The Lead project finances 10 positions for PhD Canditates with focus on the following areas:

In this sub-project we focus on material and computational modeling of the descending thoracic aorta, which can be viewed as a three-layered fibrous composite assembled by a matrix material and embedded families of dispersed collagen fibers. In particular, in the modeling effort, we consider the **micro-structure** of the aortic tissue obtained from second-harmonic imaging microscopy, and the nonlinear and anisotropic **material properties**, including **damage/failure properties**, which we receive from mechanical tests. We know that in patients who suffer from an aortic dissection the middle layer of the aorta is somehow degenerated. In particular, that layer shows a large number of gaps filled with fluid, and it is expected that the micro-structure is also changed. We will explore the influence of the micro-structure/material properties of the aortic tissues on the stress distribution of the wall under certain loading and boundary conditions. We want to find better answers to questions such as "what actually triggers an aortic dissection (AD)?", "how to predict the propagation of AD?"

The possible candidate has a strong background in **nonlinear continuum mechanics**, in the **nonlinear finite element method**, and in **modeling techniques** of **anisotropic materials** undergoing **large strains**. The candidate should be able to **implement material models** in codes such as Abaqus or FEAP, and should be familiar with** experimental verification** and **case study investigation**. The candidate should have a master's degree in computational mechanics (of materials), civil, mechanical or biomedical engineering, or applied mechanics. The candidate should also be enthusiastic to work in medical-related research, and in a multidisciplinary team with strong international cooperation. The goal for the candidate is to **write a Doctoral Thesis**.

**Contact:** Gerhard A. Holzapfel

holzapfelnoSpam@tugraz.at

www.biomech.tugraz.at

The aortic dissection is inherently associated with the rupture and delamination of aortic tissues. For the mechanical modeling, this is related to crack initiation, failure, and crack propagation. The pressure exerted by the blood flow onto the dissected aortic wall is of critical importance leading to a coupled fluid-structure interaction problem with crack propagation. The numerical modeling of the nonlinear, coupled problem is based on advanced and innovative finite element methods (FEM): space-time FEM is used to capture the time-dependent fluid and structure domains, the crack is considered based on the eXtended FEM (XFEM).

The candidate responsible for this project must have a strong background in the FEM. Advanced knowledge in the field of fluids and/or structure mechanics are required. Basic knowledge in fracture mechanics is useful.

**Contact: **Thomas-Peter Fries

friesnoSpam@tugraz.at

www.ifb.tugraz.at

Dynamical systems generally change their behavior when parameters of the system are changed. Sensitivity analysis aims at quantifying the effect of the different parameters. This may then be used in subsequent steps of the analysis to reduce the numerical effort: Focusing on the most relevant parameters and neglecting all effects which do not affect the behavior significantly makes predictions significantly faster. On the other hand, this concept has critical limits: Especially when nonlinearities are significant, parameters may change the dynamical behavior completely near bifurcation points, whereas in other parameter ranges they have little effect on the dynamical response.

The description of dynamical systems is commonly based on the assumption that parameters are known or can be measured, but this poses problems, when the response is very sensitive to parameter changes: Considering the description of aortic dissection, parameter values may to some extend be derived from experiments with tissue samples, but this leaves the question as of how much tissue in laboratories resembles the living tissue in a human being. Tests with a living person bear a risk of harming this person. This causes a level of uncertainty for the parameters of the numerical model.

In this project, statistical analysis is used in order to identify how sensitive the behavior depends on the different parameters. Special focus needs to be placed on non-continuous changes caused by bifurcations. These are to be identified by different test functions, which are then included in the analysis.

**Contact:** Katrin Ellermann

ellermannnoSpam@tugraz.at

www.tugraz.at/institute/ifm

It has been observed that the electric conductivity of blood is strongly influenced by the blood flow. This opens the possibility of using tomography techniques based on the distribution of the electric conductivity to detect changes in the blood flow, and hence indicating failure.

Electrical Impedance Tomography is the non-invasive imaging method of choice for the proposed application. Because of the complicated geometry and intricate material properties the electromagnetic field analysis will be carried out numerically by using the finite element method.

To identify the conductivity distribution inside the body, and hence to verify the rupture process, the inverse problem has to be solved. This means that the results of the finite element simulation (a forward problem) must end up meeting the observations (measurements) on the body surface. Different measurement configurations (e.g., different electrode positions or applying multiple frequencies) will be simulated to investigate possible measurement set ups.

A successful candidate should have a qualified Masters in electrical engineering or in related fields such as biomedical engineering and physics. Prior experiences in the field of electromagnetic simulations and high performance computing are beneficial, but not required.

**Contact:** Oszkár Bíró

bironoSpam@tugraz.at

www.igte.tugraz.at

The loads propagating damage and cracks of the aortic wall are due to the pulsating blood flow through the vessel. The simulation of the blood flow through vessels in organisms must account for three aspects: (i) the flow is unsteady due to the action of the heart; (ii) the flow domain varies due to the dynamic interaction between the flowing medium and the artery walls; (iii) the flowing medium is non-Newtonian and heterogeneous.

For the quantitative description of blood flow dynamics, the rheological material law of the flowing medium is essential. In the existing literature, blood is mostly characterized as a shear-thinning non-Newtonian liquid. The fluid may change its viscous properties due to chemical or other processes such as the aggregation or disaggregation of cellular contents of the liquid. Blood furthermore exhibits elastic behavior with effects on flows through small pores of a porous medium. Flows of viscoelastic media through porous media exhibit a strong increase of the effective total fluid viscosity as a critical value of about 0.5 of the Deborah number is exceeded. This effect, analog to the viscoelastic behavior of polymer solutions, is expected to be found with blood as well. Adequate rheological characterization of blood for the present purposes, therefore, must include the elastic behavior further to the influence of shear thinning. As a constitutive rheological equation, a generalized Oldroyd-B model is a good candidate, since it represents both the shear-thinning and the elastic behavior of the liquid. A first part of the project task will be to find the values of parameters in that model representing properly the material behavior upon unsteady deformation.

A second part will be to simulate a simple generic type of flow of the modelled fluid where the solution may possibly be found analytically. In a case simplified with respect to geometry and rheological material law of the fluid, the unsteady part of the axial velocity is determined by Bessel functions of the radial coordinate and an exponential function of time, where the shape of the velocity profile is determined by the Womersley number (ωR^{2}/ν)^{1/2} (pulsation frequency ω, vessel radius R, liquid kinematic viscosity ν). The results will allow the constitutive rheological equation found to be validated for the flow studied. Finally, the flow through porous media of the shear-thinning viscoelastic fluid characterized above will be investigated and simulated, again using a generic geometry, and also for validating the performance of the material model developed for both weak and strong flow.

**Contact: **Günter Brenn

brennnoSpam@fluidmech.tu-graz.ac.at

www.isw.tugraz.at

The disturbed blood flow in the so-called false lumen resulting from aortic dissection often leads to thrombus formation and growth. The thrombus and its development may strongly affect the course of disease. Thrombus development is a multiscale problem involving a complex interplay between biological, chemical and mechanical determinants. Mathematical modeling of thrombus growth is performed on various scales and with particle based and continuum methods or combinations of thereof. In the current project we aim at adopting and improving existing continuum models of thrombus deposition and growth. These models sometimes use up to ten chemical and biological species in coupled convection diffusion systems, which makes them computationally too costly for efficient simulations on realistic domains. The available models of thrombus deposition and growth also usually employ strongly simplified couplings to the changing flow field which is affected by the growing tumor. Moreover, as the thrombus is a porous medium with internal fluid flow we not only expect the thrombus to grow, but also to change its mechanical properties over time due to continuing platelet deposition in the interior. The latter relies on the description of the rate of bulk transport as a combination of convective and diffusive fluxes within the thrombus.

In the current project efficient numerical models for thrombus growth and property development shall be developed and numerically implemented in order to predict thrombus formation and growth in possibly patient-specific geometries of a dissected aorta. The pursuit of this challenging research task requires a solid background in either continuum mechanics or fluid dynamics, and in numerical methods for solving partial differential equations of continuum physics. The multidisciplinary context of the Lead project moreover presumes the ability to collaborate with researchers from various backgrounds.

**Contact:** Thomas Hochrainer

hochrainernoSpam@tugraz.at

www.ifl.tugraz.at

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.

Work program:

- 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
- Sound knowledge in continuum mechanics
- Good programming skills in C++
- High motivation to cope with a challenging topic

**Contact: **Martin Schanz

m.schanznoSpam@tugraz.at

www.mech.tugraz.at

Within this sub-project we aim to formulate, analyze, and implement new space-time finite element methods for a stable, adaptive, accurate, reliable, and efficient numerical simulation of the blood flow in arteries. The discretization is done in the space-time domain which allows for adaptive refinement strategies simultaneously in space and time, and for parallel solution strategies for the overall system of nonlinear algebraic equations. The focus of this PhD topic is in the numerical analysis of new space-time finite element methods, on aspects of scientific computing for an efficient implementation, and applications in biomechanics.

**Contact:** Olaf Steinbach

o.steinbachnoSpam@tugraz.at

www.numerik.math.tugraz.at

**Bayesian analysis: model selection, parameters estimation, and validation of computational results**

Computer simulations of the complex mutual interplay of arterial tissues with hemodynamic, as outlined in the parts of the other projects, depends on model assumptions and parameters. Most of the model parameters parameters are inferred from selected experiments, which in some cases even involve the solution of (ill-posed) inversion problems. Needless to say that the parameter assignment is based on assumptions and it suffers from uncertainties due to experimental noise and variations in the samples. Eventually the outcome of the simulations has to be compared with experiments, which in many cases again is hampered by an (ill-posed) inversion problem, in particular when imaging techniques such as MRI, CT, TEE, and EIT are applied. Parameter assignment, model assessment, validation of numerical results in the light of experimental data and the solution of (ill-posed) inversion problems require sophisticated probabilistic techniques. The only consistent frame for these tasks is provided by Bayesian probability theory. Moreover, the combination of computer simulations and Bayesian experimental design allows the optimization of the experimental setup in order optimize the diagnostic predictive power. The present subproject is an interdisciplinary issue that will be carried out in close collaboration with the other subprojects that require probabilistic analyses. The added value will be an optimal choice of parameters, confidence intervals for the results, quantification of the uncertainties in the model and parameter selection and consistent inclusion of available prior knowledge.

Requirements for the PhD student: Profound knowledge on Bayesian probability theory. Moreover, it is expected that he/she will closely cooperate with the other PhD students and is prepared to gain a thorough understanding of the underlying mechanical models, the numerical techniques, and the experimental methods, used to infer parameters and patient specific data.

**Contact: **Wolfgang von der Linden

vonderlindennoSpam@tugraz.at

http://itp.tugraz.at/

The Institute for Computer Graphics and Vision at Graz University of Technology, Austria, announces one new PhD student position in the research field of medical visualization, which is granted for three years. The designated start-date for the associated TU Graz Lead project will be January 1, 2018.

The focus of the project is on the virtual reality visualization of the results from simulations of aortic dissections. The primary task will be to conduct world-class research in visualization technology for combined medical scanner and simulation data in virtual reality.

The applicants must have a relevant background, which also must be sufficiently documented in the application, and their research interest should fit within existing activities in visualization. With this opening, we are primarily searching for a candidate in real-time medical visualization. If applicants can report experiences with related research, they should verbosely document this. Candidates are also encouraged to provide a short description of their research vision as well as letters of recommendation from their previous employers or university teachers. The project will also require excellent programming skills in C++; knowledge of VTK and ITK libraries is also preferred. Furthermore, very good spoken and written English is essential for the position.

We offer a full-time work contract, including specified time to finish a PhD Thesis, and good salary (gross salary: € 2.731,- per month, 14 times per year). The research will be carried out under Prof. Dieter Schmalstieg, who is full professor and head of the Institute for Computer Graphics and Vision at Graz University of Technology, Austria. His current research interests are augmented reality, virtual reality, real-time graphics, medical visualization and 3D user interfaces. The Institute for Computer Graphics and Vision at Graz University of Technology is the only Austrian academic group with the charter to address both Computer Vision and Computer Graphics, and is carefully nurturing a culture of Digital Visual Information Processing to resolve the artificial boundaries between computer graphics and computer vision. The research at ICG is focused on Computer Graphics, Visualization, Medical Computer Vision, Object Recognition, Object Reconstruction, Robotics, Virtual Reality and Augmented Reality.

**Contact: **Dieter Schmalstieg

schmalstiegnoSpam@icg.tu-graz.ac.at

www.icg.tu-graz.ac.at

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Openings - pdf

Application Details

**Employement:** full time**Starting date:** January 1, 2018 at the earliest**Location:** Graz University of Technology**Application to:** gccenoSpam@tugraz.at**Initial Screening:** December 1, 2017

Contact

**Gerhard A. Holzapfel**

Graz University of Technology

Institute of Biomechanics

8010 Graz, Austria

Phone: ++43 316 873 35500

holzapfelnoSpam@tugraz.at

www.biomech.tugraz.at