Final answer:
The spinal cord injury known as Brown-Séquard syndrome involves ipsilateral weakness or paralysis and contralateral loss of pain and temperature sensation, due to a hemisection of the spinal cord.
Step-by-step explanation:
The spinal cord injury that classically presents with weakness of the upper and lower extremities on the ipsilateral side and loss of pain and temperature sensation on the contralateral side is the Brown-Séquard syndrome. Brown-Séquard syndrome is a type of hemisection of the spinal cord, which means that only one half of the spinal cord is damaged. Following such an injury, the motor pathways, such as the corticospinal tract that transmits voluntary motor commands from the brain to the body, are affected ipsilaterally at the level of injury and below. This results in paralysis or weakness on the same side as the injury (ipsilateral hemiplegia).
Conversely, the sensory pathways responsible for pain and temperature sensation, namely the spinothalamic tracts, cross over to the opposite (contralateral) side of the spinal cord shortly after they enter. As such, the ability to perceive pain and temperature is lost on the side opposite to the injury (contralateral sensory loss), below the level of the hemisection. Therefore, within the clinical context of a spinal cord injury, if a patient displays ipsilateral motor deficit and contralateral pain and temperature sensory loss, it is indicative of Brown-Séquard syndrome.