Related papers: Models, measurement and inference in epithelial ti…

As biomedical sciences discover new layers of complexity in the mechanisms of life and disease, mathematical models trying to catch up with these developments become mathematically intractable. As a result, in the grand scheme of things,…

Diffusion probabilistic models have made their way into a number of high-profile applications since their inception. In particular, there has been a wave of research into using diffusion models in the prediction and design of biomolecular…

Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…

Morphological instabilities of growing tissues that impinge on passive materials are typical of invasive cancers. To explain these instabilities in experiments on breast epithelial spheroids in an extracellular matrix, we develop a…

Recent advancements in model checking have demonstrated significant potential across diverse applications, particularly in signal and image analysis. Medical imaging stands out as a critical domain where model checking can be effectively…

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…

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…

In this paper we address some modelling issues related to biological growth. Our treatment is based on a recently-proposed, general formulation for growth within the context of Mixture Theory (Journal of the Mechanics and Physics of Solids,…

Unstable dynamics characterizes the evolution of most solid tumors. Because of an increased failure of maintaining genome integrity, a cumulative increase in the levels of gene mutation and loss is observed. Previous work suggests that…

A tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a…

In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution…

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…

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…

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…

Developing clinically viable tissue-engineered cardiovascular implants remains a formidable challenge. Achieving reliable and durable outcomes requires a deeper understanding of the fundamental mechanisms driving tissue evolution during in…

In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may…

When they are damaged or injured, soft biological tissues are able to self-repair and heal. Mechanics is critical during the healing process, as the damaged extracellular matrix (ECM) tends to be replaced with a new undamaged ECM supporting…

An important aspect of astrophysical MHD turbulence research is developing diagnostics to connect simulations with the observable universe. Turbulent systems are by definition structurally complex in all fluid variables (density, velocity,…

We present a hydrodynamic theory to describe shear flows in developing epithelial tissues. We introduce hydrodynamic fields corresponding to state properties of constituent cells as well as a contribution to overall tissue shear flow due to…