Final answer:
Remifentanil is the opioid that is not affected during the anhepatic stage of liver transplant because it is metabolized by nonspecific blood and tissue esterases, rather than the liver.
Step-by-step explanation:
The opioid that is not affected in the anhepatic stage of liver transplant is Remifentanil. Unlike Morphine, Fentanyl, and Methadone, Remifentanil is metabolized by nonspecific blood and tissue esterases. This means that its metabolism and therefore its clearance from the body, is mainly independent of liver function. Therefore, during the anhepatic phase of liver transplantation, where the liver is non-functional, Remifentanil remains unaffected compared to other opioids that rely on hepatic metabolism