Purpose: The purpose of this study is to assess the importance of non-Newtonian rheological models on blood flow in the human thoracic aorta. Methods: The pulsatile flow in the aorta is simulated using the models of Casson, Quemada and Walburn-Schneck in addition to a case of fixed (Newtonian) viscosity. The impact of the four rheological models (using constant hematocrit) was assessed with respect to (i) magnitude and deviation of the viscosity relative to a reference value (the Newtonian case); (ii) wall shear stress (WSS) and its time derivative; (iii) common WSS-related indicators, OSI, TAWSS and RRT; (iv) relative volume and surface-based retrograde flow; and (v) the impact of rheological models on the transport of small particles in the thoracic aorta. Results: The time-dependent flow in the thoracic aorta implies relatively large variations in the instantaneous WSS, due to variations in the instantaneous viscosity by as much as an order of magnitude. The largest effect was observed for low shear rates (tens s-1). The different viscosity models had a small impact in terms of time- and spaced-averaged quantities. The significance of the rheological models was clearly demonstrated in the instantaneous WSS, for the space-averaged WSS (about 10%) and the corresponding temporal derivative of WSS (up to 20%). The longer-term accumulated effect of the rheological model was observed for the transport of spherical particles of 2 mm and 2 mm in diameter (density of 1200 kg/m3). Large particles' total residence time in the brachiocephalic artery was 60% longer compared to the smaller particles. For the left common carotid artery, the opposite was observed: the smaller particles resided considerably longer than their larger counterparts. Conclusions: The dependence on the non-Newtonian properties of blood is mostly important at low shear regions (near walls, stagnation regions). Time- and space-averaging parameters of interest reduce the impact of the rheological model and may thereby lead to under-estimation of viscous effects. The rheological model affects the local WSS and its temporal derivative. In addition, the transport of small particles includes the accumulated effect of the blood rheological model as the several forces (e.g., drag, added mass and lift) acting on the particles are viscosity dependent. Mass transport is an essential factor for the development of pathologies in the arterial wall, implying that rheological models are important for assessing such risks.

Cardiovascular diseases (CVD) are the most common cause of death in large parts of the world. Atherosclerosis (AS) has a major part in most CVDs. AS is a slowly developingdisease which is dependent on multiple factors such as genetics and life style (food, smoking, and physical activities). AS is primarily a disease of the arterial wall and develops preferentially at certain locations (such as arterial branches and in certain vessels like thecoronary arteries). The close relation between AS sites and blood flow has been well established over the years. However, due to multi-factorial causes, there exist no early prognostic tools for identifying individuals that should be treated prophylactically or followed up. The underlying hypothesis of this thesis was to determine if it is possible to use bloodflow simulations of patient-specific cases in order to identify individuals with risk for developing AS. CT scans from patients with renal artery stenosis (RAS) were used to get the affected vessels geometry. Blood flow in original and “reconstructed” arteries were simulated. Commonly used wall shear stress (WSS) related indicators of AS were studied to assess their use as risk indicators for developing AS. Divergent results indicated urgent need to assess the impact ofsimulation related factors on results. Altogether, blood flow in the following vessels was studied: The whole aorta with branches from the aortic arch and the abdominal aorta, abdominal aorta as well as the renal arteries, and separately the thoracic aorta with the three main branching arteries from the aortic arch. The impact of geometrical reconstruction, employed boundary conditions (BCs), effects of flow-rate, heart-rate and models of blood viscosity as function of local hematocrit (red blood cell, RBC, concentration) and shear-rate were studied in some detail. In addition to common WSS-related indicators, we suggested the use of endothelial activation models as a further risk indicator. The simulations data was used to extract not only the WSS-related data but also the impact of flow-rate on the extent of retrograde flow in the aorta and close to its walls. The formation of helical motion and flow instabilities (which at high flow- and heart-rate lead to turbulence) was also considered.

Results:

A large number of simulations (more than 100) were carried out. These simulations assessed the use of flow-rate specified BCs, pressure based BCs or so called windkessel (WK) outlet BCs that simulate effects of peripheral arterial compliance. The results showed high sensitivity of the flow to BCs. For example, the deceleration phase of the flow-rate is more prone to flow instabilities (as also expressed in terms of multiple inflection points in the streamwise velocity profile) as well as leading to retrograde flow. In contrast, the acceleration phase leads to uni-directional and more stable flow. As WSS unsteadiness was found to be pro-AS, it was important to assess the effect flow-rate deceleration, under physiological and pathological conditions. Peaks of retrograde flow occur at local temporal minima in flow-rate. WK BCs require ad-hoc adjusted parameters and are therefore useful only when fully patient specific (i.e. all information is valid for a particular patient at a particular point of time) data is available. Helical flows which are considered as atheroprotective, are formed naturally, depending primarily on the geometry (due to the bends in the thoracic aorta). Helical flow was also observed in the major aortic branches. The helical motion is weaker during flow deceleration and diastole when it may locally also change direction. Most common existing blood viscosity models are based on hematocrit and shear-rate. These models show strong variation of blood (mixture) viscosity. With strong shear-rate blood viscosity is lowest and is almost constant. The impact of blood viscosity in terms of dissipation is counter balanced by the shear-rate; At low shear-rate the blood has larger viscosity and at high shear-rate it is the opposite. This effect and due to the temporal variations in the local flow conditions the effect of blood rheology on the WSS indicators is weak. Tracking of blood components and clot-models shows that the retrograde motion and the flow near branches may have so strong curvature that centrifugal force can become important. This effect may lead to the transport of a thrombus from the descending aorta back to the branches of the aortic arch and could cause embolic stroke. The latter results confirm clinical observation of the risk of stroke due to transport of emboli from the proximal part of the descending aorta upstream to the vessels branching from the aortic arch and which lead blood to the brain.

Conclusions:

The main reasons for not being able to propose an early predictive tool for future developmentof AS are four-folded:

i. At present, the mechanisms behind AS are not adequately understood to enable to define aset of parameters that are sensitive and specific enough to be predictive of its development.

ii. The lack of accurate patient-specific data (BC:s) over the whole physiological “envelop”allows only limited number of flow simulations which may not be adequate for patientspecificpredictive purposes.

iii. The shortcomings of current models with respect to material properties of blood andarterial walls (for patient-specific space- and time-variations) are lacking.

iv. There is a need for better simulation data processing, i.e. tools that enable deducinggeneral predictive atherosclerotic parameters from a limited number of simulations, throughe.g. extending reduced modeling and/or deep learning.

The results do show, however, that blood flow simulations may produce very useful data thatenhances understanding of clinically observed processes such as explaining helical- andretrograde flows and the transport of blood components and emboli in larger arteries.

Patient specific (PS) blood flow studies have become popular in recent years but have thus far had limited clinical impact. This is possibly due to uncertainties and errors in the underlying models and simulations set-up. This study focuses on the sensitivity of simulation results due to in- and outflow boundary conditions (BC:s). Nine different inlet- and seven different outlet BC:s were applied to two variants of a healthy subject’s thoracic aorta. Temporal development of the flow is essential for the formation and development of helical/spiralling flow where the commonly observed clockwise helical motion may change direction during the heart-cycle. The sensitivity to temporal and spatial variations in the inlet conditions is significant both when expressed in terms of mean and maximal wall shear stress (WSS) and its different averaged variables, e.g. Time-Averaged WSS (TAWSS), Oscillating Shear Index (OSI) and Relative Residence Time (RRT). The simulation results are highly sensitive to BC. For example, the maximal WSS may vary over 3 orders of magnitude (1 to 1000 Pa) depending on particular combinations of BC:s. Moreover, certain formulations of outlet boundary conditions may be inconsistent with the computed flow field if the underlying assumptions of the space-time dependence are violated. The results of this study show that CFD simulations can reveal flow details that can enhance understanding of blood flows. However, the results also demonstrate the potential difficulties in mimicking blood flow in clinical situations.

Pulsatile flow in the abdominal aorta and the renal arteries of three patients was studied numerically. Two of the patients had renal artery stenosis. The aim of the study was to assess the use of four types of indicators for determining the risk of new stenosis after revascularization of the affected arteries. The four indicators considered include the time averaged wall shear stress (TAWSS), the oscillatory shear index (OSI), the relative reference time (RRT) and a power law model based in platelet activation modeling but applied to the endothelium, named endothelium activation indicator (EAI). The results show that the indicators can detect the existing stenosis but are less successful in the revascularized cases. The TAWSS and, more clearly, the EAI approach seem to be better in predicting the risk for stenosis relapse at the original location and close to the post-stenotic dilatation. The shortcomings of the respective indicators are discussed along with potential improvements to endothelial activation modeling and its use as an indicator for risks of restenosis.