Final answer:
The deep branch of the radial nerve is responsible for innervating the extensor muscles of the forearm, not for supplying blood. For arterial supply, it is the radial artery that provides blood to the lateral forearm and hand, contributing to the superficial and deep palmar arches.
Step-by-step explanation:
The deep branch of the radial nerve is not directly responsible for supplying blood to any region. However, there seems to be some confusion in the question as it mixes information about nerve supply with details pertaining to arterial blood supply. In terms of nerve supply, the deep branch of the radial nerve innervates the extensor muscles of the forearm, which are responsible for extending the wrist and fingers. It also provides sensation to part of the hand and motor functions to some muscles at the back of the forearm.If the question was intended to refer to blood supply instead of nerve supply, the information provided is more relevant to arteries than nerves. For instance, the radial artery is the one that supplies blood to the lateral aspects of the forearm and hand.
The radial artery bifurcates from the brachial artery and, after giving off smaller branches in the carpal region, fuses with the ulnar artery to form the superficial and deep palmar arches, ultimately supplying blood to the lower arm, carpal region, and hand.The deep branch of the radial nerve supplies blood to the lower arm and carpal region. It is formed at the bifurcation of the brachial artery and parallels the ulna. It gives off smaller branches until it reaches the carpal region where it fuses with the radial artery to form the superficial and deep palmar arches.