Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue

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Abstract
Bone tissue is a complex multilevel composite which has the ability to sense ad respond to its mechanical environment. It is believed that bone cells called osteocytes within the bone matrix sense the mechanical environment and determine whether structural alterations are needed. At present it is not known, however, how loads are transferred from the whole bone level to cells. A computational procedure combining representative volume element (RVE) based homogenization theory with digital imaging is proposed to estimate strains at various levels of bone structure. Bone tissue structural organization and RVE based analysis are briefly reviewed. The digital image based computational procedure was applied to estimate strains in individual trabeculae (first-level microstructure). Homogenization analysis of an idealized model was used to estimate strains at one level of bone structure around osteocyte lacunae (second-level trabecular microstructure). The results showed that strain at one level of bone structure is amplified to a broad range at the next microstructural level. In one case, a zeor-level tensile principal strain of 495 μE engendered strains ranging between -1000 and 7000 μE in individual trabeculae (first-level microstructure). Subsequently, a first-level tensile principal strains of 1325 μE within an inidividual trabecula engendered strains ranging between 782 and 2530 μE around osteocyte lacunae. Lacunar orientation was found to influence strains around osteocyte lacunae much more than lacunar ellipticity. In conclusion, the computational procedure combining homogenization theory with digital imaging can proveide estimates of cell level strains within whole bones. Such results may be used to bridge experimental studies of bone adaptation at the whole bone and cell culture level. © 1994 John Wiley & Sons, Inc.