A Voxel-based Approach for Simulating Microbial Decomposition in Soil: Comparison with LBM and Improvement of Morphological Models

This study presents a new computational approach for simulating the microbial decomposition of organic matter, from 3D micro-computed tomography (micro-CT) images of soil. The method employs a valuated graph of connected voxels to simulate transformation and diffusion processes involved in microbial decomposition within the complex soil matrix. The resulting model can be adapted to simulate any diffusion-transformation processes in porous media. We implemented parallelization strategies and explored different numerical methods, including implicit, explicit, synchronous, and asynchronous schemes. To validate our method, we compared simulation outputs with those provided by LBioS and by Mosaic models. LBioS uses a lattice-Boltzmann method for diffusion and Mosaic takes benefit of Pore Network Geometrical Modelling (PNGM) by means of geometrical primitives such as spheres and ellipsoids. This approach achieved comparable results to traditional LBM-based simulations, but required only one-fourth of the computing time. Compared to Mosaic simulation, the proposed method is slower but more accurate and does not require any calibration. Furthermore, we present a theoretical framework and an application example to enhance PNGM-based simulations. This is accomplished by approximating the diffusional conductance coefficients using stochastic gradient descent and data generated by the current approach.

Global Attractor for a Reaction-Diffusion Model Arising in Biological Dynamic in 3D Soil Structure

Partial Differential Equations (PDEs) play a crucial role as tools for modeling and comprehending intricate natural processes, notably within the domain of biology. This research explores the domain of microbial activity within the complex matrix of 3D soil structures, providing valuable understanding into both the existence and uniqueness of solutions and the asymptotic behavior of the corresponding PDE model. Our investigation results in the discovery of a global attractor, a fundamental feature with significant implications for long-term system behavior. To enhance the clarity of our findings, numerical simulations are employed to visually illustrate the attributes of this global attractor.

Segmentation of 3D pore space from CT images using curvilinear skeleton: application to numerical simulation of microbial decomposition

Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).

Generic tool for numerical simulation of transformation-diffusion processes in complex volume geometric shapes: application to microbial decomposition of organic matter

This paper presents a generic framework for the numerical simulation of transformation-diffusion processes in complex volume geometric shapes. This work follows a previous one devoted to the simulation of microbial degradation of organic matter in porous system at microscopic scale. We generalized and improved the MOSAIC method significantly and thus yielding a much more generic and efficient numerical simulation scheme. In particular, regarding the simulation of diffusion processes from the graph, in this study we proposed a completely explicit and semi-implicit numerical scheme that can significantly reduce the computational complexity. We validated our method by comparing the results to the one provided by classical Lattice Boltzmann Method (LBM) within the context of microbial decomposition simulation. For the same datasets, we obtained similar results in a significantly shorter computing time (i.e., 10-15 minutes) than the prior work (several hours). Besides the classical LBM method takes around 3 weeks computing time.

3D Quantum Cuts for Automatic Segmentation of Porous Media in Tomography Images

Binary segmentation of volumetric images of porous media is a crucial step towards gaining a deeper understanding of the factors governing biogeochemical processes at minute scales. Contemporary work primarily revolves around primitive techniques based on global or local adaptive thresholding that have known common drawbacks in image segmentation. Moreover, absence of a unified benchmark prohibits quantitative evaluation, which further clouds the impact of existing methodologies. In this study, we tackle the issue on both fronts. Firstly, by drawing parallels with natural image segmentation, we propose a novel, and automatic segmentation technique, 3D Quantum Cuts (QCuts-3D) grounded on a state-of-the-art spectral clustering technique. Secondly, we curate and present a publicly available dataset of 68 multiphase volumetric images of porous media with diverse solid geometries, along with voxel-wise ground truth annotations for each constituting phase. We provide comparative evaluations between QCuts-3D and the current state-of-the-art over this dataset across a variety of evaluation metrics. The proposed systematic approach achieves a 26% increase in AUROC while achieving a substantial reduction of the computational complexity of the state-of-the-art competitors. Moreover, statistical analysis reveals that the proposed method exhibits significant robustness against the compositional variations of porous media.