Related papers: Tumor containment as an anti-percolation process
A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments…
Despite the remarkable advances in cancer diagnosis, treatment, and management that have occurred over the past decade, malignant tumors remain a major public health problem. Further progress in combating cancer may be enabled by…
Using our previously developed model we demonstrate here, that (1) solid tumor growth and cell invasion are linked, not only qualitatively but also quantitatively, that (2) the onset of invasion marks the time point when the tumor cell…
In this paper we introduce a novel description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows us to find the expected size of the giant connected component…
A mathematical model of infiltrative tumour growth taking into account cell proliferation, death and motility is considered. The model is formulated in terms of local cell density and nutrient (oxygen) concentration. In the model the rate…
In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumour growth model. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death…
Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the…
We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the…
The clinical management of breast cancer depends on an accurate understanding of the tumor and its anatomical context to adjacent tissues and landmark structures. This context may be provided by semantic segmentation methods; however,…
Glioblastoma is among the most aggressive brain tumors in adults, characterized by patient-specific invasion patterns driven by the underlying brain microstructure. In this work, we present a proof-of-concept for a mathematical model of GBL…
Current analysis of tumor proliferation, the most salient prognostic biomarker for invasive breast cancer, is limited to subjective mitosis counting by pathologists in localized regions of tissue images. This study presents the first…
Assuming that there is feedback between an expanding cancer system and its organ-typical microenvironment, we argue here that such local tumor growth is guided by co-existence rather than competition with the surrounding tissue. We then…
Butterfly tumors are a distinct class of gliomas that span the corpus callosum, producing a characteristic butterfly-shaped appearance on MRI. The distinctive growth pattern of these tumors highlights how white matter fibers and structural…
In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…
Data clustering has been widely used in data analysis and classification. In the present work, a method based on dynamic quantum clustering is proposed for the segmentation and analysis of brain tumor MRI. The results open the possibility…
We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully…
Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology. Using an in vivo mammalian model, we show here that one can obtain useful…
Purpose: Tumor-associated vasculature differs from healthy blood vessels by its chaotic architecture and twistedness, which promotes treatment resistance. Measurable differences in these attributes may help stratify patients by likely…