Diplopia is the medical term for double vision. In multiple sclerosis, it is usually caused by lesions in the brainstem where the cranial nerves serving the eye muscles arise.
Sixth (or abducens) nerve palsy is the most common in MS and affects the nerve which operates lateral rectus muscle which pulls the eye outwards. Sixth nerve palsy causes double vision when looking from side to side. It is usually unilateral which means that the double vision occurs only when looking to one side and not to the other.
Third (or oculomotor) nerve palsy is much rarer than 6th in MS and it's not really understood why. The third cranial nerve supplies four muscles to each eye; the medial rectus (pulls the eye inwards), the superior and inferior rectus (which pull the eye up and down and tend to turn the eye inwards), and the inferior oblique.
The forth (or trochlear) nerve controls the one muscle, the superior oblique, which moves the eye down and out. Forth nerve palsy is often associated with vertical diplopia.
All three of these cranial nerves arise in the brainstem - the third and forth in the midbrain and the sixth in the pons (a favoured site for MS). Lesions to these areas will often show up in MRI scans and your neuro can often pinpoint the actual lesion that is causing the problem on the image.
A related paralysis, called internuclear ophthalmoplegia, sometimes, but not always, leads to double vision. What usually happens is that the outward-looking eye fails to move outwards. This can occur in the absence of paralysis of the sixth nerve. It is due to a lesion of the medial longitudinal bundle, which is also commonly affected by MS.
Treatment often involves wearing a patch or press-on prisms for spectacles which can help eliminate the double vision. Steroids are often used to treat diplopia associated with relapsing-remitting MS but they have been shown to only affect the rate and not the amount of recovery.
Yale- Cranial Nerve 6, pg. 1
Yale- Cranial Nerve 3, pg. 1
Yale- Cranial Nerve 4, pg. 1
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