calculating the depth of a 3D skeleton

Hi, I have a 3D Structure with x,y and goes through slices in the z direction. also i have it's 3D skeleton (or medial axis)

the task is to calculate the depth of each point of the skeleton and it's derivative to determine if there'e a sudden change in the depth..

i can't fugure out how to work through this in the 3D space.. i thought of getting the neighbours of each voxel and calculate the normal to the vector between them, then measure the depth in the direction of the normal line.. but it's all theoritical.. can u please help?

here're pictures for explanation

some consequetive slices in the skeleton:

same slices in the original structures:

both in 3d space: