Tumour-induced angiogenesis is a complex biological process that involves growth of new blood vessels within the tumour microenvironment and is an important target for cancer therapies. Significant efforts have been undertaken to develop theoretical models as well as in vitro experimental models to study angiogenesis in a highly controllable and accessible manner. Various mathematical models have been developed to study angiogenesis, but these have mostly been applied to in vivo assays. Recently, microfluidic cell culture systems have emerged as useful and powerful tools for studying cell migration and angiogenesis processes, but thus far, mathematical angiogenesis models have not yet been applied to microfluidic geometries. Integrating mathematical and computational modelling with microfluidic-based assays has potential to enable greater control over experimental parameters, provide new insights into fundamental angiogenesis processes and assist in accelerating design and optimization of operating conditions. Here, we describe the development and application of a combined mathematical and computational modelling approach tailored specifically for microfluidic cell culture systems. The objective was to allow optimization of the engineering design of microfluidic systems, where the model may be used to test the impact of various geometric parameters on cell migration and angiogenesis processes, and assist in identifying optimal device dimensions to achieve desired readouts. We employed two separate continuum mathematical models that treated cell density, vessel length density and vascular endothelial growth factor (VEGF) concentration as continuous average variables, and we implemented these models numerically using finite difference discretization and a Method of Lines approach. We examined the average response of cells to VEGF gradients inside our microfluidic device, including the time-dependent changes in cell density and vessel density, and how they were affected by changes in device geometries including the migration port width and length. Our study demonstrated that mathematical modelling can be integrated with microfluidics to offer new perspectives on emerging problems in biomicrofluidics and cancer biology.
Keywords: Angiogenesis; Chemotaxis; Computational modelling; Endothelial cells; Mathematical modelling; Migration; Vessel sprouting.