Geometric modelling of 3D pore space using curve skeleton: Application to computational microbiology of soil organic matter mineralization

Recent advances in 3D X-ray Computed Tomography (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Classical methods for the numerical simulation of biological dynamics using meshes of voxels, such as the Lattice Boltzmann Method (LBM), tend to require long computation times. The use of more compact geometrical representations of the pore space can drastically decrease the computational cost of simulations. Recent research has introduced basic analytic volume primitives to define piece-wise approximations of the pore space to simulate drainage, diffusion, and microbial mineralization of organic matter in soils. Such approaches work well but a drawback is that they give rise to significant approximation errors caused by imposing a priori shapes to represent the pores. In the present article, another alternative is proposed, where pore space is described by means of geometrically relevant connected subsets of voxels (regions) regrouped on the basis of the curve skeleton (3D medial axis). The curve skeleton has been adopted to characterize 3D shapes in various fields (e.g., medical imaging, material sciences, etc.). The few publications that have used it in the context of soils have dealt exclusively with the determination of pore throats. This technique is used mostly to describe shape and not to partition it into connected subsets like in the present work. Here, the pore space is partitioned by using the branches of the curve skeleton, then an Attributed Relational Graph (ARG) is created in order to simulate numerically the microbial mineralization of organic matter, including the diffusion of by-products. Each node of the ARG is attached to an element of the partition (pore) and each arc to an adjacency relationship between pores (connectivity). The graph is valuated in the sense that the attributes related both to geometry and dynamic are linked to nodes and arcs. This new representation can be used for graph-based simulations, which are different from voxel-based simulations.