Quantitative study on the influence of process design on the biophysical microenvironment in 3D cell cultures.

The mechanisms that biological cells exploit to organize themselves into multicellular aggregates and tissue-like structures are based on fundamental physical principles. Yet, the natural emergence of complexity in biological systems, while of great importance for many applications in biology and medicine, is still poorly understood. For this, mathematical models can be of great help by identifying key components and mechanisms that govern a system, and based on these, predict the inception of complex pattern formation. Individual cell-based models consider cells as distinct entities that interact with each other, and describe the dynamics and structure of multicellular systems by integrating an equation of motion. By doing so, they can help elucidate the interplay between mechanical forces, active cell behavior and the properties of cell aggregates.

In this dissertation, new developments and applications of individual cell-based models are presented. The central aim is to quantify the collective dynamics of cell aggregates, based on the mechanical properties of single cells, and the specific shape of intercellular forces. One of the predominant difficulties in individual cell-based modeling lies in properly taking into account cell shape. In order to address this, a novel methodology is established here for representing arbitrary cell shapes and modeling mechanical forces on the intercellular interface in great detail.

First, a general computational theory is introduced for accurately calculating contact forces between any two arbitrary shapes. For this, an expression for the contact pressure is integrated over the surface of an intersection polygon, to come up with net normal and tangential contact forces. When the shape is rounded, i.e. the radius of curvature varies smoothly between adjacent discretization points, a mechanistic contact model is obtained that can make use of shape independent material properties and a pressure formulation from classical Hertz theory. The usage of this new methodology is demonstrated in simulations at the macro scale of granular material using the Discrete Element Method. By implementing a pressure formulation from Maugis-Dugdale theory in order to model cell adhesion, and adding an approximate model for the mechanical behavior of the cytoskeleton, a deformable cell model is obtained. By performing simulations that use this model, the fundamental power laws governing initial cell spreading are analyzed. Finally, a coupling with computational fluid dynamics is realized by making use of the Immersed Boundary Method. Simulations of human periostium derived cells inside a bioreactor show the various mechanical effects of perfusion flow on cells cultured for Tissue Engineering purposes. In the future, individual cell-based models using these deformable cells can serve to relate detailed intercellular forces at the cell interface to multicellular organization.

In order to model the collective behavior of large cell numbers, more simple cell shapes are adopted, for which an explicit equation of motion is integrated. By adding a morphological description for cell division, a model is obtained that can be used to simulate proliferation in in vitro cell culture. It is shown that for cells growing on spherical microbeads, a sudden increase in mechanical stress is expected upon reaching confluence. Finally, simulations of large monolayer cultures of epithelial cells were performed in order to construct a diagram of physical phases. It is demonstrated that two cell properties are critical in governing phase behavior and the appearance of emergent complex structures: cell-cell contractile energy and the strength of contact inhibition of locomotion. The latter is shown to give rise to large-scale collective migration, as experimentally seen monolayer sheet expansion, and polarized structures with liquid-like behavior. By classifying multicellular structures in physical phases, the groundwork is provided of a structured framework for explaining the emergence of complex in vitro and in vivo tissue architectures.