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A tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a…
In this work we explore the temporal dynamics of spatial heterogeneity during the process of tumorigenesis from healthy tissue. We utilize a spatial stochastic process model of mutation accumulation and clonal expansion in a structured…
In this article we shall trace the historical development of tumour growth laws, which in a quantitative fashion describe the increase in tumour mass/volume over time. These models are usually formulated in terms of differential equations…
Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide and, as a result, they form tumours that grow in size. The immune system recognise the cancerous cells and attack them, though, it can be…
Multi-gene panel testing allows many cancer susceptibility genes to be tested quickly at a lower cost making such testing accessible to a broader population. Thus, more patients carrying pathogenic germline mutations in various…
We consider the model of interaction between the immune system and tumor cells including a memory function that reflect the influence of the past states, to simulate the time needed by the latter to develop a chemical and cell mediated…
Multidrug resistance consists of a series of genetic and epigenetic alternations that involve multifactorial and complex processes, which are a challenge to successful cancer treatments. Accompanied by advances in biotechnology and…
Clusters of genes that have evolved by repeated segmental duplication present difficult challenges throughout genomic analysis, from sequence assembly to functional analysis. Improved understanding of these clusters is of utmost importance,…
Any process in which competing solutions replicate with errors and numbers of their copies depend on their respective fitnesses is the evolutionary optimization process. As during carcinogenesis mutated genomes replicate according to their…
Recent works have stressed the important role that random mutations have in the development of cancer phenotype. We challenge this current view by means of bioinformatic data analysis and computational modelling approaches. Not all the…
Molecular circadian clocks, that are found in all nucleated cells of mammals, are known to dictate rhythms of approximately 24 hours (circa diem) to many physiological processes. This includes metabolism (e.g., temperature, hormonal blood…
Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new mathematical model is proposed for the population dynamics of heterogeneous tumor cells following external beam radiation treatment. According…
Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative…
We apply our statistically deterministic machine learning/clustering algorithm *K-means (recently developed in https://ssrn.com/abstract=2908286) to 10,656 published exome samples for 32 cancer types. A majority of cancer types exhibit…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
This paper proposes an original theory of aging of multicellular organisms. The cells of multicellular organisms, in contrast to unicellular organisms, are burdened with a two- part genome: housekeeping and specialized (multicellular),…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analyzed and…
Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours,…
Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and, when they reach a critical length, the cell will enter permanent cell cycle arrest - a state known…