Cancer stem cells, self-seeding, and decremented exponential growth: theoretical and clinical implications.

The cancer stem cell hypothesis, for all of its biological intricacy, lends itself to a simple mathematical model with intriguing theoretical and practical implications. Models of this type are neither esoteric nor computation-intensive. Indeed, they can often be expressed in words and images rather than mathematical symbols. This essay will build such a model from basic, experimentally-derived postulates and show how it could explain all of the classical features of epithelial breast cancer: histologic disorganization (dysplasia, anaplasia), rapid growth, large tumor size, angiogenesis, invasion, and metastasis. The model could also explain why anti-mitotic therapy fails to cure most malignant diseases including stage IV breast cancer, and suggests alternative and perhaps superior therapeutic approaches.

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