On the design and fabrication of nanoliter-volume hanging drop networks

Hanging drop cultures provide a favorable environment for the gentle, gel-free formation of highly uniform three-dimensional cell cultures often used in drug screening applications. Initial cell numbers can be limited, as with primary cells provided by minimally invasive biopsies. Therefore, it can be beneficial to divide cells into miniaturized arrays of hanging drops to supply a larger number of samples. Here, we present a framework for the miniaturization of hanging drop networks to nanoliter volumes. The principles of a single hanging drop are described and used to construct the fundamental equations for a microfluidic system composed of multiple connected drops. Constitutive equations for the hanging drop as a nonlinear capacitive element are derived for application in the electronic-hydraulic analogy, forming the basis for more complex, time-dependent numerical modeling of hanging drop networks. This is supplemented by traditional computational fluid dynamics simulation to provide further information about flow conditions within the wells. A fabrication protocol is presented and demonstrated for creating transparent, microscale arrays of pinned hanging drops. A custom interface, pressure-based fluidic system, and environmental chamber have been developed to support the device. Finally, fluid flow on the chip is demonstrated to align with expected behavior based on the principles derived for hanging drop networks. Challenges with the system and potential areas for improvement are discussed. This paper expands on the limited body of hanging drop network literature and provides a framework for designing, fabricating, and operating these systems at the microscale.