Related papers: Spatial evolution of tumors with successive driver…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
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…
Heterogeneity in characteristics from one region (sub-population) to another, commonly observed in complex systems, such as glasses and a collection of cells, is hard to describe theoretically. In the context of cancer, intra-tumor…
In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander,…
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…
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
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…
In this study, we model avascular tumour growth in epithelial tissue. This can help us to get a macroscopic view of the interaction between the tumour with its surrounding microenvironment and the physical changes within the tumour…
In this work, we develop a kinetic model of tumour growth taking into account the effects of clinical uncertainties characterising the tumours' progression. The action of therapeutic protocols trying to steer the tumours' volume towards a…
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…
A major challenge for cancer pathologists is to determine whether a new tumor in a patient with cancer is a metastasis or an independent occurrence of the disease. In recent years numerous studies have evaluated pairs of tumor specimens to…
In this paper we study a free boundary problem for the growth of multi-layer tumors in necrotic phase. The tumor region is strip-like and divided into necrotic region and proliferating region with two free boundaries. The upper free…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer…
Intra-tumor heterogeneity driving disease progression is characterized by distinct growth and spatial proliferation patterns of cells and their nuclei within tumor and non-tumor tissues. A widely accepted hypothesis is that these spatial…
A single solid tumor, composed of nearly identical cells, exhibits heterogeneous dynamics. Cells dynamics in the core is glass-like whereas those in the periphery undergo diffusive or super-diffusive behavior. Quantification of…
We investigate how quantum information, encoded in a quantum field, evolves during the expansion of spacetime. Due to information loss across the horizon, a local observer experiences this evolution as a nonunitary quantum channel. We…
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…
Numerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial…