Which branch is not associated with the hepatic artery?

The left gastric artery is not associated with the hepatic artery because it primarily supplies blood to the stomach rather than the liver. The left gastric artery arises from the celiac trunk, which is the major arterial supply for the stomach and the proximal part of the duodenum.

In contrast, the right gastric artery, the gastroduodenal artery, and the right gastroepiploic artery are all branches that have a direct relationship with the hepatic artery or are associated with the vascular supply to organs that receive blood from the hepatic artery. The right gastric artery also originates from the hepatic artery and supplies the lesser curvature of the stomach. The gastroduodenal artery branches from the common hepatic artery and supplies both the stomach and part of the duodenum, while the right gastroepiploic artery branches off from the gastroduodenal artery and supplies the greater curvature of the stomach.

Therefore, understanding the anatomy and origins of these arteries clarifies why the left gastric artery stands apart as it does not directly relate to the hepatic artery's branches.