The Elder's Stroll

You play as Albert, an old patient of a destroyed hospital, trying to escape the numerous guards at his pursuit. In order to run, you monitor & control the vital signs of the elderly: his saturation, his heart rate and his temperature. Raising any of those parameters with drugs will speed you up but you are then at risk of an overdosis.

That would be a breeze if it wasn't for all the factors disturbing the escape (and the health) of the old man: a nasty cat would raise the usually-quiet heart rate of Albert to give an example.

If you don't use drug though, you could just be caught by the hospital guards riding on their might Segway or run off by a stretcher.

A runner game reversing completely the dynamics so dear the the genre.