If a patient cannot shrug the shoulders against resistance, which cranial nerve (cn) requires further evaluation?

Based on the question, the cranial nerve that required further evaluation is the CN XI, spinal accessory

The spinal accessory nerve refers to the eleventh paired cranial nerve. It contains a purely somatic motor function.

The spinal accessory nerve has two roots:  

The spinal part arises from the end of the nucleus ambiguous. It also possibly arises from the dorsal nucleus within the vagus nerve. The fibers present in the nucleus are linked bilaterally with corticobulbar tract.

The corticobulbar tract is the motor neuron of the cranial nerves that connect the cerebral cortex with the brainstem.  

The cranial portion of the spinal accessory nerves is very smaller and arises from the lateral part of the medullar oblongata. It leaves the medullar oblongata as five rootlets that unite together and also join the spinal part of the accessory nerves, like it enters the jugural foramen; it can transmit fibers to the spinal part at this point.

It can only unite with the spinal portion of the accessory nerves for a short period of time before it unites with the inferior ganglion within the vague nerve.  At this point, the cranial fibers will now pass to the recurrent laryngeal and pharyngeal branches of the vagus nerve.

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