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Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells,…
Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux…
For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
Aggregation and fragmentation of single molecules in the cell environment lead to a spectrum of diffusivities and to statistical laws of movement very different from typical Brownian motion. Current models of intracellular transport do not…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic…
Spheroids are aggregates of cells that can mimic the cellular organization often found in tissues. They are typically formed through the self-assembly of cells in a culture where there is a promotion of interactions and cell-to-cell…
Diffusive molecular communication (DMC) is envisioned as a promising approach to help realize healthcare applications within bounded biological environments. In this paper, a DMC system within a biological spherical environment is…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
Diffusion of molecules in cells plays an important role in providing a biological reaction on the surface by finding a target on the membrane surface. The water retardation (slow diffusion) near the target assists the searching molecules to…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…