Related papers: Computational modelling of cancer evolution by mul…

In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution…

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…

Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…

Cancer is increasingly perceived as a systems-level, network phenomenon. The major trend of malignant transformation can be described as a two-phase process, where an initial increase of network plasticity is followed by a decrease of…

Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study…

Cancer, as the uncontrollable cell growth, is related to many branches of biology. In this review, we will discuss three mathematical approaches for studying cancer biology: population dynamics, gene regulation, and developmental biology.…

The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous…

A recently proposed single progenitor cell model for skin cell proliferation [Clayton et al., Nature v446, 185 (2007)] is extended to incorporate homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can…

In this review, we discuss recent advances on the plasticity of cancer stem cells and highlight their relevance to understand the metastatic process and to guide therapeutic interventions. Recent results suggest that the strict hierarchical…

Cancer is a very complex phenomenon that involves many different scales and situations. In this paper we consider a free boundary problem describing the evolution of a tumor colony and we derive a new asymptotic model for tumor growth. We…

Despite significant medical advancements, cancer remains the second leading cause of death, with over 600,000 deaths per year in the US. One emerging field, pathway analysis, is promising but still relies on manually derived wet lab data,…

Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…

Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving the…

Cancer is most commonly viewed as resulting from somatic mutations enhancing proliferation and invasion. Some hypotheses further propose that these new capacities reveal a breakdown of multicellularity allowing cancer cells to escape…

Motivation: Driver (epi)genomic alterations underlie the positive selection of cancer subpopulations, which promotes drug resistance and relapse. Even though substantial heterogeneity is witnessed in most cancer types, mutation accumulation…

We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…

We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…

We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…

Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tighly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting…

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…