A radial-path filter element (500, 600, 700), comprising: a wound closed membrane structure (510, 510', 610, 710) forming a continuous structure defining an interior space or portion wrapped about a core (530, 630, 730) in reciprocating clockwise and counterclockwise directions forming semicircular folds of membrane about the core, the semicircular folds of membrane having opposingly situated apical ends separated by a gap, wherein the membrane structure has an interior portion (515, 715) defining at least one feed channel and an exterior portion defining at least one permeate channel, the filter element configured to introduce feed into the interior portion of the membrane structure, and the gap defines a radial permeate discharge path (550, 750), wherein: a radial path support, configured to support said apical ends against feed-side pressure while allowing permeate to flow into the radial discharge path, is located within the radial permeate discharge path; the radial discharge path is configured to allow permeate to travel therethrough directly to the core; the wound closed membrane structure is folded upon itself and joined to itself such that it forms said continuous structure defining said interior portion and: includes a membrane sheet having a backing facing an exterior of the closed membrane structure, wherein the membrane sheet is sealed to itself at its ends, to thereby define said interior portion; or is formed from an integral loop of membrane. a wound closed membrane structure (510, 510', 610, 710) forming a continuous structure defining an interior space or portion wrapped about a core (530, 630, 730) in reciprocating clockwise and counterclockwise directions forming semicircular folds of membrane about the core, the semicircular folds of membrane having opposingly situated apical ends separated by a gap, wherein the membrane structure has an interior portion (515, 715) defining at least one feed channel and an exterior portion defining at least one permeate channel, the filter element configured to introduce feed into the interior portion of the membrane structure, and the gap defines a radial permeate discharge path (550, 750), wherein: a radial path support, configured to support said apical ends against feed-side pressure while allowing permeate to flow into the radial discharge path, is located within the radial permeate discharge path; the radial discharge path is configured to allow permeate to travel therethrough directly to the core; the wound closed membrane structure is folded upon itself and joined to itself such that it forms said continuous structure defining said interior portion and: includes a membrane sheet having a backing facing an exterior of the closed membrane structure, wherein the membrane sheet is sealed to itself at its ends, to thereby define said interior portion; or is formed from an integral loop of membrane. a radial path support, configured to support said apical ends against feed-side pressure while allowing permeate to flow into the radial discharge path, is located within the radial permeate discharge path; the radial discharge path is configured to allow permeate to travel therethrough directly to the core; the wound closed membrane structure is folded upon itself and joined to itself such that it forms said continuous structure defining said interior portion and: includes a membrane sheet having a backing facing an exterior of the closed membrane structure, wherein the membrane sheet is sealed to itself at its ends, to thereby define said interior portion; or is formed from an integral loop of membrane. includes a membrane sheet having a backing facing an exterior of the closed membrane structure, wherein the membrane sheet is sealed to itself at its ends, to thereby define said interior portion; or is formed from an integral loop of membrane.