02 Fakultät Bau- und Umweltingenieurwissenschaften
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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.