Modelling cell guidance and curvature control in evolving biological tissues

Abstract

Tissue geometry is an important influence on the evolution of many biological tissues. The local curvature of an evolving tissue induces tissue crowding or spreading, which leads to differential tissue growth rates, and to changes in cellular tension, which can influence cell behaviour. Here, we investigate how directed cell motion interacts with curvature control in evolving biological tissues. Directed cell motion is involved in the generation of angled tissue growth and anisotropic tissue material properties, such as tissue fibre orientation. We develop a new cell-based mathematical model of tissue growth that includes both curvature control and cell guidance mechanisms to investigate their interplay. The model is based on conservation principles applied to the density of tissue synthesising cells at or near the tissue's moving boundary. The resulting mathematical model is a partial differential equation for cell density on a moving boundary, which is solved numerically using a hybrid front-tracking method called the cell-based particle method. The inclusion of directed cell motion allows us to model new types of biological growth, where tangential cell motion is important for the evolution of the interface, or for the generation of anisotropic tissue properties. We illustrate such situations by applying the model to simulate both the resorption and infilling components of the bone remodelling process, and provide user-friendly MATLAB code to implement the algorithms.

Model-based data analysis of tissue growth in thin 3D printed scaffolds

“…These results highlight a potential value in designing an experiment to collect time-series observations, which will provide information about cell density and tissue coverage of each pore at multiple time points. This more detailed information will allow for the inclusion of more complicated mechanisms, such as directed migration through chemotaxis [43,62], mechanical effects at the tissue boundary [63,64], or the depletion of nutrients available to the cell population. At present, we find the complexity of the mathematical model is well suited to the level of information available in the experimental data, and we expect identifiability issues to arise if we were to interpret the current data with a more complex model.…”