Related papers: A Growth Model for Multicellular Tumor Spheroids
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…
Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are…
How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links…
Most conspicuous organisms are multicellular and most multicellular organisms develop somatic cells to perform specific, non-reproductive tasks. The ubiquity of this division of labor suggests that it is highly advantageous. In this paper,…
This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn-Hilliard-Keller-Segel tumor growth model, which incorporates complex biological processes such as species diffusion, chemotaxis,…
We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…
Monod's model describes the growth of microorganisms using a hyperbolic function of extracellular resource concentration. Under fluctuating or limited resource concentrations this model performs poorly against experimental data, motivating…
Growth drives cellular dynamics in dense aggregates including bacterial colonies, developing tissues, and tumors. We investigate the underlying physical principles emerging from the interplay of growth, steric repulsion, and motility in a…
This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et…
A general simple theory for the interspecific allometric scaling is developed in the $d+1$-dimensional space ($d$ biological lengths and a physiological time) of metabolic states of organisms. It is assumed that natural selection shaped the…
Bacteria are highly adaptive microorganisms that thrive in a wide range of growth conditions via changes in cell morphologies and macromolecular composition. How bacterial morphologies are regulated in diverse environmental conditions is a…
In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint…
We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…
Simple ideas, endowed from the mathematical theory of control, are used in order to analyze in general grounds the human immune system. The general principles are minimization of the pathogen load and economy of resources. They should…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving the…
Living systems continuously transform matter and energy through the chemical processes that constitute their metabolism. The overall metabolic rate of an organism correlates positively with its body mass, however both the exact scaling…
Tissue self-organization into defined and well-controlled three-dimensional structures is essential during development for the generation of organs. A similar, but highly deranged process might also occur during the aberrant growth of…