P. Pallav, PhD

In this page the occlusal surfaces of the molars of our theoretical set up are curved in a special way. The flow resistance is the same in all directions and there is no chance that the food will flow otherwise than straight from the center outward.

The average height is the same as it was, but with respect to the plane set up the height at the center is increased. Along a ring around the center (C) the height is decreased. Along a ring around this ring again the height is increased (B), etc. (A). We used a simple sine function to define the shapes of the surfaces.

Note that here the words in~ and decrease refer to the amount of vertical space between the surfaces, which would be the other way around when referring to the height of the surfaces of the molars.

In the plots below the sketch, the curves of the flat set up are drawn lightly for comparison. For the shape of the molars we used a sine function. The height varies between 80 and 120 % of the original flat set up.
Because the height is raised to the second power, the differences in wear rate are greatly accentuated (curve EA). At A and C the erosive activity is increased by 56 % of what it was. At B it has decreased 31 %.

Coming Closer

Of course the height variations stay the same as the surfaces come closer. Therefore the relative influences must increase. If you think of 100% as 1 mm (millimeter), the drawn variations of the height of 20% become 0.2 millimeter around 1 mm, which is as much as 40% of 0.5mm or only 13.3% of 1.5mm.
Because of this the effects of the height variations become more pronounced as the molars come closer.

With reference to the picture above, the three average heights in this picture are 150%:100%:50%, in that order, which then represents 1.5, 1, and 0.5 millimeters.

The rather large difference in the magnitude of the three curves (upper curves) effectively prevents comparison of the shapes of these curves, because the 100, and 150% curves vanish in the pixels.

This was solved with a common trick, by dividing each of the three curves by its average value (lower set).

Simulation

In the spread sheet we will use one of these curves as the key to the distribution of the wear rate (and re-evaluate it after each step), because it is not practical to simulate an entire closing motion for each successive wear progression.

Although we know that most wear occurs during the last few tenths of millimeters, we need some kind of average value of this trajectory.

It is not possible to calculate the height exactly, but equation 6 in the previous page suggests that this could be 26% of the average height before or above occlusion. For example when the average height between two molars at centric occlusion would be 0.6mm, the curve to be used is that where the height at the contacts is still 0.156mm (= 26% of 0.6mm) above occlusion.