Circulating tumor cells (CTCs) in blood stream have known to have cancer seeding effects and cause cancer metastases. Detection of CTCs plays an important role in early cancer diagnosis and treatment monitoring. A new technique of using microfluidic devices for CTC detection (CTC-chips) provides a promising solution. Among various CTC-chip designs, label-free chips based on cell size and deformability have the advantages of structural simplicity, stable performance, low cost and ease of use. In deformation-based CTC-chips, the threshold pressure required to pass CTCs through the chips is a key parameter of informing the CTC filtering capability and device sensitivity. Most existing models for the threshold pressure in deformation-based CTC-chips are based on quasi-static Young-Laplace surface tension model. However, for modeling high throughput CTC-chips, dynamic terms such as pressure drop in the surrounding flow should be taken into consideration. In the present work, we consider liquid-liquid (cell-medium) interfacial tension along with the effect of fluid flow in the threshold pressure prediction, and propose a second order relationship between the threshold pressure and the reciprocal of hydraulic diameter of the filter channel. Based on the new equation, the effect of parameters such as surface tension coefficient, viscosity, velocity and channel roundness are studied. This predicative model can be a valuable tool to aid future design of high throughput CTC-chips.

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