Complas 2023

COMPLAS 2023

3D reconstruction of an orientation distribution from planar projections according to the principle of maximum entropy

Wollner, Maximilian (Graz University of Technology)
Pukaluk, Anna (Graz University of Technology)
Holzer, Clarissa (Graz University of Technology)
Holzapfel, Gerhard (Graz University of Technology)

In session: TUa-501 - - IS501 - Advanced Modeling and Simulation in Biomechanics: from Molecules to Tissues

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The mechanical behavior of anisotropic materials is often governed by the distribution of fibrous constituents. In biological tissue, this role is predominantly taken up by collagen fibers, whose orientation plays a crucial part in constitutive modeling. A common exper- imental method for investigating such fiber networks is the two-dimensional analysis of differently oriented planar sections of the tissue in question. We show that a finite number of these two-dimensional projections is in general insufficient to unambiguously infer the full three-dimensional fiber orientation. We overcome this lack of information by choosing the distribution of maximum entropy. By approximating the fiber orientation via a series representation on the sphere, we reduce the reconstruction to a surprisingly simple optimization problem. The resulting algorithm is able to deduce the three-dimensional distribution of fibers from any number of differently oriented projections. We illustrate the validity of the approach using different sets of real data.