An in-vivo plasmapheresis and/or in-vivo ultrafiltration membrane comprises elongated hollow fibers each fiber having an interior lumen extending along the fiber length, the fiber wall having a plurality of zones between the inner and outer wall surfaces, each of the zones having a mass density different than the mass density of an adjacent zone. The fiber wall is characterized by having a lower mass density zone at the inner wall surface and a higher mass density zone at the outer wall surface. The fiber is further characterized by having an average elongation breaking force strength of at least about 0.2 lbs. and an average elongation of at least about 45%.