Type of thesis
An integrated model towards the prediction of the pathological state of ascending thoracic aortic aneurysms
Scientific disciplinary sector
SCIENZE MEDICHE - Translational Medicine
relatore Prof. RECCHIA, FABIO ANASTASIO
- Ascending thoracic aortic aneurysms
- Boundary conditions
- Computational fluid dynamics
- Magnetic resonance imaging
- Patient-specific modeling
- Polynomial chaos expansion
- Uncertainty quantification
Exam session start date
Ascending Thoracic Aortic Aneurysms (ATAAs) must be carefully managed since they are symptoms of a weak arterial wall, and thus they may eventually lead to major complications, as aortic dissection or rupture. Currently, the risk of ATAA complications is evaluated by means of the maximum diameter, surgery being generally recommended when the ascending aortic diameter reaches 5.5 cm. However, despite being an index related to the actual structural stress present on the arterial wall, the maximum diameter alone is not able to fully characterize the pathological state of the aneurysm: the literature has reported that nearly 60% of the ascending aortic dissections occur with a diameter smaller than 5.5 cm (Pape et al., 2007). In this context, the use of Computational Fluid Dynamics (CFD) tools has become more and more common in the last few years, since they allow the simulation of the hemodynamic flow and the quantification of several indicators that cannot be obtained with sufficient accuracy by means of medical imaging.<br><br>The main objective of this Ph.D. project was to develop a new platform exploring the combination between CFD models and medical imaging, in order to evaluate the pathological state of ATAAs on a patient-specific basis.<br><br>The first aim was to identify an open-source numerical solver suitable for cardiovascular<br>applications. The performance of the code was investigated in particular in terms of the following aspects: (i) the possibility to integrate complex patient-specific ATAA geometries as computational domain, (ii) the possibility to take into account wall compliance and thus to perform Fluid-Structure Interaction (FSI) and (iii) the possibility to impose physiological boundary conditions, i.e. conditions that lead to a physiological behavior of flow rates and pressures.<br>After a literature survey we chose SimVascular, a comprehensive open-source software package specific for cardiovascular applications (Updegrove et al., 2016). The software provides a complete pipeline from medical image data segmentation to patient-specific blood flow simulation. In this work, we used the meshing tool and the numerical solver. We modeled the blood as a Newtonian fluid governed by the Navier- Stokes equations for an incompressible flow, without the explicit introduction of any turbulence model. As inlet boundary condition we imposed a flow rate waveform (either derived from the literature or from medical imaging), whereas at the outlets we modeled the effect of downstream organs and vessels by means of the 3-element Windkessel. We generally performed both rigid and deformable simulations: when the wall compliance was taken into account, the aorta was modeled as a linear elastic material, with homogeneous and isotropic properties.<br><br>Since the choice of the boundary conditions to be specified in hemodynamic simulations is non-trivial, the main focus of this thesis was to investigate how uncertainties in such data affect the output quantities of interest, e.g. Wall Shear Stress (WSS) and Time- Averaged Wall Shear Stress (TAWSS). A systematic deterministic analysis would imply a large number of simulations and, thus, huge computational costs, which is practically unaffordable. Therefore, we used a stochastic approach in which the unknown parameters were considered as random variables varying in a suitable interval with a given probability density function. In particular, we adopted the generalized Polynomial Chaos method with a tensor-product approach in case of two random parameters considered together. This allows continuous response surfaces to be obtained in the parameter space starting from a few deterministic simulations. The availability of the response surfaces eventually permits to calibrate the parameters against available data.<br>We started by evaluating the effect of uncertainties in outlet boundary conditions in terms of the 3-element Windkessel model, which is defined by the RCR parameters. After a sensitivity analysis in the 0D model we selected the capacitance C and the proximal resistance Rp for the uncertainty quantification analysis on the complete 3D problem. We found that instantaneous wall shear stresses are significantly affected by outflow parameters, especially in regions characterized by large streamline curvature and flow recirculation, as e.g. in some parts of the aortic neck and of the aneurysm at early diastole. However, the effect on TAWSS is low and further reduced when taking the wall compliance into account. This indicates that, in case of lack of experimental data, the RCR parameters may be specified by using simplified models without losing significant accuracy of the results.<br>Then we investigated the effect of uncertainties in inlet boundary conditions. Reference deterministic simulations showed that the shape of the imposed inlet flow rate waveform, and in particular the quantity of blood entering the aorta, significantly affects both instantaneous and time-averaged WSS. Therefore, we evaluated the effect of varying the stroke volume and the cardiac cycle period. For these parameters we also had clinical information about 23 patients, which allowed the use of more specific probability density functions. The results showed that the parameters at the inlet affect wall shear stresses much more significantly than those at the outlet. In addition, the stroke volume was found to be the main responsible of stochastic variability of TAWSS in almost the entire arterial wall.<br>Finally, we addressed the problem of validating the code against the experimental data given by 4D-Flow Magnetic Resonance Imaging. 4D-Flow MRI is a very interesting technique since it provides time- and space-resolved velocity field. However its resolution is not sufficient for reliably deriving shear stresses on the arterial wall. We thus tested a possible strategy for using such data to calibrate unknown model parameters in the numerical simulation of blood flow inside a healthy thoracic aorta. We preliminary tuned the outflow resistances in order to match the fractions of flow rate exiting the domain outlets during an entire cardiac cycle. As expected, with a rigid-wall model the resulting flow rate waveforms at the outlets do not show the time lag respect to the inlet waveform conversely found in MRI data. We therefore evaluated the impact of wall compliance by using a linear elastic model with homogeneous and isotropic properties, finding that Young’s elastic modulus significantly affect the time delay of outlet flow rate waveforms. Comparison between measured and simulated velocity maps in some representative sections along the aorta shows good qualitative agreement.<br><br>In conclusion, in this Ph.D. project we have successfully set-up a new platform able to investigate hemodynamics on patient-specific ATAAs by integrating simulation models and in-vivo medical imaging. We have assessed the impact on the hemodynamic model<br>of boundary conditions and wall compliance with a general stochastic methodology, which can be used also for addressing other sources of uncertainty. We have also contributed to validate the numerical solver by presenting a procedure to derive the free parameter of the Windkessel model against the experimental data acquired by 4D-Flow MRI. This is a first step towards a routine use of this platform for patient-specific risk evaluation and follow-up.
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