The issue of defining "person" and "death" in Judaism

Michael Shalom
I am a hematologist by profession and my main occupation is treating people with cancer with very dynamic diseases and significant mortality. On a daily basis, I encounter the need to make difficult decisions regarding the choice of treatment, the determination of death, the determination of futility of further treatment, etc. Naturally, there are quite a few ethical and moral dilemmas in my daily life.
In some cases, I have approached and been present at discussions and even discussed specific cases with medical ethics experts who are religious people with rabbinical credentials. In many cases, I have been disappointed by the lack of logic even in the context of an ethical-religious discussion (or, more accurately, to say modestly – my disagreement with what is presented as logic by them).
I would very much like to discuss with you a number of practical issues that are important to me, because I greatly appreciate you as a logical person and certainly more knowledgeable than I am in the framework of halachic logic in which the above-mentioned experts operate.
I'm sure you're a very busy person and probably don't have time for this topic, but I decided to try anyway.
If you think that the framework of this website is not appropriate and there is another framework – I would of course be happy to know.