Fractal tumor stromal border in a nonequilibrium growth model

To examine the potential relationships of tumor growth parameters and fractal dimensionality of the resulting pattern.

A nonequilibirum tumor growth model was developed taking into account tumor cell motility, tumor and stromal proliferation, cohesion, autocrine and paracrine growth stimulation, and tumor and stromal destruction. Ten thousand simulation runs were performed with varying settings of the control parameters. Fractal dimensionality of the tumor-stroma border was assessed in each pattern by a box counting method.

Fractal dimensionality increased with overall tumor cell motility, heterotypic tumor-stroma adhesion and paracrine growth stimulation, and decreased with homotypic tumor-tumor adhesion, autocrine growth stimulation, and tumor and stroma destruction.

Fractal dimensionality of the tumor-stroma border depends on various parameters controlling tumor growth. Some growth properties considered to be associated with an increased degree of malignancy influence fractal dimensionality in opposite directions. Therefore, determination of fractal dimensionality cannot be related directly to any particular biologic feature or to the overall biologic behavior of a tumor.