Surgical Aortic Valve Replacement: Are We Able to Improve Hemodynamic Outcome?

Abstract

Aortic valve replacement (AVR) does not usually restore physiological flow profiles. Complex flow profiles are associated with aorta dilatation, ventricle remodeling, aneurysms, and development of atherosclerosis. All these affect long-term morbidity and often require reoperations. In this pilot study, we aim to investigate an ability to optimize the real surgical AVR procedure toward flow profile associated with healthy persons. Four cases of surgical AVR (two with biological and two with mechanical valve prosthesis) with available post-treatment cardiac magnetic resonance imaging (MRI), including four-dimensional flow MRI and showing abnormal complex post-treatment hemodynamics, were investigated. All cases feature complex hemodynamic outcomes associated with valve-jet eccentricity and strong secondary flow characterized by helical flow and recirculation regions. A commercial computational fluid dynamics solver was used to simulate peak systolic hemodynamics of the real post-treatment outcome using patient-specific MRI measured boundary conditions. Then, an attempt to optimize hemodynamic outcome by modifying valve size and orientation as well as ascending aorta size reduction was made. Pressure drop, wall shear stress, secondary flow degree, helicity, maximal velocity, and turbulent kinetic energy were evaluated to characterize the AVR hemodynamic outcome. The proposed optimization strategy was successful in three of four cases investigated. Although no single parameter was identified as the sole predictor for a successful flow optimization, downsizing of the ascending aorta in combination with the valve orientation was the most effective optimization approach. Simulations promise to become an effective tool to predict hemodynamic outcome. The translation of these tools requires, however, studies with a larger cohort of patients followed by a prospective clinical validation study.

Significance

Cardiovascular disease is a common cause of death in industrialized nations, with valvular heart disease being a common subtype. Although diagnosis and treatment are already advanced, most recommendations are based on general information. Only a limited amount of patient-specific data is used. Recently, computer-based models have widely been applied in clinical research to better understand the cardiovascular system and allow patient-specific analysis. However, translation of these models into clinical routine remains cumbersome. Modeling of different valve treatments before the actual intervention might help in improving the clinical outcome. Therefore, we investigated which effects different aortic valve treatments have on the blood flow. It shows that in some cases, a restoration of the physiological flow conditions is possible.

Introduction

Valvular heart disease (VHD) belongs to the structural heart diseases. In industrial countries with high income, the greatest burden is cause by aortic valve disease (1). Furthermore, the strong correlation between VHD and age, combined with an ageing population, results in a consideration of VHD as the “next cardiac epidemic” (2). The prevalence of aortic stenosis grows exponentially from ∼1% in the age group 60–69 to 4% in the 70–79 age group and 10% in the 80–89 group (3). For patients with VHD, surgical aortic valve replacement (AVR) with a biological or a mechanical valve prosthesis is a standard clinical procedure. Alternatively, a transcatheter valve implantation procedure is performed. According to the German Heart Surgery Report 2017 (4), over 34,000 isolated heart valve procedures, including ∼13,000 transcatheter interventions with an in-hospital survival rate of 96%, were performed. For patients with a significantly dilated aorta, an additional replacement of the ascending aorta is recommended (5). Surgical AVR significantly improves survival for patients of all severity groups when compared with medical therapy (6).

The major aim of VHD treatment is to restore physiological function of the heart valve as characterized by two hemodynamic aspects: transvalvular pressure gradient (TPG) and/or regurgitation because both parameters affect cardiac load. Recently, however, further aspects of the hemodynamics associated with VHD and AVR have moved into focus. VHD is also associated with abnormal and complex flow features characterized by high helicity, vorticity, recirculation regions, and turbulent jets impinging the vessel wall (7, 8). These abnormal flow features are, among others, associated with vessel dilatation, aneurysm formation, and atherosclerosis formation as well as ventricle remodeling (8, 9, 10, 11). Finally, these effects affect long-term morbidity and the need for reoperations (12, 13).

Recent studies on post-treatment hemodynamics found that the type of treatment as well as the treatment device used affect hemodynamic outcome. Furthermore, findings have shown that treating the TPG and/or valve insufficiency of a diseased valve does not restore flow profiles toward those of healthy individuals (14, 15, 16). This could possibly explain differences in the post-treatment remodeling process reported for biological and mechanical heart valve prostheses (17, 18).

Currently, the only way to predict post-treatment hemodynamics before a treatment procedure is performed are computational fluid dynamics (CFD). This approach requires, apart from a numerical flow solver, patient-specific image data for geometry and information about inlet and outlet flow conditions as well as information about a possible treatment procedure such as, for example, the known geometry of the heart valve prosthesis and its spatial orientation. All these data together allow, with some degree of uncertainty, predicting the post-treatment geometry and the post-treatment hemodynamics (19, 20). Recent developments in image-based patient-specific modeling of hemodynamics promise a translation of this method into the clinic in the near future, assuming steps will be taken toward clinical validation.

The prediction of the post-treatment procedure is challenging, however, not only because hemodynamic outcomes are sensitive to boundary conditions but also because of the large variability in treatment options for heart valve procedure, including the choice of the valve type (mechanical or biological), design, size, position, and orientation, as well as possible treatment combinations because valve treatment together with ascending aorta replacement is possible. Some of these effects were partially investigated. Hellmeier et al. compared different impacts of biological and mechanical valve prostheses on hemodynamics in the same patient-specific geometries (19). Bruening et al. investigated the impact of the LVOT inflow velocity profile on heart valve hemodynamics (21). Kauhanen et al. have shown the impact of the dilated aorta on hemodynamics (22), whereas Bongert et al. investigated the impact of the valve mounting position (23).

In this light, the primary question is about the ability of engineering methods to reliably improve the post-treatment hemodynamic outcome compared to that of a real surgical outcome. This pilot study aims to describe a virtual AVR procedure, including an optimization strategy developed in our group, in detail, prove of the optimization strategy feasibility on the one hand and elucidate possible key factors affecting the heart valve treatment optimization on the other.

Materials and Methods

The process of image-based patient-specific modeling of the transvalvular and aortic flow after the surgical AVR, from here on called virtual AVR, can generally be divided into two major steps. The first step is the generation of the patient-specific geometric model, and the second is the numerical simulation using CFD. Whereas the latter part consists of the traditional CFD steps of preprocessing, solving of the discretized equations, and postprocessing, the first part is a rather specific, in-house-developed methodology for simulating virtual AVR hemodynamic outcome and will be described in more detail.

Virtual AVR modeling

Each patient-specific model of the virtual AVR is compounded of at least two geometric entities: the patient-specific aorta, including the aortic root with a part of the left ventricle outflow tract (LVOT), and the aortic valve prosthesis. These two entities are combined to obtain the virtual AVR model used for the simulation. In some cases, a virtual replacement of the ascending aorta simulating aortic graft as third entity should be added. The aortic geometry is based on 3D Whole Heart magnetic resonance imaging (MRI) data routinely obtained by a 1.5T Philips Achieva (Philips Medical Systems, Best, The Netherlands) during end-diastolic phase with acquired voxel size 0.66 × 0.66 × 3.2 mm, reconstructed voxel size 0.66 × 0.66 × 1.6 mm, repetition time 40 ms, echo time 2.0 ms, flip angle 90°, and number of signal averages 3. Data used in this study were acquired in the context of the Systems Medicine of Heart Failure study (clinicaltrials.gov ID: NCT03172338, June 1, 2017, retrospectively registered). The study was carried out according to the principles of the Declaration of Helsinki and approved by the local ethics committee. Written informed consent was obtained from the participants and/or their legal guardians.

Image sets of four patients who underwent AVR are used in this study. Based on these data, three-dimensional (3D) label fields are created using ZIB Amira software (Zuse Institute Berlin, Germany) in a slice by slice manner: on each slice (two-dimensional image) in the set, an upper- and lower-threshold based filling is used to obtain a two-dimensional labeling of the region of interest (LVOT and aortic lumen) in that particular slice. Additionally, filling boundaries are defined where necessary to prevent regions outside of the aortic lumen from being labeled (Fig. 1 A).

Figure 1.

(A) Segmentation procedure. (B) The final 3D label field is shown. (C) Label-field-based surface is shown. (D) Surface is shown preprocessed for simulation. To see this figure in color, go online.

This labeling is performed in an extrusion-like manner from top to bottom to yield the full 3D label field. The model was constrained vertically to the apex of the left ventricle at the descending aorta and to the bifurcation of the brachiocephalic trunk at the branching vessels. At the inlet side, the aorta is modeled up until ∼1 cm upstream of the aortic valve annulus, thereby including a portion of the LVOT (Fig. 1 B).

The next step involves creation and cleanup of the triangulated surface model. An initial surface is computed with subvoxel accuracy from the 3D label field by triangulating its boundaries (Fig. 1 B). This raw surface is then smoothed with a local-volume-preserving algorithm while smoothing out the pixel-like surface structure, resulting in a more physiological representation of the vessel (Fig. 1 C; (24)). To finalize the aortic surface model, the smoothed surface is cut off at the inlet and outlet branches with planes orthogonal to the centerlines to obtain well-defined inlet and outlet boundaries for the numerical solver (Fig. 1 D).

The aortic valve prosthesis must also be represented with an appropriate surface model. Two valve types (one mechanical and one biological) of various sizes were used in this study. The mechanical valve models were reverse engineered from publicly available manufacturer information and patent drawings of the ATS Open Pivot Valve (Medtronic, Minneapolis, MN) in different size variations in the fully open position and without hinge mechanisms. The biological valves were represented by a Fisics-Incor valve (INCOR, Hospital das Clínicas, University of São Paulo, São Paulo, Brazil), constructed from a high-resolution (0.1 mm) optical scan that was published earlier (25). For these models, size variations were realized with a global scaling of the base model to fit a certain inlet diameter. The size variations are later used for patient-specific virtual AVR size matching and optimization. Fig. 2 A shows the mechanical and biological valve models, and Table 1 gives an overview of the various sizes modeled.

Figure 2.

(A) Geometry of the mechanical and biological heart valve prosthesis. (B) The process of combining two geometric entities of the aortic shape and the aortic valve prosthesis is shown. (C) Two possible changes of the mechanical valve orientation are shown: tilting (left) and axial rotation (right).

Table 1.

Geometric Information Regarding Real AVR and the Two Optimization Steps

Number	AAo D	Real AVR	Opt. I	Opt. II
1	35	25 mech.	25 mech./10° tilt	25 mech./20° tilt/27 graft
2	42	25 biol.	27 biol./10° tilt	27 biol./10° tilt/33 graft
3	38	22 mech.	22 mech./45° rot/5° tilt	25 mech./−45° rot/5° tilt/28 graft
4	42	23 biol.	23 biol./13° tilt	23 biol./−13° tilt/35 graft

The Opt. I column has multiple sections divided by slashes. The first section denotes the valve size and type and the second/third the valve positioning. The Opt. II column has an additional section for graft size. All sizes are in millimeters. AAo D, ascending aorta diameter; biol., biological; mech., mechanical; rot, rotation.

The final step in the geometry preparation process of the virtual AVR is to combine valve and aortic shapes into a single geometric model. First, a portion of the aorta is cut off at the presumed valve location, which is derived from postoperative MRI data (Fig. 2 B, a and b). The height of this cut is determined depending on valve and sinus size, aiming to prevent surface intersections between valve and aortic root surfaces while retaining as much of the original aortic shape as possible. This places the cutoff planes at a height at which the diameter of the vessel starts to drop below that of the valve ring’s outer diameter. The cutout region is then enlarged by an additional 2–3 mm to create a safety margin for the surface-generation used in the last step. Next, the valve is placed inside the cutoff region (Fig. 2 B c) and aligned to correspond to the real valve’s position, which is obtained from post-treatment imaging. Finally, the upper and lower edges of the valve ring are connected to the aorta and LVOT, respectively (Fig. 2 B d). This step is performed with Autodesk Meshmixer v11 software (Autodesk, San Rafael, CA). Using Meshmixer’s “Join” function, a smooth surface connecting the respective edges is created, resulting in a single manifold surface for the whole model.

Virtual AVR optimization

In addition to modeling patient-specific real AVRs, an attempt to optimize the hemodynamic outcome is made by introducing geometric changes to the valve prosthesis and to the aorta. These virtual AVRs are performed in two steps with increasing surgical complexity. The first step alters the valve’s orientation and size while retaining the original aorta. The choice of valve size and/or angulation was based on the results of the real AVRs. In all patients, various degrees of valve-jet eccentricity have been observed. To reduce jet eccentricity, the intuitive approach was to adjust the valve outflow angle, which in turn was presumed to be largely determined by the valve angulation. For patients 1 and 2, a change in angulation of ∼10° was found to be the maximal allowable value before the valve jet would start impinging the inner vessel wall. For patients 3 and 4, values of 5 and 13°, respectively, were found to be acceptable. Additionally, because of the large recirculation area observed at the inner wall of the ascending aorta in patient 2, this patient received an enlarged valve in an attempt to reduce the extend of this recirculation area. The increase in size was chosen to be minimal (2 mm), aiming to create a realistic setup with a valve size, which can be fitted to the anatomical size of the valve annulus and hence is also realizable by a real implantation procedure.

For this optimization step, the same aortic and valve geometries were used as for the real AVRs, with only the valve orientation altered. Here, the valve was rotated relative to the real AVRs position along two axes: the first rotation, applied only to patient 3, was performed around the valve’s horizontal axis (denoted by the rotation angle). The second rotation was performed around an axis normal to the curvature plane of the ascending aorta (denoted by the tilt angle). Both rotations are illustrated in Fig. 2 C.

The first optimization step, although showing improvement to jet eccentricity, did not reduce flow complexity to the desired level, as will be seen in the Results. Therefore, additional modifications to the valves and aortic geometries were made. This second optimization step aims to improve the flow in the ascending aorta by changing the geometry of the ascending aorta itself. These changes mimic the implantation of a vascular graft in place of the original vessel. The shapes and diameters of these grafts were constructed in an attempt to constrict the flow, thereby reducing space for potential recirculation areas. The vascular grafts were created using SolidWorks (v. 2017; Dassault Systèmes, Vélizy-Villacoublay, France) by extruding a circle along a specified path. Inserting the graft into the aorta was done similarly to inserting the valve by cutting out a portion of the ascending aorta, positioning the graft, closing the gaps, and smoothing the resulting surface patch between graft and aorta with Meshmixer.

In addition to the vascular graft, the valve of patient 3 was increased to 25 mm and rotated by 90° because we presumed that this would improve the valve’s flow diverting capabilities and thus help in moving the valve jet closer to the vessel center. As with patient 2, increase in valve size was chosen to not exceed potential implantation capabilities.

An overview of the geometric changes introduced during the optimization process is presented in Table 1, and Fig. 3 shows a view of the ascending aorta, together with the aortic valve prosthesis, for each patient at various optimization steps.

Figure 3.

Geometric shapes of the ascending aorta as well as valve prosthesis orientations for the 12 geometries simulated. Patients are arranged from top to bottom. To see this figure in color, go online.

Control subject

To assess whether and to what extent the virtual AVRs have a hemodynamical benefit, a reference solution is required. This reference is provided by simulating the hemodynamics of a healthy control subject (age 26, male). The methods used to create the patient-specific model of the aorta are the same as for the AVR patients.

CFD

Steady flow calculations were performed using StarCCM+ version 12.04 (Siemens PLM Software, Plano, TX). A pressure-based, semi-implicit solver for incompressible fluids was used to solve the Reynolds-averaged Navier-Stokes governing equations and obtain the velocity and pressure fields under peak systolic conditions. The discretization of the fluid domain was obtained with StarCCM+’s built in polyhedral mesh generator with a base size of 1 mm. Additionally, a mesh boundary layer, consisting of five prism cell layers, was created at the wall of the aorta and the aortic valve to accurately capture near-wall flow features and wall shear stress (WSS). This results in a volume mesh of ∼3–4 million cells for each patient, which was found to be a good balance between accuracy and computational cost based on a mesh independence study.

Blood was treated as a non-Newtonian fluid with a shear-rate-dependent viscosity described by a Carreau-Yasuda fluid model (26) and with parameters described by Abraham et al. (27). The density of the blood was set to 1050 kg/m³. Turbulence is accounted for by a k-ω shear stress transport model and, in the absence of reliable in vivo turbulence measurement, a uniform turbulence intensity of 5% is prescribed at the inlet.

For this study, the simulations are confined to a single point within the cardiac cycle, namely the point of peak systolic blood flow. Therefore, both the hemodynamic boundary conditions as well as the geometries of the valve and the aorta remain unchanged during runtime. Although this omits the effects of vessel compliance and valve function, it significantly reduces computational and modeling costs.

For each patient, individual patient-specific peak systolic LVOT inflow and descending aorta outflow rates have been extracted from postoperative four-dimensional (4D) phase-contrast MRI data using MEVIS Flow version 9.2 (Fraunhofer Institute for Digital Medicine MEVIS, Bremen, Germany). Additionally, peak systolic velocity profiles at the inlet boundaries are created from the same data. These were used to impose accurate velocity distributions at the inlet boundary (Fig. 4). The flow rates at the ascending and descending aorta boundaries were then adjusted to match the patient-specific flow rates obtained earlier. The rest of the outflow (i.e., the difference between measured inflow and outflow rates) is split among the three branching vessels according to Murray’s law (28). Table 2 gives an overview of the flow rates and Reynolds numbers.

Figure 4.

Patient-specific LVOT inlet vector boundary condition for patient 1. To see this figure in color, go online.

Table 2.

LVOT Inlet Flow Rates and Descending Aorta Outlet Flow Rates as Measured by MRI, as well as Reynolds Numbers Calculated for the Valve and Ascending Aorta Before and After Optimization

Patient	Inlet Flow Rate [mL/s]	Outlet Flow Rate [mL/s]	Re (Valve) AVR/Opt.	Re (Asc.Ao.) AVR/Opt.
Control	490	280	7000/–	5100/–
1	450	300	6500/–	4700/6100
2	600	340	8700/8000	6000/6400
3	520	280	8600/7300	5000/6800
4	290	180	4600/–	2500/3000

Reynolds numbers (Re) were calculated with a kinematic viscosity of 3.5 × 10⁻⁶ m²/s. Asc.Ao., ascending aorta.

For the control subject, a slightly different modeling approach had to be made. Because the aortic valve was not observable in our MRI data, it could not be included in the geometrical model. As a result, unlike the AVR cases, the inflow boundary in the healthy subject is placed above the aortic valve. Therefore, the hemodynamic effects of the aortic valve in this case are accounted for by imposing a peak systolic velocity profile specific to the control subject on the inlet boundary ∼1 cm downstream of the aortic valve.

This provides each patient with their own patient-specific set of hemodynamical boundary conditions. The boundary conditions between the three configurations per patient (i.e., real AVR, Optimization I [Opt. I], and Optimization II [Opt. II]) are not changed, thereby assuming that the virtual AVRs produce the same ventricular flow and afterload as the real ones.

Although the boundary conditions and geometry remain unchanged during simulation runtime, unsteady effects are present in areas of flow separation and high vorticity. Therefore, an unsteady solver is necessary to obtain a converged solution. For this study, an implicit backward integration scheme was used to discretize in time, with a uniform time step of 1 ms for all simulations.

Convergence was assessed by both monitoring the normalized residuals of the transported variables (i.e., momentum, mass, and turbulence) and the pressure at the inlet and outlet boundaries. A simulation was considered converged when the normalized residuals had dropped below a threshold of 10⁻⁴ and the pressure at the inlet and outlet boundaries had remained steady within a margin of 5 mmHg for several hundred iterations. The threshold values used here were derived from clinical validation study performed earlier (29), which validated the exact same CFD model against catheter-measured pressure drops.

Postprocessing

Postprocessing was performed directly within StarCCM+. The following quantitative parameters were evaluated: surface-averaged and SD of WSS, secondary flow degree (SFD), helicity, TPG, maximal velocity magnitude (V_max), and turbulent kinetic energy (TKE). Additionally, streamlines, cross-sectional velocity magnitude, and WSS magnitude plots were created to assess the flow structure qualitatively as well as to compare with 4D flow MRI acquisitions.

Surface-averaged ascending aorta WSS and WSS SD were evaluated on the vessels surface extending from the sinotubular junction (STJ) up to the brachiocephalic artery, as shown in Fig. 5.

Figure 5.

Cross sections used for SFD evaluation, depicted for patient 1. To see this figure in color, go online.

SFD, defined as the ratio of mean in-plane velocity/mean through-plane velocity, was evaluated in three separate cross sections in the ascending aorta (Fig. 5). The first cross section was placed shortly above the valve at the STJ. The other two planes were positioned caudally and cranially from the pulmonary artery bifurcation, respectively. SFD values at these three cross sections were then averaged to obtain a mean SFD in the ascending aorta.

TPG was calculated as the difference between static pressure in the LVOT and a point of maximal static pressure recovery, downstream of the aortic valve. The static pressure values were calculated by averaging over cross sections defined at the respective measuring points in the LVOT and the ascending aorta.

V_max was evaluated in the valve prosthesis region within a volume enclosing the whole valve prosthesis. It represents the maximal local velocity magnitude in this region and corresponds to the clinically used Bernoulli-based estimation of the TPG.

TKE was evaluated in the ascending aorta, with the region of interest defined similarly to that of the WSS calculation (STJ to brachiocephalic artery). Volume integrals of TKE over the whole region of interest were performed, resulting in an absolute value for TKE in that volume.

Finally, the volume-averaged values for left- and right-handed helicity, as well as the volume-averaged helicity magnitude (i.e., the mean of unsigned helicity), were computed within the same region of interest used for the TKE calculations (i.e., the ascending aorta). The helicity is defined as the scalar-product of the local (i.e., cell-centered) velocity and vorticity vector. The equation for calculating ascending aorta helicity mean is given below. Here, the index i denotes the i-th cell of the computational grid in the ascending aorta and V is the ascending aorta volume.

$$H_{asc}=\frac{{\sum }_{i=1}^{N_{cells}}\stackrel{\rightharpoonup }{v_i}\cdot \stackrel{\rightharpoonup }{{\omega }_i}\cdot V_i}{V_{asc}}$$

Results

Comparison between measured and simulated hemodynamics

To validate the computational results, a comparison between 4D MRI measured and CFD computed hemodynamics is performed. For each patient, the velocity magnitude at peak systolic flow is presented in Fig. 6 in a side-by-side comparison between 4D MRI (left column) and CFD (right column) on two cross-sectional planes (top and bottom rows). The same comparison for the control is shown in Fig. 7. The first section (top row) lies in the plane of curvature of the ascending aorta. The second (bottom row) is a vessel-orthogonal cross section located at the height of the pulmonary artery bifurcation. The exact location of this plane is marked with a magenta line in the first cross section.

Figure 6.

Comparison between 4D flow MRI and CFD velocity magnitude on the curvature plane of the ascending aorta (top row) and a cross section at the bifurcation of the pulmonary artery (bottom row). To see this figure in color, go online.

Figure 7.

Left: Comparison between 4D flow MRI and CFD velocity magnitude for the healthy subject. Right: Healthy subject’s streamlines colored by velocity magnitude. To see this figure in color, go online.

In Fig. 6, the respective MRI- and CFD-based velocity plots show a clear resemblance in both distribution and magnitude of velocity. Characteristic flow features such as valve outflow angle, valve-jet size, and eccentricity correspond well between 4D flow MRI and CFD on both section planes, as do jet impingement and jet velocity. However, some inconsistencies are also present, most notably in the area of flow separation on the inner side of the ascending aorta. In this region, the CFD generally depicts lower velocities compared to what can be seen in the 4D flow MRI images. Nevertheless, the computed AVRs are able to capture major flow features of the real AVRs at peak systolic flow, suggesting that the methods presented here hold the potential to predict hemodynamic outcome sufficiently well for clinical use.

Helicity and SFD

Quantitative results for all patients and configurations are summarized in Table 3, and Figs. 8 and 9 show streamlines and WSS magnitude contours for all four patients in all three AVR configurations, respectively. In addition to streamlines, Fig. 8 features dashed arrows highlighting major flow features, representing the jets generated by the valve prostheses as well as secondary flow features, including helical flow and recirculation areas. Finally, Fig. 7 shows a streamline plot for the control subject.

Table 3.

Quantitative Parameters Characterizing the AVR Hemodynamic Outcome

Patient	Treatment	Surface-Averaged WSS ± SD [Pa]	TPG [mmHg]	SFD Mean	Hel.+/−/mag. Mean [m/s2]	Vmax [m/s]	TKE [mJ]
Control	N/A	7.7 ± 5.6	<5	0.19	60/−57/59	1.5	0.1
1	Real	10.9 ± 7.4	7	0.87	76/−80/78	2.3	0.9
	Opt. I	11.2 ± 6.8	7	0.89	69/−79/73	2.2	0.8
	Opt. II	9.1 ± 5.1	6	0.26	53/−66/59	2.0	0.3
2	Real	6.3 ± 5.5	5	0.39	99/−57/79	2.5	0.7
	Opt. I	4.4 ± 3.1	0	0.58	52/−43/48	2.1	0.9
	Opt. II	5.2 ± 3.4	1	0.36	69/−51/60	2.2	0.6
3	Real	17.3 ± 11.4	12	1.00	86/−123/107	3.0	1.8
	Opt. I	12.9 ± 10.3	12	0.73	80/−84/83	3.2	2.7
	Opt. II	10.5 ± 6.8	2	0.79	56/−74/68	3.1	0.2
4	Real	5.7 ± 3.8	2	0.98	20/−16/18	1.3	0.6
	Opt. I	5.9 ± 4.0	2	1.30	26/−29/27	1.4	0.8
	Opt. II	6.1 ± 4.8	1	0.87	20/−20/20	1.3	0.6

Hel.+/−/mag., volume-averaged magnitude of left-handed (−), right-handed (+), and unsigned helicity. N/A, not applicable.

Figure 8.

Visualization of the flow after real AVR and both optimization steps by streamlines colored by velocity magnitude. Dashed arrows represent the major flow features. To see this figure in color, go online.

Figure 9.

WSS magnitude contours after real AVR and both optimization steps plotted on the ascending aorta. To see this figure in color, go online.

For patients 1, 2, and 3, the change in SFD and helicity suggest a reduction in flow complexity of various degrees during the optimization process. Patient 1 shows the most notable reduction in SFD and helicity toward control values at optimization step 2, whereas step 1 shows little to no improvement. This is also reflected by the streamline plots. Here, a large helical structure in the ascending aorta is present in both the real AVR and at optimization step one. The flow at step 2 reveals no such structures and appears more regular.

Patient 2 also sees a reduction of SFD throughout the optimization, although SFD remains significantly higher than the healthy patient’s SFD. However, helicity values are reduced toward control values. The streamlines show a displacement of the valve jet toward the outer wall, resulting in a large recirculation area on the inner side of the ascending aorta in the real AVR. The extent of this recirculation area is slightly reduced in step 1 as the jet moves toward the vessel’s center and even further in step 2, in which the vessel diameter is reduced by the vascular graft modeling.

The optimization also appears effective in patient 3, in whom a notable reduction in SFD and helicity is observed. Helicity was reduced by almost 40% in step 2 compared to the real AVR. SFD is lowered by 30% but remains well above the control value, although the flow in step 2 appears to be largely parallel to the vessel’s centerline in the ascending aorta. An area of recirculation is present, however, with flow separation onset in the upper half of the ascending aorta.

Unlike the other three patients, the optimization appears to be rather ineffective in patient 4. SFD remains very high compared to that of the healthy subject. The streamline plots reveal the valve jet impinging the outer vessel wall, creating large helical structures. Neither the change in valve angulation nor ascending aorta shape seem to alter this. The local helicity values in contrast are very low for all three configurations. This would not be expected from the former observations but can be attributed to the fact that this parameter is calculated by first-order spatial derivatives and is therefore unable to accurately capture large helical structures, whose size is orders of magnitude above that of the computational grid.

WSS

Mean and SD of WSS in patient 1 remain roughly unchanged at the first optimization step and decrease slightly at the second. Patient 3, in contrast, sees a continuous decrease in both mean and SD toward control values during the optimization process, with mean WSS decreasing by ∼70% and SD by ∼40% percent. A less outstanding but still notable reduction is observed in patient 2. Here, however, both optimization steps appear to reduce the mean and SD WSS to healthy values, whereas patient 3 shows elevated mean and SD values even at step 2. Patient 4, on the other hand, shows no notable difference between the three configurations, with all values being slightly below that of the healthy subject.

In addition to the quantitative results, the WSS distributions in the ascending aorta are presented in Fig. 9. These correspond well with the observations made previously; however, some hemodynamical changes are more apparent in this depiction. The most notable case is patient 3. Although a reduction in mean and SD of WSS can be seen at optimization step 1, Fig. 9 shows little change in the irregular WSS distribution, whereas the WSS distribution in step 2 appears far more regular and thus closer to that of the control.

Another noteworthy example is patient 1. Here, the WSS mean and SD values are reduced by only a few Pa at step 2 compared to the real AVR. The distribution, however, moves noticeably toward a more regular one. In contrast, patient 4 shows no apparent change in WSS distribution during the optimization procedure. Instead, the area of high WSS appears to grow during the optimization, moving hemodynamics away from those of the control case.

Patient 2 shows a slight change in WSS distribution. Although the numerous local WSS peaks seen in the real AVR seem to vanish at step 2, some of them are retained during both optimization steps, and both optimizations do not seem to alter the distribution toward a healthy one, unlike in the previous two patients.

TPG

As expected, the TPG remains unchanged for patients who retained their initial valve size during optimization (i.e., patients 1 and 4). Patients 2 and 3, whose valve sizes were increased during the optimization process, see a reduction in TPG from 12 to 2 mmHg and from 5 to 1 mmHg, respectively. Note, however, that the TPG of all real AVRs and optimizations is below a clinically acceptable threshold of 40 mmHg (30).

TKE

As with the other parameters evaluated, the TKE does not follow a uniform trend during the optimization procedure. However, all real AVRs show TKE values roughly an order of magnitude above those of the control subject. In patients 1 and 3, these are reduced toward the control value at optimization step 2. Step 1, however, shows no notable reduction. Patients 2 and 4, on the other hand, do not see a decrease in TKE gradual enough to correspond to the control value and remain highly elevated.

Maximal velocity

Maximal velocity within the valve region seems largely unaffected by the optimization procedure. The only exception is patient 2, in whom a slight reduction from 2.5 to 2.1 m/s can be observed. This is consistent with the reduction in TPG observed in that patient. Interestingly, the valve velocity in patient 3, which showed an even greater reduction in TPG, increases in both optimization steps.

Discussion

This pilot proof-of-concept numerical study aimed to improve AVR hemodynamics outcome by utilizing three major principles in the optimization process: use of a valve prosthesis with larger aortic valve area, change of the valve orientation by tilting of the biological valve prosthesis plane or by a combination of valve tilting and in-plane rotation of the mechanical valve prosthesis, and decreasing of the ascending aorta diameter. The success of the hemodynamic treatment outcome was quantified by an analysis of the following parameters: TPG, WSS, SFD, TKE, V_max, and helicity.

The rationale behind the choice of the optimization strategy and the parameters characterizing the flow optimization were associated with the current clinical understanding of normal and abnormal hemodynamics of aortic valve flow. Abnormal aortic flow is usually characterized by several factors:

• •High turbulence, which is associated with higher TPG and blood damage, causing, for example, acquired von Willebrand disease. Turbulence was quantified by TKE. Increase of valve orifice area seems to be the most effective approach to reduce TKE by reducing the Reynolds number and should also decrease the TPG by increasing the relationship between aortic valve area (AVA) and the cross-sectional area of the ascending aorta (A₀). This relationship is well described by the Borda-Carnot equation for the pressure drop behind a sudden expansion:

$$\text{dp}=\rho \times \frac{AVA}{A_0}\times \left(1-\frac{AVA}{A_0}\right)\times {v_{AVA}}^2,$$

where ρ is blood density and v_AVA is the AVA-averaged velocity. However, an associated reduction of the jet kinetic energy could contribute to jet instability and cause an undesired jet impingent, forming recirculation regions, which contribute to TPG increase.

• •A valve-formed jet directed toward the aortic wall proximal to the aortic valve, which is associated with dilatation of the aorta and aneurysm formation. Furthermore, the jet impinging the vessel wall contributes to energy dissipation and thus TPG increase and forms other flow features associated with abnormal hemodynamics: recirculation areas and regions characterized by vorticity and flow eccentricity. The effect of the flow jet can be quantified by WSS increase and by an increase in the flow swirl, which can be quantified by the SFD. A change in valve orientation should redirect the jet along the aortic centerline and thus avoid secondary flow feature, which should result in decreased WSS and SFD, whereas reduced aortic diameter should stabilize the valve jet and thus contribute toward hemodynamics without abnormal flow features and lower TPG. At the same time, a reduced aortic diameter increases mean cross-sectional velocity and contributes to the desired SFD decrease but also leads to a WSS increase, which is proportional to the velocity and inversely proportional to the diameter.

Some effects of flow optimization used in our study were also investigated earlier: Bongert et al., for example, optimized aortic flow with respect to pressure drop, shear stress, and velocity by rotating a valve prosthesis in an individual patient-specific geometry (23). Valve rotation alone allowed a change of up to 10% in velocity, 30% in shear stress, and 50% in pressure drop, showing different sensitivities of various parameters to the same optimization procedure. However, they did not consider the impact of the individual inlet velocity profile in the LVOT, whose importance was shown in a set of studies (21, 31). In this study, we present a broader range of geometric modifications, and the results show that different optimization measures have different hemodynamic effectivity.

Summarizing our experience with this AVR hemodynamic outcome optimization study, the following conclusions can be drawn:

• •Repositioning of a mechanical valve prosthesis by rotation and tilting effectively allows redirection of the jet generated by the valve. In contrast, tilting of the biological valve prosthesis results in a moderate or even negligible effect.
• •The existence of a near-wall jet flow formed in the LVOT seems to prevent an effective flow optimization by changing valve size and orientation.
• •Combination of valve positioning with downsizing of the ascending aorta was the most effective optimization step.
• •Changing valve orientation and/or ascending aorta geometry seems to have no effect on TPG and maximal valve velocity (i.e., Bernoulli-based TPG). Furthermore, a reduction of TPG is not necessarily accompanied by a decrease in maximal valve velocity.

Although the hemodynamic effects of the optimized AVR can be accurately quantified, assessing the biophysical effects and therefore treatment outcome is rather difficult, not only because of the simplifications and assumptions made in our methods (i.e., steady-state, rigid wall) but also because the relationships between hemodynamics and biophysical processes such as vessel degradation/remodeling and blood damage are not fully understood. For example, a link between abnormal WSS and aneurysm growth and/or vessel dilatation is suggested by several studies (22, 32, 33, 34), but no simple quantitative relations between these two are known and could be used in our model to predict mid or long-term vessel malformation.

The optimization strategy investigated in this study was limited to some modifications of a valve proposed by a clinician for a real treatment and an additional possible treatment of the ascending aorta. A possible optimization by using another valve type, for example, a use of the mechanical valve instead of the biological prosthesis or vice versa, was not considered. Note that differences between flows generated by a mechanical or a biological valve prosthesis are well known and were intensively investigated (19).

Other limitations originate from the steady-state approach. The process of valve opening and/or closure and any associated hemodynamic and biophysical effects such as blood damage or valve insufficiency are not modeled. This is particularly important when considering mechanical valves. Our study demonstrated superior optimization potential when using mechanical valves, but it did not show the increased blood damage potential during leaflet closure reported by other studies (35, 36). This limited scope of modeling would thus artificially favor mechanical valves over biological ones. Another issue arises from the lack of structural modeling. Here, the negative effects of graft-vessel compliance mismatch (37) are not considered.

Nevertheless, the methods presented here hold the potential for a positive clinical impact, even in this early state. The comparison between measured and simulated hemodynamics showed that the steady-state CFD, which is more likely to become clinical routine than complex unsteady fluid structure interaction methods, can reproduce peak systolic hemodynamics. In this hemodynamic state, the potential to tackle typical abnormal flow features mentioned earlier in this chapter with current surgical methods has been shown. And, although our methods are unable to quantitatively predict mid/long-term biophysical effects, a reduction of flow complexity (i.e., SFD or helicity, WSS, TKE) toward that of a healthy subject achieved through the virtual optimization is likely to benefit the patient. However, to what extend and whether such modifications of the ascending aorta and valve position can be achieved in clinical practice should be investigated further.

Furthermore, this study was restricted to a simple trial and error optimization approach, which, although successful in three of four cases, is not an efficient and reproducible optimization technique. A more systematic optimization approach is required to accurately assess the potential and increase the reliability of the methods presented here.

Finally, the small amount of patients also represents a problem. On the one hand, although optimization was successful in three out of four patients in this study, the same success rate may not necessarily be achieved in a larger cohort. On the other hand, no statistically meaningful data could be derived from such a small set of patients, and the statistical significance of the optimized results remains unknown.

Conclusions

In this pilot study, an AVR optimization aiming to improve abnormal flow found after real AVR was attempted. Valve size and orientation and ascending aorta downsizing were tested as the major personalized-flow-optimization factors. It was demonstrated that, at least in silico, abnormal flow present after AVR can be improved by changing valve size and/or position, altering the ascending aorta, or a combination of both. Therefore, outcome prediction based on patient-specific numerical modeling may hold the potential to become an effective individual therapy planning tool for AVR.

In its current state, however, it omits important physical effects because of its steady-state approach, necessitating additional work to verify and further explore the strengths and weaknesses of the methods presented here. Furthermore, other surgical techniques available for AVR such as transcatheter aortic valve implantation need to be explored, as well as a more detailed comparison between mechanical and biological valves.

Apart from improving the methods to include more physiological effects like unsteady flow and vessel compliance, a larger cohort of patients is required to statistically assess the improvement in hemodynamics achieved through the optimization. Ultimately, a prospective clinical study including short-, middle-, and long-term outcome analysis will be required to quantify the biophysical impact and validate the method for a clinical integration.

Author Contributions

P.Y. and L.G. wrote initial version of the manuscript, which was further improved by J.B. and F.H. S.N. and M.K. performed MRI acquisitions and analyzed these data. P.Y. and F.H. performed numerical simulations and analysis of these data. J.B., P.Y., and L.G. developed a methodology of virtual AVR. L.G., T.K., C.K., and V.F. designed the study and study aims. C.K. and V.F. treated patients. All authors discussed possible AVR optimization strategies.

Editor: Kenneth Campbell.