Projects in the research field of "Computational Biomechanics"

Growth and Remodeling in Arterial Walls

growth and remodeling
Lupe
growth and remodeling
growth and remodeling
© Anna Zahn

Abstract:

As living biological materials, arterial tissues have the ability to improve their load-bearing behavior by adapting to changes in their mechanobiological environment conditions.
It is for example known that arteries try to compensate for an enduring elevation of the blood pressure by increasing the thickness of their walls.
Besides such an increase of the overall tissue volume, referred to as "growth", a reorganization of the existing tissue components, a so-called "remodeling" process, might occur as a reaction to changes of the loading situation.
Arterial tissues are multi-layered, heterogeneous composites which can be idealized as matrix materials with embedded fibers of varying orientation.
Based on this idealization, a reorientation of the fibers following the local demands can be considered in the context of arterial remodeling.
As a consequence of arterial adaptation processes, which tend to reduce strain or stress peaks and/or gradients in the loaded state, residual stresses arise.
For the numerical simulation of arteries, it is necessary to include these commonly unknown, self-balancing stresses, which are present in the unloaded state, since they affect the behavior under external loading.
Modeling arterial adaptation processes allows for an estimation of growth-induced residual stresses.
Moreover, it provides an option to obtain a mechanically motivated estimate for the real distribution of the fiber angles, which is another unknown input quantity in numerical simulations.

References:
Zahn, A. & Balzani, D. (2018), "Study of model variants in a combined framework for multiplicative growth and remodeling in arterial walls", Proceedings in Applied Mathematics and Mechanics., December, 2018. Vol. 18, pp. e201800080.

Zahn, A. & Balzani, D. (2018), "A combined growth and remodeling framework for the approximation of residual stresses in arterial walls", Zeitschrift für Angewandte Mathematik und Mechanik., December, 2018. Vol. 98, pp. 2072-2100.

Balzani, D. & Zahn, A. (2017), "Residual stresses resulting from growth and remodeling in arterial walls", Proceedings of the VII International Conference on Coupled Problems in Science and Engineering., May, 2017. , pp. 167-178.

Zahn, A. & Balzani, D. (2017), "Modeling of anisotropic growth and residual stresses in arterial walls", Acta Polytechnica CTU Proceedings. Vol. 7, pp. 85-90.

Zahn, A. & Balzani, D. (2016), "Modeling residual stresses in arterial walls based on anisotropic growth", Proceedings in Applied Mathematics and Mechanics., October, 2016. Vol. 16, pp. 115-116.

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Domain-Decomposition-Based Fluid Structure Interaction Algorithms for Highly Nonlinear and Anisotropic Elastic Arterial Wall Models in 3D

DFG (Deutsche Forschungsgemeinschaft) project BA 2823/9-1, in cooperation with SNF (Swiss National Science Foundation) under the D-A-CH agreement

Artery 3d
Lupe
Results of parallel simulations of atherosclerotic arterial walls
Results of parallel simulations of atherosclerotic arterial walls
© Daniel Balzani

Cooperation with:

A. Klawonn (Universität zu Köln),
A. Quarteroni und S. Deparis (École polytechnique fédérale de Lausanne)
O. Rheinbach (Technische Universität Bergakademie Freiberg),
J. Schröder (Universität Duisburg-Essen)

Abstract:
Transmural stress distributions of in vivo arteries are a major factor driving, e.g., the processes of arteriosclerosis and arteriogenesis. Realistic predictions for transmural stress distributions require a dynamic simulation considering the interaction of the blood flow with the vessel wall. One cannot expect to obtain precise predictions for vessel wall stresses using solid models that do not reflect the global layer structure and the anisotropic fibrous microstructure of the vessel wall. Furthermore, eigenstress distributions in the vessel wall must be taken into account for the analysis of more realistic stress regimes and can be observed to have significant influence on simulations. The fluid structure interaction (FSI) problem is known to be a nontrivial problem especially when nonlinear models are used for the structural part describing the deformation of the arterial wall. In this project, algorithms for the fluid structure interaction are developed based on domain decomposition methods and applied to the computation of realistic transmural stresses in physiological models of arterial walls. The associated systems of coupled nonlinear partial differential equations are to be solved in 3D and on different parallel machines. Moreover, a biologically motivated model for the incorporation of residual stresses is constructed based on nonlocal stress measures.

References:

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Biomechanics of Arterial Walls under Supraphysiological Loading Conditions

DFG (Deutsche Forschungsgemeinschaft) project BA 2823/5-1, in cooperation with FWF (Austrian Science Fund) under the D-A-CH agreement

Artery Quer
Lupe
Damage behavior in arterial walls
Damage behavior in arterial walls
© Daniel Balzani

Cooperation with:

G. A. Holzapfel (Technische Universität Graz, Österreich)

Abstract:
This research project deals with the analysis and the modeling of traumatic degenerations of overstretched arterial walls that occur in therapeutical interventions. The data base for the qualitative and quantitative description of arterial tissues is obtained from biaxial extension tests performed on the tissue components of individual arterial layers loaded far beyond the physiological domain. Such tests enable the analysis of the macroscopic mechanical response of the tissues. In addition, structural analysis techniques such as Fourier transfer infrared spectroscopy and scanning electron microscopy are used to study damage on the smaller length scale. The macroscopic response of the fiber-reinforced tissues is described by a formulation based on micro-mechanical models characterizing the individual tissue components. These models take into account alterations of stochastic distributions of fiber properties as a consequence of the tissue overstretch. In order to obtain a quantitative prediction of the material response the model parameters are adjusted to the performed experiments based on least-square minimization. Finally, the models are validated by comparing finite element calculations with experiments performed on whole arterial wall segments.

References:

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Method for the Diagnosis of Diseased Heart Tissue based on Improved Inverse Problems

Heart
Lupe
Simulation of a simplified heart
Simulation of a simplified heart
© Daniel Balzani

Cooperation with:
L. Perotti (University of California Los Angeles, USA)
B. Klug (University of California Los Angeles, USA)

Abstract:
In order to improve diagnosis techniques to detect diseased tissues, particularly in important organs such as the heart, typically imaging-based methods are often applied. These enable a variety of information including geometry, deformation, distribution of electro-magnetic fields, etc. Based thereon, in this project a highly efficient method is developed to identify distributions of material properties within the heart as a solution of an improved reformulated inverse problem. An important focus is the guaranteed uniqueness of solutions to enable a reliable quantitative analysis.

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Determination of biomechanical parameters of the human eye

Auge
Lupe
FE-Modell des menschlichen Auges
FE-Modell des menschlichen Auges
© Stefan Münch

Cooperations with:
Dr.-Ing. Mike Röllig (Fraunhofer-Institut für Keramische Technologien und Systeme IKTS),
Prof. Dr. rer. nat. habil. E. Spörl (Augenklinik, Universitätsklinikum Carl Gustav Carus an der Technischen Universität Dresden)

Abstract:
In this research project, methods for the identification of biomechanical parameters of the human eye are to be derived based on numerical calculations. These parameters are of paramount importance in ophthalmology where they reflect pathological processes due to biochemical changes in the tissue structure.
By developing a reliable method for estimating the unknown biomechanical parameters, it is possible to diagnose various eye diseases at an early stage. This is substantial to avoid eye surgery in many cases, as most today's non-surgical treatment procedures only interrupt the progression of the disease and maintain its actual state. Furthermore, because the biomechanics of the eye tissue influences its imaging properties and thus its visual acuity, targeted changes in the biomechanics are usually conducted using techniques such as LASIK to adjust the imaging properties and, consequently, correct the refraction error. Nevertheless, through a successful identification of the patient-specific biomehcanical properties of the eye, more efficient and reliable adjustment and correction procedures can be achieved. Moreover, by a regular estimation of the biomechanical parameters the healing process can be followed and monitored.
This work focuses on the numerical simulation of the system response of the human eye during appropriate medical testing methods. In the first step, different influential biomechanical factors are identified and evaluated through significance analyses. Subsequently, by using these factors, a mathematical model describing the eye behavior is derived. This model will be used in the future in the identification process of the biomechanical properties using inverse analysis methods.
The tasks defined in this project require a realistic definition of external loads as well as a detailed geometric description of the human eye and its boundary conditions. Additionally, they require the derivation of appropriate material models of the individual eye components.

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In vivo Quantification of Cellular Stresses using Elastic Round Microgels

Bead
Bead microinjection into living tissue
© Klemens Uhlmann

Cooperation with:
J. Guck (Biotechnology Center, Center for Molecular and Cellular Bioengineering, TU Dresden),
C. Werner(Leibniz-Institute for Biofunctional Polymer Materials Dresden)

Abstract:
Mechanical stress exerted and experienced by cells during tissue morphogenesis and organ formation plays an important role in embryonic development. While techniques to quantify mechanical stresses in vitro are available, few methods exist for studying stresses in living organisms. In this project, hydrogel microbeads are injected into living tissue and imaged via fluorescence confocal microscopy. A method is developed to reconstruct the stress states of microbeads at different stages of the tissue development. In the long term, a more detailed understanding of the connection of cellular stresses and cell growth can be accomplished, supporting the diagnostics of developmental defects.

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