Here's a superb account, by David DeGrazia, of the issues pertaining to the definition of death. DeGrazia sets the scene as follows:
According to the whole-brain standard, human death is the irreversible cessation of functioning of the entire brain, including the brainstem. This standard is generally associated with an organismic definition of death. Unlike the older cardiopulmonary standard, the whole-brain standard assigns significance to the difference between assisted and unassisted respiration. A mechanical respirator can enable breathing, and thereby circulation, in a brain-dead patient—a patient whose entire brain is irreversibly nonfunctional. But such a patient necessarily lacks the capacity for unassisted respiration. On the old view, such a patient counted as alive so long as respiration of any sort (assisted or unassisted) occurred. But on the whole-brain account, such a patient is dead. The present approach also maintains that someone in a permanent (irreversible) vegetative state is alive because a functioning brainstem enables spontaneous respiration and circulation as well as certain primitive reflexes.
We may think of the brain as comprising two major portions: (1) the “higher brain,” consisting of both the cerebrum, the primary vehicle of conscious awareness, and the cerebellum, which is involved in the coordination and control of voluntary muscle movements; and (2) the “lower brain” or brainstem. The brainstem includes the medulla, which controls spontaneous respiration, the ascending reticular activating system, a sort of on/off switch that enables consciousness without affecting its contents (the latter job belonging to the cerebrum), as well as the midbrain and pons.
Whole-brain death involves the destruction of the entire brain, both the higher brain and the brainstem. By contrast, in a permanent vegetative state (PVS), while the higher brain is extensively damaged, causing irretrievable loss of consciousness, the brainstem is largely intact. Thus, as noted earlier, a patient in a PVS is alive according to the whole-brain standard. Retaining brainstem functions, PVS patients exhibit some or all of the following: unassisted respiration and heartbeat; wake and sleep cycles (made possible by an intact ascending reticular activating system, though destruction to the cerebrum precludes consciousness); pupillary reaction to light and eyes movements; and such reflexes as swallowing, gagging, and coughing. A rare form of unconsciousness that is distinct from PVS and tends to lead fairly quickly to death is permanent coma. This state, in which patients never appear to be awake, involves partial brainstem functioning. Permanently comatose patients, like PVS patients, can maintain breathing and heartbeat without mechanical assistance.
The whole-brain approach clearly enjoys advantages. First, whether or not the whole-brain standard really incorporates, rather than replacing, the traditional cardiopulmonary standard, the former is at least fairly continuous with traditional practices and understandings concerning human death. Indeed, current law in the American states incorporates both standards into disjunctive form, most states adopting the Uniform Determination of Death Act (UDDA) while others have embraced similar language. The UDDA states that “… an individual who has sustained either (1) irreversible cessation of circulatory and respiratory functions, or (2) irreversible cessation of all functions of the entire brain, including the brain stem, is dead.”
As mentioned, every American state has legally adopted the whole-brain standard alongside the cardiopulmonary standard as in the UDDA. It is worth noting, however, that a close cousin to the whole-brain standard, the brainstem standard, was adopted by the United Kingdom and various other nations (including several former British colonies). According to the brainstem standard—which has the practical advantage of requiring fewer clinical tests—human death occurs at the irreversible cessation of brainstem function. One might wonder whether a person's cerebrum could function—enabling consciousness—while this standard is met, but the answer is no. Since the brainstem includes the ascending reticular activating system, the on/off switch that makes consciousness possible (without affecting its contents), brainstem death entails irreversible loss not only of unassisted respiration and circulation but also of the capacity for consciousness. Importantly, outside the English-speaking world, many or most nations, including virtually all developed countries, have legally adopted either whole-brain or brainstem criteria for the determination of death. Moreover, most of the public, to the extent that it is aware of the relevant laws, appears to accept such criteria for death. Opponents commonly fall within one of two main groups. One group consists of religious conservatives who favor the cardiopulmonary standard, according to which one can be brain-dead yet alive if (assisted) cardiopulmonary function persists. The other group consists of those liberal intellectuals who favor the higher-brain standard, which, notably, has not been adopted by any jurisdiction.