Related papers: A level-set approach for a multi-scale cancer inva…
Multiple myeloma is a plasma cell cancer that leads to a dysregulated bone remodeling process. We present a partial differential equation model describing the dynamics of bone remodeling with the presence of myeloma tumor cells. The model…
Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring…
Multicellular tumor spheroids are an important {\it in vitro} model of the pre-vascular phase of solid tumors, for sizes well below the diagnostic limit: therefore a biophysical model of spheroids has the ability to shed light on the…
In this paper, we study a well-posedness problem on a new mathematical model for cancer invasion within the plasminogen activation system, which explicitly incorporates cooperation with host normal cells. Key biological…
Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative…
Temporally and spatially resolved measurements of protein transport inside cells provide important clues to the functional architecture and dynamics of biological systems. Fluorescence Recovery After Photobleaching (FRAP) technique has been…
We study the dynamics of epidemic and reaction-diffusion processes in metapopulation models with heterogeneous connectivity pattern. In SIR-like processes, along with the standard local epidemic threshold, the system exhibits a global…
The use of oncolytic viruses as cancer treatment has received considerable attention in recent years, however the spatial dynamics of this viral infection is still poorly understood. We present here a stochastic agent-based model describing…
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…
Clinical management of cancer has continuously evolved for several decades. Biochemical, molecular and genomics approaches have brought and still bring numerous insights into cancerous diseases. It is now accepted that some phenomena,…
The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs but not vice versa. However, an alternative paradigm of CSC theory with reversible…
Drug resistance and metastasis - the major complications in cancer - both entail adaptation of cancer cells to stress, whether a drug or a lethal new environment. Intriguingly, these adaptive processes share similar features that cannot be…
Understanding how microenvironmental heterogeneity influences tumor progression is essential for advancing both cancer biology and therapeutic strategies. In this study, we develop a cellular automata (CA) model to simulate tumor growth…
Cancer progression arises from interactions across multiple biological layers, especially beyond morphological and across molecular layers that remain invisible to image-only models. To capture this broader biological landscape, we present…
Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…
Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a…
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating).…
The primary objective of phase I cancer clinical trials is to evaluate the safety of a new experimental treatment and to find the maximum tolerated dose (MTD). We show that the MTD estimation problem can be regarded as a level set…
At present it is still quite difficult to match the vast knowledge on the behavior of individual tumor cells with macroscopic measurements on clinical tumors. On the modeling side, we already know how to deal with many molecular pathways…
We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context…