Numerical study of the oxygen transport in aorta: effect of haemoglobin and inlet velocity profile

The blood flowing in the cardiovascular system allows the transport of nutrients to cells and the removal of metabolites and toxins. Among substances carried by the blood, oxygen is one of the most relevant due to its key role in all metabolic processes. Insufficient delivery of oxygen to cells leads to hypoxia and consequent disfunction and disorganization of cells. If this condition occurs in arterial walls, it is considered to promote the origination and development of atherosclerotic lesions. Therefore, studying mechanisms that rule oxygen transport in blood may allow to localize regions of arterial wall with a non-negligible probability to develop atherosclerosis. In particular, this study focused on the oxygen effects in the largest human body artery: the aorta. It must be considered that oxygen is present in the blood in two forms: dissolved in blood or bound to haemoglobin. Moreover, oxygen can move from blood to cells by two mechanisms: a diffusive mechanism and a transport mechanism mediated by flowing blood, called advection. These two mechanisms have been linked together and with the haemoglobin dependant oxygen properties in a differential equation describing oxygen transport. This equation has been numerically solved together with the Navier-Stokes equations considering four cases: two cases with a 3D velocity profile set at the inlet section of the model and two cases with a parabolic velocity profile. One of each pair was performed neglecting the effect of the haemoglobin. The advection and diffusion terms of the equation were described by two distinct (one for each term) user-defined functions (UDFs), to customize the modeling. The results of each simulation were used to calculate the Sherwood Number (Sh) and the Wall shear stress (WSS) which give information on the entity of oxygen transport and on stresses occurring on the aortic walls. This was made in order to localize regions of the aorta with the higher risk, that is, regions where Sh and WSS are both low. Also the Damkohler (Daw) number was considered to make an estimation of areas which risk to undergo hypoxia, that is, areas where Sh is lower than Daw. The results of the four cases were analysed and compared in order to evaluate the effects of inlet velocity profile and haemoglobin to the localization of regions at risk.