Short-term rhythmic proliferation of human breast cancer cell lines: surface effects and fractal growth patterns

Kinetic studies of cell proliferation rates shed light on the growth dynamics of cancer. Most such studies are based on measurements of cell numbers that were evaluated in time intervals of about 12 h. Studies of the initial tumour growth with short measuring intervals are rare. This study was therefore designed with 1 h measuring intervals over a 24 h period. Human breast cancer cell lines (ZR-75-1, SK-BR-3, MCF-7) and a benign cell line (HBL-100) were used to study the hourly thymidine uptake as a measure of cells in synthesis. In parallel experiments, the same cell lines were also exposed to tumour necrosis factor alpha (TNF-alpha) to explore the effect of an apoptosis-inducing substance on initial tumour growth kinetics. In time-evolution plots, there was an oscillation of the labelling index of thymidine uptake for all investigated cell lines, with and without TNF-alpha. Based on the results obtained, a mathematical model was developed mimicking the real experiment. To describe the system dynamically a cellular automaton model was studied. The growth kinetics revealed by the simulation were in accordance with our experimental data. Two- and three-dimensional growth simulations of this computer model yielded objects morphologically similar to real images of human breast cancer. Almost identical fractal dimensions of the virtual and real tumours further supported this visual similarity. The cellular automata models could, therefore, be seen as a bridge towards realistic in vivo scenarios. From a clinical point of view, the results obtained may be applicable not only to primary tumours, but even to tumour cell microfoci and small metastases, which are a major concern in early metastasizing tumours such as breast cancer.