Related papers: Study on Multicellular Systems Using a Phase Field…
We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe…
Coupled natural systems are generally modeled at multiple abstraction levels. Both structural scale and behavioral complexity of these models are determinants in the kinds of questions that can be posed and answered. As scale and complexity…
It is demonstrated that the description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach previously used in the literature is shown to…
We present a continuum model trained on molecular dynamics (MD) simulations for cellular membranes composed of an arbitrary number of lipid types. The model is constructed within the formalism of dynamic density functional theory and can be…
During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology that defines how living organisms form. Establishing tissue-level morphology critically relies on how…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
We simulate the electrical response of multiple disjoint biological 3D cells undergoing an electropermeabilization process. Instead of solving the boundary value problem in the unbounded volume, we reduce it to a system of boundary…
In this work, we study the adhesion of multi-component vesicle membrane to both flat and curved substrates, based on the conventional Helfrich bending energy for multi-component vesicles and adhesion potentials of different forms. A phase…
While analyzing mobile systems we often approximate the actual coverage surface and assume an ideal cell shape. In a multi-cellular network, because of its tessellating nature, a hexagon is more preferred than a circular geometry. Despite…
To model mechanically-driven phase transformations using the phase-field theory, suitable models are needed for describing the mechanical fields related to individual phase-fields in the interfacial regions. They play a crucial role in…
We present a multiphase mathematical model for tumor growth which incorporates the remodeling of the extracellular matrix and describes the formation of fibrotic tissue by tumor cells. We also detail a full qualitative analysis of the…
We consider the shape optimization of flow fields for electrochemical cells. Our goal is to improve the cell by modifying the shape of its flow field. To do so, we introduce simulation models of the flow field with and without the porous…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
Cellular signaling is essential in information processing and decision making. Therefore, a variety of experimental approaches have been developed to study signaling on bulk and single-cell level. Single-cell measurements of signaling…
We review theoretical results for the adhesion-induced phase behavior of biomembranes. The focus is on models in which the membranes are represented as discretized elastic sheets with embedded adhesion molecules. We present several…
Microphase separation of membrane components is thought to play an important role in many physiological processes, from cell signaling to endocytosis and cellular trafficking. Here, we study how variations in the membrane composition can be…
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…
Over the last two decades, scientific literature has been blooming with various means of simulating epithelial cell colonies. Each of these simulations can be separated by their respective efficiency (expressed in terms of consumed…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
We consider a family of multi-phase Stefan problems for a certain 1-d model of cell-to-cell adhesion and diffusion, which takes the form of a nonlinear forward-backward parabolic equation. In each material phase the cell density stays…