we find that the sectioned form can be described by its size together with two meaningful relative warps of shape. The pattern of this shape variation is not novel. It is closely aligned with two of the standard footprint measurements, the Chippaux-Šmiřák arch index and the Clarke arch angle, whose geometrical foci (the former in the ball of the foot, the latter in the arch) it apparently combines. Thus a strong contemporary analysis complements but does not supplant the simpler anthropometric analyses of half a century ago, with implications for applied anthropology.</p></div

Regression of the semilandmark polygon on the difference of the first two RW scores, versus regressions on our version of the classic arch index.

<p>Left, predictions from the difference of RW’s; right, from the classic measure as implemented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133303#pone.0133303.g002" target="_blank">Fig 2</a>. The patterns seem synonymous.</p

The data for the GMM computations.

<p>Shown are slipped Procrustes coordinates of 158 36-gons for 79 pairs of sectioned laserscan surfaces of adult female feet.</p

Relative warp 1 versus Chippaux’s index.

<p>Left, regression profile of semilandmark locations on the RW1 score; right, on the Chippaux-Šmiřák arch index as implemented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133303#pone.0133303.g002" target="_blank">Fig 2</a>. The Chippaux index shows a comparable effect at its locus of measurement, but falls off inefficiently toward the ball of the foot. The word “normed” in the title of this figure means that the regression coefficient is not in the usual units of the predictor variable per se (here, the RW score on the left, or the index score on the right) but instead takes on units of the predictor’s standard deviation. The arch index in the figure title is the ratio of the length of the lower straight-line segment length in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133303#pone.0133303.g002" target="_blank">Fig 2</a> to the length of the upper segment.</p

The same as Fig 6 for the comparison with arch angle.

<p>Clarke’s measure shows the same pattern as RW1 in the vicinity of the corner of the anteromedial arc, but falls off inefficiently toward the posterior arch.</p

The first two relative warp scores for 79 pairs of insole outlines.

<p>Dashes link left and right foot of each subject.</p

Operationalization of the arch angle, after the examples in Clarke [5].

<p>The image, from Amira, shows a footprint and the associated section at 2 mm above the plane of support.</p

The same for Clarke arch angle (Fig 1) vis-à-vis the sum of the first two relative warp scores.

<p>Panels are as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133303#pone.0133303.g008" target="_blank">Fig 8</a>. Again the actions seem synonymous.</p