Porous media, including soil, catalysts, rocks, and organic tissue, are ubiquitous in nature, acting as complex environments through which heat, ions, and chemicals travel. Diffusion, often coupled to interfacial reactions, constitutes a fundamental transport process in porous media. It plays an important role in the transport of fertilizer and contaminants in soil, heat conduction in insulators, and natural phenomena such as geological rock transformations and biological signaling and patterning. This thesis aims to enable a deeper understanding of reaction-diffusion processes in porous media by developing a flexible and computationally efficient numerical modeling and simulation workflow.
Numerical modeling is required whenever the problem is too complex for mechanistic insight by quantitative experiments or analytical theory. Reaction-diffusion processes in porous media are such a complex problem, as transport is coupled to the intricate pore geometry. In addition, they involve different scales, from microscale tortuous diffusion pathways and local reactions to macroscale gradients, requiring models that resolve multiple scales.
Multiscale modeling is, however, challenging due to its large memory requirement and computational cost. In addition, realistic porous media geometries, as can be derived from microscopy images or µCTs, are not parametrizable, requiring algorithmic representation.
We address these issues by developing a scalable, multi-GPU accelerated numerical simulation pipeline that enables memory-efficient multiscale modeling of reaction-diffusion processes in realistic, image-based geometries. This pipeline takes volumetric images as input, from which it derives implicit geometry representations using the level-set method. The diffusion domain is discretized in a geometry-adapted, memory-efficient way using distributed sparse block grids. Reaction-diffusion PDEs are solved in the strong form using the finite difference method with scalable multi-GPU acceleration, enabling the simulation in large, highly resolved 3D samples.
We demonstrate the versatility of the present pipeline by simulating reaction-diffusion processes in the image-derived 3D geometries of four applications: fertilizer diffusion in soil, heat conduction with surface dissipation in reticulate porous ceramics, fluid-mediated mineral replacement in rocks, and morphogen gradient formation in the extracellular space of a gastrulating zebrafish embryo. The former two are used to benchmark the performance of our pipeline, whereas the latter two address real-world problems from geology and biology, respectively.
The geological problem considers a process called dolomitization, which converts calcite into dolomite. Determining the geophysical characteristics of the earth's most abundant rocks, dolomitization plays an important role in engineering and geology. Predicting dolomitization is hampered by the extreme scales involved, as mountain-scale dolomite is produced by ion-scale reactions over millions of years. Using the presented pipeline, we derive rock geometries from µCTs and simulate dolomitization as an inhomogeneous reaction-diffusion process with moving reaction fronts and phase-dependent diffusion. The simulation results show that reaction and diffusion are not sufficient to explain the reaction-front roughness observed experimentally, implying that other processes, such as advection, porosity fingering, or sub-resolution geometric features, such as microcracks in the rock, play an important role in dolomitization.
The biological problem, which constitutes the main application of this thesis, is the formation of morphogen gradients during embryonic development. This is a particularly complex problem influenced by several factors, such as dynamically changing tissue geometries, localized sources and sinks, and interaction with molecules of the extracellular matrix (e.g., HSPG). The abundance of factors involved and the coupling between them makes it difficult to quantify how they modulate the gradient individually and collectively.
We use the present pipeline to reconstruct realistic extracellular space (ECS) geometries of a zebrafish embryo from a light-sheet microscopy video. In these geometries, we simulate the gradient formation of the morphogen Fgf8a, showing for the first time in realistic embryo geometries that a source-diffusion-degradation mechanism with HSPG binding is sufficient for the spontaneous formation and maintenance of robust long-range morphogen gradients. We further test gradient sensitivity against different source, sink, and HSPG-binding rates and show that the gradient becomes distorted when ECS volume or connectivity in the model changes, demonstrating the importance of considering realistic embryo geometries.
In summary, this thesis shows that modeling highly resolved, realistic 3D geometries is computationally feasible using geometry-adapted sparse grids, achieving an 18-fold reduction in memory requirements for the zebrafish model compared to a dense-grid implementation. Multi-CPU/GPU acceleration enables pore-scale simulation of large systems. The pipeline developed in this thesis is fully open-source and versatile, as demonstrated by its application to different kinds of porous media, and we anticipate its future application to other reaction-diffusion problems in porous media, in particular from biology.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:94327 |
| Date | 06 November 2024 |
| Creators | Stark, Justina |
| Contributors | Sbalzarini, Ivo F., Shvartsman, Stanislav Y., Technische Universität Dresden, Max Planck Institute of Molecular Cell Biology and Genetics, Center for Systems Biology Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 10.1016/j.jocs.2023.102118, 18777503 |
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