GAMM Mitteilungen最新文献

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.

Dielectric elastomers are a promising technology for wave energy harvesting. An optimal system operation can allow maximizing the extracted energy and, simultaneously, reducing wear that would lead to a reduction in the wave harvester lifetime. We pursue a model-based optimization approach to identify optimal controls for wave energy harvesters based on dielectric elastomers. First, a direct method is used for time-discretization of the dielectric elastomer wave energy harvester in the optimal control problem. The two conflicting objectives are considered in a multiobjective optimization framework. Considering a periodic, sinusoidal wave excitation, the optimal solution shows turnpike properties for the optimal periodic mode of operation. However, since real wave motion is neither monochromatic nor predictable on longer time horizons, further extensions are pursued. First, we introduce a stochastic wave excitation. Second, an iterative model-predictive control scheme is designed. Due to multiple objectives, the control scheme has to include an automated adaption of the corresponding priorities. Here, we propose and evaluate a heuristic rule-based adaption in order to maintain the damage below target levels. The approach presented here might be used in the future to guarantee for autonomous operation of farms of wave energy harvesters.

The current special issue of the GAMM Mitteilungen, which is the second of a two-part series, contains several contributions on the topic of Applied and Nonlinear Dynamics. We are very happy that several teams of authors have accepted our invitation to report on recent developments, research highlights and emerging application areas in Applied and Nonlinear Dynamics.

This second part of the topical issue on Applied and Nonlinear Dynamics includes five interesting papers. These are devoted to numerical and experimental methods in applied and nonlinear dynamics as well as advanced applications of multibody systems and optimal control methods to dynamical systems.

Contribution 3 deals with stationary solutions in applied dynamics. Thereby a unified framework for the numerical calculation and stability assessment of periodic and quasi-periodic solutions based on invariant manifolds is presented. Paper 2 gives an overview of dynamic human body models in vehicle safety, a unique application of multibody dynamics. In paper 1, a family of total Lagrangian Petrov-Galerkin Cosserat rod finite element formulations is presented. Paper 5 discusses continuation methods for lab experiments of nonlinear vibrations. Finally paper 4 deals with the optimal operation of dielectric elastomer wave energy converters under harmonic and stochastic excitation.

In this work, we will give an overview of our recent progress in experimental continuation. First, three different approaches are explained and compared which can be found in scientific papers on the topic. We then show S-Curve measurements of a Duffing oscillator experiment for which we derived optimal controller gains analytically. The derived formula for stabilizing PD-controller gains makes trial and error search for suitable values unnecessary. Since feedback control introduces higher harmonics in the driving signal, we consider a harmonization of the forcing signal. This harmonization is important to reduce shaker-structure interaction in the treatment of nonlinear frequency responses. Finally, the controlled nonlinear testing and harmonization is enhanced by a continuation algorithm adapted from numerical analysis and applied to a geometrically nonlinear beam test rig for which we measure the nonlinear forced response directly in the displacement-frequency plane.

The standard in rod finite element formulations is the Bubnov–Galerkin projection method, where the test functions arise from a consistent variation of the ansatz functions. This approach becomes increasingly complex when highly nonlinear ansatz functions are chosen to approximate the rod's centerline and cross-section orientations. Using a Petrov–Galerkin projection method, we propose a whole family of rod finite element formulations where the nodal generalized virtual displacements and generalized velocities are interpolated instead of using the consistent variations and time derivatives of the ansatz functions. This approach leads to a significant simplification of the expressions in the discrete virtual work functionals. In addition, independent strategies can be chosen for interpolating the nodal centerline points and cross-section orientations. We discuss three objective interpolation strategies and give an in-depth analysis concerning locking and convergence behavior for the whole family of rod finite element formulations.

The determination of stationary solutions of dynamical systems as well as analyzing their stability is of high relevance in science and engineering. For static and periodic solutions a lot of methods are available to find stationary motions and analyze their stability. In contrast, there are only few approaches to find stationary solutions to the important class of quasi-periodic motions–which represent solutions of generalized periodicity–available so far. Furthermore, no generally applicable approach to determine their stability is readily available. This contribution presents a unified framework for the analysis of equilibria, periodic as well as quasi-periodic motions alike. To this end, the dynamical problem is changed from a formulation in terms of the trajectory to an alternative formulation based on the invariant manifold as geometrical object in the state space. Using a so-called hypertime parametrization offers a direct relation between the frequency base of the solution and the parametrization of the invariant manifold. Over the domain of hypertimes, the invariant manifold is given as solution to a PDE, which can be solved using standard methods as Finite Differences (FD), Fourier-Galerkin-methods (FGM) or quasi-periodic shooting (QPS). As a particular advantage, the invariant manifold represents the entire stationary dynamics on a finite domain even for quasi-periodic motions – whereas obtaining the same information from trajectories would require knowing them over an infinite time interval. Based on the invariant manifold, a method for stability assessment of quasi-periodic solutions by means of efficient calculation of Lyapunov-exponents is devised. Here, the basic idea is to introduce a Generalized Monodromy Mapping, which may be determined in a pre-processing step: using this mapping, the Lyapunov-exponents may efficiently be calculated by iterating this mapping.