Ultherapy creates a focused wound which creates and inflammatory healing reaction. This is what results in the skin tightening and collagen production. Prednisone could theoretically impact your response to Ultherapy treatment.
It is likely that steroids will reduce the amount of collagen deposition and thus reduce tightening. I would postpose the treatment if possible.
In theory the prednisone can interfere with collagen remodeling, but the effect of the Ultherapy is a months-long process so the effect if any of prednisone is likely to be small. However, it has not been studied specifically so there is no real way to know, and the results are variable depending on individual factors. Probably best to prioritize your back issue.
Steroids cause thinning of the skin in general. They affect wound healing and this is from emperical observation from hundreds of thousands of patients.
I believe that the Ultherapy effects (results) will be diminished in patients on prednisone.
Read the Ultherapy ebook provided on the link below.
Ultherapy is an fda approved treatment for lifting the face the neck. Consult with your physician to discuss medications that may interfere with tissue remodeling.