An endovascular microvalve device for use in a vessel during a therapy procedure includes an outer catheter, an inner catheter displaceable within the outer catheter, and a filter valve coupled to the distal ends of the inner and outer catheters. The valve is constructed of a braid of elongate first filaments coupled together at their proximal ends in a manner that the first filaments are movable relative to each other along their lengths. A filter is provided to the braid formed by electrostatically depositing or spinning polymeric second filaments onto the braided first filaments. The lumen of the inner catheter delivers a therapeutic agent beyond the valve. The device is used to provide a therapy in which a therapeutic agent is infused into an organ.