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Computational Modeling of Extravascular Flow in Bone

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Computational Modeling in Biomechanics

Abstract

The resident cells of bone tissue are the micromachines responsible for maintaining and adapting the tissue structure to meet needs associated with bone’s dynamic, physiologic function. Mechanical load induced extravascular fluid flow provides the mechanical and chemical signals that modulate bone cell activity. However, the mechanisms by which cell scale processes are translated to functional adaptation at the organ scale are not clear. Predictive multi-scale models provide a means to test virtually the effects of specific model parameters, increasing efficiency and speeding the discovery of mechanisms underlying functional adaptation. This chapter reviews top-down computational modeling approaches to predict the interplay between mechanical loading of bone, load-driven fluid flow, and associated augmentation of molecular transport within bone. As underscored in recent studies, typically applied idealizations in geometry, as well as spatial distribution (anisotropy) and material properties of cells and tissues, deteriorate the fidelity of extravascular flow predictions. For example, idealization of pericellular fluid space geometries causes orders of magnitude underprediction of stresses imparted by fluid drag on cell surfaces. New, bottom-up approaches will help to elucidate the mechanical and chemical signals comprising the mechanophysiological environment of bone at multiple length scales, which is key to understanding mechanotransduction and how cells adapt bone tissue in health and disease.

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Notes

  1. 1.

    Interestingly, the diffusion constant for water in the pores of the bone matrix has recently been measured in rabbit bone to be on the order of \(3 \times 1{0}^{-7}\,{\mathrm{cm}}^{2}/\mathrm{s}\) [17]. The measured diffusion coefficient for rabbit bone is an order of magnitude higher than our estimate, but it does not alter the validity of the theoretical model. In addition, diffusion coefficients in human cortical bone are likely to be significantly less than those in rabbit or rat bone due to human cortical bone’s compact and osteonal structure (After [31, 34]).

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Authors and Affiliations

  1. Departments of Mechanical & Aerospace and Biomedical Engineering, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH, 44106-7222, USA

    Melissa L. Knothe Tate (Joint Professor)

  2. Professor Emeritus, Institute of Biomedical Engineering and Medical Informatics, Swiss Federal Institute of Technology, Zurich, Switzerland

    Peter Niederer

Authors
  1. Melissa L. Knothe Tate
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  2. Roland Steck
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  3. Andrea Tami
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  4. Hans-Jörg Sidler
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  5. Eric J. Anderson
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  6. Peter Niederer
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Correspondence to Melissa L. Knothe Tate .

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Editors and Affiliations

  1. Dept. Mechanical, Aerospace &, Rensselaer Polytechnic Institute, 8th Street 110, Troy, 12180-3590, U.S.A.

    Suvranu De

  2. Div. Orthopaedic Surgery, Duke University Medical Center, Durham, 27710, U.S.A.

    Farshid Guilak

  3. Dept. Bioengineering, University of California, Berkeley, Evans Hall 479, Berkeley, 94720-1762, U.S.A.

    Mohammad Mofrad R. K.

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Tate, M.L.K., Steck, R., Tami, A., Sidler, HJ., Anderson, E.J., Niederer, P. (2010). Computational Modeling of Extravascular Flow in Bone. In: De, S., Guilak, F., Mofrad R. K., M. (eds) Computational Modeling in Biomechanics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3575-2_10

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