Numerical modeling of mechanically driven emergent behavior in biological systems

Bringing a mechanical modeling approach to biological systems offers a powerful lens through which to view challenges associated with scale, emergent behavior, and nonlinear material response. In this thesis, we present numerical methods and computational studies designed to elucidate mechanically driven emergent behavior in biological systems. Within this broad area, the first focus is multi-layer wrinkling. Wrinkling, when a thin stiff film adhered to a compliant substrate deforms sinusoidally out of plane due to compression, is a well understood phenomenon in bi-layer systems. However, when there are more than two layers, the wrinkling behavior of the multi-layer system is, at present, not fully understood. Here we provide an analytical solution for wrinkling in tri-layer systems where the additional layers can contribute to either the film stiffness or substrate stiffness. Then, we provide an algorithmic approach for extending this tri-layer analytical solution to systems with multiple additional layers. Our analytical solution and algorithmic approach are verified numerically using the finite element method. Using our methodology, wrinkling can be predicted and controlled in multi-layer systems, with applications ranging from buckling based metrology, to engineered device design, to organism morphogenesis. In particular, we show that a tri-layer model can predict surface wrinkling as a potential mechanism to explain anchoring center initiation and positioning in the developing cerebellum. This is important because cerebellar foliation has been extensively studied; yet, the mechanisms that control anchoring center initiation and position remain insufficiently understood. The proposed tri-layer wrinkling model provides insight into the hierarchical formation of anchoring centers and establishes an essential missing link between gene expression and evolution of shape. The second focus is creating numerical methods and implementing computational studies to understand the connection between unit cell operations and cell population behavior. This is motivated by a desire to better understand the mechanics of tumor growth and tumor response to intervention. In tumors, growth is driven primarily by a change in the number of cells. Tumor enlargement is driven by cell division, and tumor shrinkage is driven by cell death. Critically, analogous phenomena occur in many other biological systems, such as developing organisms and in vitro cell culture. Despite the prevalence of these phenomena, the connection between cell division and cell death on the microscale and the resulting population and tissue scale behavior is far from fully understood. Computational modeling is uniquely positioned to address this issue by connecting system behavior on multiple scales. Here we focus on our recently formulated computational framework for studying multiscale emergent behavior in stochastic biological systems. This framework is based on peridynamics, a theoretical and computational approach designed to unify the mechanics of discrete and continuous media. In this this thesis, we focus on specific examples where the interaction of algorithmic rules and mechanical behavior on the cellular level gives rise to phenomena that can be quantified on the population scale. Beyond these specific examples, the methods and results presented here are a starting point for significant future investigation toward understanding and predicting the mechanical behavior of biological systems across scales.

Advisor: Linder Christian (Engineering professor) 
Borja Ronaldo I. (Ronaldo Israel)
Kuhl Ellen