A mathematical model for metastatic growth illustrated by in vivo and in vitro growth of a transplantable mammary carcinoma in mice.

We analysed the growth pattern of metastases in C3H-mice produced by i.v. injection (tail vein) of tumor cell suspensions of mammary carcinoma HB. Although the ordinary Gompertz equation generally corresponds well to tumor growth in animals and men, we found it inadequate to describe the growth of lung metastases in our model. The morphometric analysis and growth kinetics (LI/GF) of the metastases show a biphasic pattern. The first phase is characterized by a strictly avascular growth and nutrition by diffusion, the second phase is initiated by tumor angiogenesis. To analyze these observations we developed a new mathematical equation which fits particularly well to the metastatic growth curve. We conclude that the present model is appropriate for the analysis of tumor angiogenesis, especially to study factors, which influence the development of a tumor specific vascular system.