84 research outputs found
A multi-scale sub-voxel perfusion model to estimate diffusive capillary wall conductivity in multiple sclerosis lesions from perfusion MRI data.
We propose a new mathematical model to learn capillary leakage coefficients from dynamic susceptibility contrast MRI data. To this end, we derive an embedded mixed-dimension flow and transport model for brain tissue perfusion on a sub-voxel scale. This model is used to obtain the contrast agent concentration distribution in a single MRI voxel during a perfusion MRI sequence. We further present a magnetic resonance signal model for the considered sequence including a model for local susceptibility effects. This allows modeling MR signal-time curves that can be compared to clinical MRI data. The proposed model can be used as a forward model in the inverse modeling problem of inferring model parameters such as the diffusive capillary wall conductivity. Acute multiple sclerosis lesions are associated with a breach in the integrity of the blood brain barrier. Applying the model to perfusion MR data of a patient with acute multiple sclerosis lesions, we conclude that diffusive capillary wall conductivity is a good indicator for characterizing activity of lesions, even if other patient-specific model parameters are not well-known. This article is protected by copyright. All rights reserved
Coupling DuMuX and DUNE-PDELab to investigate evaporation at the interface between Darcy and Navier-Stokes flow
An implementation of a coupled Navier-Stokes/Darcy model based on different Dune discretization modules is presented. The Darcy model is taken from DuMuX, the Navier-Stokes model is implemented on top of Dune-PDELab, and the coupling is done with help of Dune-MultiDomain together with some project-specific auxiliary code. The Navier-Stokes model features one fluid phase, the Darcy model two fluid phases. Each fluid phase may be composed of two components, in addition, non-isothermal processes are considered. The coupling between free and porous-medium flow uses a sharp interface between both subdomains and conserves mass, momentum, and energy by accounting for the corresponding fluxes across the interface. A cell-centered finite volume method (FVM) is combined with a marker and cell (MAC) scheme. It solves the coupled problem in one monolithic system using a Newton method and a direct linear solver. Numerical results demonstrate the basic functioning and a lab-scale reference application
Uncertainty-aware Validation Benchmarks for Coupling Free Flow and Porous-Medium Flow
A correct choice of interface conditions and useful model parameters for
coupled free-flow and porous-medium systems is vital for physically consistent
modeling and accurate numerical simulations of applications. We consider the
Stokes--Darcy problem with different models for the porous-medium compartment
and corresponding coupling strategies: the standard averaged model based on
Darcy's law with classical or generalized interface conditions, as well as the
pore-network model. We study the coupled flow problems' behaviors considering a
benchmark case where a pore-scale resolved model provides the reference
solution and quantify the uncertainties in the models' parameters and the
reference data. To achieve this, we apply a statistical framework that
incorporates a probabilistic modeling technique using a fully Bayesian
approach. A Bayesian perspective on a validation task yields an optimal
bias-variance trade-off against the reference data. It provides an integrative
metric for model validation that incorporates parameter and conceptual
uncertainty. Additionally, a model reduction technique, namely Bayesian Sparse
Polynomial Chaos Expansion, is employed to accelerate the calibration and
validation processes for computationally demanding Stokes--Darcy models with
different coupling strategies. We perform uncertainty-aware validation,
demonstrate each model's predictive capabilities, and make a model comparison
using a Bayesian validation metric
Surrogate-based Bayesian Comparison of Computationally Expensive Models: Application to Microbially Induced Calcite Precipitation
Geochemical processes in subsurface reservoirs affected by microbial activity
change the material properties of porous media. This is a complex
biogeochemical process in subsurface reservoirs that currently contains strong
conceptual uncertainty. This means, several modeling approaches describing the
biogeochemical process are plausible and modelers face the uncertainty of
choosing the most appropriate one. Once observation data becomes available, a
rigorous Bayesian model selection accompanied by a Bayesian model
justifiability analysis could be employed to choose the most appropriate model,
i.e. the one that describes the underlying physical processes best in the light
of the available data. However, biogeochemical modeling is computationally very
demanding because it conceptualizes different phases, biomass dynamics,
geochemistry, precipitation and dissolution in porous media. Therefore, the
Bayesian framework cannot be based directly on the full computational models as
this would require too many expensive model evaluations. To circumvent this
problem, we suggest performing both Bayesian model selection and justifiability
analysis after constructing surrogates for the competing biogeochemical models.
Here, we use the arbitrary polynomial chaos expansion. We account for the
approximation error in the Bayesian analysis by introducing novel correction
factors for the resulting model weights. Thereby, we extend the Bayesian
justifiability analysis and assess model similarities for computationally
expensive models. We demonstrate the method on a representative scenario for
microbially induced calcite precipitation in a porous medium. Our extension of
the justifiability analysis provides a suitable approach for the comparison of
computationally demanding models and gives an insight on the necessary amount
of data for a reliable model performance
Visual Ensemble Analysis of Fluid Flow in Porous Media across Simulation Codes and Experiment
We study the question of how visual analysis can support the comparison of
spatio-temporal ensemble data of liquid and gas flow in porous media. To this
end, we focus on a case study, in which nine different research groups
concurrently simulated the process of injecting CO2 into the subsurface. We
explore different data aggregation and interactive visualization approaches to
compare and analyze these nine simulations. In terms of data aggregation, one
key component is the choice of similarity metrics that define the relation
between the different simulations. We test different metrics and find that a
fine-tuned machine-learning based metric provides the best visualization
results. Based on that, we propose different visualization methods. For
overviewing the data, we use dimensionality reduction methods that allow us to
plot and compare the different simulations in a scatterplot. To show details
about the spatio-temporal data of each individual simulation, we employ a
space-time cube volume rendering. We use the resulting interactive, multi-view
visual analysis tool to explore the nine simulations and also to compare them
to data from experimental setups. Our main findings include new insights into
ranking of simulation results with respect to experimental data, and the
development of gravity fingers in simulations.Comment: arXiv preprin
Visual Analysis of Hyperproperties for Understanding Model Checking Results
Model checkers provide algorithms for proving that a mathematical model of a system satisfies a given specification. In case of a violation, a counterexample that shows the erroneous behavior is returned. Understanding these counterexamples is challenging, especially for hyperproperty specifications, i.e., specifications that relate multiple executions of a system to each other. We aim to facilitate the visual analysis of such counterexamples through our HYPERVIS tool, which provides interactive visualizations of the given model, specification, and counterexample. Within an iterative and interdisciplinary design process, we developed visualization solutions that can effectively communicate the core aspects of the model checking result. Specifically, we introduce graphical representations of binary values for improving pattern recognition, color encoding for better indicating related aspects, visually enhanced textual descriptions, as well as extensive cross-view highlighting mechanisms. Further, through an underlying causal
analysis of the counterexample, we are also able to identify values that contributed to the violation and use this knowledge for both improved encoding and highlighting. Finally, the analyst can modify both the specification of the hyperproperty and the system directly within HYPERVIS and initiate the model checking of the new version. In combination, these features notably support the analyst in
understanding the error leading to the counterexample as well as iterating the provided system and specification. We ran multiple case studies with HYPERVIS and tested it with domain experts in qualitative feedback sessions. The participants’ positive feedback confirms the considerable improvement over the manual, text-based status quo and the value of the tool for explaining hyperproperties
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