Medical seems to suggest high reliability and probably a very good 24V supply. You need to consider how critical it is, how long (and whether) you can operate if it fails, whether the equipment has internal batteries (and how long they will last), and what happens if it fails. You then need to balance that against how far you are going from a reliable mains supply, and how long it would take to get to one in the event of a problem.
If the answer is that reliable supply is totally critical and the loss is life threatening then I think you ought to probably contact your equipment supplier to see if they can suggest a solution - a 'home brew' is unlikely to stand up to scrutiny in the worst case scenarios.
Otherwise if the unit has internal batteries that will last longer than a worst case rescue (plus 100% safety margin) some sort of 12 - 24V DC-DC converter would probably suffice, e.g. something from someone like Alfatronix (
DD Series 12-24V UP Voltage Converters, Convertisseur) but I would go and speak to them about the application and the criticality. There are converters on EBay (e.g.
DC 12V to 24V 3A 72W -STEP UP- Converter Regulator Waterproof BOOST POWER Module | eBay) but I wouldn't consider EBay as source in safety critical applications.
You could also consider a 12-24V converter such as the ones above into a 2x12V battery with enough capacity to run the equipment for the expected rescue time (+100% safety margin) - I use 12V 7.2Ah batteries in UPS's (from EBay, Amazon, etc) and they are reasonably reliable, but you do need to check the current rating of the equipment against the capacity and I would also recommend a full discharge test, probably every 4-6 months, and if the discharge time is less than recover time plus about 80% then it is definitely time to think about changing the batteries.
I'm sorry if this all sounds a bit anal - and it may well be over the top - but as a Chartered Electronic Engineer with experience in Health and Safety, and also design in military applications, I am conservative in design (but not in politics!). Drop me a PM if you want any more thoughts
Bob