Oxygen and carbon dioxide transport in time-dependent blood flow past fiber rectangular arrays

Abstract

The influence of time-dependent flows on oxygen and carbon dioxide transport for blood flow past fiber arrays arranged in in-line and staggered configurations was computationally investigated as a model for an artificial lung. Both a pulsatile flow, which mimics the flow leaving the right heart and passing through a compliance chamber before entering the artificial lung, and a right ventricular flow, which mimics flow leaving the right heart and directly entering the artificial lung, were considered in addition to a steady flow. The pulsatile flow was modeled as a sinusoidal perturbation superimposed on a steady flow while the right ventricular flow was modeled to accurately depict the period of flow acceleration (increasing flow) and deceleration (decreasing flow) during systole followed by zero flow during diastole. It was observed that the pulsatile flow yielded similar gas transport as compared to the steady flow, while the right ventricular flow resulted in smaller gas transport, with the decrease increasing with Re. The pressure drop across the fiber array (a measure of the resistance), work (an indicator of the work required of the right heart), and shear stress (a measure of potential blood cell activation and damage) are lowest for steady flow, followed by pulsatile flow, and then right ventricular flow. The pressure drop, work, shear stress, and Sherwood numbers (a measure of the gas transport efficiency) decrease with increasing porosity and are smaller for AR<1 as compared to AR>1 (AR is the distance between fibers in the flow direction/distance between fibers in direction perpendicular to flow), although for small porosities the Sherwood numbers are of similar magnitude. In general, for any fiber array geometry, high pressure drop, work, and shear stresses correlate with high Sherwood numbers, and low pressure drop, work, and shear stresses correlate with low Sherwood numbers creating a need for a compromise between pressure drop/work/shear stresses and gas transport.