SO! Your stones have white pockets inside??? I've never heard of that, so far. Fascinating. Are the white pockets powdery or solid or crystally?
Most people's cholesterol stones seem to be emerald or pea green inside. But they can be tan/golden on the outside or any shade of green on the outside.
Some people have passed calcified stones, of course. They are white inside, crystally and I've heard some described as 'malt ball'y inside. Totally wild.