Revision as of 21:22, 4 April 2007

research statement

one of the most challenging applications of the mechanics of solid materials today is certainly the field of computational biomechanics, a well-recognized, fast-growing but not yet clearly defined subject that is unquestionably an interdisciplinary science par excellence. It provides a vast number of new and fascinating areas of application such as the internal and external remodeling of bones, the healing of fracture, the growth of tumors, wound healing of the epidermis, the regeneration of microdamaged muscles, functional adaptation and general repair processes of the cardiovascular system to name but a few. besides a basic knowledge in medicine, biology and chemistry, research in the field of computational biomechanics requires a profound theoretical background in thermodynamics, continuum mechanics and structural mechanics paired with the ability to develop efficient robust and stable computational simulation tools.

my ultimate goal is to establish an interactive computer-based biomechanical lab that supports the solution of medically and technologically challenging biomechanical problems.

selected research accomplishments

in contrast to traditional engineering materials, living organisms show the remarkable ability to adapt not only their geometry, but also their internal architecture and their material properties to environmental changes. although this functional adaptation of biological tissues has been known since julius wolff published his fundamental law of bone remodeling in 1892, research in biomechanics mainly focuses on the passive behavior of tissues rather than taking into account their active response to changes in mechanical loading. instead of following mainstream research and applying standard classical constitutive equations to biological materials, my personal research was driven by the desire to formulate appropriate continuum equations that properly account for the functional adaptation of living tissues. this adaptation is known to occur in three different forms which have dominated my previous research:

density growth

when characterizing engineering structures with the help of classical continuum field theories, we typically think of closed thermodynamic systems for which the amount of matter within a fixed material domain is constant throughout the entire thermodynamical process. the appropriate characterization of living biological structures, however, goes far beyond this traditional point of view. it falls within the framework of open system thermodynamics. in order to account for biological growth, the traditional balance of mass is enriched by additional mass source and flux terms that account for cell growth, cell shrinkage, cell division or cell migration on a phenomenological level. it is obvious, that the exchange of matter with the environment not only effects the balance of mass itself since the newly generated or inflowing mass typically carries a specific amount of momentum, energy and entropy. we have developed a general theoretical framework for open system thermodynamics which has been implemented in a finite element based simulation tool for density growth in biological tissues. for example, a medically relevant application of this model that has led to a pronounced industrial interest in our work is the optimization of modern implant design in hip replacement surgery.

volume growth

while growth phenomena in hard biological tissue can essentially be attributed to local changes in density, growth in soft biological tissues typically takes place in the form of huge volumetric changes. motivated by the classical ideas in large strain plasticity, we have adopted the concept of a fictitious configuration to characterize the kinematics of growth. we have developed an efficient simulation tool for volumetric growth which has been applied to the simulation of atherosclerosic plaque growth. the model was implemented in a commercial finite element package and applied it to the simulation of in-stent restenosis. the results of the simulation are based on patient-specific geometries generated from computer tomography.

microstructural remodeling

by virtue of their collagenous microstructure, soft biological tissues show a pronounced anisotropic response. In the early stages of tissue development, the underlying collagenous scaffold is found to reorient itself with respect to the principal loading directions. in a corresponding continuum model, characteristic microstructural orientations can be represented by fiber vectors. guided by minimization principles, we have developed a concept of fiber reorientation in which a single characteristic microstructural orientation is allowed to gradually align with the maximum principal strain direction. a typical application of this model can be found within the field of tissue engineering where tissue replacements are grown outside the human body. due to the absence of mechanical loading, these in vitro engineered functional tissue constructs typically lack a pronounced microstructural orientation. however, the formation of this orientation can be stimulated by subjecting the growing tissue to different mechanical loading scenarios. In close collaboration with experts intissue engineering from the university of michigan, we have been able to qualitatively validate our fiber reorientation model. the long term goal of this project is the optimal stimulation of microstructural growth. conceptually speaking, we strive for finding the optimal amount, frequency and direction of loading with the aim of reproducing the in vivo conditions as realistic as possible.

short term goals - immediate research interests

based on our expertise in computational biomechanics, we would like to pursue the following immediate research areas

on the tissue level - optimal implant design

based on our expertise in simulating the functional adaptation in bones, we have started an industrial collaboration aiming at improving implant design in artificial hip replacement surgery. since our computational tools have proven extremely powerful in predicting bone remodeling and implant loosening, I would like to continue this research guided by the following fundamental questions: how can we gain qualitative three-dimensional patient-specific information about the response to hip replacement surgery? how can the prosthesis' material and its geometry be improved to increase long-term biocompatibility? how can aseptic loosening of the prosthesis be avoided?

on the tissue level - simulation of atherosclerosis

to diagnose and localize atherosclerosis it is important to know the medical history of each individual patient. we are collaborating with radiologists who provide patient-specific geometries in the form of computer tomography images. these images typically consist of two-dimensional data sets at cutting distances of several millimeters. as such, they can be used to generate individual three-dimensional finite element models for patient-specific simulations. hoping to improve the understanding of atherosclerotic plaque growth, we would like to address a number of open questions: how can realistic in vivo boundary conditions for the artery be simulated? how can the vivo loading conditions be modeled appropriately? how can the concept of pre-stress be incorporated in the formulation?

on the cellular level - improved understanding of migration phenomena

the theoretical tools and computational models that have been proven successful in previous research have to face the criticism of lacking a profound micromechanical basis. to gain a better understanding of the phenomenological parameters of growth, we would like to dedicate part of our immediate research to an improved understanding of the transport phenomena taking place on the cellular level. based on previous research on nonlinear diffusion phenomena coupled with surface tension of cahn-hilliard type, we particularly aim at elaborating the following issues: how are transport phenomena driven? how does cell migration occur? how can cell migration be related to a phenomenologically introduced mass flux on the continuum level?

current projects

sunt in culpa
"Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum."
Link 1
Link 2