Complications such as cavernous sinus thrombosis and Ludwig's angina can be life-threatening.
From the en.wikipedia.org
The major blood supply to the brain, the carotid artery, passes through the centre of the cavernous sinus, a pool of venous blood that links the jugular vein and the tissues of the face.
From the newscientist.com
The network weaves through the large cavernous sinus in their heads, so as blood is pumped through the arterial network, it loses heat to the cooler venous blood in the cavernous sinus.