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Jim Mcmahon
07-09-1996, 01:35 PM
Dear Colleagues,

I hope one, or several, of you can help me with a problem I've
encountered. I'm trying to estimate max. bite force using measurements on
a series of dry skulls; so I need to construct a biomechanical model of
mastication in order to determined what measurements are appropriate.
I've "dabbled" in biomechanics but have no formal training, and thus must
rely on the experts. I'm making the assumption that the jaw acts as a
Class III lever (an assumption made by many of the people who do this
kind of work). The general formula should apply:

Resultant Muscle Force=F
Angle betweeen resultant force and line of bite resistance=A
Lever Arm length=LEVER
Load Arm length=LOAD

(F cosine A) x LEVER
Bite Force = ---------------------
LOAD

This much seems to be clear. But my review of the literature has turned
up numerous different measurements for these values.

Most models place the fulcrum at the TMJ and the "weight" at the bite
point, so that the Load arm length should be the distance between the TMJ
and the bite point (some specified tooth).

But Dechow and Carlson (Amer J. Phys. Anthr. vol 83,2) calculate Bite
force using the occlusal plane (OP) as the lever. They simply extend a
vertical line down from TMJ until it intersects OC. Likewise, the load
arm of the temporalis mm. is the intersect of a vertical line drawn down
from the "tip" of the coronoid process to OP. How can this be?

Demes and Creel (J Hum Evo. vol 17) and Anapol and Lee (Amer J. Phys. Anthr.
vol 94,2) use the Frankfort Horizontal: "lever arm of temporalis--estimated
to be one-half the distance along the FH from the most caudal extent of the glenoid fossa to
the most rostral limit of the temporal fossa on the dorsal aspect of the
zygomatic arch" (Anapol and Lee, p. 241).

I think, in a biomechanical model it should be the actual line connecting
the TMJ and bite point NOT the occlusal plane nor the Frankfort
Horizontal, that represents the lever arm, and that the load arm is also
measured along this line. Greaves (J. Zool. Lond. vol 184) uses this
type of model. I also think that in the (F cosine A) part of the equation
A should be taken between the Muscle Resultant vector and a line
perpendicular to the occlusal plane, since this is the direction of bite
force reaction. Am I right? OK, my big problem is how to locate the load
arm along this line. Well one point is clearly fulcrum (TMJ), and the
other point should be the intersection of the resultant muscle
vector algon the TMJ-bite point line. Right?

If I'm right about all this so far, then
a resultant vector acting perpendicular to the occlusal plane will have a
cosine of 1 and the full magnitude of the force will be transmitted to
the bite point. But that means that the intersection of this vector and
TMJ-bite point line will be posteriorly place making for a short load arm
and decreased mechanical advantage; compared to a muscle vector that
intersects the bite point, which would have an optimum mechanical
advantage (lever arm=load arm), but whose angle relative to the bite
reaction force (perpendicular to occlusal plane) would be oblique
resulting in an angle cosine of much less than 1. In other words, there
is a trade off between the two vector situations.

Any comments on any of this, references, etc, would be greatly
appreciated. I'd really like to know if I'm on the right track. None of
the biomechanics or mechanics books I've come across address this precise
problem. Thanks in advance,

James McMahon
Doctoral Student
Biological Anthropology Program
City University of New York