Of the various possibilities available, English-speaking medical people seem to prefer to the expression "extreme elevation" (over 3,000 Google hits when combined with the term "swelling") to the more literal "extremely elevated position" (a mere 2 hits totally unrelated to medicine). In other words, "The patient is given anti-swelling treatment with extreme elevation."

E.G.: See below sample sentence taken from the International Journal of Surgery, vol. 22, p. 259.

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Note added at 20 hrs (2009-09-03 14:33:57 GMT)
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"Maximum" versus "extreme" elevation: Note that the two meanings aren't quite the same. "Extreme" emphasizes that a certain value is quite high while leaving open the possibility that it isn't the highest value one can obtain in a given situation ("I thought my translation was extremely good, but someone else's turned out even better"), whereas "maximum" could conceivably be the highest value possible while still not being very high ("This CD yields a maximum interest rate of 2%"; interest rates in general are low nowadays). In other words, one must exercise care even when choosing commonly recognized phrasing, keeping in mind the original intended meaning of the source text.