I've had my mechanical valve for eight years. My cardiologist encouraged me to cut back on my pre-op weight-lifting routine and focus on aerobic exercise instead. He has not limited my running (or anything else), but doesn't like for my heart rate to get too high for extended periods of time.
I always wear a heart rate monitor (HRM) when running or cycling. My HRM has high/low alarms for my target zones and beeps when my HR gets too high or too low. Most of my workouts are done in Zone 2, which is optimal for building aerobic endurance and burning calories. In less technical terms, this is a "conversational pace" which will let you carry on a conversation while running, although with some effort.
I had my lactic threshhold measured in a lab a couple of years ago, and used those results to determine my HR zones for working out. My lactic threshhold heart rate (LTHR), the point at which you go from aerobic to anaerobic, was measured at 159 bpm. We then used the HR charts in Joe Friel's The Triathlete's Training Bible to determine specific heart rate zones.
One thing I have found living in FL is that my HR is very sensitive to heat. When I run on hot days I often have to slow down to keep my HR in my target range.
Mark