Authors:

Kaley Roe

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About Paper:

Allometric scaling laws are used to describe how geometric properties of organisms change with body mass. These laws typically follow a basic equation of Y=aM^b, with M representing mass, a a constant, and b the allometric scaling exponent. This project focuses on scaling laws in bone. Two sets of geometric properties describe bone: (1) macroscale properties, such as length and diameter, as well as (2) microscale properties describing bone building blocks, i.e., osteons. Previous studies have explored how body mass relates to macroscale bone properties and how body mass correlates with microscale features. The objective of this study is to link micro and macro data on bone allometric scaling and to build new allometric scaling laws. Data was gathered from established literature using a plot digitizer and compiled into a cross- linked database for further analysis. We hypothesize that ratios between bone size parameters (diameter, length, cortical bone thickness) and osteon size parameters (osteon diameter, infill length, canal diameter) are independent of body mass, i.e., possess b = 0.0. This hypothesis is based on the consideration of bone as a quasi-brittle material, and the mechanics of failure of quasi-brittle materials guides the testing of the hypothesis. The initial analysis considered outer bone diameter and osteon diameter and did not verify the hypothesis; rather, b = 0.2. Future work seeks to expand the data set, to consider additional micro-macro scaling laws, and to combine the size scaling laws with additional factors. This work was supported by NSF award 1952993. Keywords: Allometric Scaling; Bone Properties; Ratios

Source:

Purdue University / 2025

Topics:

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Co-authors:

Kaley Roe