A combustor system comprising: an annular combustor dome arranged around a centerline for a gas turbine engine, the annular combustor dome comprising an annular dome plate having a first axial side and a second axial side opposite the first axial side, wherein a plurality of injection holes in the annular dome plate extend from the first axial side to the second axial side, the injection holes in fluid communication with a combustion chamber at least partially defined by the second axial side, wherein the annular dome plate further comprises: an inlet channel that extends from the first axial side toward the second axial side; a plurality of internal cooling channels enclosed within the annular dome plate, the internal cooling channels defined inside of the annular dome plate between the first axial side and the second axial side, the internal cooling channels in fluid communication with the inlet channel, wherein air received by the inlet channel is split between the internal cooling channels, wherein the internal cooling channels include a plurality of circumferential cooling channels and a radial cooling channel, the circumferential cooling channels concentric with at least one f the injection holes, each circumferential cooling channel positioned at a different radial distance from the at least one injection hole, and wherein the radial cooling channel extends away from the at least one injection hole and intersects the plurality of circumferential cooling channels at a plurality of cooling junctions; a plurality of pockets located on the second axial side of the annular dome plate, wherein each of the pockets includes a side having a shadow surface and the shadow surface includes a corresponding cooling outlet in fluid communication with the internal cooling channels, the corresponding cooling outlet configured to release air from the internal cooling channel onto the second axial side of the annular dome plate; and an outlet channel that extends from at least one of the internal cooling channels toward the second axial side of the annular dome plate, wherein the outlet channel is configured to receive air from at least one of the internal cooling channels and convey the air to at least one of said cooling outlets of the annular dome plate on the second axial side. an annular combustor dome arranged around a centerline for a gas turbine engine, the annular combustor dome comprising an annular dome plate having a first axial side and a second axial side opposite the first axial side, wherein a plurality of injection holes in the annular dome plate extend from the first axial side to the second axial side, the injection holes in fluid communication with a combustion chamber at least partially defined by the second axial side, wherein the annular dome plate further comprises: an inlet channel that extends from the first axial side toward the second axial side; a plurality of internal cooling channels enclosed within the annular dome plate, the internal cooling channels defined inside of the annular dome plate between the first axial side and the second axial side, the internal cooling channels in fluid communication with the inlet channel, wherein air received by the inlet channel is split between the internal cooling channels, wherein the internal cooling channels include a plurality of circumferential cooling channels and a radial cooling channel, the circumferential cooling channels concentric with at least one f the injection holes, each circumferential cooling channel positioned at a different radial distance from the at least one injection hole, and wherein the radial cooling channel extends away from the at least one injection hole and intersects the plurality of circumferential cooling channels at a plurality of cooling junctions; a plurality of pockets located on the second axial side of the annular dome plate, wherein each of the pockets includes a side having a shadow surface and the shadow surface includes a corresponding cooling outlet in fluid communication with the internal cooling channels, the corresponding cooling outlet configured to release air from the internal cooling channel onto the second axial side of the annular dome plate; and an outlet channel that extends from at least one of the internal cooling channels toward the second axial side of the annular dome plate, wherein the outlet channel is configured to receive air from at least one of the internal cooling channels and convey the air to at least one of said cooling outlets of the annular dome plate on the second axial side.