I have a "mild" case of spinal cord compression from disc herniation at C4/5 in my neck. This diagnosis certainly isn't based on my symptoms, which are very severe. What does it mean?

When the disc bulges backwards, it can put pressure on the spinal cord in the cervical and thoracic spines. In the low back or lumbar spine, the disc is more likely to press against a spinal nerve as the nerve leaves the spinal cord and travels down the back or
leg.

Cord compression is seen using magnetic resonance imaging (MRI). Mild cord compression means there is an indentation into the space where the spinal cord is housed.
The spinal cord itself isn't touched yet.

In moderate encroachment the cord is being pressed by the disc, but there's no obvious deformity of the spinal cord. A severe indentation leaves a lasting dent in the spinal cord and may even cause the cord to twist or buckle.

Several things can cause changes of this type. It isn't always just a protruding or herniated disc. There are ligaments in the spine that can come in contact with the spinal cord. Hardening or buckling of the ligament can cause mild to severe pressure on the
spinal cord in the neck, too.

It's long been reported that severe changes seen on MRI don't always cause symptoms, whereas a mild change can cause severe symptoms. Doctors don't know yet why this happens.
That's how you can have a mild case of spinal cord compression with severe symptoms.

Reference: 

Vaijayantee Kulkarni, MCh (Neuro), et al. Accelerated Spondylotic Changes Adjacent to the Fused Segment Following Central Cervical Corpectomy: Magnetic Resonance Imaging Study Evidence. In Journal of Neurosurgery: Spine. January 2004. Vol. 100. No. 1. Pp. 2-6.

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