A prosthesis (100, 600A, 600B, 600C, 800) having a compressed configuration for delivery within a vasculature and a radially-expanded configuration for deployment within a target blood vessel in a patient, the prosthesis comprising: a tubular body (110, 110C, 610A, 610B, 610C, 810) having a first end (121, 821) and a second end (125, 825), the first end (121, 821) having an anchoring structure to engage an inner wall of the target blood vessel in the radially-expanded configuration; and an elongated mid-portion between the first (121, 821) and second ends (125, 825) and including a channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818) formed in a wall (112, 112C, 812) thereof, wherein the channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818) is at least partially oriented circumferentially about the tubular body (110, 110C, 610A, 610B, 610C, 810); and a fluid-absorbable composition (310, 410, 510) deposited within the channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818), the fluid-absorbable composition (310, 410, 510) having a first volume when the prosthesis (100, 600A, 600B, 600C, 800) is in the compressed configuration and configured to swell to a second volume within the channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818) upon deployment of the prosthesis (100, 600A, 600B, 600C, 800) within the target blood vessel to thereby transition at least the elongated mid-portion into the radially-expanded configuration. a tubular body (110, 110C, 610A, 610B, 610C, 810) having a first end (121, 821) and a second end (125, 825), the first end (121, 821) having an anchoring structure to engage an inner wall of the target blood vessel in the radially-expanded configuration; and an elongated mid-portion between the first (121, 821) and second ends (125, 825) and including a channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818) formed in a wall (112, 112C, 812) thereof, wherein the channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818) is at least partially oriented circumferentially about the tubular body (110, 110C, 610A, 610B, 610C, 810); and a first end (121, 821) and a second end (125, 825), the first end (121, 821) having an anchoring structure to engage an inner wall of the target blood vessel in the radially-expanded configuration; and an elongated mid-portion between the first (121, 821) and second ends (125, 825) and including a channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818) formed in a wall (112, 112C, 812) thereof, wherein the channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818) is at least partially oriented circumferentially about the tubular body (110, 110C, 610A, 610B, 610C, 810); and a fluid-absorbable composition (310, 410, 510) deposited within the channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818), the fluid-absorbable composition (310, 410, 510) having a first volume when the prosthesis (100, 600A, 600B, 600C, 800) is in the compressed configuration and configured to swell to a second volume within the channel (118, 118a, 118b, 118c, 418, 618A, 618B, 618C, 818) upon deployment of the prosthesis (100, 600A, 600B, 600C, 800) within the target blood vessel to thereby transition at least the elongated mid-portion into the radially-expanded configuration.