Apparatus and methods are disclosed for supporting ischemic tissue of the heart using scaffolds that may be placed within the heart percutaneously. A scaffold assembly may include a layer of biocompatible material detachably secured to a placement rod, such that the placement rod may be used to urge the layer of biocompatible material through a catheter to adjacent an area of ischemic tissue. Anchors may secure the layer of material to the myocardium. Multiple layers of biocompatible material may be placed in the ventricle separately to form the scaffold. In some embodiments, a scaffold is formed or reinforced by injecting a polymer, such as a visco-elastic foam, around an inflatable member inflated within a ventricle.