The data show the opposite. Type “TK brain dead” into your search engine.
If the brain is the integrating principle of the body then the integrating effects would cease when the brain is dead. Our immunological system is a complex organized multi cellular activity that launches when foreign substances attack the body. TK, certified brain dead but maintained on a ventilator, lived 20 years without a functioning brain.
Our pathologic findings at autopsy confirmed that his brain had been destroyed by the events associated with the episode of H influenzae type b meningitis, whereas his body remained alive (brain death with living body) for an additional two decades, a duration of survival following brain death that far exceeds that of any other reports.
hods.org/pdf/Long%20Survival%20Following%20Baterial%20Meningits-Associated%20Brain%20Destruction1.pdfDuring his 20 years TK contracted infections which his immune system handled quite well. The immune system’s many components, carried in peripheral blood, offer hundreds of cell types to combat infection and perhaps thousands of molecules that are monitored as known prior invaders. The immense heterogeneity and variability in immune cells and proteins could not function without an integrating, organizing and conducting principle.
Such integrating principle was at work in TK and it was not his brain.