By Dominik Wodarz
The booklet goals to supply an creation to mathematical types that describe the dynamics of tumor development and the evolution of tumor cells. it may be used as a textbook for complicated undergraduate or graduate classes, and likewise serves as a reference publication for researchers. The publication has a robust evolutionary part and displays the perspective that melanoma will be understood rationally via a mixture of mathematical and organic instruments. it may be used either by means of mathematicians and biologists. Mathematically, the publication begins with fairly easy usual differential equation versions, and to that end explores extra complicated stochastic and spatial types. Biologically, the ebook starts off with explorations of the elemental dynamics of tumor progress, together with aggressive interactions between cells, and for that reason strikes directly to the evolutionary dynamics of melanoma cells, together with eventualities of melanoma initiation, development, and therapy. The ebook finishes with a dialogue of complicated themes, which describe how a few of the mathematical thoughts can be utilized to achieve insights right into a number of questions, comparable to epigenetics, telomeres, gene remedy, and social interactions of melanoma cells.
Readership: Researchers in mathematical biology, mathematical modeling, biology, mathematical oncology.
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Additional info for Dynamics of Cancer : Mathematical Foundations of Oncology
Iii) Modeling of cancer initiation and progression as somatic evolution. In this area of research, methods of population dynamics and evolutionary game theory are applied to study cancer. First developed by ecologists and evolutionary biologists, these methods have been used to understand the collective behavior of a population of cancer cells, see [Gatenby and Gawlinski (2003); Gatenby and Vincent (2003b)]. In this chapter we review basic mathematical tools necessary to undertake different types of cancer modeling.
The development of cancer can thus be seen as a conspiracy between tumor cells and their altered environment which allows uncontrolled growth. Under non-pathogenic conditions, the tissue environment can prevent tumor cells from growing to significant levels. Interestingly, autopsies have revealed that people who die without ever developing cancers show microscopic colonies of cancer cells which are referred to as in situ tumors [Folkman and Kalluri (2004)]. Data suggest that >30% of women in the age range between 40 and 50 who do not develop cancer in their life-time are characterized by small colonies of breast cancer cells.
Each niche contains multiple stem cells, and niche stem cells are lost at random with replacement. It is assumed that each stem cell can either divide asymmetrically, or give rise to two stem cells, or to two differentiated cells. This loss and replacement dynamics eventually leads to the loss of all stem cell lineages except one. The average time to cancer is calculated with this model, using five successive mutational steps. The results are compared with the existing age-incidence statistics.