A honeycomb body with a honeycomb structure having an inner zone of a first plurality of walls and an outer zone of a second plurality of walls at least partially surrounding the inner zone. The honeycomb structure has Pi that is greater than Po and MPSi that is greater than MPSo, wherein Pi is an average bulk porosity of the first plurality of walls, Po is an average bulk porosity of the second plurality of walls, MPSi is a median pore size of pores in the first plurality of walls, and MPSo is a median pore size of pores in the second plurality of walls. Various honeycomb structures, honeycomb extrusion apparatus, and co-extrusion methods are disclosed.