Related papers: Reaction-Diffusion Models for Glioma Tumor Growth
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…
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…
A fundamental model of tumor growth in the presence of cytotoxic chemotherapeutic agents is formulated. The model allows to study the role of the Norton-Simon hypothesis in the context of dose-dense chemotherapy. Dose-dense protocols aim at…
Low grade gliomas (LGGs) are a group of primary brain tumors usually encountered in young patient populations. These tumors represent a difficult challenge because many patients survive a decade or more and may be at a higher risk for…
We derive a full 3-dimensional (3-D) model of inhomogeneous -- anisotropic diffusion in a tumor region coupled to a binary population model. The diffusion tensors are acquired using Diffusion Tensor Magnetic Resonance Imaging (DTI) from a…
In this paper, we tackle the problem of reconstructing earlier tumour configurations starting from a single spatial measurement at a later time. We describe the tumour evolution through a diffuse interface model coupling a…
Spatial agent-based models are increasingly used to investigate the evolution of solid tumours subject to localised cell-cell interactions and microenvironmental heterogeneity. Here we present a non-technical step by step guide to…
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…
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…
The development of mathematical models of cancer informed by time-resolved measurements has enabled personalised predictions of tumour growth and treatment response. However, frequent cancer monitoring is rare, and many tumours are treated…
We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035, 2020). The model captures memory effects in diffusive…
Generative tasks about molecules, including but not limited to molecule generation, are crucial for drug discovery and material design, and have consistently attracted significant attention. In recent years, diffusion models have emerged as…
Adaptive therapy is a dynamic cancer treatment protocol that updates (or "adapts") treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific…
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…
Diffusion models have achieved remarkable success in generative modeling. Despite more stable training, the loss of diffusion models is not indicative of absolute data-fitting quality, since its optimal value is typically not zero but…
Employing a novel two-dimensional computational model we have simulated the feedback between angiogenesis and tumor growth dynamics. Analyzing vessel formation and elongation towards the concentration gradient of the tumor-derived…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…
It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression…
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have…
Research into somatic mutations in cancer cell DNA and their role in tumour growth and progression between successive stages is crucial for improving our understanding of cancer evolution. Mathematical and computer modelling can provide…