Related papers: Simulation of morphogen and tissue dynamics
Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…
The organization of cells within tissues plays a vital role in various biological processes, including development and morphogenesis. As a result, understanding how cells self-organize in tissues has been an active area of research. In our…
Evolution and development operate at different timescales; generations for the one, a lifetime for the other. These two processes, the basis of much of life on earth, interact in many non-trivial ways, but their temporal hierarchy --…
Epigenetic Tracking is a mathematical model of biological cells, originally conceived to study embryonic development. Computer simulations proved the capacity of the model to generate complex 3-dimensional cellular structures, and the…
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…
We present a topology grounded, multiscale simulation platform for morphogenesis and biological active matter. Morphogenesis and biological active matter represent keystone problems in biology with additional, far-reaching implications…
During the development of an organism, cells must coordinate and organize to generate the correct shape, structure, and spatial patterns of tissues and organs, a process known as morphogenesis. The morphogenesis of embryonic tissues is…
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte…
The inverse geometric approach to the modeling of the growth of circular objects revealing required features, such as the velocity of the growth and fractal behavior of their contours, is presented. It enables to reproduce some of the…
We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which combines cell proliferation and cell differentiation. We derive a hydrodynamic limit when the number of…
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…
A two-dimensional mathematical model for dynamics of endothelial cells in angiogenesis is investigated. Angiogenesis is a morphogenic process in which new blood vessels emerge from an existing vascular network. Recently a one-dimensional…
During development, epithelial tissues undergo extensive morphogenesis based on coordinated changes of cell shape and position over time. Continuum mechanics describes tissue mechanical state and shape changes in terms of strain and stress.…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of…
Following the ideas of L.N.Gumilev, we introduce the mathematical model of ethnogenesis which describes the dynamics of subgroups in the developing polity in terms of ordinary differential equations. The bust dynamics associated with the…
This paper is placed at the intersection-point between the study of theoretical computational models aimed at capturing the essence of genetic regulatory networks and the field of Artificial Embryology (or Computational Development). A…
The aim of this paper is to provide a mathematical model for spatial distribution of membrane electrical potential changes by fluorescence diffuse optical tomography. We derive the resolving power of the imaging method in the presence of…
Urban morphogenesis is the process of formation of its elements and the specialization of its suburbs. Street networks are the structural part of the system. Understand their formation reveals crucial information about urban transformation…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…