Open position for a PhD canditate in the following area:
Thrombus mechanics and growth
In stage 5 of the aortic dissection (AD), a thrombosis may develop in the false lumen. This process changes the mechanical behavior of the whole system and needs to be considered. Mostly, the thrombus is classified in the literature as a porous material, i.e. as consisting of two phases. Either simple Biot type models, as found in soil mechanics for consolidation processes, or more sophisticated and more easily extendable two-phase models based on the Theory of Porous Media (TPM) for soft tissues are used.
The latter approach is adopted to model the thrombus in the false lumen of AD. The TPM is especially suited because in this theory a nonlinear geometric and material model is already available for soil mechanics and can be adjusted to model the behavior of the thrombus. The consistent continuum mechanical description allows to take only the necessary nonlinearities into account. An extension to a dynamic model is straightforward. The numerical realization is carried out by the FEM to study the behavior of the model also in complex geometries. The new and challenging part is the model for the thrombus growth.
The above shows the basic approach to model a thrombosis with several aspects bridging as well several scales. As mentioned above, the TPM is used to establish essentially a two-phase model. This model is inherently a macroscopic model based on continuum mechanics. All effects on the different scales can be incorporated into such a model by special techniques like homogenization. This is the final goal. However to- start, the TPM-based model will use only the macroscopic level, and the growth of the thrombosis is modeled by a mass production term in the continuity equations. In principle, the model established to describe the growth of a tumor is used as a starting point. The first step is to establish a sound two-phase model of the thrombus, and, as a next step, growth can be modeled. The effects studied on the micro level, i.e. the transport processes of sub-projects V and VI, is then used in the first step to calibrate a phenomenological macroscopic model. This macroscopic approach will allow to compute 3D models of a false lumen. A direct coupling of the detailed model is then performed in a second step.
As an example, Fig. 9 in this paper (please click the [pdf]) shows a computational analysis of the time evolution of thrombus growth in comparsion with clinical CT scans.
Familiarization with two-phase continua
Literature review on growth modeling of phenomena similar to thrombus growth
Formulation of a first simple model within the TPM
Realization of this model in a FE formulation
Refinement of the model in cooperation with the other subprojects, especially with subprojects V and VI
Qualifications of the candidate:
MSc/Diplom in computational mechanics, civil- or mechanical engineering, or similar