Related papers: Modeling Tumor Angiogenesis with Cellular Automata
Malignant cancers that lead to fatal outcomes for patients may remain dormant for very long periods of time. Although individual mechanisms such as cellular dormancy, angiogenic dormancy and immunosurveillance have been proposed, a…
Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies…
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…
Since the discovery of a cancer initiating side population in solid tumours, studies focussing on the role of so-called cancer stem cells in cancer initiation and progression have abounded. The biological interrogation of these cells has…
This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model…
We discuss the characteristics of the patterns of the vascular networks in a mathematical model for angiogenesis. Based on recent in vitro experiments, this mathematical model assumes that the elongation and bifurcation of blood vessels…
We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the…
Cancer research has shifted from a purely gene-centric view to a more holistic understanding that recognizes the critical role of the tumour microenvironment, where mechanics and metabolism are key drivers of disease progression. However,…
Resection of primary tumors is often followed by accelerated growth of metastases. Here we propose that this effect may be due to the fact that resection of primary tumor results in a decrease in the total systemic amount of angiogenesis…
\emph{In vitro} experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an…
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…
Breast cancer is one of the most challenging global health problems among women. This study investigates the intricate breast tumor microenvironment (TME) dynamics utilizing data from Mammary-specific Polyomavirus Middle T Antigen…
Age-related macular degeneration (AMD) may cause severe loss of vision or blindness particularly in elderly people. Exudative AMD is characterized by angiogenesis of blood vessels growing from underneath the macula, crossing the…
We present a mathematical study of the emergence of phenotypic heterogeneity in vascularised tumours. Our study is based on formal asymptotic analysis and numerical simulations of a system of non-local parabolic equations that describes the…
Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but…
Tumor synthesis enables the creation of artificial tumors in medical images, facilitating the training of AI models for tumor detection and segmentation. However, success in tumor synthesis hinges on creating visually realistic tumors that…
Autologous chemotaxis, in which cells secrete and detect molecules to determine the direction of fluid flow, is thwarted at high cell density because molecules from other cells interfere with a given cell's signal. Using a minimal model of…
Metastatic tumors often invade healthy neighboring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model…
Cytotoxic chemotherapy is a common treatment for advanced prostate cancer. These tumors are also known to rely on angiogenesis, i.e., the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical…
The stochastic discrete space-time model of an immune response on tumor spreading in a two-dimensional square lattice has been developed. The immunity-tumor interactions are described at the cellular level and then transferred into the…