Related papers: Turing pattern induced by cross-diffusion in cance…
Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Alan Turing proposed an elegant mechanism for pattern formation based on spontaneous breaking of the spatial translational symmetry in the underlying…
Cell competition is recognized to be instrumental to the dynamics and structure of the tumor-host interface in invasive cancers. In mild competition scenarios, the healthy tissue and cancer cells can coexist. When the competition is…
Chimeric antigen receptor (CAR) T-cell based immunotherapy has shown its potential in treating blood cancers, and its application to solid tumors is currently being extensively investigated. For glioma brain tumors, various CAR T-cell…
Cancer is a disease driven by random DNA mutations and the interaction of many complex phenomena. To improve the understanding and ultimately find more effective treatments, researchers leverage computer simulations mimicking the tumor…
We develop a field theory-inspired stochastic model for description of tumour growth based on an analogy with an SI epidemic model, where the susceptible individuals (S) would represent the healthy cells and the infected ones (I), the…
The combination of cytotoxic therapies and anti-angiogenic agents is emerging as a most promising strategy in the treatment of malignant tumors. However, the timing and sequencing of these treatments seem to play essential roles in…
Upcoming immunotherapies for cancer treatment rely on the ability of the immune system to detect and eliminate tumors in the body. A highly simplified version of this process can be studied in a Petri dish: starting with a random…
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
Contact inhibition is the process by which cells switch from a motile growing state to a passive and stabilized state upon touching their neighbors. When two cells touch, an adhesion link is created between them by means of transmembrane…
The objective of this work is to apply the H\"anggi-Klimontovich stochastic differential equations to model and study the effects of anti-tumor chemotherapy in the case of continuous infusion delivering. The fluctuations generated by…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…
It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply, and chemotherapy. The subdiffusion of the system…
Chimeric antigen receptor (CAR) T cell therapy is revolutionizing the treatment of blood cancers. Mathematical models that can predict the effectiveness of immunotherapies such as CAR T are of increasing interest due to their ability to…
Targeted therapeutic interventions utilizing low-inten\-sity ultrasound (LIUS) exhibit substantial potential for hindering the proliferation of cancer stem cells. This investigation introduces a multiscale model and computational framework…
We study a tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues into the exterior vacuum. The model features two moving…
Chemotherapy is one of the most important therapeutic options used to treat human cancers, either alone or in combination with radiation therapy and surgery. Recent studies have indicated that intra-tumoural heterogeneity has a significant…
Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide and, as a result, they form tumours that grow in size. The immune system recognise the cancerous cells and attack them, though, it can be…