An endoluminal filter including a first support member having a first end and a second end and a second support member attached to the first end of the first support member or the second end of the first support member and forming a crossover with the first support member. The endoluminal filter also includes a material capture structure extending between the first and second support members, the crossover and the first end or the second end of the first support member and at least one tissue anchor on the first support member or the second support member. The material capture structure can be formed by, for example, joining intersecting filaments, laser cutting a sheet of material, or additive manufacturing. A perimeter of the material capture structure can include attachments to join the material capture structure to the first or second support member.
