Final answer:
A mid-shaft humerus fracture may injure the radial nerve and the brachial artery, both of which are important for the motor and sensory function of the lower arm and hand.
Step-by-step explanation:
A mid-shaft humerus fracture may injure the radial nerve. This nerve runs in close proximity to the mid-shaft of the humerus and is commonly associated with injuries in this area. The nerve is responsible for innervating the forearm muscles and is crucial for the motor and sensory function of the lower arm and hand. In terms of vascular injury, the brachial artery is the major blood vessel at risk of being compromised due to its location near the humerus. Damage to the brachial artery can lead to ischemia and lack of oxygen to the forearm muscles if compression occurs, potentially causing irreparable damage.