The invention provides apheresis devices and their use for substantial removal of all types of cfDNA for treatment of various diseases and during perfusion of an organ and/or anatomical cavity, to limit the negative effects of circulating cfDNA during organ transplantation and thus improve the quality and survival of transplanted organs, and reduce unfavorable transplantation outcomes such as transplant dysfunction, ischemia-reperfusion injury, graft rejection, and organ failure.