A fastening system includes a membrane assembly which can comprise a pair of body panels secured together at a seam. The membrane panels can comprise a semi-permeable material. A sheath assembly has a tubular configuration with proximate and distal ends and a sheath passage extending therebetween. The sheath assembly can be fastened to the membrane assembly by adhesively securing the sheath assembly adjacent to its proximate end between the membrane panels at the membrane assembly seam. A sheath-to-tube fastener is provided for fastening the sheath assembly to a tube. A fastening method includes the steps of fastening two panels of a membrane assembly together at a seam, fastening a sheath assembly to the membrane assembly between the panels at the seam, and fastening a tube to the sheath. In one embodiment of the present invention a surgical sponge is fastened to the membranes in fluidic connection with the sheath, which is fastened to a suction tube for drawing blood from a surgical site.