The method is described as the removal of mediators that contribute to the pathogenesis of cancer from blood by contacting the blood with a solid, essentially non-micro-porous substrate which has been surface treated with heparin, heparan sulfate and, optionally, other molecules or chemical groups (the adsorbent media or media) having a binding affinity to the mediator, and wherein the size of the interstitial channels within said substrate are balanced with the amount of interstitial substrate surface area such that high flow rates of blood past said substrate creates a flow transport that is characterized by convection transport more than Brownian diffusion transport.