I'm not going to bother discussing Rashi's view, because he wasn't aware of the correct scientific reality as discovered by modern science.
Now, many people reading that last sentence will see it as further evidence of my unacceptable approach. How could I have the audacity to dismiss Rashi? Rashi was written with ruach hakodesh!
But that sentence in bold is not mine. It was the statement of no less an authority than the Chasam Sofer, discussing Rashi's commentary on a different matter relating to physiology:
"What are the meanings of the anatomical terms mentioned in this Mishna? After I researched medical books and medical writers as well as scholars and surgical texts, I have concluded that we cannot deny the fact that reality is not as described by Rashi, Tosfos and the drawings of the Maharam of Lublin. We have only what the Rambam wrote in the Mishna Torah and his Commentary to the Mishna - even though the latter has statements which are unclear. However, you will find correct drawings in the book Maaseh Tuviah and Shevili Emuna…. Therefore, I did not bother at all with the commentaries of Rashi and Tosfos in this matter since it is impossible to match them with true reality. You should know this." (Chasam Sofer to Nidah 18a)
If Chasam Sofer recognized that we can't use Rashi's explanations if they are affected by his lack of medical knowledge, why can't Poskim today?
Even more ironic is that the Poskim also analyze the Chasam Sofer's statements about death in order to reach their conclusion. But Chasam Sofer also did not have the modern understanding of physiology, nor the modern possibilities for maintaining organs and physiological systems.
Now, some will immediately point to the statement of Chasam Sofer rejecting any alternative to the Gemara's rule of declaring death based upon the absence of respiration. He claims that this must have been based on the superior scientific knowledge of the ancients and/or on Scripture. As Chasam Sofer famously stated:
"All the winds of the world will not move us from the standards established by our Torah." (Teshuvos Chatam Sofer, Yoreh Deah 338)
Yet the fact is that nobody follows the Gemara's rule in this regard. According to the Gemara, if the person is not breathing, he is considered dead. That was a reasonable position for Chazal to take. But nowadays, we would do CPR! Some people attempt to argue that the Gemara is talking about someone who has irreversibly stopped breathing. But this is sticking a contemporary position into the Gemara - it's not what Chazal said or meant. Yes, if Chazal would have known about CPR, they would have formulated their ruling differently. But by the same token, if they would have known that the heart is nothing more than a blood-pumping organ, and that all cognitive action takes place in the brain, and that a brain-dead person can have his organs used to save others, they would have said many things differently.
Dismissing Rashi due to his lack of knowledge of anatomy? Chasam Sofer already did it. Undermining the Chasam Sofer's principle? Every posek has already done it. So why when it comes to brain death, all the Poskim - on both sides - are reaching their conclusions by analyzing the positions of Chazal, the Rishonim and Acharonim? Especially since when it comes to kidney donation, most Poskim freely ignore Chazal, where Chazal likewise based themselves on Scripture.