In order to inhibit thrombotic processes locally rather than systemically, higher levels of antithrombotic drugs in the deep veins of the legs than in the systemic circulation are obtained using devices and methods that provide venous cannulation in the dorsum of the foot of a patient while applying pressure to the foot proximal to the venous cannulation, potentially as far up the leg as the knee, in an amount sufficient to compress the superficial veins and divert the venous drainage in the deep venous system into the venous plexus.