Arm and leg modelling

No, I’m not looking for people with lithe limbs to be photographed for money. Much more sexily, I’m referring to a recent paper (Pietak et al., 2013) that’s found that the relative length of the segments of human limbs can be modeled with a log-periodic function:

Figure 2 from Pietak et al. 2013. Human within-limb proportions are such that the length of each segment (e.g., H1-6) of a limb, from  fingertip to shoulder (A) and to to hip (B), can be predicted by a logarithmic periodic function (C).

In other words, within a limb, the length of each segment is mathematically fairly predictable on the basis of the segment(s) before and after it. As the authors state, “Being able to describe human limb bone lengths in terms of a log-periodic function means that only one parameter, the wavelength λ, is needed to explain the proportional configuration of the limb.”

The biological significance of this pattern is difficult to discern. The length of a limb segment is determined by a number of factors, including the spacing between the initial limb condensations embryonically, and thereafter the growth rates and duration of growth at proximal and distal epiphyses. As a result, limb proportions aren’t static throughout life, but change from embryo to adult. For instance, here are limb proportion data for the coolest animal ever – gibbons! – from the great anatomist Adolph Schultz.

ResearchBlogging.orgAn important question, and follow-up to Pietak et al’s study, is whether human limb proportions can be described by such log-periodic functions throughout ontogeny, and if so how these change. Plus, it’s also not clear to what extent human proportions might happen to be describable by log periodic functions, simply because each segment is shorter than the one preceding it proximally. In short, this study raises really interesting and pursuable questions about how and why animal limbs grow to the size and proportions that they do.

References
Pietak A, Ma S, Beck CW, & Stringer MD (2013). Fundamental ratios and logarithmic periodicity in human limb bones. Journal of anatomy, 222 (5), 526-37 PMID: 23521756

Schultz, A. (1944). Age changes and variability in gibbons. A Morphological study on a population sample of a man-like ape American Journal of Physical Anthropology, 2 (1), 1-129 DOI: 10.1002/ajpa.1330020102

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