With the help of a friend, the exerted watts on an indoor biker were monitored and the heart beats per minute (bpm) were recorded using my trustful Polar RS300X watch. At the end of the test, I took the data from the paper and I inputted it on an excel spreadsheet to draw the graph that is shown below. The test was performed 2 Feb. 2014.
The threshold is the point where a 'break in the knee" is observed (shown with the red lines on the graph).
This is roughly the point where your body shifts from an aerobic into an anaerobic state.
For your info, my resting heart rate is around 51bpm, while my maximum (running) pulses are 183bmp.
Hence it can be observed that the the maximum HR on the bike is less than the maximum HR on the run (this is to be expected as less muscles are activated during cycling) - this comes in agreement with the findings provided on many textbooks in the subject of sport's science (although I would expect that the bike HRmax should be about 10bmp or so less than the HRmax achieved of the run, perhaps this was influenced from the fact that I had completed some endurance training sessions the days towards the fitness test).
Bike fitness test
It is recommended to repeat such tests every 4-5 weeks or so to assess progress and overlay the results on the same XY graph to compare them with the previous tests. An improvement on the performance is noticed when the most recent line is shifted on the right compared to the previous test. You won't necessarily observe a significant change on the position of the threshold point, otherwise the other data points should shift. For a given effort (watts) a lower bpm is recorded when your fitness has improved.
Execute a fitness test at your own responsibility! Always seek a medical advice before putting yourself under an excessive effort.