Seeing pulsation of the artery at the completion of this dissection.

1. This is a run-on that can be fixed with a period.
2. This is a run-on that can be fixed by adding a comma and a conjunction.
3. This is a fragment that can be fixed by adding a subject and verb after this long introductory element.
4. This is a fragment that can be fixed by removing the word seeing from the beginning of the sentence.
5. The sentence is fine as it is.

Seeing pulsation of the artery at the completion of this dissection, I ran.

so #3.

The correct answer is 3. This is a fragment that can be fixed by adding a subject and verb after this long introductory element.

Explanation:
A fragment is an incomplete sentence that is missing either a subject or a verb. In this case, the phrase "Seeing pulsation of the artery at the completion of this dissection" is a long introductory element that does not have a subject or verb. To fix this fragment, you need to add a subject and verb after the introductory element. For example, you could rewrite the sentence as follows: "Seeing the pulsation of the artery at the completion of this dissection, I realized the importance of careful surgical techniques."