A. Iomin

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The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model. The balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration are derived. The transport of tumor cells is formulated in terms of the CTRW with an(More)
We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW), we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated(More)
A toy model for glioma treatment by a radio frequency electric field is suggested. This low-intensity, intermediate-frequency alternating electric field is known as the tumor-treating field (TTF). In the framework of this model the efficiency of this TTF is estimated, and the interplay between the TTF and the migration-proliferation dichotomy of cancer(More)
Fractional reaction-diffusion equations are derived by exploiting the geometrical similarities between a comb structure and a spiny dendrite. In the framework of the obtained equations, two scenarios of reaction transport in spiny dendrites are explored, where both a linear reaction in spines and nonlinear Fisher-Kolmogorov-Petrovskii-Piskunov reactions(More)
This chapter is a contribution in the"Handbook of Applications of Chaos Theory"ed. by Prof. Christos H Skiadas. The chapter is organized as follows. First we study the statistical properties of combs and explain how to reduce the effect of teeth on the movement along the backbone as a waiting time distribution between consecutive jumps. Second, we justify(More)