I want to answer you, but I'm at work right now, and your question deserves a detailed answer.
The short answer (as far as I'm concerned), is, many specialties will be very sparsely populated, simply due to the lack of imaging technology. If you can't see what's wrong, if invasive surgery is generally discouraged except in dire emergencies, and if you have only primitive tests for the more serious ailments in a specialty, that makes it more difficult to treat patients and is likely to attract fewer practitioners below the master level.
I could be way off base, here; this is just my opinion. We didn't have many cardiac specialists before adequate technology was developed to detect and treat heart ailments, for example.
Will add more when I get home and have hopefully been able to think about this in more detail. Even then, my answer might evolve, based on the responses of anyone more knowledgeable than myself.
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Okay, I'm home from work and voice lesson. Let's see... Here's the list:
- Dermatology
- ENT
- Toxicology
- Pulmonolgy
- Nephrology
- Pharmacology (I'm certain that some herbalism falls into this, but what about Healer Hall/Healers trying to develop new combinations? How much of this can they do before it becomes complicated and needs scientific equipment?)
- Pathology
- Palliative care (I'm supposing--but not certain--that all aspects of hc in pern currently have training related to this?)
Dermatology - Since they do have microscopes, I'm going to presume that dermatology is possible, as would be certain lab tests, like urine and blood cultures.
ENT - Yes, possible, though some people might go through their entire lives with mild degrees of sinus infections--because those are hard to get rid of, today, if the infection goes deep enough or has an antibiotic-resistant strain of bacteria.
Toxicology - I think this would most likely fall under the more general branch of herbalism/pharmacology and would probably be the sort of thing a person would become a master in.
Pulmonology - I think this would more likely be in the realm of general medicine. They probably have enough technology to have developed a breathing capacity test and maybe other simple tests that I'm not aware of. Most of the testing would be done by auscultation. A healer might even have to build his own equipment to perform respiratory tests.
Nephrology - Another specialty that I think would fall more under the umbrella of general medicine. They can probably diagnose kidney stones, but they'd have no way of treating them, short of telling the patient to drink a lot of water and hope they'll pass them. I don't think the Pernese would be eager to cut blindly into an organ as important as the kidney. Up for debate. I'd want to have an MD's opinion on whether they would do kidney surgery. I'm doubting it, though, unless a Threadscore gives them a convenient opportunity to go in. I hate to think of someone having to live with that kind of pain, though.
Pharmacology - In my opinion, pharmacology and herbalism are pretty much the same thing, on Pern. If there's no plant or natural compound that can heal it, it's unlikely to get healed with medicine.
Pathology - I think yes--because the Pernese have no taboo about dissecting cadavers, and they would consider it a vital way to learn medicine. They would want to study the ways in which the body responds to disease so they can more accurately recognize them in living patients.
Palliative care - Probably something that all healers learn to do. I wouldn't expect it to be a specialty. I remember joint-ail (arthritis) being mentioned frequently in Anne's books, so I'm guessing this is a common occurrence needing palliative treatment.
I'm not even sure that geriatrics and pediatrics would necessarily be specialties; it would just be that some healers are known to be better with children or with the elderly than others. I think Pernese healers treat people of all ages--because, typically, you have one Healer in a minor Hold. You might not even have a healer at all, except for the circuit healer, who comes around once a month. So you would treat everybody, no matter what age. There might be masters who specialize in treating children and the elderly, but I think their main function would be to teach the general healers how to relate to those patients, rather than to function as a Hold's gerontologist or pediatrician.
Dentistry - Yes, though obviously not much beyond teeth cleaning and extractions, maybe some fillings and making dentures; I don't know enough about the history of dentistry to answer you.
Some specialties I think would be possible that you didn't mention:
Plastic surgery - I think the Romans were the ones who first used plastic surgery for their soldiers. The American Civil War and WWII also saw great strides made in this area. War has always been a primary mover in medical advancement on Earth. Pern has few, if any, wars, so Passes would be the times of the greatest Pernese medical advancement in this field.
Orthopedics and physical therapy - I think this would be absolutely vital for dragonriders as well as for people in the crafts and in holds, who have to do hard work to survive.
Ophthalmology and optometry - I figure, if the ancient Egyptians could do cataract surgery, the Pernese should also be able to. Again, you're not likely to have a hold ophthalmologist; you're more likely to have someone who visits from the local healerhall when a hold's healer informs him/her of a need.
Neurosurgery (brain) - I think it is more likely that brain surgery would be reserved for treating head trauma, subural hematomas, etc. than for treating brain tumors. The only method you would have for diagnosing a tumor would be to observe the behavioral and affect damage it causes to the patient--and even then, I think that could be an inexact science. There are a lot of things which can be learned from a thorough neurological exam, though.
(nerves) - I'm thinking you might have surgeons who could perform hand surgery or treat something like sciatica, among other ailments.
Neurology - Yes. See remark about neuro exam above. A general practitioner would be able to diagnose a lot of things (I would hope), but s/he might consult with a healer from a healerhall on difficult cases.
Forensic medicine - I'm guessing the Hold Guard or whoever would consult with the local healer, who might perform an autopsy him/herself and/or would consult with a pathologist.
Oncology - I'd rather leave that up to an MD to decide. The Pernese are supposed to come from a very, very good gene pool, but you can always get DNA transcription errors, so I'd say cancer is quite possible, though likely not a common disease.
I hope that helps!