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Tumor growth, which plays a central role in cancer evolution, depends on both the internal features of the cells, such as their ability for unlimited duplication, and the external conditions, e.g., supply of nutrients, as well as the…

Is cancer a disease that can be cured or a degenerative disease which comes predominantly with old age? We give an answer based on a two-dimensional representation of diseases. These two dimensions are defined as follows. In mortality…

Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors,…

We propose a multiscale chemo-mechanical model of cancer tumour development in an epithelial tissue. The model is based on transformation of normal cells into the cancerous state triggered by a local failure of spatial synchronisation of…

Is it possible to understand cancer? Or more specifically, is it possible to understand cancer from genetic side? There already many answers in literature. The most optimistic one has claimed that it is mission-possible. Duesberg and his…

It is proposed that cancer results from the breakdown of universal control mechanisms which developed in mutual association as part of the historical process that brought individual cells together into multi-cellular communities. By…

Primary tumors often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical observations have suggested that these premalignant fields…

Risk evaluation to identify individuals who are at greater risk of cancer as a result of heritable pathogenic variants is a valuable component of individualized clinical management. Using principles of Mendelian genetics, Bayesian…

We investigate a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telomere length structure, which is applicable to the clonal…

We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…

Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype…

Compiled data for the stem cell numbers, Ns, and division rates, ms, is reanalized in order to show that we can distinguish two groups of human tissues. In the first one, there is a relatively high fraction of maintenance (stem and transit)…

Cancer progression is driven by a small number of genetic alterations accumulating in a neoplasm. These few driver alterations reside in a cancer genome alongside tens of thousands of other mutations that are widely believed to have no role…

The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…

Drug resistance and metastasis - the major complications in cancer - both entail adaptation of cancer cells to stress, whether a drug or a lethal new environment. Intriguingly, these adaptive processes share similar features that cannot be…

This manuscript has been written to address questions related to our recent publication (Science 347:78-81, 2015). We appreciate the many reactions to this paper that have been communicated to us, either privately or publicly. The following…

We have analyzed gene expression data from 3 different kinds of samples: normal human tissues, human cancer cell lines and leukemic cells from lymphoid and myeloid leukemia pediatric patients. We have searched for genes that are over…

First, we revisit the stochastic Luria-Delbr\"uck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes, and number of…

In this study, we develop consistent estimators for key parameters that govern the dynamics of tumor cell populations when subjected to pharmacological treatments. While these treatments often lead to an initial reduction in the abundance…

Cancer is one of the most feared diseases in the world it has increased disturbingly and breast cancer occurs in one out of eight women, the prediction of malignancies plays essential roles not only in revealing human genome, but also in…