Advances in microfluidics inaugurate a new possibility of designing diagnostic devices for early cancer detection. There is a growing interest in deformation-based microfiltration for capturing circulating tumor cells (CTCs) from peripheral blood due to its simplicity and low cost. Fundamental understanding of CTC passing through a microfilter is critical, as it helps optimize the design for achieving high isolation purity. Previous research has modeled CTC as a simple droplet for deformation-based CTC separation. Here, we use a compound droplet model to study the flow dynamics more realistically. An adaptive-mesh-refinement (AMR) method is used here, using the open-source code, gerris, after modification for droplet dynamics and contact angle model. The developed code is validated with results compared with ansysfluent and available theory. The effects of various parameters such as the nuclear-to-cytoplasmic (N/C) ratio, operating flow rate, and cell viscosity are investigated. It is found that the compound droplet behaves like a homogeneous droplet when the nucleus size is smaller than the filtering channel. However, the pressure profile is greatly influenced by the nucleus when it is larger than the channel size. In addition, there is a linear correlation between the pressure drop in the channel and the operating flow rate. Similarly, critical passing pressure increases linearly with the increase of the cell viscosity. Our study suggests that for having an accurate prediction of cell transport behavior inside the microchannel, it is of great importance to consider the effects of the nucleus and its possible deformation.