For those who want to keep track of the Muslim sources related to this issue, here they are. (Note: I didn't use all of these in the video. Note also: I typed these in by hand, so let me know if you spot any typos.)
I. QUR'AN TRANSLATIONS
Qur’an 69:44-46—And if he (Muhammad) had forged a false saying concerning Us We surely should have seized him by his right hand (or with power and might), and then certainly should have cut off his life artery (Aorta). (Hilali-Khan)
Qur’an 69:44-46—And if he had invented false sayings concerning Us, We assuredly had taken him by the right hand and then severed his life-artery. (Pickthall)
Qur’an 69:44-46—Had he invented lies concerning Us, We would have seized him by the right hand and severed his heart’s vein. (Dawood)
Qur’an 69:44-46—And if he had fabricated against Us some of the sayings, We would certainly have seized him by the right hand, then We would certainly have cut off his aorta.(Shakir)
II. MUSLIM COMMENTARIES
Tafsir Ibn Abbas on Qur’an 69:44-46—(And if he had invented) and had Muhammad invented (false sayings concerning Us) lies against Us and attributed to Us that which We did not say, (We assuredly had taken him) We assuredly had taken revenge against him (by the right hand) by means of truth and proofs; it is also said this means: We assuredly had vehemently taken him. (And then severed his life artery) the life artery of Muhammad (pbuh).
Tafsir Jalalayn on Qur’an 69:44-46—And had he, namely, the Prophet (s), fabricated any lies against Us, by communicating from Us that which We have not said, We would have assuredly seized him, We would have exacted vengeance [against him], as punishment, by the Right Hand, by [Our] strength and power; then We would have assuredly severed his life-artery, the aorta of the heart, a vein that connects with it, and which if severed results in that person’s death.
Tafsir Ibn Kathir on Qur’an 69:46—(And then We certainly would have cut off Al-Watin from him,) Ibn ‘Abbas said, “It (Al-Watin) refers to the artery of the heart, and it is the vein that is attached to the heart.” This has also been said by ‘Ikrimah, Sa’id bin Jubayr, Al-Hakim, Qatadah, Ad-Dahhak, Muslim Al-Batin and Abu Sakhr Humayd bin Ziyad.
III. HADITH REFERENCES
Sahih al-Bukhari 2588—Aisha said, “When the Prophet became sick and his condition became serious, he requested his wives to allow him to be treated in my house, and they allowed him. He came out leaning on two men while his feet were dragging on the ground.”
Sahih al-Bukhari 2617—A Jewess brought a poisoned (cooked) sheep for the Prophet who ate from it. She was brought to the Prophet and was asked, “Shall we kill her?” He said, “No.” Anas added: “I continued to see the effect of the poison on the palate of the mouth of Allah’s Messenger.”
Sahih al-Bukhari 2797—The Prophet said, . . . “By Him in Whose Hands my soul is! I would love to be martyred in Allah’s Cause and then come back to life and then get martyred, and then come back to life again and then get martyred and then come back to life again and then get martyred.”
Sahih al-Bukhari 4428—The Prophet in his ailment in which he died, used to say, “O Aishah! I still feel the pain caused by the food I ate at Khaibar, and at this time, I feel as if my aorta is being cut from that poison.”
Sahih Muslim 5430—A Jewess came to Allah’s Messenger with poisoned mutton and he took of what had been brought to him. (When the effects of this poison were felt by him) he called for her and asked her about that, whereupon she said: I had determined to kill you. Thereupon he said: Allah will never give you the power to do it.
Sunan Abu Dawud 4498—A Jewess presented [Muhammad] at Khaibar a roasted sheep which she had poisoned. The Apostle of Allah ate of it and the people also ate. He then said: Lift your hands (from eating), for it has informed me that it is poisoned. Bishr b. al-Bara b. Ma’rur al-Ansari died. So he (the Prophet) sent for the Jewess (and said to her): What motivated you to do the work you have done? She said: If you were a prophet, it would not harm you; but if you were a king, I would rid the people of you. The Apostle of Allah then ordered regarding her and she was killed. He then said about the pain of which he died: I continued to feel pain from the morsel which I had eaten at Khaibar. This is the time when it has cut off my aorta.
Sunan Abu Dawud 4449—Umm Bishr said to the Prophet during the sickness of which he died: What do you think about your illness, Apostle of Allah? I do not think about the illness of my son except the poisoned sheep of which he had eaten with you at Khaibar. The Prophet said: And I do not think about my illness except that. This is the time when it cut off my aorta.
Sunan Ibn Majah 1622—Aishah said: “I never saw anyone suffer more pain than the Messenger of Allah.”
IV. SIRA REFERENCES
Ibn Ishaq, p. 516—When the apostle had rested, Zaynab d. al-Harith, the wife of Sallam b. Mishkam prepared for him a roast lamb, having first inquired what joint he preferred. When she learned that it was the shoulder she put a lot of poison in it and poisoned the whole lamb. Then she brought it in and placed it before him. He took hold of the shoulder and chewed a morsel of it, but he did not swallow it. Bishr b. al-Bara b. Ma’rur who was with him took some of it as the apostle had done, but he swallowed it, while the apostle spat it out, saying, ‘This bone tells me that it is poisoned.’ Then he called for the woman and she confessed, and when he asked her what had induced her to do this she answered: ‘You know what you have done to my people. I said to myself, If he is a king I shall ease myself of him and if he is a prophet he will be informed (of what I have done).’ So the apostle let her off. Bishr died from what he had eaten.
Ibn Ishaq, p. 516—Marwan b. Uthman b. Abu Sa’id b. al-Mu’alla told me: The apostle had said in his illness of which he was to die when Umm Bishr d. al-Bara came to visit him, ‘O Umm Bishr, this is the time in which I feel a deadly pain from what I ate with your brother at Khaybar.’
At-Tabari, Volume 8, p. 124—The Messenger of God said during the illness from which he died—the mother of Bishr b. al-Bara had come in to visit him—“Umm Bishr, at this very moment I feel my aorta being severed because of the food I ate with your son at Khaybar.”
Ibn Sa’d, Volume 2, pp. 251-252—When the Apostle of Allah, may Allah bless him, conquered Khaybar and he had peace of mind, Zaynab Bint al-Harith, the brother of Marhab, who was the spouse of Sallam Ibn Mishkam, inquired: Which part of the goat is liked by Muhammad? They said: The foreleg. Then she slaughtered one from her goats and roasted it (the meat). Then she wanted a poison which could not fail. The Jews discussed about poisons and became united on one poison. She poisoned the she-goat putting more poison on the forelegs, and shoulder. When the sun had set and the Apostle of Allah, may Allah bless him, returned after leading the people in Maghrib (sun-set) prayers, she sat by his feet. He asked her about her. She said: O Abu al-Qasim! Here is a present which I wish to offer to you. The Prophet, may Allah bless him, ordered it to be taken. It was served to him and to his Companions who were present and among those who were present was Bishr Ibn al-Bara Ibn Ma’rur. Then the Apostle of Allah, may Allah bless him, said: Come closer and have night meal. The Apostle of Allah, may Allah bless him, took the foreleg, a piece of which he put into his mouth. Bishr Ibn al-Bara took another bone and put it into his mouth. When the Apostle of Allah, may Allah bless him, ate one morsel of it Bishr ate his and other people also ate from it. Then the Apostle of Allah, may Allah bless him, said: Hold back your hands! Because this foreleg; and according to another version, the shoulder of the goat, has informed me that it is poisoned. Thereupon Bishr said: By Him Who hath made you great! I discovered it from the morsel I took. Nothing prevented me from emitting it out, but the idea that I did not like to make your food unrelishing. When you had eaten what was in your mouth, I did not like to save my life after yours, and I also thought you would not have eaten it if there was something wrong. Bishr did not rise from his seat but his color changed to that of taylsan (a green cloth). For a year the pain did not permit him to change his sides but with the help of others and then he expired. According to another version, he died before leaving his seat. He (Ibn Sa’d) said: A peace of it was dropped before a dog who ate it and died (instantaneously) without being able to move its foreleg. The Apostle of Allah sent for Zaynab Bint al-Harith and said to her: What induced you to do what you have done? She replied: You have done to my people what you have done. You have killed my father, my uncle, and my husband, so I said to myself. If you are a prophet, the foreleg will inform you; and others have said: If you are a king we will get rid of you. The Jewess returned as she had come. He (Ibn Sa’d) said: The Apostle of Allah, may Allah bless him, handed her over to the heirs of Bishr Ibn al-Bara who put her to death.
For further study on this topic, see the following articles:
Sam Shamoun, "How Allah Killed His Prophet"
Silas, "The Death of Muhammad"