This section is from the book "Anatomy Of The Arteries Of The Human Body", by John Hatch Power. Also available from Amazon: Anatomy of the Arteries of the Human Body, with the Descriptive Anatomy of the Heart.
The Cervicalis Profunda Artery is a small but constant branch which passes backwards through the brachial plexus, and between the transverse process of the seventh cervical vertebra and the first rib :* it is situated underneath the last cervical nerve, and separates this nerve from the neck of the first rib. It then ascends on the back of the neck, in the groove between the spinous and transverse process of the cervical vertebrae, lying on the spino-transverse muscle and covered by the great complexus. It supplies the deep-seated muscles on the back of the neck, and anastomoses with the vertebral and descending cervical of the occipital arteries.
* When there is a cervical rib, it passes between this rib and the first dorsal.