A finite difference model of load-induced fluid displacements within bone under mechanical loading

Load-induced fluid flow in the lacunocanalicular network, induced by the me chanical loading of bone, is believed to play an important role in bone mod elling, remodelling and adaptation processes. There are strong indications that this fluid flow is responsible for the mechanotransduction from extern al mechanical loads to the cells responsible for bone apposition or removal . Since direct how measurements (especially in compact bone, in vivo and in situ) are not yet possible, theoretical modelling offers an alternative ap proach to determine the fluid flow velocities, displacements and effects of interstitial fluid flow. In this model, the fluid displacements in a middi aphyseal slab of a rat tibia under a cyclic four-point-bending load were ca lculated by applying Blot's theory of poroelasticity. The resulting differe ntial equations were solved numerically for the fluid displacement vectors using the finite difference method. Thereby, the cross section located in t he middle between the two inner points of force application was chosen for examination, such that the problem, although formulated in three dimensions , reduced itself to an essentially planar form. The maximal fluid displacem ents for the vector components in the cross sectional plane were found in t he proximity of the neutral axis of bending. The direction of the displacem ent vectors was from the: lateral aspect, which was in compression in the e xamined loading situation, towards the medial aspect in tension. In a param eter study it was found that the fluid displacement pattern and the distrib ution of fluid displacements remained constant for all the examined paramet ers, while the magnitude was influenced by the model parameters Young's mod ulus, Poisson's ratio and porosity. This study represents a further step in the examination of load-induced fluid displacements in loaded bone using t heoretical models, aiming to understand the relationship between mechanical loading and bone modelling, remodelling and functional adaptation. (C) 200 0 IPEM. Published by Elsevier Science Ltd. All rights reserved.