Has this been reported as trolling?
Perhaps a bit harsh but it does sound a very odd question.
A mid foot position will actually use the knee more as you reduce the work the muscles around the ankle do. If you have had a knee replacement then a mid foot cleat position won’t make the slightest bit of difference and might actually make any pain worse. For those with ankle issues like stuey then it might help alleviate some issues. Saddle position will make the biggest change to the amount of knee flexion throughout each pedal stroke.
From Joe Friels blog:
Another advantage is that the biggest muscles of your body – the quads and glutes – are used more since the calf – a relatively small muscle – is now less active and no longer serves as a “transmission” for the biggest muscles. This latter point is especially beneficial for triathletes who rely on those calf muscles as their primary mover when they start the run. Fresh calf muscles mean a better run.
PS: A singlespeed also insn’t going to make a knee replacement very happy either (based on the Gorrick thread)