Appendix B

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If O is a point is space representing the sphincter, a force F, representing the tension applied to it by LM contraction, will be opposed in the plane by the phrenoesophageal ligaments represented by the two vectors b1 and b2 . The projections of b1 and b2 on the vertical are a1 and a2. The vertical components are both in the opposite direction to F and counteract its tendency to elevate point O. In the same way, c1 and c2 are the projections of b1 and b2 in the horizontal direction.

From the geometry we can write:

a1 = b1 cos sigma
a2 = b2 cos sigma

c1 = b1 sin sigma
c2 = b2 sin sigma

a1 = a2

c1 = -c2

The sum of the a1 and a2 vectors will prevent upward translation of point O. The effect of the c1 and c2 vectors, which are of opposite sign, will be to pull point O in opposite directions.

If O, instead of being a point, is a minute annulus representing the inner surface of a closed sphincter, the effect of the c vectors will be to separate the opposite walls. If the whole diagram is rotated about the vertical axis distributing these vectors in 3 dimensions, all of the periphery of the closed sphincter will be spread open without any lateral translation of the sphincter itself.

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, D1 and D2 by the diaphragmatic contraction of a hiccup, the resulting distribution of forces will be identical. Thus a hiccup is the mechanical equivalent of a contraction of the LM and has the same effect in releasing the sphincter.The PEL is essential to this force resolution. When it ruptures, reflux is alleviated.

Last Updated July 31 2007 by David PJ Stiennon