LONDON — By inserting itself on Sunday into the case of a brain-damaged, terminally ill British infant, the Vatican drew attention to the precarious intersection of ethics and biomedicine, an area in which both theology and regulation have struggled to keep pace with technological advances.

The infant, Charlie Gard, is on life support in a London hospital. He has a rare genetic disorder that prevents his cells from producing the energy needed to sustain his organs. He cannot move or breathe on his own.

The hospital has won a series of court rulings — the final one was last week — allowing it to turn off the ventilation and feeding machines that keep Charlie alive.

Charlie’s parents, however, have fought a battle to prolong his life, maintaining that an experimental therapy in the United States might possibly save him, even though courts have reviewed the evidence and decided that terminating life support is the only humane option. Although the parents, Connie Yates and Chris Gard, exhausted their legal appeals last week, they found new allies in Pope Francis and President Trump, who offered statements of support.