02 Fakultät Bau- und Umweltingenieurwissenschaften
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/3
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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 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.