Methods of treating, inhibiting and/or preventing instant blood-mediated inflammatory reaction (IBMIR) comprise administering, to a subject, a dextran sulfate characterized by a number average molecular weight (Mn) as measured by nuclear magnetic resonance (NMR) spectroscopy within an interval of 1850 and 3500 Da; an average sulfate number per glucose unit within an interval of 2.5 and 3.0; and an average sulfation of C2 position in the glucose units of said dextran sulfate of at least 90%, or a salt of such a dextran sulfate.