The biomechanical effect of the O-A angle on the aortic valve under left ventricular assist device support: a primary fluid-structure interaction study

Introduction

Heart failure is the terminal stage of cardiovascular diseases (1). And left ventricular assist device (LVAD) has become one of the main treatments for heart failure (2). However, the valve complications caused by LVAD support remain great concerns. For example, aortic regurgitation is a common complication in patients with LVAD support, which requires surgical intervention (3,4). In addition, patients under LVAD support usually have reduced aortic valve compliance, and the expression of multiple proteins associated with valve activation and damage are increased in patients with LVAD support compared with the control patients (5,6).

Cumulative studies have revealed that LVAD support is associated with the hemodynamic status of the aortic valve. It has been shown that LVAD support leads to high transvalvular pressure, which seriously affects aortic valve function (7,8). What’s more, the support level of LVAD was positively correlated to the stress on the aortic valve. And reducing the support level of LVAD may be beneficial in preventing aortic valve dysfunction (9,10).

Recent studies suggested that the angle between LVAD outflow graft and the aorta, known as the O-A angle was a crucial determinant on aortic valve function (11,12). It was shown that the large O-A angle aggravated aortic regurgitation and caused high wall shear stress (WSS) on aortic leaflets. And the reverse-flow region extending up to the aortic valve was considered as one cause of aortic valve dysfunction (13,14). Additionally, it was indicated that LVAD outflow grafts should be placed toward the aortic arch lumen, thus reducing retrograde stress on the aortic valve (4,15). Therefore, elucidating the biomechanical effect of the O-A angle on the aortic valve can provide valuable insights for clinicians to optimize the strategies for LVAD implantation. Computational analysis is an important and widely used method to investigate the biomechanical status of the aortic valve. For example, the finite element method (FEM) has been widely used in medical research, including aortic leaflet dynamics (16-18). And computational fluid dynamics method (CFDM) has been reported to analyze the hemodynamics of different prostheses (19,20). However, the evaluation of the aortic valve’s structural and hemodynamic response is not feasible using the FEM and the CFDM due to a strong coupling effect between blood and flexible valve leaflets (16,21). The Lattice Boltzmann method (LBM) is an enhanced approach derived from the Lattice Gas Automata, which effectively mitigates statistical noise and achieves improved Galilean invariance. Compared with traditional CFDM, the LBM is highly applicable to complex fields and readily adaptable for parallel processing calculations. The LBM has been successfully applied to a diverse range of hemodynamic problems, such as aorta (22) and intracranial aneurysm (23), which employs the mesoscopic approach derived from statistical physics.

Currently, the fluid-structure interaction (FSI) model has been actively developed (24,25). It was reported that FSI model was employed to investigate the hemodynamic status of the bicuspid aortic valve (16,26), and to compare the hemodynamic performance and mechanical stress between polymeric surgical aortic valve replacement and newer versions of valves specifically designed for transcatheter aortic valve replacement (27,28). In addition, a novel immerso Geometric FSI framework has also been proposed to investigate the anchoring ability of the transcatheter aortic valve (29) and to examine the effects of severe aortic stenosis and transcatheter aortic valve implantation on coronary blood flow under resting conditions (30,31). Thus far, the reports on the application of FSI model to evaluate the effect of LVAD support on the aortic valve function are very limited. Morany et al. reported the hemodynamic effect of LVAD support on the aortic valve (16) and El-Nashar et al. investigated the biomechanical effects of LVAD support on the aortic valve (28). However, the evaluation of biomechanical effect of the O-A angle on the aortic valve using the FSI model has not been reported.

In the current study, we employed a novel FSI model, which integrates the LBM and the FEM to investigate the biomechanical effect of the O-A angle on the aortic valve under LVAD support. The findings of this study will favor to identify the optimal O-A angle and relieve aortic valve dysfunction under LVAD support.

Methods

Construction of the FSI model

The geometric model of the aortic valve with a LVAD outflow cannula used in this study was constructed based on a previous report (16). The geometric model comprises the aortic valve leaflets, the sinus of Valsalva, ascending aorta, and LVAD outflow cannula (Figure 1A) The ascending aorta and LVAD outflow cannula are considered as rigid bodies, and the aortic valve leaflets as isotropic hyperelastic materials. In the geometric model, the aortic valve leaflets are situated between the left ventricle and the ascending aorta, while the three protuberances are referred to the sinus of Valsalva. In this study, three different O-A angle (45, 90, and 135 degrees) conditions were designed according to Karmonik’s report (Figure 1A) (32). And the diameter of LVAD outflow cannula was set at 12 mm based on clinical practice. The geometric model incorporates two distinct inlets (the ventricular inlet and the LVAD inlet) and one outlet (the ascending aortic outlet). To mitigate the impact of boundary conditions on the flow pattern, an extension is applied to both the inlets and outlet of the model. The aortic valve consists of three leaflets that are affixed to the aortic wall. The leaflet attachment refers to the surface contact where the two leaflets meet at the root wall (Figure 1B) (33).

Figure 1 Construction of the FSI model. (A) The geometric model of the ascending aorta and the sinus of valsalva with three O-A angles. (B) The geometric model of the leaflets. (C) The mean stress on the leaflets in the three element size conditions. (D) A schematic sketch of the experiment. (E) A 3D printed prosthetic heart valve (21 mm). (F) The boundary condition. LVAD, left ventricular assist device; LVP, left ventricular pressure; AP, aortic pressure; FSI, fluid-structure interaction; 3D, three-dimensional.

The LBM

Hemodynamic parameters, such as the pressure and velocity, are represented as a series of discrete populations fi(i=1,2,…,k−1)fi, which are discrete representations of statistical particle distribution functions of molecular velocities (25). In this theory, the density and the velocity µ of the fluid are governed by Eqs. [1,2]:

ρ=∑ifi[1]

u=∑ifiei[2]

where the vector ei represents the discrete velocity model in the velocity space discretization process.

In the study, the lattice Bhatnagar-Gross-Krook was used, in which the distribution function fi is a set of discrete equilibrium distribution functions governed by fie Hence, the LBM equation is expressed as Eq. [3]:

fi(x+Δtei,t+Δt)−fi(x,t)=−1τ[fi(x,t)−fie(x,t)][3]

where τ represents the relaxation time, and fie is governed by Eq. [4]:

fie=ωiρ[1+ei⋅uCs2+(ei⋅u)22Cs4−u⋅u2Cs2][4]

where Cs represents the speed of sound in lattice, and ωi is the weight coefficients corresponding to the lattice direction considered. In this study, the three-dimensional (3D) lattice model D3Q27 (i=0,1,…,26) was used. In addition, the relaxation time τ is governed by Eq. [5]:

μ=Cs2(τΔt−0.5)[5]

where µ represents the kinematic viscosity. For the D3Q27 model, the blood pressure and shear stress tensor are controlled by Eqs. [6,7] (26):

p=Cs2ρ[6]

σxy=−Pδxy−(1−12τ)∑i=026(fi−fieq)eixeiy[7]

where Cs represents the sound speed of the system, and the WSS was calculated according to Eq. [8]:

τω=σ⋅n−((σ⋅n)⋅n)n[8]

where τω represents the WSS, and n represents the normal vector of the wall boundary surface.

The aortic valve constitutive equation

The biomechanical property of the aortic leaflets can be simulated by the Ogden model (34). In this study, we chose the isotropic, hyperelastic incompressible, second-order Ogden model to reflect the biomechanical property of the leaflets, as shown in Eq. [9]:

W=∑i=1W2uiαi2(λ¯1ai+λ¯2ai+λ¯3ai−3)[9]

where W represents the strain energy function λ¯i, represents the deviatoric principal stretches, ui, and ai represents the material parameters. According to Mao’s work, α1=67.14, α2=27.47, μ1=19.58kPa, and μ2=260.56kPa. In addition, the density of the leaflet is set to 1,100 kg/m³. To minimize computational expenses, it is assumed that the sinus of Valsalva, ascending aorta, and LVAD outflow cannula exhibit rigid behavior.

The discretization of the FSI model

To maintain the simulation accuracy, the leaflets are discretized into 20,352 10-node quadratic tetrahedrons (C3D10). The aortic vessel and the LVAD outflow cannula were modeled as separate rigid components in this study to optimize computational efficiency. The leaflet element sizes are the same as those employed in a previous study (16), in which the element size was shown not to affect the accuracy of the simulation solution. The octree lattice structure is employed for the blood domain, enabling 4^th order spatial discretization and facilitating the utilization of a non-uniform lattice structure for the intricate blood domain. To determine the appropriate numbers of grids for this work, grid independency tests were performed on the volume-weight average stress (mean stress) of the aortic leaflets. An average error of less than 5% in mean stress is considered acceptable. This test used three element sizes of 0.2 mm (2.5 million elements), 0.3 mm (0.75 million elements) and 0.5 mm (0.16 million elements). The result is shown in Figure 1C. Notably, when the element size was less than 0.3 mm, the element size had little influence on the simulation results. Therefore, the element size in this study was set to 0.3 mm.

The FSI model setup and boundary condition

In this study, the configuration of the FSI model refers to previously published literatures, and its accuracy has been verified (35,36). Briefly, two commercial CAE software programs, Abaqus 2019 (Simulia, Providence, RI, USA) and Xflow 2019 (Simulia), were combined to study the biomechanical status of the aortic valve under LVAD support. The Abaqus/Explicitsolver was used to solve the structural problem, and XFlow was used as the fluid solver. The conventional LBM assumes the compressibility of the fluid. Conversely, the flow pattern of an incompressible fluid can be determined by XFlow through the implementation of a novel LBM (37). To manage the coupling between the two solvers, the Co-Simulation Engine (Simulia) was used.

The boundary conditions applied in this study were obtained from an in vitro experiment. The schematic sketch of the experimental setup was shown in Figure 1D. Briefly, a 3D printed prosthetic heart valve (21 mm) was mounted in an idealized aortic root model (Figure 1E). An axial flow pump was implanted in the experiment setup. The left ventricular (LV) chamber was driven by a pneumatic pump to mimic physiological left ventricular pressure (LVP) (Figure 1F). The compliance chamber was placed in series with the aortic valve to generate the aortic pressure (AP) (Figure 1F). Two pressure probes, used to measure the instantaneous pressure waveform, were located at 2 cm upstream and 5 cm downstream, respectively. The transonic flow probe was placed between the LV chamber and aortic valve chamber to measure the instantaneous outflow of LVAD. And LVAD controller regulated the rotational speed of the LVAD to maintain a constant outflow of LVAD. In this study, LVAD worked in a fully supported condition, in which all the blood was pumped, and the aortic valve was closed during the entire cardiac cycle. During the experiment, the outflow speed was set to 4.5 L/min. The heart rate was set to 75 bpm.

Notably, LVP was found to be less than AP during the entire cardiac cycle. LVP was applied as the pressure boundary condition at the ventricular inlet, and AP was applied as the pressure boundary condition at the aortic outlet. Meanwhile, the mass flow boundary condition was applied at the pump inlet to simulate the constant outflow of the LVAD. Additionally, the physiological parameters, such as the blood density (ρ=1050kg∕m3) and the blood viscosity (u=0.0035Pa⋅s), were fixed. The blood was assumed to be Newtonian fluid. The time step for both the structure solver and the fluid solver was set to 1 microsecond. The Wall-Adapting Local Eddy-viscosity model was chosen as the turbulence model. The cardiac cycle was set to 0.8 s (75 bpm), and three cycles were calculated to eliminate the influence of the initial condition. The results calculated during the third cardiac cycle were extracted and used to evaluate the motion and biomechanical status of the aortic valve. The simulation was performed on an Intel Xeon (E2667) workstation with 32 cores and required 96hours for computation.

The biomechanical effect evaluation

To evaluate the biomechanical effect of the O-A angle on the aortic valve leaflets, four indicators, including stress distribution, the mean stress, the axial hemodynamic force (AHF). and the WSS distribution were investigated at three time points (28, 133, and 266 ms), 28 ms represents the time point at which the difference between the LVP and AP is at the minimum (AP-LVP, 12.5 mmHg); 133 ms represents the midpoint of the rapid diastolic phase of the left ventricle (AP-LVP, 50.8 mmHg); 266 ms represents the time point at which the difference between the LVP and AP is at the maximum (AP-LVP, 97 mmHg).

The volume weighted average stress (mean stress) is a factor that reflects the average stress on the aortic leaflets. The mean stress is governed by Eq. [10]:

stressm=∑stressi∗voli∑voli[10]

where stressm is the volume weighted mean stress of the aortic leaflets, stressi denotes the stress on the ithi element of the aortic leaflet, and voli represents the volume of the ithi element of the aortic leaflets.

AHF is used to evaluate the hemodynamic force (HF) exerted by blood flow on the leaflets, which is calculated as shown in Eq. [11]:

AHF(t)=1S∫SRFaorta(t)ds−1S∫SRFventricle(t)ds[11]

where the AHF(t) denotes the AHF at t time point, RFaorta(t) and RFventricle(t) are the reaction force exerted on both sides of the leaflet, and s represents the surface area of the leaflet.

Results

The stress and AHFon the aortic valve

In this study, the LVAD was used in the fully supported condition, the aortic valve remained closed throughout the entire cardiac cycle. As shown in Figure 2, the aortic insufficiency was observed during the systolic phase (28 ms) in the 135-degree O-A angle (arrow a). Moreover, the stress on the aortic leaflets increased as the O-A angle increased. Similarly, the stress on the aortic leaflets increased as the difference between the LVP and AP increased. At 133 ms (the rapid diastolic phase), the high-stress region was located at the leaflet attachment (arrow b), and the region area increased as the O-A angle increased, and the maximum stress on the leaflets was 0.45 MPa. In addition, when the difference between the LVP and AP reached its maximum (266 ms), the stress on the aortic leaflets also reached its maximum, and the high-stress region was located at the belly of the leaflets (arrow c), and the region area increased as the O-A angle increased. The maximum stress at the attachment and the belly of the leaflets were 0.7 and 0.5 MPa, respectively.

Figure 2 The stress distribution on the aortic valve. Arrow a, the aortic valve insufficiency phenomenon. Arrow b, the high-stress region of the aortic valve located at the leaflet attachment. Arrow c, the high-stress region located at the belly of the leaflet.

Then, the mean stress and AHF on the leaflets were further evaluated. As shown in Figure 3A, the tendency of the mean stress were similar in the three O-A angle conditions, and the mean stress increased when the O-A angle increased. The maximum mean stress in the three O-A angle conditions were 0.225, 0.252, and 0.262 MPa, respectively. When the O-A angle was 90 or 135 degrees, significant fluctuation in the mean stress was observed during the systolic phase (0–100 ms, arrow a). However, no significant fluctuation in the mean stress was observed when the O-A angle was 45 degrees. During the diastolic phase, the mean stress in the three O-A angle conditions increased as the difference between the LVP and AP increased. As shown in Figure 3B, the tendency of the AHF was similar in the three O-A angle conditions. And, an obvious fluctuation of the AHF was observed during the systolic phase (0–100 ms) in the 135-degree condition (arrow b). During the diastolic phase, the AHF increased in the three O-A angle conditions when the difference between the LVP and AP increased. And the peak values of the AHF in the three O-A angle conditions were −12.3, −12.7 and −13.9 N, respectively.

Figure 3 The mean stress and the axial hemodynamic force of the aortic valve in the three O-A angle conditions. (A) The tendency of the mean stress on the leaflets. (B) The tendency of the axial hemodynamic force. Arrow a, the significant fluctuation observed in the mean stress on the leaflets during the systolic phase. Arrow b, the obvious fluctuation observed in AHF during the systolic phase. AHF, axial hemodynamic force.

The flow patterns in the three O-A angle conditions

The flow contour field was evaluated in a cross-section through the symmetry plane of the valve at three timepoints throughout the cardiac cycle (Figure 4). Notably, the outflow of LVAD directly hit the ascending aorta when the O-A angle was 90 degrees (arrow b). And, when the O-A angle was 45 degrees, the outflow of LVAD directly jetted into the ascending aorta. Notedly, a retrograde flow (toward the aortic valve) was observed (arrow a) in the entire cardiac cycle when the O-A angle was 135 degrees. In addition, the blood flow velocity in the sinus of Valsalva also gradually increased as the O-A angle increased (arrow c).

Figure 4 The flow contour field evaluated at three O-A angel conditions throughout the cardiac cycle. Arrow a, the retrograde blood flow (toward the aortic valve). Arrow b, LVAD outflow directly hit the ascending aorta when the O-A angle was 90 degrees. Arrow c, the blood flow velocity in the sinus of Valsalva gradually increased as the O-A angle increased. LVAD, left ventricular assist device.

To further evaluate the differences in the flow patterns among the three O-A angle conditions, the flow velocity vector field was examined. As shown in Figure 5, at 28 ms (systolic phase), an obvious retrograde flow was observed when the O-A angle was 135 degrees (arrow a). At 133 ms (the rapid diastolic phase), a significant turbulence was observed in the aortic root when the O-A angle was 135 degrees (arrow b). In addition, at 266 ms (the difference between the LVP and AP reaching its maximum), an obvious retrograde flow was observed when the O-A angle was 135 degrees), resulting in a significant turbulence in the sinus of Valsalva (arrow c).

Figure 5 The flow velocity vector field evaluated at three O-A angel conditions throughout the cardiac cycle. Arrow a, an obvious retrograde flow observed in the 135-degree O-A angle. Arrow b, significant turbulence observed in the aortic root in the 135-degree O-A angle. Arrow c, obvious turbulence observed in the sinus of Valsalva.

The WSS distribution on the leaflets

Then, the WSS distribution on the aortic leaflets was evaluated. , As shown in Figure 6, it was noted that the leaflets were deformed at 28 ms (the systolic phase) in the 135-degree O-A angle, and the WSS on the free edge of the leaflets was relative high and reached a maximum of 11.5 Pa). At 133 ms (the rapid diastolic phase), a high WSS was observed at the free edge of the leaflets when the O-A angles were 45 or 90 degrees (arrow b, maximum WSS 8.9 and 9.3 Pa, respectively). And, when the O-A angle was 135 degrees, a high WSS was observed at both free edge (arrow b, maximum WSS 11 Pa) and belly (arrow c, maximum WSS 10 Pa) of the leaflets.

Figure 6 The WSS distribution on the aortic valve. Arrow a, deformed leaflet observed at 28 ms (the systolic phase) in the 135-degree O-A angle. Arrow b, the high-WSS region observed at the free edge of the leaflet, when the O-A angle was 45 or 90 degrees. Arrow c, the high-WSS region observed at the belly of the leaflets in the 135-degree O-A angle. WSS, wall shear stress.

Discussion

The present study was the first report to investigate the biomechanical effects of O-A angles on the aortic valve using a novel FSI model, which integrates the LBM with the FEM. The results revealed a close correlation between the O-A angle and the biomechanical status of the aortic valve, and indicated that a small O-A angle was favorable to maintain the normal function of the aortic valve under LVAD support. The findings of this study provide valuable insights for clinicians to optimize the anastomotic angle of LVAD implantation, in order to reduce the risk of LVAD-induced aortic valve dysfunction.

Aortic regurgitation is a concerning complication under LVAD support (38,39), which leads to LVAD-LV recirculation and requires surgical intervention (30). Reportedly, the LVAD outflow significantly affected the flow pattern of the aorta (40), and the WSS (41) and turbulent energy dissipation (42) in the ascending aorta. However, these studies only focused on the hemodynamic effects of the LVAD outflow on the aorta and did not evaluate the biomechanical effect on the aortic valve. Meanwhile, the aortic valve in these studies was neglected or was considered a rigid body. The overload stress on the aortic valve is considered as an important factor associated with aortic regurgitation. A recent study indicated that O-A angle was correlated with aortic valve regurgitation (43). And our results further demonstrated that the biomechanical effect of the O-A angle on the aortic valve using a novel FSI model. It was revealed that the biomechanical status was directly regulated by the O-A angle and a small O-A angle provided better biomechanical status for the aortic valve.

The biomechanical status has been confirmed to be an important factor associated with the function of the leaflets. For instance, cyclic stretch and stress act together to modulate the aortic valve interstitial cell phenotype (44). Similarly, elevated mechanical stretch on aortic valve cusps may detrimentally alter proteolytic enzyme expression and activity in valve cells (45). In our study, the stress on the aortic leaflets was significantly regulated by the O-A angle. When the O-A angle increased, the peak mean stress on the aortic leaflets and the area of the high-stress region were all significantly increased. In addition, significant fluctuation in the mean stress and the AHF was observed when the O-A angle was 90 or 135 degrees, indicating that a small O-A angle favor to maintain a normal biomechanical status of the aortic leaflets.

It has been verified that the flow pattern directly regulates the mechanobiology of the aortic leaflets (46). And the stronger the turbulence in the sinus of Valsalva, the higher risk of lesions in the leaflets (47). WSS is considered an important factor that regulates valve endothelial phenotypes (48). Many studies have confirmed that the abnormal function of the endothelium affects the mechanical properties of the aortic valve cusps (49), leading to the formation of valvular calcification (50). In this study, we found that the blood flow velocity in the sinus of Valsalva gradually increased when the O-A angle increased. At the same time, the intensity and the distribution of WSS was increased when the O-A angle increased, which may explain the deformed leaflet and the retrograde flow (toward the aortic valve) observed when the O-A angle was 135 degrees. Therefore, a small O-A angle under LVAD support may favor to prevent the aortic valve dysfunction.

Compared with previous findings (7,21,51), the mean stress and the area of the high-stress region was smaller in our study. This is because LVP and AP were applied in our study. In addition, the AHF calculated in our study was significantly higher (peak value at the O-A angle of 45 degrees −12.7 N vs. peak value −7 N). This may be due to the fact that the patients in previous reports were those received aortic valve implantation but not those received LVAD support. And this may explain the high incidence of valvular complications in patients under LVAD support.

Limitations

There are some limitations in this study. Firstly, as a preliminary study, statistical analysis and sensitivity analysis were not used in this study, and. energy losses analysis, vorticity analysis, and oscillatory shear index were not included. More repeated studies and in-depth analysis are needed to verify the results of this study. Secondly, in the FSI model, the ascending aorta was assumed to be a rigid part, and the elastic properties were ignored. This is because that the deformation of the ascending aorta is very small throughout the cardiac cycle according to a recent report (52). Thirdly, blood is actually a non-Newtonian fluid; which was assumed to be a Newtonian fluid in this study. This is because that, this assumption is widely used in macroscopic hemodynamic studies. Lastly, more work is needed to verify the FSI model predictions in a direct experiment.

Conclusions

The O-A angle is an important factor that regulates the biomechanical states of the aortic valve under LVAD support. And a large O-A angle caused high stress and WSS on the aortic leaflets, as well as broad stress and WSS distribution, thus leading to deformed leaflets and retrograde flow. Therefore, optimization of the O-A angle will favor to maintain aortic valve function.

Acknowledgments

Funding: This study was partly funded by the National Key Research and Development Program of China (No. 2022YFC2704804) and the National Natural Science Foundation of China (Nos. 61931013, 82171886, 81701644, and 11832003).

Footnote

Data Sharing Statement: Available at https://jtd.amegroups.com/article/view/10.21037/jtd-24-1650/dss

Peer Review File: Available at https://jtd.amegroups.com/article/view/10.21037/jtd-24-1650/prf

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://jtd.amegroups.com/article/view/10.21037/jtd-24-1650/coif). W.W. is from Jiangsu STMed Technology Co., Ltd., Suzhou, China. The other authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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