Fractal tumours: their real and virtual images

Autonomous and uncoordinated proliferation of epithelia leads to various well-known growth patterns such as expansive (cauliflower-like), radiating infiltrative, polycyclic, and roundish-ovoid figures. All attempts to describe such natural growth patterns graphically by Euclidean geometry have failed and remain no more than works of art. However, fractal geometry is a new tool for the characterization of irregularly-shaped and complex figures. Moreover, behind a fractal structure there is a basic power-law which provides the opportunity to simulate these forms artificially. A prerequisite for achieving this goal of simulating tumour growth by computer is to establish whether typical tumour growth patterns are fractal. Hence, an investigation was undertaken of 20 tumours (malignant, metastases or benign) exhibiting the above-mentioned typical patterns. If tumour outlines are fractal they have to possess a fractal non-integer dimension which significantly exceeds the integer Euclidean dimension. The fractal dimension of tumour outlines was determined using the box-counting method. Almost all tumours presented a fractal dimension and virtual tumour images were created by utilizing available fractal software. In conclusion, the determination of the fractal dimension of solid neoplasms may be an additional morphometric parameter for growth assessment and it probably provides further opportunity to simulate cancer growth and infiltration by computer animation.