Organic Transplants: Of Hearts and Palms invokes the following eight laws.
1. The human body is sacred. Benefitting from a cadaver is almost always forbidden even with the prior consent of the individual [Yoreh De'ah 349:1].
2. To save a deathly ill patient, it is permissible to benefit from a cadaver [ibid. Pischei Teshuva 1].
3. It is forbidden to terminate the life of a terminally ill patient in order to save the life of another patient [Rambam Hilchos Rotzeach 1: 9].
4. Do not destroy a fruit-bearing tree so long as it produces sufficient fruit from which one can benefit (Devarim 20: 19, 20, see Maseches Bava Kama 91b for minimum production quantity).
5. Man is an inverted tree. His/her roots; the conduits of his/her life source are in the heavens, his/her arms and legs are its branches[Maharal Netzach Yisrael 7]. Man is comparable to a fruit bearing tree, bearing eternal fruit [Gur Aryeh Bereishis 9:21].
Rebbi Chanina testified that his righteous son Shivchis died young because he felled a palm tree while it was still productive [Maseches Bava Kama ibid.].
6. If the tree is damaging other fruit, or if it is more profitable to market the wood than the fruit thereof, one may cut down the tree [e.g. hearts of palms] (Maseches Bava Kama ibid.)
7. Similarly, if one needs the area, one may eliminate the tree [Rosh 8: ].
Needing the space means for necessity and not for luxurious consumption [Chavos Yair 195].
8. When it is permissible to eliminate a productive fruit tree, need one concern him/herself with the mystical danger documented in the Talmud?
Though, Binyan Tzion (Aruch Laner, Rav Yaakov Ettlinger) says one need not worry; common custom is to be wary of such danger as per Yaavetz 1: 76, Taz, and Chasam Sofer.
Application:
Of Hearts
In the late nineteen sixties and early seventies, most heart transplant recipients did not survive [Professor Shimon Glick Head of Dept. of Internal Medicine, Soroka Medical Center].
Even after medical advances increased success rates dramatically; as of yet, the heart must be harvested while the donor patient cannot definitively be proclaimed as halachically dead. As such, as of yet, it would be forbidden to allow the practitioner to transplant Lori's heart, even to benefit her mother [Rav Shlomo Zalman Auerbach].
And Palms
Roy may only fell the productive Sylvester tree if he needed the space. Even so, many are wary of potential mystical dangers associated with the untimely cutting down of fruit bearing trees. If Roy did not need the pool per se; rather, he merely wished to pamper himself with luxury and comfort, it would be in fact forbidden for him to cut down the tree. Instead, numerous approaches are available, one of which is to effectively transplant the tree to an alternative area, while not jeopardizing the longevity of the tree.