Final answer:
Extraocular muscles are not directly innervated by the contralateral side of the brain, but eye movement coordination involves interhemispheric connections through pathways like the medial longitudinal fasciculus, which can be affected in conditions such as internuclear ophthalmoplegia.
Step-by-step explanation:
The extraocular muscles are innervated by three cranial nerves: the oculomotor, trochlear, and abducens nerves. None of these muscles are directly innervated by the contralateral side of the brain; however, the pathways involving the control of eye movements involve complex interactions across both sides of the brain. For instance, certain gaze functions require the coordination of the medial longitudinal fasciculus (MLF), which connects nuclei of cranial nerves involved in eye movements. Internuclear ophthalmoplegia is a condition that affects the MLF and can lead to problems with conjugate lateral gaze, such as the lateral rectus muscle failing to contract due to damage. This condition demonstrates the importance of interhemispheric connections, as damage to the MLF can affect the ability of the abducens nerve on one side to coordinate with oculomotor functions on the other side.