Robust and Efficient Cell-Based Models of Tissue Mechanics

Mathias, S. 2022. Robust and Efficient Cell-Based Models of Tissue Mechanics. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 2164. 76 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-1544-7. Cell-based models of tissue mechanics have become an important tool in cancer research and developmental biology. Complementary to wet-lab experiments, they allow for cost-efficient in-silico evaluation of mechanisms not easily probed in the lab. However, if these models are to be useful for understanding how complex tissues are formed, their simulation needs to be numerically efficient in order to scale to realistic problem sizes. Moreover, the simulation behavior needs to be robust with respect to numerical parameter settings and modelers need to be aware of how different modeling choices can affect model conclusions. In this thesis we address the above issues for the center-based model, a type of off-lattice cellbased model. For a population of cells, the center-based model represents each cell individually as a point mass interacting mechanically with its neighbors. Cell shape is approximated using simple spheres that potentially overlap, for example after cell division. Cells eliminate overlap by pushing on each other. The resulting cell movement is governed by a system of ordinary differential equations which are solved numerically. In Paper I, we study how different combinations of the pairwise interaction force with first and second-order numerical solvers affect the numerical efficiency of the simulation. We illustrate the importance of resolving daughter cell trajectories after division in a both numerically stable and physically correct manner to prevent geometrical differences at the population level. In Paper II, we eliminate the need for manual determination of a suitable time step size by considering adaptive time stepping methods. In these methods, the time step is chosen dynamically to satisfy a pre-defined error threshold on the accuracy of the cell positions, thereby significantly increasing simulation efficiency. There exist several open-source implementations of center-based models aimed at different biological applications. These are feature-rich software in which numerical components typically are not exposed to the user. In Paper III, we present CBMOS, a Python package focusing on facilitating the numerical study of center-based models through a flexible and easily accessible interface. Moreover, CBMOS allows to transfer the computionally most expensive parts of the simulation to a graphics processing unit, if available. In Paper IV, we apply the center-based model to the process of cartilage formation during embryonic development. We perform an in-silico study to evaluate how the geometrical arrangement of the initial ancestor population and the orientation of cell division affect the observed shape of clonal columns in sheet-like cartilage. To conclude, this thesis contributes to making center-based models more efficient and robust, as well as providing modelers with tools to better understand the impact of numerical parameters on model predictions. Additionally, we demonstrate the utility of center-based models in biological research at the example of cartilage morphogenesis.