An internal and external medical closure system for a separation of first and second tissue portions is provided, which includes a mesh screen comprising tubular vertical risers, vertical strands with barbed filaments, and horizontal spacers connecting the risers and strands in a grid-like configuration. An optional perimeter member partly surrounds the screen and can comprise a perimeter tube fluidically coupled with the vertical risers to form a tubing assembly. Various input/output devices can optionally be connected to the perimeter tube ends for irrigating and/or draining the separation according to methodologies of the present invention. Separation closure, irrigation and drainage methodologies are disclosed utilizing various combinations of closure screens, tubing, sutures, fluid transfer elements and gradient force sources. The use of mechanical forces associated with barbed strands for repositionably securing separated tissues together is disclosed. The use of same for eliminating or reducing the formation of subcutaneous voids or pockets, which can potentially form hematoma and seroma effects, is also disclosed. Further disclosed are alternative embodiment medical closure screen installation systems and methods.