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5.4 CONCLUSION 91

diameters, we obtained 2.7% and 1.9%, respectively. These values are computed with respect to the loaded configu-
ration, that is, when the diastolic pressure has been reached. During the load of the artery until diastolic pressure, the
diameter variations of the locations, shown in Fig. 5.9, are of about 21.8% for the AA and 15.1% for the DA. For the
carotid artery (Fig. 5.9B), the maximal diameter variations during a cardiac cycle are 0.1 and 0.13 mm on the CCA and
ECA, respectively. By normalizing these changes with their corresponding diameters, we obtained 2.4% and 3.1%,
respectively. The obtained values are smaller than those measured by Studinger et al. [43]. However, the latter have
been obtained using healthy and young patients during intense exercise conditions while the results presented here are
obtained using rest conditions. It has to be noted that again, these values refer to the diameter variation during the
cardiac cycle. The maximal diameter variation of each branch from the initial configuration to the beginning of the
cycle is, in fact, much higher (about 20% and 17%), respectively. As for the case of the aorta, this is due to the pres-
surization of the artery until the diastolic pressure and it has not been considered for comparison purposes.
The presented results agree with those obtained in other works, which show that the arterial wall compliance for the
carotid remains limited during the cardiac cycle [9]. Evidently, the WSS magnitude is reduced in the distensible model
so that the compliance may play a crucial role when computing WSS and related indices for assessing atherosclerotic
risk. The results of the flow study have been compared as far as possible with the numerical results found in the lit-
erature. However, this comparison can be performed only in a qualitative manner due to the different conditions
in which the compared results have been obtained. These differences include pressure pulse wave, wall parameter,
Reynolds number, and rheological blood property, among others. The qualitative comparison shows agreements
in the essential features. For instance, during diastole, a reduction of the internal axial flow velocity is registered so
that the pressure and, thus, the vessel lumen increase, as previously reported by Perktold and Rappitsch [9].
On the contrary, during systole, local accelerations and pressure decreases cause vessel lumen contractions so that
the internal axial flow velocity tends to increase.

5.3.5 Limitations
The main limitation of the provided work that is based on FSI simulations is related to the increased computational
costs with respect to the CFD and CSM techniques. This aspect may limit the introduction of the FSI to the clinical
practice, contrary to the CFD, for instance. Furthermore, patient-specific boundary conditions would be of advantage
for more precisely studying the presented hemodynamics. The computed impedance-based boundary conditions are
specific to measured data that unfortunately have not been obtained from the same patients as those of the CT data.
Additionally, the conditions are imposed as flat profiles on the inlet and outlet surfaces. However, the entrance and exit
profiles are more complicated. The boundary conditions of the solids model also play a very important role. In this
work, we have constrained the extremities of the structural domains. In this way, even the movement as a rigid body is
impeded; the models tend to provide a certain displacement that could be avoided with the use of elastic springs. We
are currently working on this issue for dumping this nonphysiological movement. Finally, the structural material
models, even hyperelastic, anisotropic, and fiber-reinforced, are considered as passive, neglecting the active behavior
of the muscular tissue.
However, with all these assumptions, the presented computational models shed light on the role and the arterial
compliance for vessel hemodynamics, quantifying the differences with the usual rigid wall models.

5.4 CONCLUSION

Human cardiovascular hemodynamics is a complex problem that is usually treated separately regarding the anal-
ysis of vessel structural behavior and the arterial hemodynamics. In this chapter, a comprehensive FSI model of two
human arteries is presented. The model, which considers the aorta and the carotid artery, includes the most important
flow and structural features of human hemodynamics and presents a fully coupled approached between the fluid and
solid domain. Arterial flow has been computed as quasisteady and non-Newtonian while the vessel wall has been
modeled as anisotropic, hyperelastic, and fiber-reinforced. Arterial compliance has been evaluated in the analyzed
cases as well as the WSS. As previously shown by experimental and computational studies [44, 45], the temporal var-
iation of the vessel lumen is in phase with the pressure waveform while the temporal variation of the WSS is in phase
with the flow waveform. The WSS, being a well-known biomarker for atherosclerosis, was used for computing derived
variables that are frequently used for assessed atherosclerotic risk such as the time average WSS. A comparison
between CFD and FSI analyses has been carried out in order to quantify the impact of the compliant vessel wall when

I. BIOMECHANICS