Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

Abstract

In this paper we present an overview of agentbased models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations, and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent-based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings, and capabilities of the major agent-based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center-based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results.

Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles

“…(1) describe damping mechanisms related to the friction forces resulting from the contact of cell i with, respectively, the substrate and the other individuals, as λ cs i and λ cc i j are the corresponding coefficients (which may be, for instance, constant parameters in common for all cells ( Costanzo et al, 2015 ) or time-dependent individuallyspecific tensors ( Liedekerke et al, 2015 )). These contributions have the effect to slow down individual movement and eventually to increase the characteristic time scale of the overall cell collective patterning.…”

“…On the right hand side, F i instead denotes the sum of all forces influencing cell behavior. However, in order to simplify the picture, we can first notice that cells move in extremely viscous environments, characterized by very small Reynolds numbers: inertial effects in cell dynamics can therefore be neglected, if a sufficiently large observation time is considered ( Liedekerke et al, 2015;Odell et al, 1981 ). In fact, in these conditions, biological cells can maintain a persistent ballistic locomotion only for a substantially small time, giving rise to straight displacements shorter than their typical dimensions.…”

Model Prediction and Validation of an Order Mechanism Controlling the Spatiotemporal Phenotype of Early Hepatocellular Carcinoma

“…Here, F C X ij denotes the interaction force between a cell i and object j (X denotes an object which can be a cell or a piece of the sinusoid, see A-8), u ij the normal vector pointing from cell i to object j, A ij the interface between cell i and object j. An extension to tensors able to measure shear contributions is straightforward but not needed here (Liedekerke et al 2015). Table 1).…”

“…There is in the meanwhile a wide range of different single-cell-based models both on lattices and in lattice-free space. The pros and cons of different types of agentbased models have been discussed in-depth in Liedekerke et al (2015). Simulations with single-cell-based models can be considered as experiments in silico, i.e., on the were used, which had been constructed based on the following pipeline: (a) A stack of confocal laser scanning micrographs were transformed by image processing into a full 3D volume data set.…”

Theoretical approaches to understanding root vascular patterning: a consensus between recent models

“…In general, vertex-based and Cellular Potts models have similar capabilities in a static setting; the major differences emerge when they are used to model cellular growth. This discussion is not within the scope of this paper and is covered in detail elsewhere (Prusinkiewicz and Runions, 2012;Liedekerke et al, 2015).…”