Related papers: Levy model of cancer
We present a general computational theory of cancer and its developmental dynamics. The theory is based on a theory of the architecture and function of developmental control networks which guide the formation of multicellular organisms.…
Five-year cancer survival rates are widely reported and often interpreted to mean that early detection saves lives, that a late fatal diagnosis would have been prevented by earlier detection, and that increasing survival over time proves…
One of many important features of the tumour microenvironment is that it is a place of active Darwinian selection where different tumour clones become adapted to the variety of ecological niches that make up the microenvironment. These…
Cancer cells are widely known to be protected from apoptosis, which is a major hurdle to successful anti-cancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to…
The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is…
We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term…
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…
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…
Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on…
We examine a lattice model of tumor growth where survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the…
Cancer prognosis can be regarded as estimating the risk of future outcomes from multiple variables. In prognostic signatures, these variables represent expressions of genes that are summed up to calculate a risk score. However, it is a…
Cancer and its subtypes constitute approximately 30% of all causes of death globally and display a wide range of heterogeneity in terms of clinical and molecular responses to therapy. Molecular subtyping has enabled the use of precision…
Williams and Bjerknes proposed a simple stochastic growth model to describe the tumor growth in the basal layer of an epithelium. In this work we generalize this model by including the possibility of saturation in the tumor growth as it is…
In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumor-environment interaction. In particular, oxygen concentration plays a central role in the determination of the…
In many situations, the gene expression signature is a unique marker of the biological state. We study the modification of the gene expression distribution function when the biological state of a system experiences a change. This change may…
Although the survival rate of cancer patients has significantly increased due to advances in anti-cancer therapeutics, one of the major side effects of these therapies, particularly radiotherapy, is the potential manifestation of…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
The mechanisms leading cells to acquire a fitness advantage and establish themselves in a population are paramount to understanding the development and growth of cancer. Although there are many works that study separately either the…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
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…