Analyses of tumor cells by mathematical models

Mathematical models of tumor growth ∗

In the lecture we describe some elements of mathematical modeling of tumor growth. We present deterministic mathematical models most often used for description of tumor growth. Development of a model, based on some biological assumption, is also illustrated by one example. Described models are tested and compared by ability to describe experimental data.

Properties of Tumor Spheroid Growth Exhibited by Simple Mathematical Models

Solid tumors, whether in vitro or in vivo, are not an undifferentiated mass of cells. They include necrotic regions, regions of cells that are in a quiescent state (either slowly growing or not growing at all), and regions where cells proliferate rapidly. The decision of a cell to become quiescent or proliferating is thought to depend on both nutrient and oxygen availability and on the presence...

Mathematical Models of Avascular Tumor Growth

This review will outline a number of illustrative mathematical models describing the growth of avascular tumors. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modeling of avascular tumor development are ...

Singularity and symmetry analyses of mathematical models of epidemics

Single-cell analyses of circulating tumor cells

Circulating tumor cells (CTCs) are a population of tumor cells mediating metastasis, which results in most of the cancer related deaths. The number of CTCs in the peripheral blood of patients is rare, and many platforms have been launched for detection and enrichment of CTCs. Enumeration of CTCs has already been used as a prognosis marker predicting the survival rate of cancer patients. Yet CTC...