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A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…

In early-phase cancer clinical trials, the limited availability of data presents significant challenges in developing a framework to efficiently quantify treatment effectiveness. To address this, we propose a novel utility-based Bayesian…

Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…

Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…

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…

Intracellular structural alterations are hallmark of several disease conditions and treatment modalities. However, robust methods to quantify these changes are scarce. In view of this, we introduce a new method to quantify structural…

We develop statistically based methods to detect single nucleotide DNA mutations in next generation sequencing data. Sequencing generates counts of the number of times each base was observed at hundreds of thousands to billions of genome…

The homeostasis of epithelial tissue relies on a balance between the self-renewal of stem cell populations, cellular differentiation, and loss. Although this balance needs to be tightly regulated to avoid pathologies, such as tumor growth,…

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least…

Tissue self-organization into defined and well-controlled three-dimensional structures is essential during development for the generation of organs. A similar, but highly deranged process might also occur during the aberrant growth of…

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…

Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On…

In cancer genomics, it is of great importance to distinguish driver mutations, which contribute to cancer progression, from causally neutral passenger mutations. We propose a random-effect regression approach to estimate the effects of…

The collective chemotaxis of multicellular clusters is an important phenomenon in various physiological contexts, ranging from embryonic development to cancer metastasis. Such clusters often display interesting shape dynamics and…

Brain-related experiments are limited by nature, and so biological insights are often restricted or absent. This is particularly problematic in the context of brain cancers, which have very poor survival rates. To generate and test new…

Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size…

We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…

Recent studies of cancer somatic mutation profiles seek to identify mutations for targeted therapy in personalized medicine. Analysis of profiles, however, is not trivial, as each profile is heterogeneous and there are multiple confounding…

Cancer cells are known to modify their micro-environment such that it can sustain a larger population, or, in ecological terms, they construct a niche which increases the carrying capacity of the population. It has however been argued that…

Movement behavior of biological entities plays a crucial role in their destiny through regulating their intraspecific and interspecific interactions as well as their interaction with surrounding environment. In spite of various models for…