Travelling wave and asymptotic analysis of a multiphase moving boundary model for engineered tissue growth

We derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy's law to relate the velocity of the cell and liquid phases to their respective pressures. Cell-cell and cell-scaffold interactions which can drive cellular motion are accounted for by utilising relevant constitutive assumptions for the pressure in the cell phase. We reduce the model to a nonlinear reaction-diffusion equation for the cell phase, coupled to a moving boundary condition for the tissue edge, the diffusivity being dependent on the cell and scaffold volume fractions, cell and liquid viscosities, and parameters that relate to cellular motion. Numerical simulations reveal that the reduced model admits three regimes for the evolution of the tissue edge at large-time: linear, logarithmic and stationary. Employing travelling wave and asymptotic analysis, we characterise these regimes in terms of parameters related to cellular production and motion. The results of our investigation allow us to suggest optimal values for the governing parameters, so as to stimulate tissue growth in an engineering scaffold.

Substrate-rigidity dependent migration of an idealized twitching bacterium

An analytical model reveals generic physical mechanisms for substrate-rigidity dependence of cellular motion. Key ingredients are a tight surface adhesion and forced adhesion rupture.

Motion Sensing Superpixels (MOSES): A systematic framework to quantify and discover cellular motion phenotypes

Cellular motion is fundamental in tissue development and homeostasis. There is strong interest in identifying factors that affect the interactions of cells in disease but analytical tools for robust and sensitive quantification in varying experimental conditions for large extended timelapse acquisitions is limited. We present Motion Sensing Superpixels (MOSES), a method to systematically capture diverse features of cellular dynamics. We quantify dynamic interactions between epithelial cell sheets using cell lines of the squamous and columnar epithelia in human normal esophagus, Barrett’s esophagus and esophageal adenocarcinoma and find unique boundary formation between squamous and columnar cells. MOSES also measured subtle changes in the boundary formation caused by external stimuli. The same conclusions of the 190 videos were arrived at unbiasedly with little prior knowledge using a visual motion map generated from unique MOSES motion ‘signatures’. MOSES is a versatile framework to measure, characterise and phenotype cellular interactions for high-content screens.