posterior interosseous artery
The posterior interosseous artery is one of the two terminal branches of the short common interosseous artery (from the ulnar artery). The artery courses deep in the proximal anterior compartment of the forearm to pierce the upper aspect of the interosseous membrane and enter the posterior compartment of the forearm. Here it gives off a recurrent branch, the interosseous recurrent artery that anastomoses proximally with the middle collateral artery (from the deep brachial artery), contributing to the arterial anastomosis of the elbow.
The posterior interosseous artery itself descends on the posterior surface of the interosseous membrane alongside the posterior interosseous nerve (from the radial nerve) between the supinator (superficially) and abductor pollicis longus (deeply) muscles, supplying both. In the distal forearm it terminates by anastomosing with a branch of the anterior interosseous artery having just pierced the interosseous membrane and together they contribute to the dorsal carpal arch.