The above link will get you answers to this broad question.
The individual is worried about an overdose of medication during the procedure, while that is possible, it is also highly unlikely if the anesthesia team are doing what they do on a daily basis. I would suggest that the person have the surgeon ask for an anesthesia consult preoperatively during a less than stressful day, and have the patient list a series of questions that they want answered. That way, the two principals will have a chance to understand each other face to face. That is the best solution for the question about ways to lessen the impact for the anxious patient.
The American Society of Anesthesiologist has a web page that might help:
Over the past century, physician anesthesiologists have advanced patient safety through innovative research, science and technology advancements. Whether in the operating room, procedure room, intensive care unit or pain clinic, physician anesthesiologists are committed to delivering the safest medical care that every patient deserves before, during and after surgery.
Even though anesthesia is safer than ever, the administration of anesthesia is a complex and technically demanding medical procedure. It requires a physician who has the extensive medical education (up to 14 years) and clinical training (12,000-16,000 hours) to evaluate your medical condition, recommend an appropriate anesthesia plan, diagnose and treat problems that might surface during a procedure, and make critical, split-second decisions that can save your life.
*Who is in charge of your life?*
You have a right to know. Before undergoing a surgical procedure, you need to know who will be providing your anesthesia and ask for your physician anesthesiologist. Be sure your physician anesthesiologist is aware of your prior anesthesia and medical history, as well as any medications you currently take.
For more information visit *asahq.org/WhenSecondsCount
I hope this might help in your quest for knowledge and ease your anxiety.