Abstract: The invention relates generally to methods of improving function of a transplanted organ, treating or preventing primary graft dysfunction of a transplanted organ, treating or preventing acute rejection of a transplanted organ, treating or preventing delayed graft function, or achieving a clinical endpoint indicative of a successful organ transplant in a recipient of the transplanted organ which comprise contacting blood from the recipient with an extracorporeal membrane having a plurality of pores having an average pore size of at least 40 kDa, 50 kDa or 60 kDa to permit inflammatory cytokines and other inflammatory molecules to pass through the pores and out of the blood that is returned back to the recipient.