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A Biphasic Poroelasticity Model for Soft Tissue

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Quantification of Biophysical Parameters in Medical Imaging

Abstract

Poroelastic media are characterized by biphasic structure, consisting of a solid matrix permeated by a fluid-filled pore space. Originally conceived for soil mechanics, poroelastic models have been used to study the mechanics of biological tissues, where the matrix consists of cells or the extracellular matrix, and the fluid compartment is comprised of the vascular tree, interstitial fluid, cerebro-spinal fluid, or a combination of these. Unlike simpler monophasic models, poroelasticity predicts two longitudinal (compressional) wave modes with different wave speeds. The poroelastic equations of motion depend on two interaction or coupling parameters that describe the transfer of energy or momentum between the two phases, thus leading to a system of coupled equations. In this chapter, we will explain the poroelastic tissue model, present a poroelastic version of the wave equation, and complement this theoretical part with numerical simulations.

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Notes

  1. 1.

    Tortuosity is the ratio of the length of a curve (in this case, a pore) to the Euclidean distance of its end points. Therefore, T ≥ 1, with larger values indicating a more “curled” shape of the pore space.

  2. 2.

    The value of 2.2 GPa is the bulk modulus of pure water, which is the main constituent of biological tissues. We neglect the influence of the solid shear modulus in the formula \( {M}^{\mathrm{s}}={K}^{\mathrm{s}}+\frac{4}{3}{\mu}^{\mathrm{s}} \), since, in biological tissues, μ s is three orders of magnitude smaller than compression modulus K s. We thus approximate M s ≈ K s.

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Authors and Affiliations

  1. Institute of Medical Informatics, Charité – Universitätsmedizin Berlin, Berlin, Germany

    Sebastian Hirsch

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  1. Sebastian Hirsch
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Correspondence to Sebastian Hirsch .

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Editors and Affiliations

  1. Department of Radiology, Humboldt University of Berlin Charité University Hospital, Berlin, Germany

    Ingolf Sack

  2. Medical Physics and Metrological Information Technology, Physikalisch-Technische Bundesanstalt , Berlin, Germany

    Tobias Schaeffter

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Hirsch, S. (2018). A Biphasic Poroelasticity Model for Soft Tissue. In: Sack, I., Schaeffter, T. (eds) Quantification of Biophysical Parameters in Medical Imaging. Springer, Cham. https://doi.org/10.1007/978-3-319-65924-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-65924-4_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65923-7

  • Online ISBN: 978-3-319-65924-4

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