The purpose of this double-blind, placebo-controlled, dose-escalation study is to evaluate the safety, tolerability and effectiveness of Thymosin Beta 4 (Tβ4), administered topically, in patients with Pressure Ulcers (PU). PU is caused by prolonged pressure or rubbing of the body in areas prone to moisture and friction. PU affects primarily elderly, bedridden patients. Tβ4 is a synthetically-produced copy of a naturally-occurring 43 amino acid peptide that has wound healing and anti-inflammatory properties and can up-regulate the expression of laminin-5.