Publikationen

Zusammenfassung

Sea ice in the polar oceans plays a significant role in regulating global climate and biological ecosystems. During the winter months, seawater freezes to form porous ice, which also serves as a habitat for sea ice algae to survive in harsh winter conditions. However, accurate description of mechanisms and interactions associated with formation of ice, and its interaction with photosynthesis and carbon assimilation have not been well understood. This paper presents a modeling framework to describe coupled small scale Physical (P) and BioGeoChemical (BGC) processes associated with sea ice. Critical processes associated with photosynthesis along with growth and loss of algal carbon are considered. Appropriate parametrization for environmental factors such as temperature, light, salinity, and nutrients are employed to model the photosynthetic rate. Summer and winter environmental conditions are presented and discussed in detail. Finally, monthly data is taken from literature to simulate a typical year in the Southern Ocean.

Zusammenfassung

Laser therapy is extensively utilized in dermatology and medicine due to its ability to precisely target tissues, particularly for skin rejuvenation and colla-gen stimulation. However, the complex interactions between laser irradiation and multilayered skin structures remain insufficiently understood. This study presents a two-dimensional dual-phase-lag heat conduction model to simu-late the temperature distribution in multilayered skin subjected to pulsating laser irradiation. The model incorporates the distinct optical and thermal properties of different skin layers, enhancing the accuracy of heat transfer analysis. To regulate laser intensity and maintain surface temperature within a predefined range, a proportional-integral-derivative (PID) control system is implemented. Experimental validation using an agar-based phantom shows strong agreement with simulation results, confirming the model's reliability. The results further indicate that the PID control system effectively maintains the target temperature with minimal overshoot. However, while surface temperature remains regulated, deeper skin layers may experience higher peak temperatures, emphasizing the need for improved subsurface thermal monitoring, particularly in high absorption treatments. Additionally, the study systematically analyzes the influence of PID gain parameters on temperature regulation, highlighting their impact on system stability and response time. These findings underscore the critical role of integrated control systems in laser-based thermal therapies, enhancing precision, safety, and clinical efficacy. The proposed framework provides a robust foundation for real-time temperature management, contributing to more reliable and effective medical applications of laser technology.

Zusammenfassung

Laser therapy in dermatology has become a popular method in treatment of skin related issues. However, an improper administration of laser beam on skin can lead to negative effects on the patients’ physical and emotional well-being. While quite a fair bit of experimental data is available for laser-skin interactions, the inherent bias due to geographical developments of these techniques have led to a neglect towards skins of color. Hence, for a large section of the society and skin types, the existing methods are no better than an educated guess. Mathematical models performing simulations of various effects of laser on the skin tissue while also considering different skin properties and melanin content can fill the gaps in the dermatological knowledge. In this paper, a numerical study is conducted to investigate the temperature profiles induced by various lasers commonly used in dermatological therapies within a multi-layered skin tissue model. The model, constructed using the Virtual Element Method with Voronoi meshing, incorporated three primary skin layers along with an underlying muscle layer. To account for the heterogeneous nature of the epidermis, sublayers including stratum corneum, epidermis, basal layer, and melanin were considered, with melanin modeled as dispersed particles within the epidermis. Additionally, a vascular layer was included in specific simulations to investigate the effects of vascular targeting. The simulations provide detailed temperature profiles generated by four different lasers, highlighting the impact of laser parameters and tissue properties on thermal response. The findings of this study contribute to a better understanding of laser-tissue interactions and can inform the development of more effective and targeted dermatological treatments.

Zusammenfassung

Stabkonstruktion, Balkentragwerke, Fachwerk, Biegebalken, Stabbiegebalken, Torsionswellen, Bauingenieurwesen, Maschinenbau Dieses Lehr- und Übungsbuch ermöglicht Ihnen, die Finite-Elemente-Methode (FEM) mit neuen Augen zu sehen und nicht nur in der Theorie nachzuvollziehen, sondern sie fundiert zu verstehen und selbst anzuwenden. Die Inhalte sind so aufgebaut, dass a priori die Theorie mit allen mathematischen Anforderungen und Beispielen dargelegt und a posteriori der gelernte Stoff anhand von Aufgaben tiefgehend geübt wird, sodass er sich nachhaltig festigen kann. Das Buch behandelt Stabtragwerke, Balkentragwerke, Stabbalkenkonstruktionen und Torsionswellen. Es berücksichtigt – im Unterschied zu anderen Lehrmitteln – als Belastung nicht nur Kräfte und Momente, sondern auch Linienlängskräfte, Linienquerkräfte und Temperaturen. Darüber hinaus wird die herausragende Bedeutung von Symmetrie und Antimetrie für die FEM hervorgehoben. Abgerundet wird der Inhalt durch die Darstellung der Vorgehensweise bei nicht konstanten Material- und Geometrieparametern, eingeprägten Verschiebungen, der Spannungsberechnung und der Berechnung von Lagerreaktionen. Die Abbildungen und Texte folgen einem didaktischen Farbcode. Kontrollfragen ermöglichen es, das Gelernte zu überprüfen. Das Buch richtet sich an Studierende der Ingenieurwissenschaften, insbesondere des Bauingenieurwesens, des Maschinenbaus, der Fahrzeugtechnik sowie der Luft- und Raumfahrttechnik. Es ist aber auch für Studierende der Mathematik und der Naturwissenschaften sowie für Berufsfachleute von großem Nutzen und hilft beim Verstehen der numerischen Werkzeuge.

Zusammenfassung

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. To address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Zusammenfassung

Stroke is one of the leading causes of adult disability affecting millions of people worldwide. Post-stroke cognitive and motor impairments diminish quality of life and functional independence. There is an increased risk of having a second stroke and developing secondary conditions with long-term social and economic impacts. With increasing number of stroke incidents, shortage of medical professionals and limited budgets, health services are struggling to provide a care that can break the vicious cycle of stroke. Effective post-stroke recovery hinges on holistic, integrative and personalized care starting from improved diagnosis and treatment in clinics to continuous rehabilitation and support in the community. To improve stroke care pathways, there have been growing efforts in discovering biomarkers that can provide valuable insights into the neural, physiological and biomechanical consequences of stroke and how patients respond to new interventions. In this review paper, we aim to summarize recent biomarker discovery research focusing on three modalities (brain imaging, blood sampling and gait assessments), look at some established and forthcoming biomarkers, and discuss their usefulness and complementarity within the context of comprehensive stroke care. We also emphasize the importance of biomarker guided personalized interventions to enhance stroke treatment and post-stroke recovery.

Zusammenfassung

Introduction Joint deformities, whether neurologic or idiopathic, can lead to muscle shortening and movement restrictions. While surgical interventions are often necessary for both patient groups, the approaches and outcomes can vary. Achilles tendon lengthening (ATL) is a common procedure for addressing foot deformities; however, the lack of a standardized method for objectively measuring the required tendon lengthening without significant muscle weakening impedes optimal surgical outcomes. Research Question Understanding how ATL affects the force production of targeted muscles across their lengths is essential. In this study, we developed an intraoperative method to assess the forces of calf muscles pre- and post-ATL 1, aiming to demonstrate surgery’s effect on ankle range of motion (ROM) and muscle forces, particularly between patients with neurological conditions and idiopathic foot deformities. Our goal is to present representative patient data for a passive state and propose a clinically applicable method.

Zusammenfassung

Laser therapies embody cutting-edge advances in non-invasive medical techniques. This study concentrates on enhancing precision thermal therapy via a modeling approach for the investigation of the intricate interplay between laser radiation and the complex layers of human skin. Our method involves a representation the skin as three layers—epidermis, dermis, and subcutaneous tissue—and strategically changing a range of wavelengths. We explore the subtle workings of absorption and extinction coefficients, with a specific focus on unraveling the scattering dynamics between these layers. The purpose of this research is to advance the development of thermal therapies, facilitating precise targeting of tissue depths. To simulate heat distribution in multilayered skin tissue, we use a stepwise Heaviside Function to outline thermal and optical properties. We also incorporate a three-phase lag model to capture the finite speed of heat conduction, delayed response, and heterogeneous characteristics of skin tissue. The solution to the governing equation, obtained via numerical simulation, indicates the possibility of selecting optimal laser wavelengths and characteristics. Based on the results, most types of lasers with different wavelengths are absorbed in the first layer and then in the second layer. There are a few lasers that can pass through the first and second layers of the skin and cause a significant temperature increase in the third layer because some of the components of the skin layers are common.This approach enables us to attain desired temperatures at precise depths within the tissue, advancing our comprehension of customized thermal interventions in medical procedures involving laser technology.

Zusammenfassung

Phase transition in porous materials is relevant within different engineering applications, such as freezing in saturated soil or pancake sea ice. Mathematical descriptions of such processes can be derived based on Biot's consolidation theory or the Theory of Porous Media. Depending on parameters such as density ratio, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the general, finite deformation case, suffers from instabilities and high computational costs. Simplifications, assuming small deformations, increases stability and computational efficiency. Within this work shortcomings of simplified theories based on Biot and linearisations of the Theory of Porous Media (TPM) are systematically studied. In order to determine the interaction of the different model parameters a non-dimensional model for poro-elasticity is presented. Based on a characteristic test-case including phase-transition and consolidation, the simplified models are compared to the fully non-linear TPM, focusing on mass errors as well as the time behaviour of the solution. Taking further into account the efficiency of discretisation based on different primal variables and finite-element-spaces, a guideline for selecting an appropriate combination of model, kinematic assumption and discretisation scheme is presented.

Zusammenfassung

This dataset contains the code and produced result files for the investigations presented in Suditsch et al. (DOI-LINK). In this work a biphasic model in the framework of the Theory of Porous Media (doi:10.1007/978-3-662-04999-0) is combined with a kinematic description according to Rodriguez et al. (doi:10.1016/0021-9290(94)90021-3). The script comparision_Growth_Formulations.py produces all used data and with create_plots.ipynb all plots can be created. In TPM_2Phase_MAo_LMo_MAs_Growth.py and Rodriguez1994.py calculation routines for the respective theories are written. For convenience, general functions are outsourced into the helper.py file. In README, a rough summary of the basic equations of the coupled kinematic-multiphasic growth model are shown. It is followed by an installation guide. Additionally to the github (https://github.com/masud-src/biphasic-kinematic-growth) repository, the generated result files can be found in the output folder.

Zusammenfassung

There is no general consensus on evaluating disease progression in facioscapulohumeral muscular dystrophy (FSHD). Recently, shear wave elastography (SWE) has been proposed as a noninvasive diagnostic tool to assess muscle stiffness in vivo. Therefore, this study aimed to characterize biceps brachii (BB) muscle mechanics in mild-FSHD patients using SWE. Eight patients with mild FSHD, the BB were assessed using SWE, surface electromyography (sEMG), elbow moment measurements during rest, maximum voluntary contraction (MVC), and isometric ramp contractions at 25%, 50%, and 75% MVC across five elbow positions (60°, 90°, 120°, 150°, and 180° flexion). The mean absolute percentage deviation (MAPD) was analyzed as a measure of force control during ramp contractions. The shear elastic modulus of the BB in FSHD patients increased from flexed to extended elbow positions (e.g., p < 0.001 at 25% MVC) and with increasing contraction intensity (e.g., p < 0.001 at 60°). MAPD was highly variable, indicating significant deviation from target values during ramp contractions. SWE in mild FSHD is influenced by contraction level and joint angle, similar to findings of previous studies in healthy subjects. Moreover, altered force control could relate to the subjective muscle weakness reported by patients with dystrophies.

Zusammenfassung

Metabolic zonation refers to the spatial separation of metabolic functions along the sinusoidal axes of the liver. This phenomenon forms the foundation for adjusting hepatic metabolism to physiological requirements in health and disease (e.g., metabolic dysfunction-associated steatotic liver disease/MASLD). Zonated metabolic functions are influenced by zonal morphological abnormalities in the liver, such as periportal fibrosis and pericentral steatosis. We aim to analyze the interplay between microperfusion, oxygen gradient, fat metabolism and resulting zonated fat accumulation in a liver lobule. Therefore we developed a continuum biomechanical, tri-phasic, bi-scale, and multicomponent in silico model, which allows to numerically simulate coupled perfusion-function-growth interactions two-dimensionally in liver lobules. The developed homogenized model has the following specifications: (i) thermodynamically consistent, (ii) tri-phase model (tissue, fat, blood), (iii) penta-substances (glycogen, glucose, lactate, FFA, and oxygen), and (iv) bi-scale approach (lobule, cell). Our presented in silico model accounts for the mutual coupling between spatial and time-dependent liver perfusion, metabolic pathways and fat accumulation. The model thus allows the prediction of fat development in the liver lobule, depending on perfusion, oxygen and plasma concentration of free fatty acids (FFA), oxidative processes, the synthesis and the secretion of triglycerides (TGs). The use of a bi-scale approach allows in addition to focus on scale bridging processes. Thus, we will investigate how changes at the cellular scale affect perfusion at the lobular scale and vice versa. This allows to predict the zonation of fat distribution (periportal or pericentral) depending on initial conditions, as well as external and internal boundary value conditions.

Zusammenfassung

The unique features conferred by negative Poisson's ratio have made auxetic materials the focus of considerable attention among mechanical metamaterials. This study experimentally investigates the mechanical properties of a 3D printed soft auxetic structure under tensile loading conditions, highlighting the strain and temperature distributions and the dynamic Poisson's ratio, focusing on the elongation domain with the maximum auxetic effect. The study uses a combination of experimental testing with a DIC system to measure the strain field and an IRT camera to record temperatures over time. The study results show that the mechanical properties of auxetic structures can be controlled by adjusting the design and material parameters. This research contributes to understanding the behaviour of flexible auxetic structures and can be used in several fields, such as aerospace, biomedical engineering, and energy storage.

Zusammenfassung

Abstract Auxetic materials are mostly known for their negative Poisson's ratio, a parameter used to describe the deformation behavior of structures. This ratio serves a similar role as a material constant, detailing behavior on a microscopic scale. However, the deformation behavior of complex auxetic structures cannot be described completely using the classical Poisson's ratio approach. While it may suffice to describe auxetic behavior in foams or crystals, it fails for larger scales like the auxetic lattice structures, discussed in this study. To address this limitation, an extension to the classical Poisson's ratio is proposed to better describe the behavior of such structures. The developed method shows the different dependencies, namely the directional dependency, the frequency dependency and the position dependency of auxetic unit cells.

Zusammenfassung

Vertebroplasty is a minimally invasive surgical procedure used to treat vertebral fractures, which conventionally involves injecting poly(methyl methacrylate) (PMMA) bone cement into the fractured vertebra. A common risk associated with vertebroplasty is cement leaking out of the vertebra during the injection, which may occur due to a lack of understanding of the complex flow behavior. Therefore, experiments to quantify the cement's flow properties are necessary for understanding and proper handling of the bone cement. In this study, we aimed to characterize the behavior of PMMA bone cement in its curing stages to obtain parameters that govern the flow behavior during injection. We used rotational and oscillatory rheometry for our measurements, as well as a custom-made injector setup that replicated a typical vertebroplasty setting. Our results showed that the complex viscoelastic behavior of bone cement is significantly affected by deformations and temperature. We found that the results from rotational tests, often used for characterizing the bone cement, are susceptible to measurement artifacts caused by wall slip and "ridge"-like formations in the test sample. We also found the Cox-Merz rule to be conditionally valid, which affects the use of oscillatory tests to obtain the shear-thinning characteristics of bone cement. Our findings identify important differences in the measured flow behavior of PMMA bone cement when assessed by different rheological methods, an understanding that is crucial for its risk-free usage in downstream medical applications.

Zusammenfassung

Vertebroplasty is a minimally invasive surgical procedure used to treat vertebral fractures, which conventionally involves injecting poly(methyl methacrylate) (PMMA) bone cement into the fractured vertebra. A common risk associated with vertebroplasty is cement leaking out of the vertebra during the injection, which may occur due to a lack of understanding of the complex flow behavior. Therefore, experiments to quantify the cement's flow properties are necessary for understanding and proper handling of the bone cement. In this study, we aimed to characterize the behavior of PMMA bone cement in its curing stages to obtain parameters that govern the flow behavior during injection. We used rotational and oscillatory rheometry for our measurements, as well as a custom-made injector setup that replicated a typical vertebroplasty setting. Our results showed that the complex viscoelastic behavior of bone cement is significantly affected by deformations and temperature. We found that the results from rotational tests, often used for characterizing the bone cement, are susceptible to measurement artifacts caused by wall slip and \textquotedblridge\textquotedbl-like formations in the test sample. We also found the Cox-Merz rule to be conditionally valid, which affects the use of oscillatory tests to obtain the shear-thinning characteristics of bone cement. Our findings identify important differences in the measured flow behavior of PMMA bone cement when assessed by different rheological methods, an understanding that is crucial for its risk-free usage in downstream medical applications.

Zusammenfassung

In this repository the data files of OncoFEM are collected. The data corresponds to OncoFEM version 1.0.The up-to-date Version of oncofem can be obtained from github or Version 1.0 from DaRUS, which comes in a pre-installed virtual box. For usage, download and unzip file next to the oncofem folder or adjust the paths stored in the config.ini file if the files need to be somewhere else.

Zusammenfassung

Physics-informed neural networks (PINNs) leverage data and knowledge about a problem. They provide a nonnumerical pathway to solving partial differential equations by expressing the field solution as an artificial neural network. This approach has been applied successfully to various types of differential equations. A major area of research on PINNs is the application to coupled partial differential equations in particular, and a general breakthrough is still lacking. In coupled equations, the optimization operates in a critical conflict between boundary conditions and the underlying equations, which often requires either many iterations or complex schemes to avoid trivial solutions and to achieve convergence. We provide empirical evidence for the mitigation of bad initial conditioning in PINNs for solving one-dimensional consolidation problems of porous media through the introduction of affine transformations after the classical output layer of artificial neural network architectures, effectively accelerating the training process. These affine physics-informed neural networks (AfPINNs) then produce nontrivial and accurate field solutions even in parameter spaces with diverging orders of magnitude. On average, AfPINNs show the ability to improve the L2 relative error by 64.84% after 25,000 epochs for a one-dimensional consolidation problem based on Biot’s theory, and an average improvement by 58.80% with a transfer approach to the theory of porous media.

Zusammenfassung

Glaucoma as an eye disease influences the optic nerve, resulting in progressive vision loss and, thus, blindness. For this disease, the most important risk factor is high intraocular pressure. Therefore, it is important to accurately measure the intraocular pressure. The present work aimes to present a mathematical description of a capacitive pressure sensor based on a Micro-Electro-Mechanical-Systems (MEMS) to measure intraocular pressure (IOP). The relatively high working bias voltage of MEMS capacitive pressure sensors restricts their potential applications as implantable sensors. Hence, Polydimethylsiloxane (PDMS) is employed as a porous elastomeric substance between the deformable and fixed electrodes of the capacitor. With a low young modulus and a higher dielectric constant, it reduces the sensor's working bias voltage. The PDMS's permittivity and young modulus are a function of the porosity volume fraction based on displacement in terms of a power law with fractional power constant. The dynamic equation of the microplate's transversal motion is used in the developed model, taking mid-plane stre-tching into account along with the generated force owing to the PDMS film squeezing. To decompose the governing nonlinear equation, a weak formulation is used with appropriate basis functions, thus integrating the attained ordinary differential equations over time. The sensor response to static pressure and step-wise alteration of the applied pressure is examined by dynamic and static analysis. The results of pull-in voltage reveal that using the PDMS as a dielectric causes a considerable reduction. Additionally, the effect of the PDMS elasticity on the capacitance and displacement was assessed along with the effects of the geometrical parameters on the sensor response.

Zusammenfassung

Physics-informed neural networks~(PINNs) leverage data and knowledge about a problem. They provide a nonnumerical pathway to solving partial differential equations by expressing the field solution as an artificial neural network. This approach has been applied successfully to various types of differential equations. A major area of research on PINNs is the application to coupled partial differential equations in particular, and a general breakthrough is still lacking. In coupled equations, the optimization operates in a critical conflict between boundary conditions and the underlying equations, which often requires either many iterations or complex schemes to avoid trivial solutions and to achieve convergence. We provide empirical evidence for the mitigation of bad initial conditioning in PINNs for solving one-dimensional consolidation problems of porous media through the introduction of affine transformations after the classical output layer of artificial neural network architectures, effectively accelerating the training process. These affine physics-informed neural networks~(AfPINNs) then produce nontrivial and accurate field solutions even in parameter spaces with diverging orders of magnitude. On average, AfPINNs show the ability to improve the Formula: see text relative error by Formula: see text after 25,000 epochs for a one-dimensional consolidation problem based on Biot's theory, and an average improvement by Formula: see text with a transfer approach to the theory of porous media.

Zusammenfassung

Goal: Skeletal muscle mechanics can be assessed in vivo using shear wave elastography. However, the impact of pennation angle on shear wave velocity (SWV) remains unclear. This study aims to quantify the effect by automatically aligning the ultrasound probe with muscle fiber orientation. Methods: We propose an automatic ultrasound probe alignment system and compare it to manual and no alignment. SWV of the gastrocnemius medialis muscle of ten volunteers was measured during rest and isometric contractions. Results: The SWV was different between the conditions (p = 0.008). The highest SWV was obtained during the automatic alignment and differences between the conditions were most pronounced during high-level contractions. The automatic system yielded more accurate alignment compared to a manual operator (p = 0.05). Conclusions: The present study indicates that pennation angle affects SWV, hence muscle fiber orientation must be considered to reliably interpret SWV. Using automatic alignment systems allows for more accurate alignment, improving the methodology of ultrasound elastography in skeletal muscles.