Pressure vs. neck shortening of a balloon

[dislect]

Pressure vs. "neck" shortening of a balloon

I swear this is not a homework question

The purpose of this question is to simulate the shortening of the cervix ("neck") as a result of the increase of pressure -> volume of the female womb.

I would like to come up with a set of equations connecting between the:
1. cervix ("neck") length - shown as 40mm and 25mm in pics
2. overall thickness - shown as 15mm in pics
3. womb radius - shown as 100mm and 105mm in pics (random approximate numbers)
4. material properties (young's modulus, yield strength, density if relevant)

We can assume the:
a. Thickness stays approximately constant
b. material properties stays constant

So in theory I would be able to input the pressure inside the balloon and receive the cervix "neck" new length (shortening) as a result of the balloon inflating and taking away from that neck's length.

I would love someone to guide me and send me the right way. I can't really use laplace's/pascal law because the thickness is not negligible.

Thanks a lot!

Pics for demonstration

 

[SteamKing]

Are we talking about people or balloons? Your post is confusing.

 

[dislect]

Are we talking about people or balloons? Your post is confusing.

Balloon is the analogy simplification of the human womb.
Let's stick with balloons.

 

[SteamKing]

Sorry, don't see the similarity.

 

[dislect]

http://www.shinesa.org.au/images/dmImage/SourceImage/Stages-of-pregancy.gif