Mechanisms of polymyxin B endotoxin removal from extracorporeal blood flow: hydrodynamics of sorption

The removal of blood endotoxins with the Toraymyxin extracorporeal sorption device exploits the capability of immobilized polymyxin B (PMB) to bind endotoxins stably with a high specificity. Although adsorption is a molecular-scale mechanism, it involves hydrodynamic phenomena in the whole range from the macroscopic down to the supramolecular scales. In this paper we summarize our experience with a computational, multiscale investigation of this device's hydrodynamic functionality. 3D computational fluid dynamics models were developed for the upper-scale studies. The flow behavior in the sorbent material was either modeled as a homogeneous Darcy's flow (macroscale study), or described as the flow through realistic geometrical models of its knitted fibers (mesoscale study). In the microscale study, simplified 2D models were used to track the motion of modeled endotoxin particles subjected to the competition of flow drag and molecular attraction by the fiber-grafted PMB. The results at each scale level supplied worst-case input data for the subsequent study. The macroscale results supplied the peak velocity of the flow field that develops in the sorbent. This was used in the mesoscale analysis, yielding a realistic range for the shear stresses in the fluid next to the fiber surface. With wall shear stresses in this range, endotoxin particle tracking was studied both in the vicinity of a single immobilized PMB molecule, and in the presence of a layer of PMB molecules evenly distributed at the fiber surface. Results showed that the capability to seize endotoxin molecules extends at least at a distance of 10-20 nm from the surface, which is one order of magnitude greater than the stable intermolecular bond characteristic distance. We conclude that a multiscale approach has the power to provide a comprehensive understanding, shedding light both upon the physics involved at each scale level and the mutual interactions of phenomena occurring at different scales.