Influence of aortic valve tilt angle on flow patterns in the ascending aorta

Abstract

Transcatheter aortic valve implantation (TAVI) has become the alternative procedure to high-risk patients who are diagnosed with aortic valve stenosis. Differently from the traditional open-chest surgical procedure, a small variation on the prosthetic aortic valve deployment angle is expected with the TAVI procedure. The hemodynamic patterns of the blood flow in the ascending aorta are related to the development of many cardiovascular diseases. There are, however, few data available in the literature correlating the aortic valve tilt angle to hemodynamic effects. In this work, a 3D printed aorta model made of a transparent silicon resin was produced, based on the anatomy of a specific patient submitted to a TAVI procedure. The stereoscopic Particle Image Velocimetry technique was employed to measure three-component velocity fields at closely spaced cross-sectional planes, along the ascending aorta. The measurements were performed for a constant flow rate corresponding to the peak of the systolic phase of the cardiac cycle. Averaged velocity fields and turbulent quantities were determined for both, the base case, with no valve tilt, and for cases with an inclination of 4° and 8°, oriented at the four anatomical directions of the human body reference system, namely anterior, posterior, right and left. The results revealed the dominant flow patterns in the ascending aorta formed by a jet-like inlet flow impinging on the curved aorta right wall, inducing a significant eccentricity on the axial velocity profile. Regions of reverse flow were identified and linked to the abrupt area change associated with the typical reduced inlet diameter of TAVI implants. The impinging flow and wall curvature effects established circulation patterns defining a helical flow structure. The influence of the inlet flow orientation on the flow turbulent characteristics was assessed by the spatial evolution of the turbulent kinetic energy (TKE), Reynolds and viscous stresses. The maximum values of TKE were found around the inlet jet boundaries and concentrated in the neighborhood of the right aorta wall where the eccentric axial flow prevailed. Spatial distributions of the maximum Reynolds stresses were similar to the TKE distributions and presented maximum stresses typically one order of magnitude higher than the maximum average viscous shear stresses. Maximum average viscous stress distributions were revealed at the jet-like flow boundaries and in the vicinity of the right wall, displaying moderate stress levels that, according to the literature, can be sufficient to produce cell damage and platelet activation. The complex nature of the flow field was revealed by streamlines obtained from the measured flow fields, allowing the identification of the influence of the inlet flow orientation and tilt angle on the position of the stagnation point on the aorta right wall, as well as the angle of incidence of the jet-like flow on the wall. A simple model based on momentum balance was used to estimate the pressure increment on the wall due to flow impingement. The model captured the influence of the inlet flow orientation, indicating that pressure increases of the order of 40% in relation to the base case condition were obtained for the 8°, left inlet flow orientation.

Graphic abstract

Appendices

Appendix

Appendix A: Experimental uncertainty estimation

The experimental standard uncertainty for a generic measured quantity X was estimated by combining the random and systematic components of the uncertainty, also known as type A and type B uncertainty components, according to ISO-GUM (2018) as,

$$U^{2}_{X} = U_{X,A}^{2} + U_{X,B}^{2}$$

(9)

The uncertainty on each velocity component was estimated by neglecting the contributions of the uncertainties from the image calibration and light pulse interval, as compared to the uncertainty on the particle displacement calculation (Sciacchitano and Wieneke 2016; Sciacchitano 2019; Raffel et al. 2018). The uncertainties on the fluid density and viscosity were not considered. The type A uncertainty on the velocity components was estimated from the standard deviation of the velocity measurements as (Sciacchitano and Wieneke 2016),

$$U_{{\overline{u},A}} = \frac{{\sigma_{u} }}{\sqrt N }\quad {\text{with}}\quad \sigma_{u} = \left( {\frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \left( {u_{i} - \overline{u}} \right)} \right)^{1/2}$$

(10)

and similarly for $U_{{\overline{v},A}}$ and $U_{{\overline{w},A}}$. N is the number on uncorrelated measured samples: 1500 in the present experiments.

The systematic or type B component of the uncertainty was estimated by calibration experiments using a similar SPIV setup and processing software (Fernandes et al. 2018), leading to an uncertainty of ± 0.008 m/s for the in-plane components. The out-of-plane component displayed a larger uncertainty due to the stereoscopic displacement calculation, ± 0.014 m/s. The combined standard uncertainties on the velocity components were obtained by using Eq. (9).

The type A uncertainty components of diagonal and off-diagonal terms of the Reynolds stress tensor, R_ww and R_uw were estimated by Sciacchitano and Wieneke (2016) as,

$$U_{{R_{{ww,A}} }} = R_{{ww}} {\sqrt {\frac{2}{N}}} \quad U_{{R_{{uw,A}} }} = {\sqrt {R_{{ww}} R_{{uu}} \frac{{1 + \gamma_{{uw}}^{2} }}{N}}}$$

(11)

where $\gamma_{uw}$ is the cross-correlation coefficient between u and v. The type B uncertainty on the Reynolds stress components were estimated based on the density and the uncertainty on each velocity component, since calibration experiments were not available for those quantities. For a diagonal and an off-diagonal component, these conservative estimates were computed as $\rho \overline{{U_{w}^{2} }}$ and $\rho \sqrt {\overline{{U_{u}^{2} }} \ \overline{{U_{w}^{2} }} }$, respectively. The combined standard uncertainty on a Reynolds stress tensor component was obtained by Eq. (9).

The type A uncertainty on the turbulent kinetic energy was computed as Sciacchitano and Wieneke (2016),

$$U_{{{\text{TKE}},A}} = {\sqrt {R_{{uu}}^{2} + R_{{vv}}^{2} + R_{{ww}}^{2} }} \cdot {\sqrt {\frac{1}{{2N}}}}$$

(12)

The type B uncertainty on the TKE measurements was estimated as $\rho \overline{{U^{2} }}$, where U is the square-root combination of the uncertainties on the three velocity components. The combined standard uncertainty on TKE was obtained using Eq. (9).

The uncertainty on the components of the shear stress tensor was estimated assuming equal and non-correlated uncertainties for the neighboring velocity components involved in the spatial derivatives (Sciacchitano and Wieneke 2016). Thus,

$$U_{{\tau_{yx} }} = \mu \frac{U}{d}\sqrt {1 - \gamma \left( {2d} \right)}$$

(13)

where $\gamma \left( {2d} \right)$ is the normalized cross-correlation coefficient of the measurement error at the two points separated from two grid spaces, 2d (derivative by central difference scheme). U is the uncertainty on the velocity measurements assumed to have the same magnitude for each component. The type B uncertainty on the shear stress measurements was estimated by propagating the uncertainties on the equations defining each shear stress tensor component, as exemplified in equation Eq. 5 for the $\tau_{yx}$ component (ISO-GUM 2018). Uncertainties on the velocity components and displacements were considered, while the uncertainty on the fluid viscosity was neglected. The combined standard uncertainty on each shear stress tensor component was obtained using Eq. (9).

The combined standard uncertainties estimated as described above were expanded to be associated with a 95% confidence level by using a coverage factor k = 2, obtained from a t-student distribution corresponding to a large number of measurement samples (ISO-GUM 2018).

A sample calculation of the uncertainty estimates obtained following the procedure described is presented in Table 2. It is interesting to note in the data displayed in Table 2 that the type B uncertainties dominate the combined uncertainties for the measurements of the three components of the average velocity vector, due to the large amount of independent samples N used in the present work. For the Reynolds stress tensor components and the turbulent kinetic energy, the type A uncertainty components dominate. For the shear stress tensor components, both type A and B uncertainty components have equivalent influence on the combined uncertainty estimate.

Table 2 Uncertainty estimate for data from a typical experiment

Appendix B: Spatial distribution of maximum Reynolds stress

Fig. 23

Maximum Reynolds stress in the ascending part of the aorta model for the different inlet flow orientations and the base case, for planes 1, 4, 5 and 6 and for tilt angle of 8^o