Promising but challenging tumour growth simulation experiments at TU Dresden

Dresden 29 June 2006Cancer is a system, so we should be able to address it as a mathematical model in order to study its genesis and evolution, according to Dr. Andreas Deutsch from the Technical University of Dresden, Germany. He shared some of the recent findings of his team on tumour growth simulation with the ISC2006 audience. At the same time Dr. Deutsch warned the conference participants to not have their expectations rise too high as yet.


The speaker started out to define the precise nature of cancer. Cancer actually is a group of more than 100 diseases that develop across time and involve the uncontrolled division of cells. From the etymological point of view cancer comes from the Greek word "karkinoma", which means "a cancer". The root is "karkinos", referring to "crab". In turn, the Latin word "tumre" means "to swell".

Cancer already is an old disease which can also threaten animals. Dr. Deutsch showed a tumour in a dinosaur that lived some 200 million years ago. If we look at the leading causes of death in 2001, cancer is the number two after heart disease. Together with heart disease and stroke, cancer is responsible for 50 percent of the casualties caused by disease. Cancer often is due to lifestyle problems as becomes clear in the top three list of cancer types. In the male population, lung, colon and prostate cancers are the killers; in the female population it are breast, lung and colon cancers.

Cancer develops in stages, starting with a cell showing a genetic mutation, and runs through the hyperplasia and dysplasia phases to amount into in situ cancer and eventually into invasive cancer, as the speaker explained. In order to analyse cancer dynamics researchers are using experimental models to simulate the in vitro analysis of a cancer invasion.

This in silico analysis demonstrates a strong analogy with a chess game of white and black pieces. The black pieces are comparable to the invading cancer. As a researcher you have to know the rules of the game. The strategy is provided by the mathematical model.

Dr. Deutsch tried to answer the question why scientific research is using mathematical models and computer simulations. Mathematical models can help to explain the co-operative behaviour in the genesis of cancer. Cancer development and invasion constitute a collective, emergent phenomenon arising from the interplay between healthy cells and malignant cells attacking the immune system.

There are two routes in the analysis of biological systems: the first one is the discovery of the molecular-biological code and the second one the discovery of cell formation, morphogenesis, and spatial patterns. The level of approach is the cell to study the interaction between particles and cells.

Dr. Deutsch especially likes the analogy with ocean waves and their rippling wave pattern of interaction. The components are identical in ocean waves but there is a different rippling pattern in cells. The interactions are in fact collisions and next to the conservation laws, we see phenomena such as alignment, adhesion, contact inhibition, and chemotaxis. Their function is evolvability.

How do scientists compute an organism? They are confronted with the life cycle of a dictyostelium disc. The simulation has to visualize the interaction rules, including chemotaxis and differential adhesion. For the computation of a disease, what exactly do the researchers need? Is it a model or an algorithm?

Cancer is a spatial-temporal pattern formation system and at the TU Dresden an IBM computer is used to go through the different models by cellular automaton, as the speaker explained. Time, state space and dynamics are identified by rules. The rules are survival, death and birth. The emergent patterns are not present at the level of the rules.

Are simple rules sufficient to explain biological phenomena? Dr. Deutsch showed the presence of proliferant cells and quiescent cells in cancer development as well as the necrotic material. In the tumour model, a hybrid lattice-gas cellular automaton is used. The states are discrete tumour cells. The model dynamics are shown at each time step and lattice node. The simulation is coarse grain and shows the evolution of nutrient concentration with no necrotic signal.

Eventually, the team aims to perform a simulation of "treatments" showing the results of surgery, lowering the adhesion and enhancing the necrotic rate. The Glioma invasion constitutes a biomedical problem. In brain tumours the glioblastoma tumour is the most frequent and malignant primary brain tumour. Current imaging techniques identify max. 90 percent of gloma, as the speaker explained.

There is a linear growth because of the invasion of cancer cells. A Lattice-Boltzmann equation is used. The simulation linearizes around the fixed point and the empty lattices denote the healthy tissue. The simulation visualizes the travelling front. The visualization of fiber bundles shows a diffusion of the ellipsoids. The TU Dresden team is using a fiber tracking toolbox, as Dr. Deutsch pointed out.

An article on mathematical oncology appeared in Nature 2003. Dr. Deutsch referred to cancer as a system that has to be treated as a mathematical model to study the organisational principle of cancer and to show its growth using 3D simulations.

Researchers are trying to build evolutionary models showing the mutations and the micro-environment to better understand carcinogenesis or the birth of cancer; to achieve pattern recognition of the cancer surface; and to scale the analysis to recognize the type of cancer.

The work of the TU Dresden team is funded by the EU Marie Curie network and the simulations are the work of Sabine Dormann, David Basanta, Lutx Brusch, and Joachim Peter.

Leslie Versweyveld

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