A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determining factor in generating papillary tumor morphology.

In the past 30 years we have witnessed an extraordinary progress on the research in the molecular biology of cancer, but its medical treatment, widely based on empirically established protocols, still has many limitations. One of the reasons for that is the limited quantitative understanding of the dynamics of tumor growth and drug response in the organism. In this review we shall discuss in general terms the use of mathematical modeling and computer simulations related to cancer growth and its applications to improve tumor therapy. Particular emphasis is devoted to multiscale models which permit integration of the rapidly expanding knowledge concerning the molecular basis of cancer and the complex, nonlinear interactions among tumor cells and their microenvironment that will determine the neoplastic growth at the tissue level.

Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility, and death [S. C. Ferreira, Jr., M. L. Martins, and M. J. Vilela, Phys. Rev. E 65, 021907 (2002)], which qualitatively reproduces commonly observed morphologies for carcinomas in situ. In the present work, we analyze the effects of distinct chemotherapeutic strategies on the patterns, scaling, and growth laws obtained for the nutrient-limited model. Two kinds of chemotherapeutic strategies were considered, namely, those that kill cancer cells and those that block cell mitosis but allow the cell to survive for some time. Depending on the chemotherapeutic schedule used, the tumors are completely eliminated, reach a stationary size, or grow following power laws. The model suggests that the scaling properties of the tumors are not affected by the mild cytotoxic treatments, although a reduction in growth rates and an increase in invasiveness are observed. For the strategies based on antimitotic drugs, a morphological transition in which compact tumors become more fractal under aggressive treatments was seen.

Desmosomes are intercellular adhesive junctions that occur in almost all epithelia and should therefore be useful as epithelial markers in tumour diagnosis. Here, we describe a monoclonal antibody, 32-2B, to a major desmosomal glycoprotein (dgl) which reacts with human tissues in paraffin sections. This antibody was tested for its ability to stain epithelia and tumours. It reacted with all epithelia tested and with every specimen of a wide range of carcinomas. It also stained meningiomas, another desmosome-containing tumour. It did not stain other types of tumours including lymphomas, melanomas, and various sarcomas, or normal tissues which lack desmosomes. These characteristics demonstrate that 32-2B is a reliable epithelial marker that may have a useful role in diagnostic histopathology.