Related papers: Parameter Estimation in Recurrent Tumor Evolution …
The site frequency spectrum (SFS) is a popular summary statistic of genomic data. While the SFS of a constant-sized population undergoing neutral mutations has been extensively studied in population genetics, the rapidly growing amount of…
Multiplicative noise is found to divide the growth law of tumors into two parts in a logistic model, which is driven by additive and multiplicative noises simultaneously. The Fokker-Planck equation was also derived to explain the fact that…
While cancer has traditionally been considered a genetic disease, mounting evidence indicates an important role for non-genetic (epigenetic) mechanisms. Common anti-cancer drugs have recently been observed to induce the adoption of…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
The influence of random fluctuations on the recruitment of effector cells towards a tumor is studied by means of a stochastic mathematical model. Aggressively growing tumors are confronted against varying intensities of the cell-mediated…
The time delayed cytotoxic T-lymphocyte response on the tumor growth has been developed on the basis of discrete approximation (2-dimensional map). The growth kinetic has been described by logistic law with growth rate being the bifurcation…
Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe…
Neuroblastoma is a paediatric extracranial solid cancer that arises from the developing sympathetic nervous system and is characterised by an abnormal distribution of cell types in tumours compared to healthy infant tissues. In this paper,…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance,…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
The interplay between tumor cells and macrophages plays a central regulatory role in cancer progression. In this study, we developed a mathematical model that incorporates tumor cells, M1 type macrophages, M2 type macrophages and an M3 type…
The ability to estimate how a tumor might evolve in the future could have tremendous clinical benefits, from improved treatment decisions to better dose distribution in radiation therapy. Recent work has approached the glioma growth…
Primary tumors infrequently lead to demise of cancer patients; instead, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs (metastasis). It is well-known that malignant tumors induce…
The understanding of the macroscopic phenomenological models of the population growth at a microscopic level is important to predict the population behaviors emerged from the interactions between the individuals. In this work we consider…
This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…
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…
The recent advances in cancer immunotherapy boosted the development of tumor-immune system models aiming to provide mechanistic understanding and indicate more efficient treatment regimes. However, the complexity of such models, their…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
We present a stochastic computational model of avascular tumors, emphasizing the detailed implementation of the first four so-called hallmarks of cancer: self-sufficiency in growth factors, resistance to growth inhibitors, avoidance of…