Curved surface from points

I am trying make a surface that will pass through each set of 4 divided points on each of the circles. Another option is to create horizontal interpolated curves through each horizontal set of points on each grid level and do the same vertically (in this example it would end up as 3 horizontal curves and 4 vertical).

I have tried the "surface from points" method but with no luck. I have also tried some tree branching stuff but that hasn't worked either.

Any ideas would be much appreciated.

Thanks