Getting ribcage to behave right.

I’m rigging a model (a Cow skelton) and I have a problem.

In the ribcage, I don’t know the scientific term but the bone linking the ribs down the side, I’m having a problem with them.

Model not posed.

Model posed.

See how the ribs come out of alignment with that linking bone?

I want that to not happen, I want it so that the end of the ribs stay firmly within that bone, I assume I have to use some kind of modifier which “Skins” (to use a Max term) the ends of the ribs to the connecting bone.

What do?