Kiran Manjunatha, Anna Ranno, Jianye Shi, Nicole Schaaps, Pakhwan Nilcham, Anne Cornelissen, Felix Vogt, Marek Behr, Stefanie Reese
{"title":"A continuum chemo-mechano-biological model for in-stent restenosis with consideration of hemodynamic effects","authors":"Kiran Manjunatha, Anna Ranno, Jianye Shi, Nicole Schaaps, Pakhwan Nilcham, Anne Cornelissen, Felix Vogt, Marek Behr, Stefanie Reese","doi":"10.1002/gamm.202370008","DOIUrl":"https://doi.org/10.1002/gamm.202370008","url":null,"abstract":"<p>The occurrence of in-stent restenosis following percutaneous coronary intervention highlights the need for the creation of computational tools that can extract pathophysiological insights and optimize interventional procedures on a patient-specific basis. In light of this, a modeling framework encompassing the chemo-mechano-biological interactions in the arterial wall and the effects of hemodynamic perturbations is introduced in this work.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202370008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guozhi Dong, Moritz Flaschel, Michael Hintermüller, Kostas Papafitsoros, Clemens Sirotenko, Karsten Tabelow
{"title":"Data-driven methods for quantitative imaging","authors":"Guozhi Dong, Moritz Flaschel, Michael Hintermüller, Kostas Papafitsoros, Clemens Sirotenko, Karsten Tabelow","doi":"10.1002/gamm.202470014","DOIUrl":"https://doi.org/10.1002/gamm.202470014","url":null,"abstract":"<p>In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as quantitative magnetic resonance imaging (qMRI), where quantitative maps of biophysical parameters can characterize the imaged tissue and thus lead to more accurate diagnoses. Such quantitative values can also be useful in subsequent, automatized classification tasks in order to discriminate normal from abnormal tissue, for instance. The accurate reconstruction of these quantitative maps is typically achieved by solving two coupled inverse problems which involve a (forward) measurement operator, typically ill-posed, and a physical process that links the wanted quantitative parameters to the reconstructed qualitative image, given some underlying measurement data. In this review, by considering qMRI as a prototypical application, we provide a mathematically-oriented overview on how data-driven approaches can be employed in these inverse problems eventually improving the reconstruction of the associated quantitative maps.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Regularizations of forward-backward parabolic PDEs","authors":"Carina Geldhauser","doi":"10.1002/gamm.202470001","DOIUrl":"https://doi.org/10.1002/gamm.202470001","url":null,"abstract":"<p>Forward-backward parabolic equations have been studied since the 1980s, but a mathematically rigorous picture is still far from being established. As quite a number of new papers have appeared recently, we review in this work the current state of the art. We focus our analysis on the status quo regarding the three most common types of regularizations, namely semidiscretization, the viscous approximation, and regularization with higher order spatial derivatives.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Omar Lakkis, Adrian Muntean, Omar Richardson, Chandrasekhar Venkataraman
{"title":"Parallel two-scale finite element implementation of a system with varying microstructure","authors":"Omar Lakkis, Adrian Muntean, Omar Richardson, Chandrasekhar Venkataraman","doi":"10.1002/gamm.202470005","DOIUrl":"https://doi.org/10.1002/gamm.202470005","url":null,"abstract":"<p>We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed pullback operator, we are able to model the different microscopic domains as macroscopically dependent deformations of a reference domain. This allows for a relatively simple finite element framework to approximate the underlying system of partial differential equations with a parallel computational structure. We apply this technique to a model problem where we focus on transport in plant tissues. We illustrate the accuracy of the implementation with convergence benchmarks and show satisfactory parallelization speed-ups. We further highlight the effect of the heterogeneous microscopic structure on the output of the two-scale systems. Our implementation (publicly available on GitHub) builds on the <span>deal.II</span> FEM library. Application of this technique allows for an increased capacity of microscopic detail in multiscale modeling, while keeping running costs manageable.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Low Mach number limit of a diffuse interface model for two-phase flows of compressible viscous fluids","authors":"Helmut Abels, Yadong Liu, Šárka Nečasová","doi":"10.1002/gamm.202470008","DOIUrl":"https://doi.org/10.1002/gamm.202470008","url":null,"abstract":"<p>In this paper, we consider a singular limit problem for a diffuse interface model for two immiscible compressible viscous fluids. Via a relative entropy method, we obtain a convergence result for the low Mach number limit to a corresponding system for incompressible fluids in the case of well-prepared initial data and same densities in the limit.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mathematical analysis of a mesoscale model for multiphase membranes","authors":"Jakob Fuchs, Matthias Röger","doi":"10.1002/gamm.202470009","DOIUrl":"https://doi.org/10.1002/gamm.202470009","url":null,"abstract":"<p>In this article, we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author (<i>Arch. Ration. Mech. Anal. 193</i>, 2009) for the one-phase case. We present a mathematical analysis of the asymptotic reduction to the macroscale when a key length parameter becomes arbitrarily small. We identify two main contributions in the energy: one that can be connected to bending of the overall structure and a second that describes the cost of the internal phase separations. We prove the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 </mrow>\u0000 <annotation>$$ Gamma $$</annotation>\u0000 </semantics></math>-convergence towards a perimeter functional for the phase separation energy and construct, in two dimensions, recovery sequences for the convergence of the full energy towards a 2D reduction of the Jülicher–Lipowsky bending energy with a line tension contribution for phase separated hypersurfaces.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Moritz Piening, Fabian Altekrüger, Johannes Hertrich, Paul Hagemann, Andrea Walther, Gabriele Steidl
{"title":"Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction","authors":"Moritz Piening, Fabian Altekrüger, Johannes Hertrich, Paul Hagemann, Andrea Walther, Gabriele Steidl","doi":"10.1002/gamm.202470002","DOIUrl":"https://doi.org/10.1002/gamm.202470002","url":null,"abstract":"<p>The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by using methods from machine learning, in particular deep neural networks. Most of these methods require a huge amount of data and computer capacity to train the networks, which often may not be available. Our paper addresses the issue of learning from small data sets by taking patches of very few images into account. We focus on the combination of model-based and data-driven methods by approximating just the image prior, also known as regularizer in the variational model. We review two methodically different approaches, namely optimizing the maximum log-likelihood of the patch distribution, and penalizing Wasserstein-like discrepancies of whole empirical patch distributions. From the point of view of Bayesian inverse problems, we show how we can achieve uncertainty quantification by approximating the posterior using Langevin Monte Carlo methods. We demonstrate the power of the methods in computed tomography, image super-resolution, and inpainting. Indeed, the approach provides also high-quality results in zero-shot super-resolution, where only a low-resolution image is available. The article is accompanied by a GitHub repository containing implementations of all methods as well as data examples so that the reader can get their own insight into the performance.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alexander Auras, Kanchana Vaishnavi Gandikota, Hannah Droege, Michael Moeller
{"title":"Robustness and exploration of variational and machine learning approaches to inverse problems: An overview","authors":"Alexander Auras, Kanchana Vaishnavi Gandikota, Hannah Droege, Michael Moeller","doi":"10.1002/gamm.202470003","DOIUrl":"https://doi.org/10.1002/gamm.202470003","url":null,"abstract":"<p>This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one-dimensional toy problem are provided, showing the robustness of different approaches and empirically verifying theoretical guarantees. Another focus of this review is the exploration of the subspace of data-consistent solutions through explicit guidance to satisfy specific semantic or textural properties.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Neural-network-based regularization methods for inverse problems in imaging","authors":"Andreas Habring, Martin Holler","doi":"10.1002/gamm.202470004","DOIUrl":"10.1002/gamm.202470004","url":null,"abstract":"<p>This review provides an introduction to—and overview of—the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for regularizing inverse problems in imaging. Distinguishing features of this review are, among others, an easily accessible introduction to learned generators and learned priors, in particular diffusion models, for inverse problems, and a section focusing explicitly on existing results in function space analysis of neural-network-based approaches in this context.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling of fluid-rigid body interaction in an electrically conducting fluid","authors":"Jan Scherz, Anja Schlömerkemper","doi":"10.1002/gamm.202470012","DOIUrl":"https://doi.org/10.1002/gamm.202470012","url":null,"abstract":"<p>We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical assumptions under which a mathematical analysis of the model becomes feasible. Our main focus lies on the derivation of the boundary and interface conditions for the electromagnetic fields as well as the derivation of the magnetohydrodynamic approximation carried out via a nondimensionalization of the system.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}