The ascending cervical artery is a small branch which arises from the inferior thyroid artery

Inferior thyroid artery

The inferior thyroid artery arrises from the thyrocervical trunk and passes upward, in front of the vertebral artery and Longus colli, then turns medially behind the carotid sheath and its contents, and also behind the sympathetic trunk, the middle cervical ganglion resting upon the...

 as that vessel is passing behind the carotid sheath

Carotid sheath

The carotid sheath is an anatomical term for the fibrous connective tissue that surrounds the vascular compartment of the neck. It is part of the deep cervical fascia of the neck, below the superficial cervical fascia meaning the subcutaneous adipose tissue immediately beneath the skin.The deep...

; it runs up on the anterior tubercles of the transverse processes of the cervical vertebræ in the interval between the Scalenus anterior

Scalenus anterior

The Scalenus anterior , also known as anterior scalene muscle, lies deeply at the side of the neck, behind the Sternocleidomastoideus.-Anatomy:...

 and Longus capitis.

To the muscles of the neck it gives twigs which anastomose with branches of the vertebral, and it sends one or two spinal branches into the vertebral canal through the intervertebral foramina to be distributed to the medulla spinalis and its membranes, and to the bodies of the vertebræ, in the same manner as the spinal branches from the vertebral.

It anastomoses with the ascending pharyngeal and occipital

Occipital artery

The occipital artery arises from the external carotid artery opposite the facial artery, its path is below the posterior belly of digastric to the occipital region. This artery supplies blood to the back of the scalp and sterno-mastoid muscles...

arteries.