DeepAI AI Chat
Log In Sign Up

A surface finite element method for computational modelling of cell blebbing

03/02/2020
by   Björn Stinner, et al.
University of Warwick
0

Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of blebbing in terms of a force balance. It is abstract and flexible in that it allows for amending force contributions related to membrane tension or the presence of linker molecules between membrane and cell cortex. The deforming membrane and all forces are expressed by means of a parametrisation over a stationary reference surface. A variational formulation is presented and analysed for well-posedness. For this purpose, we derive a semi-discrete scheme based on the surface finite element method. We provide a convergence result and estimates of the error due to the spatial discretisation. Furthermore, we present a computational framework where specific models can be implemented and later on conveniently amended if desired, using a domain specific language implemented in Python. While the high level program control can be done within the Python scripting environment, the actual computationally expensive step of evolving the solution over time is carried out by binding to an efficient software backend. Cell membrane geometries given in terms of a parametrisation or obtained from image data can be accounted for. A couple of numerical simulation results illustrate the approach.

READ FULL TEXT
02/06/2020

An Object-Oriented Library for Heat Transfer Modelling and Simulation in Open Cell Foams

Metallic open cell foams have multiple applications in industry, e. g. a...
11/05/2020

Analysis of finite element methods for surface vector-Laplace eigenproblems

In this paper we study finite element discretizations of a surface vecto...
06/12/2021

Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap

We investigate the convergence of the Crouzeix-Raviart finite element me...
07/20/2021

Finite Element Method for Solution of Credit Rating Migration Problem Model

In this paper, we propose a finite element method to study the problem o...
06/23/2022

Predicting Fracture in the Proximal Humerus using Phase Field Models

Proximal humerus impacted fractures are of clinical concern in the elder...