Thanks to the Podcast Parlor, I have found out about the podcasts that the University of Warwick puts out. From the site of Warwick you can access all podcasts (feed), but I have not yet figured out how to access the separate subjects in separate feeds from there. It is possible to go through iTunes U though. Seek out the University of Warwick (under U in the universities and colleges list) and there you will find various history subjects laid out to you.
The first series I took up was Islamic Medicine (iTunes feed) by Peter Pormann. This series consists of seven short podcasts (10-20 minutes. Monologues by Pormann) about medieval medicine in the Islamic tradition. In many respects this is a continuation of classical Greek Medicine on which the sages in the Islamic world continued and to which they added. Among these sages are not only Muslims. There are Christians and Jews involved in the activities as well. The Jew Maimonides (Rambam) is part of this culture and in the translation movement that delivered a huge amount of Greek texts to Arabic, are quite a few Syriac Christians.
The importance of the Islamic Medicine is that eventually it is the bridge from the Greeks to the modern west. In spite of the fact that modern scientific evidence based medicine has been added to this tradition, some of its basics are still alive today. In culture and in various practices.
More history of medicine:
Four Humour Medicine (BBC's In Our Time),
Pain (Missing Link),
Medical History (medicalhistory podcast).