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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. [ABSTRACT FROM AUTHOR]

Ground Source Heat Pump (GSHP) systems, if improperly designed may lead to overheating or overcooling of the ground. Good designs ensure properly balanced energy storage through adequately sizing ground-loops. Hybrid systems combine conventional Heating, Ventilating, and Air Conditioning (HVAC) with GSHPs in order to significantly reduce the high installation costs of GSHPs. The hybrid systems are designed in such a way that GSHPs provide the base building energy demands while the conventional HVAC is used only during the peak hours. In general, all buildings can be divided into two main categories: cooling dominant and heating dominant. If a building is cooling dominant, ground temperature increases with time and in heating dominant cases it decreases. A severe ground temperature increase/decrease is referred to as ‘ground fouling’ because it can render the GSHP inoperable, as temperature differences are required to maintain controlled heat flow. This paper compares long-term operation of hybrid and non-hybrid GSHP systems in order to investigate the effectiveness of hybridization at alleviating ‘ground fouling’. A homespun 2D finite-volume model is proposed to study heat transfer in ground coupled heat pump systems and is verified against an analytical solution as well as experimental data. Through simulation of different building types, it is demonstrated that hybridization has potential to reduce ‘ground fouling’ but only in limited cases for which a large portion of the energy demands is being met by the conventional HVAC. [ABSTRACT FROM AUTHOR]