Visualization of spatial patterns of cells using a 3-D simulation model for multicellular tissue growth

Abstract

In this paper, we apply a previously developed computational model for the growth of multicellular tissues using a discrete approach based on cellular automata to simulate the tissue growth rates and visualize the spatial patterns of three populations of proliferating and migrating cells. We use the obtained 3-D time-varying data to visualize the generated spatial patterns of the simulated grown tissue. We then briefly compare the tissue growth rates for two seeding modes, mixed and segmented, using a uniform cell distribution. Slow, moderate, and fast moving cells are utilized with each cell population having its own division characteristics. Our visualization results show that the placement of fast cells may impact not only the tissue growth rate but also the spatial characteristics of the grown tissue pattern. The developed computational model contains a number of system parameters that allow us to explore their effects on many other aspects of cell behavior as well as to study the temporal dynamics of such a complex system.

Computationally modelling cell proliferation: A review

“…As previously mentioned, mathematical models are used to describe real problems through mathematics, which allows to validate hypotheses and to make predictions 20 . They swiftly allow to test and compare hypotheses and choose the most promising ones for laboratory research, which speeds up the scientific progress 17,19 …”

“…To obtain them, the use and progress in computing are indispensable 20 . The advances in computer power and 3D modelling software promote a continuous evolution of such mathematical models, allowing them to be more complex and realistic and capable to incorporate more data 19 . Today, the available computational efficiency allows to develop models crossing distinct spatial–temporal scales and complex discretization approaches, which can be selected to describe the problem under analysis, with regards to the focus of the study 18 …”

“…Despite the fact that mathematical methods are a powerful tool that allows for a better understanding of the cell cycle, they depend on a large number of factors such as the type of cells or the species involved, which makes it difficult to find the mathematical law of the model 19,25 …”

“…The study of other biological problems such as tumour growth, tissue regeneration, embryogenesis and wound healing can also benefit from cell proliferation models, in fact, several studies have been reported using these types of models 44 . In the literature, numerous models concerning these problems can be found 19,31,45–51 …”

“…In this model, the division of a cell occurs if an empty space in the vicinity of a cell exists and the new cells acquire new parameters, based on the cell population that gave rise to them. Their positions are chosen according to a random algorithm 19 …”