A balloon catheter for dilation of stenotic tissue within a tubular member of the body such as a blood vessel provides fluid flow such as blood flow through the balloon while it is being inflated and after it has been inflated. For valvuloplasty applications or for predilitation prior to a TAVI procedure the balloon is placed across the stenotic aortic valve leaflets and inflated to push the leaflets aside to create a greater blood flow area or allow improved subsequent passage of the large TAVI catheter across the stenotic aortic valve leaflets. As the balloon is inflated in diameter, it is required to reduce in length; this length reduction causes a braided inner tubing to also reduce in length. The braided inner tube is thereby required it to increase in diameter during the balloon inflation and create a suitably large blood flow path through the inner tubing. The continuous perfusion through the inner tubing of the balloon allows greater balloon inflation times, improved valvular dilation, and obviates the need for rapid pacing during the valvuloplasty procedure.