A nonlinear two-degree-of-freedom mass–damper–spring model to predict the isolation of circulating tumor cells in microfluidic-elasto-filtration devices

Circulating tumor cell (CTC) isolation has made positive impacts on metastatic detection and therapy analysis for cancer patients. Microfluidic-elasto-filtration (MEF) device based on the critical elasto-capillary number (Ca_e^*) has been proposed to utilize the optimal multi-parameter conditions, including cell diameter (d_c), the diameter of cylindrical filter pores (d_p), nonlinear cell elasticity and hydrodynamic drag force, for selectively capturing CTCs and depleting white blood cells (WBCs). In this paper, we propose a novel two-degree-of-freedom nonlinear mass–damper–spring (m–c–k) model to predict the dynamic behaviors of CTCs and WBCs in a generic MEF device. This model enables the optimization of the device design to achieve extremely high CTC capture efficiency and WBC depletion efficiency. In particular, the function of nonlinear cell stiffness specific to different cell types and MEF’s pore diameters is first determined by finite element method with neo-Hookean hyperelastic model, based on which the mechanical behaviors of CTCs and WBCs in MEF devices are systematically studied. Herein, the predicted normalized deformations of a CTC and WBC as a function of Ca_e are used to determine the optimized Ca_e of 0.043, consistent with the experimental results from the fabricated MEF devices using MCF-7 cells (0.04 ± 0.006). In addition, the normalized cell diameter versus Ca_e phase diagram is proposed for the first time as a useful tool for design optimization of MEF devices and other microfiltration devices.