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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 Permeability estimation of regular porous structures : a benchmark for comparison of methods(2021) Wagner, Arndt; Eggenweiler, Elissa; Weinhardt, Felix; Trivedi, Zubin; Krach, David; Lohrmann, Christoph; Jain, Kartik; Karadimitriou, Nikolaos; Bringedal, Carina; Voland, Paul; Holm, Christian; Class, Holger; Steeb, Holger; Rybak, IrynaThe intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny-Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.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 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 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.)