A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells

Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical model and a finite element formulation are proposed for the simulation of adhesive contact interactions between myocytes across the so-called gap junctions. A multi-field interface constitutive law is proposed for their description, integrating the adhesive and contact mechanical response with their electrophysiological behavior. From the computational point of view, the initial and boundary value problem is formulated as a structure-structure interaction problem, which leads to a straightforward implementation amenable for parallel computations. Numerical tests are conducted on different couples of myocytes, characterized by different shapes related to their stages of growth, capturing the experimental response. The proposed framework is expected to have impact on the understanding how imperfect mechano-transduction could lead to emergent pathological responses.Comment: 31 pages, 17 figure

Simulation of cell movement through evolving environment: a fictitious domain approach

A numerical method for simulating the movement of unicellular organisms which respond to chemical signals is presented. Cells are modelled as objects of finite size while the extracellular space is described by reaction-diffusion partial differential equations. This modular simulation allows the implementation of different models at the different scales encountered in cell biology and couples them in one single framework. The global computational cost is contained thanks to the use of the fictitious domain method for finite elements, allowing the efficient solve of partial differential equations in moving domains. Finally, a mixed formulation is adopted in order to better monitor the flux of chemicals, specifically at the interface between the cells and the extracellular domain

Individual and collective dynamics of self-propelled soft particles

Deformable self-propelled particles provide us with one of the most important nonlinear dissipative systems, which are related, for example, to the motion of microorganisms. It is emphasized that this is a subject of localized objects in non-equilibrium open systems. We introduce a coupled set of ordinary differential equations to study various dynamics of individual soft particles due to the nonlinear couplings between migration, spinning and deformation. By introducing interactions among the particles, the collective dynamics and its collapse are also investigated by changing the particle density and the interaction strength. We stress that assemblies of self-propelled particles also exhibit a variety of non-equilibrium localized patterns

Haptic Rendering of Interacting Dynamic Deformable Objects Simulated in Real-Time at Different Frequencies

International audienceThe dynamic response of deformable bodies varies significantly in dependence on mechanical properties of the objects: while the dynamics of a stiff and light object (e. g. wire or needle) involves high-frequency phenomena such as vibrations, much lower frequencies are sufficient for capturing dynamic response of an object composed of a soft tissue. Yet, when simulating mechanical interactions between soft and stiff deformable models, a single time-step is usually employed to compute the time integration of dynamics of both objects. However, this can be a serious issue when haptic rendering of complex scenes composed of various bodies is considered. In this paper, we present a novel method allowing for dynamic simulation of a scene composed of colliding objects modelled at different frequencies: typically, the dynamics of soft objects are calculated at frequency about 50 Hz, while the dynamics of stiff object is modeled at 1 kHz, being directly connected to the computation of haptic force feedback. The collision response is performed at both low and high frequencies employing data structures which describe the actual constraints and are shared between the high and low frequency loops. During the simulation, the realistic behaviour of the objects according to the mechanical principles (such as non-interpenetration and action-reaction principle) is guaranteed. Examples showing the scenes involving different bodies in interaction are given, demonstrating the benefits of the proposed method