---

Cancer cells display characteristic traits acquired in a step-wise manner during carcinogenesis. Some of these traits are autonomous growth, induction of angiogen- esis, invasion and metastasis. In this thesis, the focus is on one of the latest stages of tumor progression, tumor invasion. Tumor invasion emerges from the combined effect of tumor cell-cell and cell-microenvironment interactions, which can be studied with the help of mathematical analysis. Cellular automata (CA) can be viewed as simple models of self-organizing complex systems in which collective behavior can emerge out of an ensemble of many interacting "simple" components. In particular, we focus on an important class of CA, the so-called lattice-gas cellular automata (LGCA). Here, the principal tools of mathematical analysis of LGCA are the mean-field approximation and the corresponding Lattice Boltzmann equation. The main objective of this thesis is to investigate important aspects of tumor invasion, under the microscope of mathematical modeling and analysis: -Impact of the tumor environment -Effect of tumor cell proliferation and migration -Mechanisms of tumor invasion emergence -Computing in vivo tumor invasion

---

Haralampos Hatzikirou was borned in Thessaloniki, Greece, in1978. After school in 1996, he studied Mathematics in AristotleUniversity of Thessaloniki. In 2001, he enrolled in the programof Technomathematik in TU Kaiserslautern. After 1,5 year, heaccomplished his MSc thesis at the ITB in Berlin. From 2004-2009he wrote his PhD at TU Dresden.

---