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Blood flow presents several interesting phenomena in microcirculation that can be used to develop microfluidic devices capable to promote blood cells separation and analysis in continuous flow. In the last decade there have been numerous microfluidic studies focused on the deformation of red blood cells (RBCs) flowing through geometries mimicking microvessels. In contrast, studies focusing on the deformation of white blood cells (WBCs) are scarce despite this phenomenon often happens in the microcirculation. In this work, we present a novel integrative microfluidic device able to perform continuous separation of a desired amount of blood cells, without clogging or jamming, and at the same time, capable to assess the deformation index (DI) of both WBCs and RBCs. To determine the DI of both WBCs and RBCs, a hyperbolic converging microchannel was used, as well as a suitable image analysis technique to measure the DIs of these blood cells along the regions of interest. The results show that the WBCs have a much lower deformability than RBCs when subjected to the same in vitro flow conditions, which is directly related to their cytoskeleton and nucleus contents. The proposed strategy can be easily transformed into a simple and inexpensive diagnostic microfluidic system to simultaneously separate and assess blood cells deformability.