On the Gamblin website I found some information:
Managing solvents is the key to studio safety. Oil painting studios are immediately safer when artists remove strong solvents, especially turpentine, from their painting processes.
I've been trying to answer Nigel's question, are all alkyds toxic? Everything I look up says that Walnut Alkyd Medium by M. Graham is "Certified to be NONTOXIC!"
I received some good advice from Jeff Hein today. His classes and studio are strictly non-toxic due to allergies he has developed. He said he's heard a lot of stories lately about studio related illnesses. He rarely cleans his brushes so he doesn't really need turpentine at all. Jeff claims that his brushes hold up longer if he sets them to soak in a tray of mineral oil when he's not painting. I'm going to try it. The walnut oil is great for that too but it does go rancid after a while.