MALIGNANT INVASION MODEL WITH A SMALL AMOUNT OF DIFFUSION IN THE FRAMEWORK OF THE NON-STANDARD SCALE RELATIVITY THEORY. Part I – EVOLUTION EQUATIONS

A particular model of tumor progression (extended Perumpanani’s model), assuming that the invasive cells, the connective tissue and the proteases are moving through a non-differential medium governed by the Non-Standard Scale Relativity Theory (Scale Relativity Theory with arbitrary constant fractal dimension) is analyzed. In such context an action-reaction type law acting on the complex system formed by the extracellular matrix and the non-differential medium is considered. As a result, artificial cancer cell proliferation satisfies a logistic law accounting for the competition for space with the non-differential medium. Moreover, the connective tissues concentration increases proportionally to the real fractal velocity, squared. Over small distances, it results that even in avascular stages, malignant tumors might propagate and invade healthy tissues.