This is a very good question regarding the anatomy of the ICA. I would only add to the previously posted expert answer that looking at the structure/function correlate of the ICA, my thinking is to understand the ICA once it passes through the foramen lacerum into the brain.
This final distal route of the ICA is its communicating segment that becomes the posterior communicating arteries and then dividing into the anterior and middle cerebral arteries.
The middle cerebral arteries (MCA) supply most of the lateral surface of the cerebral hemispheres, except the medial/superior contours of the frontal lobe and superior contour of the anterior parietal lobe which are supplied by the anterior cerebral artery (ACA) and the inferior contour of the temporal/occipital lobes supplied by the posterior cerebral artery (PCA).
Study of the ACA is significantly relevant for understanding saccular and dissecting aneurysms, called berry aneurysms (BA). The important anatomical correlate here is the anterior communicating artery that connects the two ACAs. This communicating artery is relatively small and permits collateral blood flow into the contralateral hemisphere if the ICA is occluded or stenotic on either side. Because this is a collateral communicating and connecting artery, it is also not uncommon for arteriovenous malformations (AVM) to occur.
The clinical significance of BA/AVM of the anterior communicating artery where it joins the ACA is quite important in the construct sequelae of cerebral ischemic and/or thrombotic events in stroke, presenting as a lightning bolt headache, visual disturbances, unilateral facial paresthesia/weakness, loss of balance, difficulty speaking, and memory problems.
-jq