a. brachial artery
b. radial artery
c. ulnar artery
d. profunda brachial artery
e. common carotid artery
f. digital arteries
g. all of the pulses noted above would be absent
h. all of the pulses except "e" would be absent
As in problems involving peripheral nerves, when dealing with lesions of the peripheral vascular system it's useful to apply a proximal-to-distal or upstream-downstream logic. Of course if you are concerned about a venous problem the inverse (distal-to-proximal flow) would be true. The rule would be that: structures distal to the site of the occlusion will suffer diminised or absent vascular supply depending on the extent of involvement of the vessel. Alternately, vascular supply to structures proximal to the site of the lesion will not be affected.
In this problem the arterial occlusion involves the axillary artery in the axilla. The head of the humerus is compressing the vessel. While a number of glenohumeral joint dislocations are described there are two basic patterns: anterior and posterior subluxations or dislocations. The anterior dislocations, which are clincially more common, present less often with nerve or vessel involvement. When the humeral head subluxes anteriorly there are no vessels nor nerves which could be impinged. On the other hand, posterior dislocations (less common) often manifest as neurovascular impingement. The acromium process and subacromial structures offer a block or restraint to the backwardly moving humeral head. When dislocation occurrs the humeral head frequently ends up resting on the axillary artery and/or the posterior cord of the brachial plexus.
In this case all of the vessels cited in choices "a" through "d" are located distal to the site of vessel impingement and therefore (assuming a complete lesion) would not fill with blood. In checking any one of these vessels one would not find a pulse (i.e., pulse obliterated). In the case of the common carotid artery - choice "e", this vessel derives from the brachiocephalic trunk on the right side and directly from the aortic arch on the left side and proximal to the site of the axillary artery's comrpession. As such, this vessel would continue to fill with blood and therefore checking the pulse adjacent to the larynx or along the side of the head (temporal branch of the external carotid artery) would yield a normal finding.