Firstly my apologies to those who read my first post on this subject "Do You Measure Where the Condyle Goes from Centric Relation?" as it has taken much longer than I intended to write this follow-up post on the calculations I've put together.
What this post shows you is that if you measure what happens to the patient's teeth when they move from a first interference encountered in centric relation to the point of maximum intercuspation, you can calculate where the condylar axis moves. It's not a question for debate; it's just the result of applying simple high-school-level geometry. How the teeth move completely determine how the condyle moves.
Because of questions I received following the earlier blog post I decided it would be most helpful if I explained the basic principles in a video which you can watch by clicking on the video here (with my apologies for my rather jerky commentary - I decided it was better to communicate what I could put together quickly rather than aim to provide a polished production):
After watching the video you might like to download the paper "Condyle Movement Calculations from Centric Relation to Maximum Intercuspation" that contains the details of my calculations and download the spreadsheet "Calculating-Condyle-Position-From-Centric-Relation-to-MIP.xlsx" which implements those calculations and lets you enter measurements from your own patients.
I believe the calculations are correct - they were checked by one of my sons who recently achieved 100% in a SAT math subject test. Also I should probably say that my background is that I studied mathematics (we use the plural in the UK) at Cambridge University reckoned (by Cambridge graduates) to be one of the foremost math schools in the world. That doesn't actually mean a lot in the calculations I present as they only use basic high school math.
It is important to note that the calculations are based only on the observed movements of the lower teeth, so they only deal with what happens. They do not deal with how it happens (how the muscles move the teeth). I agree that it is interesting to know how the muscles navigate the jaw from its starting position to its finishing position, but understanding the "how" does not affect the "what" (unless you are attempting to predict how the jaw moves, in which case it is necessary to have a good understanding of the "how" in order to predict the "what"). I say this because some people have argued with me because they don't see how the muscles can move the condylar axis down and back (a result I show happens based on certain observed tooth movements). You will see in the video and calculations that geometry shows that the axis position is deteremined by observing the motion of the teeth. If we cannot explain how the axis gets to where it does, we need to review our understanding of the forces exerted by the muscles and not deny the facts of basic geometry! Jaw muscle function is a complex subject, so I am doing more research in this area and may postulate in a future post how the muscles can move the jaw in the manner demonstrated by these geometrial calculations.
Comments and discussion on this subject are most welcome. If you use the spreadsheet to enter your own observed figures, please share your measurements and results!