Catheters or other tubular devices and methods for using them to perform a medical procedure are provided. In an exemplary embodiment, a tubular device includes an elongate tubular member comprising a proximal end, a distal end sized for introduction into a patient's body, and a lumen extending between the proximal and distal ends； an expandable member on the distal end comprising an outer impermeable membrane with an inner surface surrounding a substantially enclosed interior space； and a fiber network within the interior space coupled to the inner surface and configured to limit expansion of the membrane when inflation media is directed into the interior space from the lumen to expand the membrane to an expanded configuration.
