Branched stent-graft system

A method comprising:

• providing an endovascular stent-graft, which includes a generally tubular hourglass-shaped body, which includes (a) a flexible stent member, which includes a plurality of structural stent elements, and (b) a tubular fluid flow guide, which comprises a fabric, and is attached to the structural stent elements;
• transvascularly introducing the stent-graft into a blood vessel of a human subject while the hourglass-shaped body is in a radially-compressed delivery configuration;
• thereafter, transitioning the hourglass-shaped body to an intermediate deployment configuration, in which the hourglass-shaped body is shaped so as to define a narrow waist portion longitudinally surrounded by and adjacent to wider first and second longitudinal portions of the hourglass-shaped body, and the fabric along the second portion is shaped so as to define at least first and second lateral apertures;
• and
• thereafter, transitioning the hourglass-shaped body to a radially-expanded deployment configuration in the blood vessel, in which radially-expanded configuration the hourglass-shaped body is shaped so as to define the narrow waist portion longitudinally surrounded by and adjacent to the wider first and second longitudinal portions, and the fabric along the second portion is shaped so as to define at least the first and the second lateral apertures,
• wherein, when the hourglass-shaped body, including the waist portion, is in the intermediate deployment configuration, an average diameter of the waist portion is at least 10% less than when the hourglass-shaped body, including the waist portion, is in the radially-expanded deployment configuration.