Dr Dietmar Oelz

Lecturer

Mathematics
Faculty of Science
d.oelz@uq.edu.au
+61 7 336 53262

Overview

I studied Technical Mathematics at the Vienna University of Technology. I also earned a Master's degree in Law and I finished the first ("non-clinical") part of Medical Studies at the University of Vienna. I earned my PhD in Applied Mathematics at the University of Vienna in 2007. My PhD advisor was Christian Schmeiser, my co-advisor was Peter Markowich. I spent several months at the University of Buenos Aires working with C. Lederman and at the ENS-Paris rue d'Ulm in the group of B. Perthame.

Before coming to UQ, I held post-doc positions at the Wolfgang Pauli Insitute (Vienna), University of Vienna and the Austrian Academy of Sciences (RICAM). In 2013 I won an Erwin Schrödinger Fellowship of the Austrian Science Fund (FWF). I was a post-doc researcher in the group of Alex Mogilner first at UC Davis, then at the Courant Institute of Math. Sciences (New York University).

Research Interests

  • Mathematical and Computational Biology
    Cell Biology, Collective Behaviour, Multi-scale Modelling, mechanobiology of cells and tissues, cell movement, intra-cellular transport, cytoskeleton dynamics, actomyosin contractility
  • Applied Mathematics
    perturbation methods, multi-scale modelling, numerical schemes
  • Partial Differential Equations
    Biomathematics

Research Impacts

Biological systems integrate a multitude of processes on various spatial and temporal scales. The output of biological processes is typically robust to a range of random perturbations. Mathematics is an outstanding tool to investigate such cooperative mechanisms on the molecular level which can hardly be assessed experimentally.

Building on a sound applied mathematics and partial differential equations (PDE) background, the area of my research is to identify and describe biological processes by formulating mathematical models, to evaluate them using numerical simulation and mathematical analysis and to validate such models against experimental data.

A ubiquitous example for a highly complex biological system are cells. They use cytoskeletons composed of long fibers on the micron length scale to sustain their shape mechanically. Molecular processes on the nanoscale which change the structure of these fibers as well as force generation by motor proteins promote remodeling of cell shape, cell migration and intracellular transport. This is the basis for vital processes such as muscle contraction, cell division, immune system response, wound healing and embryogenesis, and it plays a crucial role in pathological processes such as tumor metastasis and neurodegenerative deseases.

The central question of my research is: how do proteins on the nanoscale and larger protein complexes on the micronscale cooperate in living cells to promote cell movement, shape changes, force generation and intra- cellular transport? This type of research contributes to the development of new techniques in bioengineering and of new therapeutic approaches in clinical fields such as oncology and immunology.

One important aspect of biological mechanisms is insensitivity to random perturbations. Hence mathe- matical models on the microscopic level are necessarily stochastic and I employ mathematical analysis and numerical simulation such as Brownian Dynamics to analyze the sensitivity of models and to identify robust characteristics of a systems output. Especially the smallness of the molecular length scales interferes with experimental imaging techniques to assess these biological processes in vivo. For this reason an essential aspect of my research is to use asymptotic analysis to derive and justify macroscopic coarse-grained models based on thoroughly formulated microscopic models. In general this process yields partial differential equations such as reaction-drift-diffusion models and fluid dynamics models. I analyze these models, which often exhibit amazingly rich mathematical properties, analytically and by numerical simulation in order to relate the experimentally measurable macroscopic features to the microscopic dynamics of interest.

Qualifications

  • PhD inMathenatics, University of Vienna

Publications

View all Publications

Publications

Book Chapter

  • Manhart, Angelika , Oelz, Dietmar , Schmeiser, Christian and Sfakianakis, Nikolaos (2017). Numerical treatment of the Filament-Based Lamellipodium Model (FBLM). In Frederik Graw, Franziska Matthäus and Jürgen Pahle (Ed.), Modeling cellular systems (pp. 141-159) Cham, Switzerland: Springer. doi:10.1007/978-3-319-45833-5_7

  • Ölz, Dietmar and Schmeiser, Christian (2010). How do cells move? Mathematical modeling of cytoskeleton dynamics and cell migration. In Arnaud Chauviere, Luigi Preziosi and Claude Verdier (Ed.), Cell mechanics: from single scale-based models to multiscale modelling (pp. 133-157) Boca Raton, FL, United States: Chapman and Hall / CRC Press. doi:10.1201/9781420094558-c5

Journal Article