Fig 1.
Top left: 2D cross-section of the sandy loam soil (dataset 1, voxels; where the voxels associated with the pore space are colored in black (of the whole image).
Top middle: perspective view of a small part of the whole pore space. Top right: perspective view of the corresponding curve skeleton. Bottom left: segmentation of the curvilinear skeleton into simple branches; zoom on some simple branches (18508 simple branches in total). Bottom right: cross section of the partitioning of the pore space based on the curve skeleton where each color is attached to a region.
Fig 2.
Left: perspective view of the pore space.
Right: 2D cross section of Fontainebleau sand (dataset 3, low porosity, ;
); pore space voxels are colored in black (
of the whole image).
Fig 3.
Fitting of the ball and curve skeleton models; left figure (a): A zoom-in of the 3D projection of a portion of the partitioned image depicted in Fig 1. The 3D projection shows better than the 2D images (Fig 1) how the partitioned pore regions are connected. Each color corresponds to a region attached to a simple branch of the curve skeleton.; right figure (b): balls labeled with the corresponding region.
Fig 4.
Illustration of the two biggest balls where the micro-organisms are located (dataset 3) for the microbial decomposition simulation (2D cross sections); up left: the biggest ball colored by the parts of the regions which intersect it; up right: the (entire) regions intersecting the biggest ball; bottom left: the second biggest ball colored by the parts of the regions which intersect it; bottom right: the regions intersecting the second biggest ball.
Round 85% of the ten biggest regions are included within the two biggest balls. https://free3d.com/.
Fig 5.
Schematic representation of the main steps from gray images to the corresponding graph of the segmented regions.
Fig 6.
Simulation results for diffusion only (data set 1) used to calibrate the overall conductance to be used in later simulations.
The X-axis displays the number of planes within the image (512 planes in total), whereas the Y-axis displays the total mass of organic matter within each plane. At the start, 100 µg of carbon were introduced within the first two planes. The total simulation time was 1.783 hours. The optimal value of the diffusive overall conductance coefficient was determined to be equal to 0.35, with an intercorrelation of 0.9818. We notice that after 1.783 hours only the 300 first planes were reached.
Fig 7.
Comparison of different simulations of the microbial mineralization for dataset 1 over a total simulation time of 5 days.
The Y axis displays the mass of several components of the system expressed as a percentage of the total initial carbon mass. Simulations were carried out in the “curve skeleton” method with a diffusive conductance coefficient equal to 0.35.
Fig 8.
Comparison of the simulations of microbial mineralization for dataset 3 (low sand porosity) using the ball based MOSAIC program and the novel approach introduced here, based on the partitioning of the pore voxels on the basis of the curve skeleton.
The simulations extended over 5 days and were carried out in the “curve skeleton” method with a diffusive conductance coefficient equal to 0.35 for the curve skeleton method and 0.6 for the balls method. The initial masses (micro-organisms, dissolved organic matter) and also the diffusion coefficient were adjusted according to the image resolution. X-axis and Y-axis represents respectively time expressed in hours and the masses expressed in percentage of the total initial masses. Solid line curves and dotted line curves correspond respectively to the curve skeleton model and to the balls model. Dark blue curves, green curves, red curves, light blue curves correspond respectively to microorganisms, dissolved organic matter (DOM), carbon dioxide (CO2), slow organic matter (SOM). Same as for dataset 1 the microbial degradation model take into account DOM and SOM but not FOM.
Table 1.
Comparative table about the characteristics of the different datasets.
Fig 9.
Comparison of 3D and 0D (non-spatialized) models for microbial decomposition.
For this specific simulation, we set Vsom = 0, that explains why DOM drops to 0 although MB and SOM are positive.
Fig 10.
Comparison of different spatializations for the 3D model.
The principle of our method consists of segmenting the curve skeleton into simple branches, and afterward attaching to each simple branch a connected set of points. The result is a partition of the pore space, which can be represented by an attributed relational graph. In this graph, each node corresponds to a pore, and each arc to an adjacency between a couple of pores. We show that this geometrical representation of the pore space can be used directly to simulate the microbial mineralization dynamics including diffusion and transformation processes. We assess the soundness of the approach by comparison with other methods that have been developed and used in the past in the same context. A possible drawback of the novel approach, compared with geometrical primitives-based modeling, is that each pore is defined by a set of connected voxels with no explicit geometric properties. On the other hand, the advantages of the pore space modeling based on the curve skeleton are fourfold. It does not impose specific shapes for a pore as do primitive-based modeling methods, involving balls or ellipsoids. It defines an exact piece-wise representation of the pore space, without losing any part of it, since it is based strictly on a partitioning of the pore space into distinct regions. On the other hand, the computations on the basis of the curve skeleton use reduced information attached to the valuated graph (inertia center, region size, contact surface) that is the limitation of this framework. When implementing diffusion processes, it involves an exact computation of the area of the contact surfaces between adjacent regions. Finally, the number of nodes (pores) is much less than the ball network used in a previous work. To maximize the advantages and minimize the drawbacks, it might be possible in the future to implement hybrid geometric modeling algorithms using both skeletonization and geometric primitives.