BG Medicine, which markets a biomarker diagnostic test for heart failure and is developing others, priced its downsized IPO on Thursday. The Waltham, MA-based company raised $35 million by offering 5 million shares at $7 per share. The offering price represented half the midpoint of its previously proposed $13 to $15 range. The company had attempted to go public in December of last year before postponing the deal. BG Medicine, which was founded in 2000 and booked $1 million in sales for the 12 months ended September 30, 2010, will begin trading on Friday on the NASDAQ under the symbol BGMD. Lazard Capital Markets acted as the sole bookrunner on the deal. Baird and Cowen & Company were co-managers.