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Continuum-mechanical modelling and numerical simulation of multi-component biological tissues

The enormous complexity of the microscopical composition of biological tissues encourages the application of the Theory of Porous Media (TPM), which represents a well-suited way to model the tissue aggregate in a compact and elegant manner. Using the TPM, a volumetrical homogenisation procedure (smearing) of the underlying microscopical structure over a representative elementary volume (REV) leads to an idealised macroscopical model of superimposed and mutually interacting constituents. More precisely, the modelling approach contains immiscible and miscible constituents, which are treated in the framework of the so-called extended TPM.

In this presentation, the focus is laid on modelling the multiphasic human brain tissue in order to study clinical interventions, such as the extra-vascular infusion of therapeutics within tumor treatments (commonly known as convection-enhanced drug delivery). However, this model can also be applied to various other (vascularised or non-vascularised) biological tissues, such as, e. g., porous (osteoporotic) vertebral bones in order to simulate bone-cement spreading during vertebroplasty. For the numerical solution of the arising coupled partial differential equations, the system is discretised in space by the Finite-Element (FE) Method (using Taylor-Hood elements) and in time by an implicit (Euler) time-integration scheme. Finally, the system is solved monolithically by use of the in-house FE tool PANDAS. Numerical examples demonstrate the applicability of the presented model.

In conclusion, the present contribution aims to predict the expected impacts of a scheduled clinical procedure via numerical simulations based on a suitable and reliable constitutive model for porous biological materials. Furthermore, the possibility to include patient-specific material parameters, which are estimated from medical imaging, is given.

Author(s):

Arndt Wagner    
University of Stuttgart, Institute of Applied Mechanics (CE)
Germany

Wolfgang Ehlers    
University of Stuttgart, Institute of Applied Mechanics (CE)
Germany