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- Sergei Fedotov, Alexander Iomin
- Physical review. E, Statistical, nonlinear, and…
- 2008

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)

- Sergei Fedotov, Alexander Iomin
- Physical review letters
- 2007

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 Iomin
- The European physical journal. E, Soft matter
- 2012

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)

- A. Iomin, S. Dorfman, L. Dorfman
- 2004

A growth of malignant neoplasm is considered as a fractional transport approach. We suggested that the main process of the tumor development through a lymphatic net is fractional transport of cells. In the framework of this fractional kinetics we were able to show that the mean size of main growth is due to subdiffusion, while the appearance of metaphases… (More)

- A Iomin
- Physical review. E, Statistical, nonlinear, and…
- 2004

Chaotic dynamics of a nonlinear oscillator is considered in the semiclassical approximation. The Loschmidt echo as a measure of quantum stability to a time dependent variation is calculated. It is shown that an exponential decay of the Loschmidt echo is due to a Lyapunov exponent and it has a pure classical nature. The Lyapunov regime is observed for a time… (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)

We suggest a modification of a comb model to describe anomalous transport in spiny dendrites. Geometry of the comb structure consisting of a one-dimensional backbone and lateral branches makes it possible to describe anomalous diffusion , where dynamics inside fingers corresponds to spines, while the backbone describes diffusion along dendrites. The… (More)

- A. Iomin
- 2015

A theory of fractional kinetics of glial cancer cells is presented. A role of the migration-proliferation dichotomy in the fractional cancer cell dynamics in the outer-invasive zone is discussed an explained in the framework of a continuous time random walk. The main suggested model is based on a construction of a 3D comb model, where the… (More)

- Trifce Sandev, Alexander Iomin, Holger Kantz
- Physical review. E, Statistical, nonlinear, and…
- 2015

A grid comb model is a generalization of the well known comb model, and it consists of N backbones. For N=1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1/2. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that… (More)

- V. M'endez, A. Iomin
- 2014

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)