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Introduction
Chronic pancreatitis (CP) may be caused by oxidative stress. An important source of reactive oxygen species (ROS) is the methylglyoxal-derived formation of advanced glycation endproducts (AGE). Methylglyoxal is detoxified by Glyoxalase I (GLO1). A reduction in GLO1 activity results in increased ROS. Single nucleotide polymorphisms (SNPs) of GLO1 have been linked to various inflammatory diseases. Here, we analyzed whether common GLO1 variants are associated with alcoholic (ACP) and non-alcoholic CP (NACP).
Methods
Using melting curve analysis, we genotyped a screening cohort of 223 ACP, 218 NACP patients, and 328 controls for 11 tagging SNPs defined by the SNPinfo LD TAG SNP Selection tool and the functionally relevant variant rs4746. For selected variants the cohorts were extended to up to 1,441 patient samples.
Results
In the ACP cohort, comparison of genotypes for rs1937780 between patients and controls displayed an ambiguous result in the screening cohort (p = 0.08). However, in the extended cohort of 1,441 patients no statistically significant association was found for the comparison of genotypes (p = 0.11), nor in logistic regression analysis (p = 0.214, OR 1.072, 95% CI 0.961–1.196). In the NACP screening cohort SNPs rs937662, rs1699012, and rs4746 displayed an ambiguous result when patients were compared to controls in the recessive or dominant model (p = 0.08, 0.08, and 0.07, respectively). Again, these associations were not confirmed in the extended cohorts (rs937662, dominant model: p = 0.07, logistic regression: p = 0.07, OR 1.207, 95% CI 0.985–1.480) or in the replication cohorts for rs4746 (Germany, p = 0.42, OR 1.080, 95% CI 0.673–1.124; France, p = 0.19, OR 0.90, 95% CI 0.76–1.06; China, p = 0.24, OR 1.18, 95% CI 0.90–1.54) and rs1699012 (Germany, Munich; p = 0.279, OR 0.903, 95% CI 0.750–1.087).
Conclusions
Common GLO1 variants do not increase chronic pancreatitis risk.

Based on Onsager's variational principle, the motion of superparamagnetic nanoparticles – which are suspended in an incompressible carrier fluid and subjected to an external magnetic field – is described by systems of partial differential quations. Various modeling assumptions lead to three different systems denoted by "model GW", "model W" and "model B". When proposed in our joint work (2019), "model GW" was – to the best of our knowledge – the first one to include evolution equations for the magnetization field and for the magnetic particle density – all of them are nonlinearly coupled to the magnetostatic and the Navier-Stokes equations. The other two models use algebraic equations to determine the magnetization based on the linearized Langevin formula and are derived by us for the purpose of comparison. In case of "model W", we assume that the suspension yields a single-phase flow with negligible mass of magnetic nanoparticles. The other model is derived under the assumption that fluid particles and magnetic particles set up a two-phase fluid. It shows similarities to the model from Himmelsbach et al. (2017). All three models follow a two-domain approach – considering the magnetic field on a possibly larger domain compared to the fluid domain – of which we expect higher accuracy in determining the total magnetic field. The case when the two domains coincide requires some slight changes which are discussed when needed.
In contrast to other works in the mathematical literature, the boundary conditions of the magnetization equation in "model GW" are motivated by physical arguments only, not by practical aspects with respect to mathematical analysis. They entail H(div,curl)-regularity of the magnetic quantities – magnetization and (total) magnetic field – but possibly not H1-regularity. To establish existence of solutions to this model, the absence of H1-regularity is compensated by an intricate approximation procedure. For this, we give a meaning to the Kelvin force (m*nabla)h in the distributional sense. Existence of distributional global-in-time solutions is guaranteed under appropriate assumptions. The latter include nonlinear diffusion to be used in the evolution equation for the magnetic particles' density and the restriction to the two-dimensional setting. An existence result of global-in-time weak solutions to a regularized model is presented also in the three-dimensional setting.
To each of the three models, we propose an unconditionally energy stable finite element scheme. The discretization of "model GW" has already been published in our joint work (2019). Here, non-conforming finite elements are used to approximate the magnetization – similar as in a paper of Nochetto et al. (2015). For the first time, however, the second order differential operators nabla div and curl curl in the magnetization equation have been discretized by introducing the operators divh and curlh – discrete versions of div and curl. The latter are defined by duality and yield H1-conforming approximations of the divergence and curl of a vector field. By means of Schaefer's fixed point theorem, existence of discrete solutions is guaranteed for all three schemes. The existence results are independent of the discretization parameters.
The thesis concludes with simulations that serve as a proof of concept for the models and their numerical schemes. The three models are compared in the case of linear diffusion and the case of nonlinear diffusion which has been used in the analysis part of this thesis. For simplicity, most simulations are performed under the assumption that the domain of the magnetic field coincides with the fluid domain. Using "model W" – for practical reasons – the effects of multiple different external magnetic fields are examined as well as the impact of using a strictly larger domain for the magnetic field.