GAMM Mitteilungen最新文献

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.

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.

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.

Predicting the long-term success of endovascular interventions in the clinical management of cerebral aneurysms requires detailed insight into the patient-specific physiological conditions. In this work, we not only propose numerical representations of endovascular medical devices such as coils, flow diverters or Woven EndoBridge but also outline numerical models for the prediction of blood flow patterns in the aneurysm cavity right after a surgical intervention. Detailed knowledge about the postsurgical state then lays the basis to assess the chances of a stable occlusion of the aneurysm required for a long-term treatment success. To this end, we propose mathematical and mechanical models of endovascular medical devices made out of thin metal wires. These can then be used for fully resolved flow simulations of the postsurgical blood flow, which in this work will be performed by means of a Lattice Boltzmann method applied to the incompressible Navier–Stokes equations and patient-specific geometries. To probe the suitability of homogenized models, we also investigate poro-elastic models to represent such medical devices. In particular, we examine the validity of this modeling approach for flow diverter placement across the opening of the aneurysm cavity. For both approaches, physiologically meaningful boundary conditions are provided from reduced-order models of the vascular system. The present study demonstrates our capabilities to predict the postsurgical state and lays a solid foundation to tackle the prediction of thrombus formation and, thus, the aneurysm occlusion in a next step.

The functioning of the neuromuscular system is an important factor for quality of life. With the aim of restoring neuromuscular function after limb amputation, novel clinical techniques such as the agonist-antagonist myoneural interface (AMI) are being developed. In this technique, the residual muscles of an agonist-antagonist pair are (re-)connected via a tendon in order to restore their mechanical and neural interaction. Due to the complexity of the system, the AMI can substantially profit from in silico analysis, in particular to determine the prestretch of the residual muscles that is applied during the procedure and determines the range of motion of the residual muscle pair. We present our computational approach to facilitate this. We extend a detailed multi-X model for single muscles to the AMI setup, that is, a two-muscle-one-tendon system. The model considers subcellular processes as well as 3D muscle and tendon mechanics and is prepared for neural process simulation. It is solved on high performance computing systems. We present simulation results that show (i) the performance of our numerical coupling between muscles and tendon and (ii) a qualitatively correct dependence of the range of motion of muscles on their prestretch. Simultaneously, we pursue a Bayesian parameter inference approach to invert for parameters of interest. Our approach is independent of the underlying muscle model and represents a first step toward parameter optimization, for instance, finding the prestretch, to be applied during surgery, that maximizes the resulting range of motion. Since our multi-X fine-grained model is computationally expensive, we present inversion results for reduced Hill-type models. Our numerical results for cases with known ground truth show the convergence and robustness of our approach.

This article aims to present some novel experimental approaches and computational methods providing detailed insights into the mechanical behavior of skeletal muscles relevant to clinical problems associated with managing and treating musculoskeletal diseases. The mechanical characterization of skeletal muscles in vivo is crucial for better understanding of, prevention of, or intervention in movement alterations due to exercise, aging, or pathologies related to neuromuscular diseases. To achieve this, we suggest an intraoperative experimental method including direct measurements of human muscle forces supported by computational methodologies. A set of intraoperative experiments indicated the major role of extracellular matrix (ECM) in spastic cerebral palsy. The force data linked to joint function are invaluable and irreplaceable for evaluating individual muscles however, they are not feasible in many situations. Three-dimensional, continuum-mechanical models provide a way to predict the exerted muscle forces. To obtain, however, realistic predictions, it is important to investigate the muscle not by itself, but embedded within the respective musculoskeletal system, for example, a 6-muscle upper arm model, and the ability to obtain non-invasively, or at least, minimally invasively material parameters for continuum-mechanical skeletal muscle models, for example, by presently proposed homogenization methodologies. Botulinum toxin administration as a treatment option for spasticity is exemplified by combining experiments with modeling to find out the mechanical outcomes of altered ECM and the controversial effects of the toxin. The potentials and limitations of both experimental and modeling approaches and how they need each other are discussed.

All digital objects that result from the modeling and simulation field are valid sets of research data. In general, research data are the result of intense intellectual activity that is worth communicating. This communication is an essential research practice that, whether with the aim of understanding, critiquing or further developing results, smoothly leads to collaboration, which not only involves discussions, and sharing institutional resources, but also the sharing of data and information at several stages of the research process. Data sharing is intended to improve and facilitate collaboration but quickly introduces challenges like reproducibility, reusability, interoperability, and standardization. These challenges are deeply rooted in an apparent reproducibility standard, about which there is a debate worth considering before emphasizing how the modeling and simulation workflow commonly occurs. Although that workflow is almost natural for practitioners, the sharing practices still require special attention because the principles (known as FAIR principles) that guide research practices towards data sharing also guide the requirements for machine actionable results. The FAIR principles, however, do not address the actual implementation of the data sharing process. This implementation requires careful consideration of characteristics of the sharing platforms for benefiting the most of the data sharing activity. This article serves as an invitation to integrate data sharing practices into the established routines of researchers and elaborates on the perspectives, and guidelines surrounding data sharing implementation.

Computational fluid dynamics (CFD) carry the potential to provide detailed insights into intraventricular hemodynamics and complement in vivo flow measurement techniques. A variety of CFD approaches emerged in recent years, mostly building solely on medical image data as patient-specific input. While the utilized medical imaging method and chosen CFD approach both influence the computed hemodynamics, thereto related differences are rarely investigated. The present study addresses this issue with an inter-(imaging)-modality and inter-model comparison of intracardiac flow computations. Magnetic resonance imaging (MRI) and transthoracic echocardiography (TTE) data of a volunteer were acquired and used to reconstruct the anatomical structures. For each modality, the reconstructed shapes were applied in two previously introduced CFD approaches to compute whole-cycle ventricular flow patterns. While both methods involved benefits and challenges, similar valve velocities were computed, being in accordance with in vivo 4D flow MRI and pulsed-wave Doppler velocity measurements (systolic peak velocity: 1.24–1.26 m/s (MRI), 0.9–1.25 m/s (TTE); diastolic peak velocity: 0.54 m/s (MRI), 0.59–0.75 m/s (TTE)). A detailed flow analysis with vortex formation, kinetic energy, and mid-ventricular velocities indicated the computed inter-modality differences to be larger than inter-method ones. Quantitatively, this could be observed in the direct flow rate ($��\Delta �$ inter-modality: 13$��\%�$, $��\Delta �$ inter-method, 3$��\%�$). These results help to gain trust in CFD approaches to compute intraventricular flow and emphasize the importance of standardized input data. Future studies, however, should consider a broader data base.

The SIMulation supported LIVer Assessment for donor organs (SimLivA) project aims to develop a mathematical model to accurately simulate the influence of mechanical alterations in marginal liver grafts (specifically steatotic ones) and cold ischemia on early ischemia-reperfusion injury (IRI) during liver transplantation. Our project tackles significant research challenges, including the co-development of computational methodologies, experimental studies, clinical processes, and technical workflows. We aim to refine a continuum-biomechanical model for enhanced IRI prediction, collect pivotal experimental and clinical data, and assess the clinical applicability of our model. Our efforts involve augmenting and tailoring a coupled continuum-biomechanical, multiphase, and multi-scale partial differential equation-ordinary differential equation (PDE-ODE) model of the liver lobule, allowing us to numerically simulate IRI depending on the degree of steatosis and the duration of ischemia. The envisaged model will intertwine the structure, perfusion, and function of the liver, serving as a crucial aid in clinical decision-making processes. We view this as the initial step towards an in-silico clinical decision support tool aimed at enhancing the outcomes of liver transplantation. In this paper, we provide an overview of the SimLivA project and our preliminary findings, which include: a cellular model that delineates critical processes in the context of IRI during transplantation; and the integration of this model into a multi-scale PDE-ODE model using a homogenized, multi-scale, multi-component approach within the Theory of Porous Media (TPM) framework. The model has successfully simulated the interconnected relationship between structure, perfusion, and function—all of which are integral to IRI. Initial results show simulations at the cellular scale that describe critical processes related to IRI during transplantation. After integrating this model into a multiscale PDE-ODE model, first simulations were performed on the spatial distribution of key functions during warm and cold ischaemia. In addition, we were able to study the effect of tissue perfusion and temperature, two critical parameters in the context of liver transplantation and IRI.

A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja–Smith–Widlund) and RGDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed.