Question

What is the purpose of the highlighted vessels? what is the purpose of the highlighted vessels? to drain fluid from the tissues of the lower limb back towards blood vessels near the heart to bring oxygenated blood out to the muscles of the lower limb to provide somatic sensory innervation to the muscles of the thigh to return deoxygenated blood from the lower limb to the heart?

Answer 1

The purpose of the highlighted vessels is to drain fluid from the tissues of the lower limb back towards the blood vessels near the heart.

The lymphatic system is referred to as the circulatory system for lymphatic fluid which comprises of the network of conduits which are called lymphatic vessels which carry the fluid in one direction towards the heart.
Some of its function is too fascinating plasma and they are most densely distributed near the lymph nodes.