The nervous system is organized in funny fashion. Information that comes to and from the brain is "flipped," so that the left side of the brain controls and receives information from the right side of the body. Similarly, the left side of the body is controlled by the right side of the brain.
Nerves in the spinal cord follow set paths as they run towards the brain. Similar types of nerves run together in an organized fashion.
For example, the nerves that detect vibration, light touch, and proprioception (where the body is in space) all enter the spinal cord and ascend in what are called the dorsal columns towards the brain on the same side as the innervated limb. For the left leg, for example, the fibers run up along the left side of the spinal cord. Near the brainstem, though, the fibers cross over to the opposite side.
This is similar to how the nervous system organizes fibers that tell part of the body to move. In the brain, the fibers are on the opposite side of the body as the innervated limb, but they switch over at the bottom of the brainstem. For example, the left side of the brain sends signals that then travel down the right side of the spinal cord before exiting into the right arm. The left side of the brain, then, controls the right side of the body.
In contrast, nerve fibers that detect sensations like pain and temperature don't cross over at the base of the brainstem, but instead cross almost as soon as they enter the spinal cord from the arm or leg. Fibers in the left side of the spinal cord contain pain and temperature nerve fibers from the right arm and leg. The fibers may ascend a few levels before crossing, however.
So what happens if just half of the spinal cord is damaged? Interrupted fibers include vibration, light touch, and proprioception from the same side of the body as the lesion. Control of the body is also damaged on that side. However, pain and temperature sensation will be lost from the opposite side of the body,often one or two segments down from the injury.
This phenomenon was first described by Charles Édouard Brown-Seéquard in 1850, who described what is now known as Brown-Séquard syndrome when studying farmers injured while cutting sugar cane in the republic of Mauritius. The most common cause of this syndrome remains traumatic injury to just part of the back. Because the wound needs to precisely sever just half of the spinal cord, it remains relatively rare, but is useful for illustrating the workings of spinal cord.
If someone suffers from Brown-Seéquard syndrome, magnetic resonance imaging can be used to confirm the cause and location of the injury. In addition to trauma, lesions such as infections, inflammation, or tumors may lead to Brown-Seéquard. THe treatment will depend on the nature of the lesion.
Hal Blumenfeld, Neuroanatomy through Clinical Cases. Sunderland: Sinauer Associates Publishers 2002.
Ropper AH, Samuels MA. Adams and Victor's Principles of Neurology, 9th ed: The McGraw-Hill Companies, Inc., 2009.