02 Fakultät Bau- und Umweltingenieurwissenschaften
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/3
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Item Open Access Multiphasic modelling and computation of metastatic lung-cancer cell proliferation and atrophy in brain tissue based on experimental data(2021) Ehlers, Wolfgang; Rehm, Markus; Schröder, Patrick; Stöhr, Daniela; Wagner, ArndtCancer is one of the most serious diseases for human beings, especially when metastases come into play. In the present article, the example of lung-cancer metastases in the brain is used to discuss the basic problem of cancer growth and atrophy as a result of both nutrients and medication. As the brain itself is a soft tissue that is saturated by blood and interstitial fluid, the biomechanical description of the problem is based on the Theory of Porous Media enhanced by the results of medication tests carried out in in-vitro experiments on cancer-cell cultures. Based on theoretical and experimental results, the consideration of proliferation, necrosis and apoptosis of metastatic cancer cells is included in the description by so-called mass-production terms added to the mass balances of the brain skeleton and the interstitial fluid. Furthermore, the mass interaction of nutrients and medical drugs between the solid and the interstitial fluid and its influence on proliferation, necrosis and apoptosis of cancer cells are considered. As a result, the overall model is appropriate for the description of brain tumour treatment combined with stress and deformation induced by cancer growth in the skull.Item Open Access Patient‐specific simulation of brain tumour growth and regression(2023) Suditsch, Marlon; Ricken, Tim; Wagner, ArndtThe medical relevance of brain tumours is characterised by its locally invasive and destructive growth. With a high mortality rate combined with a short remaining life expectancy, brain tumours are identified as highly malignant. A continuum‐mechanical model for the description of the governing processes of growth and regression is derived in the framework of the Theory of Porous Media (TPM). The model is based on medical multi‐modal magnetic resonance imaging (MRI) scans, which represent the gold standard in diagnosis. The multi‐phase model is described mathematically via strongly coupled partial differential equations. This set of governing equations is transformed into their weak formulation and is solved with the software package FEniCS. A proof‐of‐concept simulation based on one patient geometry and tumour pathology shows the relevant processes of tumour growth and the results are discussed.Item Open Access Analysing the bone cement flow in the injection apparatus during vertebroplasty(2023) Trivedi, Zubin; Gehweiler, Dominic; Wychowaniec, Jacek K.; Ricken, Tim; Gueorguiev-Rüegg, Boyko; Wagner, Arndt; Röhrle, OliverVertebroplasty, a medical procedure for treating vertebral fractures, requires medical practitioners to inject bone cement inside the vertebra using a cannula attached to a syringe. The required injection force must be small enough for the practitioner to apply it by hand while remaining stable for a controlled injection. Several factors could make the injection force unintuitive for the practitioners, one of them being the non‐Newtonian nature of the bone cement. The viscosity of the bone cement varies as it flows through the different parts of the injection apparatus and the porous cancellous interior of the vertebra. Therefore, it is important to study the flow of bone cement through these parts. This work is a preliminary study on the flow of bone cement through the injection apparatus. Firstly, we obtained the rheological parameters for the power law model of bone cement using experiments using standard clinical equipment. These parameters were then used to obtain the shear rate, viscosity, and velocity profiles of the bone cement flow through the cannula. Lastly, an analysis was carried out to understand the influence of various geometrical parameters of the injection apparatus, in which the radius of the cannula was found to be the most influential parameter.Item Open Access A thermodynamically consistent quasi-double-porosity thermo-hydro-mechanical model for cell dehydration of plant tissues at subzero temperatures(2021) Eurich, Lukas; Schott, Rena; Shahmoradi, Shahla; Wagner, Arndt; Borja, Ronaldo I.; Roth-Nebelsick, Anita; Ehlers, WolfgangMany plant tissues exhibit the property of frost resistance. This is mainly due to two factors: one is related to metabolic effects, while the other stems from structural properties of plants leading to dehydration of their cells. The present contribution aims at assessing the impact of ice formation on frost-resistant plant tissues with a focus on structural properties specifically applied to Equisetum hyemale. In this particular case, there is an extracellular ice formation in so-called vallecular canals and the pith cavity, which leads to a dehydration of the tissue cells to avoid intracellular ice formation, what would be fatal for the cells and subsequently for the whole plant. To address the underlying phenomena in the plant, a coupled thermo-hydro-mechanical model based on the Theory of Porous Media is introduced as the modelling framework. The dehydration of the tissue cells is referred to as of quasi-double-porosity nature, since the water is mobile within the intercellular space, but confined to the cells in the intracellular space and consequently kinematically coupled to them. However, the mass exchange of water across the cell wall is considered. The presented numerical example shows the strong coupling of the underlying processes as well as the quasi-double-porosity feature. Finally, it supports the experimental finding of the vallecular canals as the main location of ice formation.Item Open Access Extended modelling of the multiphasic human brain tissue with application to drug-infusion processes(2014) Wagner, Arndt; Ehlers, Wolfgang (Prof. Dr.-Ing.)The brain is the most significant and complex organ of human beings and plays a key role as the control centre of the nervous system. At first glance, the brain seems to be adequately protected against external influences by the rigid skull. However, severe situations may arise if the functionality of the system is compromised within the intracranial cavity itself. For example, a life-threatening situation is caused by solid neoplasm, commonly known as brain tumours. It is obvious that an adequate theoretical modelling of the brain allows a simulation of the occurring biomechanical effects under certain circumstances. This contributes to a profound understanding of the complex processes within the tissue aggregate. Moreover, it provides the possibility to numerically study new medical treatment options and their clinical results in order to support and assist the practising surgeons. However, the biomechanical modelling of the brain is a challenging task. Certainly, this is caused by the patient-specific structural complexity of the three-dimensional anatomical shape of the brain. Moreover, the brain-tissue aggregate is a complex subject of multicomponent nature with electro-chemical properties. In this respect, the tissue characteristics of the brain-matter constituents show significant anisotropic and heterogeneous properties, which require an extended description within the framework of porous materials. In this monograph, the relevant anatomical and physiological aspects of the human brain are briefly summarised. Therein, the main focus is placed on the composition of the brain’s tissue-aggregate and the specific characteristics of its components, as far as needed for the modelling approach. The research rationale is considered by means of tumour diseases and their current treatment options. Related medical-imaging methods are introduced, which enable an insight into living tissues and, therefore, provide the possibility for a patient-specific determination of material parameters. Afterwards, the continuum-mechanical fundamentals, required for the description of the brain matter, are given. Therefore, the basic concept of the Theory of Porous Media (TPM) is applied to the multicomponent tissue-aggregate. In particular, a four-constituent model is investigated, which consists of three immiscible phases and one miscible component. The immiscible phases of the tissue-aggregate are represented by the solid skeleton (i. e. tissue cells and vascular walls), the blood and the overall interstitial fluid. Moreover, the interstitial fluid is constituted by a liquid solvent and a dissolved therapeutic solute (as a result of a medical administration). For this purpose, elements of the Theory of Mixtures are embedded in the standard TPM in order to enable the description of miscible components. Furthermore, the kinematical relations of superimposed constituents are provided, and the balance equations for the overall aggregate as well as for its particular constituents are presented. Based on that, the specific adaptation of the material-independent balance equations by an appropriate constitutive setting is discussed. Therefore, constitutive relations are derived, which describe the characteristic material behaviour of the brain’s tissue. In this regard, the constitutive assumptions for the constituents involved, is examined by means of a thermodynamically consistent framework in terms of an evaluation process of the entropy inequality. On this theoretical basis, the numerical realisation of the developed model is investigated. Therefore, the finite-element method is chosen as a suitable numerical methodology to approximate the solution of the arising set of coupled partial differential equations. For this purpose, the weak formulations of the governing balance relations are discretised in space and time. This numerical part is concluded by the description of the applied monolithic solution strategy. Finally, the application of the derived theoretical and numerical investigations to the human brain is carried out. Therein, capabilities for a patient-specific estimation of required simulation parameters, such as local anisotropic permeabilities and diffusivities, are studied in detail. Next, the possibilities for a customised creation of geometries for the simulation of realistic initial-boundary-value problems are discussed. This finally allows the study of selected numerical examples, demonstrating the feasibility of the presented modelling approach. These examples start with the basic material behaviour of brain tissue and then face the invasive delivery process of therapeutics. In this regard, the therapeutical distribution is shown for realistic geometries of the human brain and, afterwards, a survey on the influence (by a local numerical sensitivity analysis) of several involved simulation parameters is examined.Item Open Access Hydraulically induced fracturing in heterogeneous porous media using a TPM‐phase‐field model and geostatistics(2023) Wagner, Arndt; Sonntag, Alixa; Reuschen, Sebastian; Nowak, Wolfgang; Ehlers, WolfgangHydraulically induced fracturing is widely used in practice for several exploitation techniques. The chosen macroscopic model combines a phase‐field approach to fractures with the Theory of Porous Media (TPM) to describe dynamic hydraulic fracturing processes in fully‐saturated porous materials. In this regard, the solid's state of damage shows a diffuse transition zone between the broken and unbroken domain. Rocks or soils in grown nature are generally inhomogeneous with material imperfections on the microscale, such that modelling homogeneous porous material may oversimplify the behaviour of the solid and fluid phases in the fracturing process. Therefore, material imperfections and inhomogeneities in the porous structure are considered through the definition of location‐dependent material parameters. In this contribution, a deterministic approach to account for predefined imperfection areas as well as statistical fields of geomechanical properties is proposed. Representative numerical simulations show the impact of solid skeleton heterogeneities in porous media on the fracturing characteristics, e. g. the crack path.Item Open Access Continuum mechanics of multicomponent materials : modelling, numerics and applications for biological materials in the framework of the theory of porous media(Stuttgart : Institut für Mechanik (Bauwesen), Lehrstuhl für Kontinuumsmechanik, Universität Stuttgart, 2021) Wagner, Arndt; Ehlers, Wolfgang (Prof. Dr.-Ing. Dr. h. c.)Item Open Access A continuum mechanical porous media model for vertebroplasty : numerical simulations and experimental validation(2023) Trivedi, Zubin; Gehweiler, Dominic; Wychowaniec, Jacek K.; Ricken, Tim; Gueorguiev, Boyko; Wagner, Arndt; Röhrle, OliverThe outcome of vertebroplasty is hard to predict due to its dependence on complex factors like bone cement and marrow rheologies. Cement leakage could occur if the procedure is done incorrectly, potentially causing adverse complications. A reliable simulation could predict the patient-specific outcome preoperatively and avoid the risk of cement leakage. Therefore, the aim of this work was to introduce a computationally feasible and experimentally validated model for simulating vertebroplasty. The developed model is a multiphase continuum-mechanical macro-scale model based on the Theory of Porous Media. The related governing equations were discretized using a combined finite element-finite volume approach by the so-called Box discretization. Three different rheological upscaling methods were used to compare and determine the most suitable approach for this application. For validation, a benchmark experiment was set up and simulated using the model. The influence of bone marrow and parameters like permeability, porosity, etc., was investigated to study the effect of varying conditions on vertebroplasty. The presented model could realistically simulate the injection of bone cement in porous materials when used with the correct rheological upscaling models, of which the semi-analytical averaging of the viscosity gave the best results. The marrow viscosity is identified as the crucial reference to categorize bone cements as ‘high- ’or ‘low-’ viscosity in the context of vertebroplasty. It is confirmed that a cement with higher viscosity than the marrow ensures stable development of the injection and a proper cement interdigitation inside the vertebra.Item Open Access Modelling and simulation of natural hydraulic fracturing applied to experiments on natural sandstone cores(2024) Wang, Junxiang; Sonntag, Alixa; Lee, Dongwon; Xotta, Giovanna; Salomoni, Valentina A.; Steeb, Holger; Wagner, Arndt; Ehlers, WolfgangUnder in-situ conditions, natural hydraulic fractures (NHF) can occur in permeable rock structures as a result of a rapid decrease of pore water accompanied by a local pressure regression. Obviously, these phenomena are of great interest for the geo-engineering community, as for instance in the framework of mining technologies. Compared to induced hydraulic fractures, NHF do not evolve under an increasing pore pressure resulting from pressing a fracking fluid in the underground but occur and evolve under local pore-pressure reductions resulting in tensile stresses in the rock material. The present contribution concerns the question under what quantitative circumstances NHF emerge and evolve. By this means, the novelty of this article results from the combination of numerical investigations based on the Theory of Porous Media with a tailored experimental protocol applied to saturated porous sandstone cylinders. The numerical investigations include both pre-existing and evolving fractures described by use of an embedded phase-field fracture model. Based on this procedure, representative mechanical and hydraulic loading scenarios are simulated that are in line with experimental investigations on low-permeable sandstone cylinders accomplished in the Porous Media Lab of the University of Stuttgart. The values of two parameters, the hydraulic conductivity of the sandstone and the critical energy release rate of the fracture model, have turned out essential for the occurrence of tensile fractures in the sandstone cores, where the latter is quantitatively estimated by a comparison of experimental and numerical results. This parameter can be taken as reference for further studies of in-situ NHF phenomena and experimental results.