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Arch Hellen Med, 31(3), May-June 2014, 365-371


Mathematical models for tumor creation, development and metastasis

M. Kiakou, N. CHolis, N. Tsoukalas
Department of Medical Oncology, 401 General Military Hospital of Athens, Athens, Greece

Scientific data indicate that for the secrets of tumor behavior to be elucidated, tumors should not be regarded as a single collection of identical tumor cells, but as part of a "dynamic society" consisting of both normal and mutant cells, which differ also in their types of mutation. The development of cancer is considered to be the consequence of the inability of the immune system to successfully overcome the mutations that occur as a result of a variety of factors. After the creation of a small cancer-cell society, a fine balance between the cancer and the immune system is installed. This balance can easily be disturbed after chemotherapy, which in addition to acting on the tumor also impairs the immune response, by preventing its innate efforts, if not to eradicate the tumor, at least to limit its progression. Carcinogenesis starts with the accumulation of multiple genetic alterations that promote genetic instability, resulting in the disruption of normal cell differentiation and the genesis of one or more tumor clones, which have a life span proportional to the survival advantage offered by the specific mutations. The development of these neoplastic clones occurs at a higher rate than that of normal cells, because cancer cells develop adaptive responses (the "Warburg'' phenomenon, increment of angiogenesis) which make their population viable despite the continuing accumulation of cells. The invasive and metastatic phenotype, characterized by the development of mechanisms of invasion into the extracellular matrix, dispersion and establishment of tumor cells at remote sites, is what turns a mutant into a cancerous cell. An increased proliferation rate usually results in increased depth of invasion into the extracellular matrix. This is a review of the basic mechanisms of carcinogenesis and their explanation with reference to mathematical models derived from the findings of other researchers.

Key words: Cancer, Development, Mathematical models, Metastasis, Neoplasm.

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