Mean-intercept anisotropy analysis of porous media. I. Analytic formulae for anisotropic Boolean models

Journal article

Publication Details

Author(s): Klatt MA, Schroder-Turk GE, Mecke K
Journal: Medical Physics
Publication year: 2017
Volume: 44
Journal issue: 7
Pages range: 3650-3662
ISSN: 0094-2405
eISSN: 2473-4209


Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors that quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, for example, of trabecular bone in medical physics.
We analyze the orientation-biased Boolean model, a versatile stochastic model that represents microstructures as overlapping grains with an orientation bias towards a preferred direction. This model is an extension of the isotropic Boolean model, which has been shown to truthfully reproduce multi-functional properties of isotropic porous media. We explain the close relationship between the concept of intersections with test lines to the elaborate mathematical theory of queues, and how explicit results from the latter can be directly applied to characterize microstructures.
In this series of two papers, we provide analytic formulas for the anisotropic Boolean model and demonstrate often overlooked conceptual shortcomings of this approach. Queuing theory is used to derive simple and illustrative formulas for the mean intercept length. It separates into an intensity-dependent and an orientation-dependent factor. The global average of the mean intercept length can be expressed by local characteristics of a single grain alone.
We thus identify which shape information about the random process the mean intercept length contains. The connection between global and local quantities helps to interpret observations and provides insights into the possibilities and limitations of the analysis. In the second paper of this series, we discuss, based on the findings in this paper, short-comings of the mean intercept analysis for (bone-)microstructure characterization. We will suggest alternative and better defined sensitive anisotropy measures from integral geometry.

FAU Authors / FAU Editors

Mecke, Klaus Prof. Dr.
Lehrstuhl für Theoretische Physik

Additional Organisation
Exzellenz-Cluster Engineering of Advanced Materials

External institutions with authors

Karlsruhe Institute of Technology (KIT)
Murdoch University

Research Fields

A3 Multiscale Modeling and Simulation
Exzellenz-Cluster Engineering of Advanced Materials

How to cite

Klatt, M.A., Schroder-Turk, G.E., & Mecke, K. (2017). Mean-intercept anisotropy analysis of porous media. I. Analytic formulae for anisotropic Boolean models. Medical Physics, 44(7), 3650-3662.

Klatt, Michael A., Gerd E. Schroder-Turk, and Klaus Mecke. "Mean-intercept anisotropy analysis of porous media. I. Analytic formulae for anisotropic Boolean models." Medical Physics 44.7 (2017): 3650-3662.


Last updated on 2019-16-03 at 06:10