3D Grid Distortion

Hello there I am a bit stuck right now...
I have a 2 dimentional grid thats been distorted by some Attractor points. I want this distortion to happen 3 dimensionally  as if this attarctor points are bubles and not just circles. I want the grid to get distorted in x,y and aslo Z direccion...
Hope this can get done...


Any ideas would be great!!!
Check my definition and if something can help, feel free to tell me