## Appendix B
If O is a point is space representing the sphincter, a force b . The projections of _{2}b
and _{1}b on the vertical are_{2} a
and_{1} a. The vertical components are both in the
opposite direction to_{2} F and counteract its tendency to elevate
point O. In the same way, c and _{1}c
are the projections of _{2}b and _{1}bin the horizontal direction. _{2}
From the geometry we can write:
b_{1} cos sigma
a =_{2} bcos sigma _{2 }
bsin sigma _{1} c
= _{2}b sin sigma
_{2 }
a
_{2}
-c _{2}The sum of the a
vectors will prevent upward translation of point O. The effect of the _{2}cand _{1
}cvectors, which are of opposite
sign, will be to pull point O in opposite directions._{2} _{ } If O, instead of being a point, is a minute annulus representing the inner
surface of a closed sphincter, the effect of the The detailed distribution is extremely difficult to model mathematically because
the diaphragm, the esophagus and the PEL are all elastic, not rigid structures.
Because of this, point O is elevated as the PEL stretches and the angle changes.
Nevertheless, it is clear that the pull of the contraction LM will have two
effects: 1.) It will open the sphincter and 2.) It will stretch the PEL producing
a "sliding hiatus hernia." If equivalent force is applied at the endpoints of the PEL, D
Last Updated July 31 2007 by David PJ Stiennon |