Analysis of shear stress related hemolysis in a ventricular assist device

Abstract

BACKGROUND:

Implantable devices such as ventricular assist devices provide appropriate treatment for patients with advanced heart failure. Unfortunately, these devices still have many problems, particularly related to blood damage.

OBJECTIVE:

The aim of this research is to examine two new ventricular assist devices in terms of induced shear stress, exposure time, and induced hemolysis.

METHOD:

Reverse engineering was used on multiple axial flow ventricular assist devices to collect all the details related to the designs (diameters, lengths, blade angles…), which were used to build two prototypes: Model A and Model B.

RESULTS:

The obtained results were close to a large extent, except for static pressure rise, where the difference was clear.

CONCLUSION:

Compared with what has been published in other studies, the overall performance of both models was excellent.

Keywords

Computational fluid dynamics hemolysis index hemolysis shear stress hemodynamics VAD CFD

1. Introduction

Heart failure has many treatments in its early stages (A, B, and C). These include lifestyle changes (diet, exercise) and medications (beta-blockers, angiotensin-converting enzyme inhibitors). However, in end-stage heart failure (D), the most effective solution is a heart transplant. In this case, the problem of lack of organ donation arises. Therefore, researchers began developing artificial organs (artificial hearts, ventricular assist devices, mechanical valves) to compensate for this deficiency. Implantable assist devices have thus become an alternative to organ transplantation and a means of stabilizing patients’ lives.

Since the first successful long-term implantation of a ventricular assist device in 1988, research to develop new ventricular assist devices and improve existing devices’ performance has increased [1–8]. The expansion of the field of use was one of the aspects covered by this research. In addition to their use as a bridge to decision (BTD), bridge to candidacy (BTC), and as a bridge to transplantation (BTT), it has become possible to use ventricular assist devices as a bridge to recovery (BTR) and as destination therapy (DT). However, even with various designs, many ventricular assist devices have not been approved for implantation. Besides, even those approved still face some problems, including hemolysis and thrombosis [9–11].

Blood damage or hemolysis is the rupture of the red blood cell membrane. This rupture leads to the release of the cytoplasm stored within it into the surrounding plasma. Medically speaking, hemolysis can be related to many pathologies. Nevertheless, in this article, the focus will be on ventricular assist device-induced hemolysis, which is often the result of severe shear stress. Exposure to high shear stress can either entirely or partially tear the red blood cell membrane or create pores in it [12]. In addition, the red blood cell membrane can be damaged even at low shear stress if combined with a prolonged exposure time [13].

The present paper will investigate and analyze the induced shear stress, exposure time, hemolysis, and the hydraulic performance of two newly designed ventricular assist devices.

2. Methods

2.1. Geometry

As in the study by Bounouib et al. [14], reverse engineering was used on multiple axial flow ventricular assist devices to collect all the details related to the designs (diameters, lengths, blade angles…). These details were used to build two prototypes (Model A and Model B) presented in Fig. 1. These two models were selected after analyzing dozens of proposed models.

Fig. 1.

Computer-aided design (CAD) models: Model A (top), Model B (bottom).

After validating the derived details, BladeGen has been used to reconstruct the two models. Since BladeGen was designed explicitly for turbomachines, allowing reasonable control over geometric shapes. The control covers many variables such as the shroud shape, the hub shape, the blade angle, the blade thickness, the leading edge, the trailing edge, and many other variables.

After finalizing the geometry, three files containing all the data related to the part (hub, shroud, and blade profile) are exported for each part of both models. The same files were imported later to Tubogrid to create the mesh.

2.2. Meshing

Turbogrid being a grid generation tool specially designed for turbomachinery, the grid it generates has particular properties. For example, in the areas around the blades, Turbogrid generates a fine grid. On the other hand, it generates a slightly coarse grid in the spacing between the blades (Fig. 2).

Fig. 2.

Meshes of the rotors: Model A rotor (top), Model B rotor (bottom).

Taking advantage of the unique properties of Turbogrid, the grids were created independently for each part of the two models. The grids were constructed using a size factor of 0.8 to eliminate any negative element volume. In addition, the clearance between the blade tips and the inner wall of the housing was set to 0.15 mm. As a result, grids with hexahedral elements ranging in number from 19000 to 450000 for each part were generated.

2.3. Computational fluid dynamics

After finalizing the grids, the data extracted from Turbogrid was imported and assembled into ANSYS CFX based on the assembly design for each model.

The simulations were performed under steady-state flow conditions using blood as the circulating fluid. To solve this problem, we used ANSYS CFX solver which uses Navier–Stokes equations as governing equations $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle \frac{\partial {\upsilon}_{x}}{\partial x}+\frac{\partial {\upsilon}_{y}}{\partial y}+\frac{\partial {\upsilon}_{z}}{\partial z}=0\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \displaystyle \frac{\partial {\upsilon}_{x}}{\partial t}+{\upsilon}_{x}\frac{\partial {\upsilon}_{x}}{\partial x}+{\upsilon}_{y}\frac{\partial {\upsilon}_{x}}{\partial y}+{\upsilon}_{z}\frac{\partial {\upsilon}_{x}}{\partial z}=-\frac{1}{{\rho}}\frac{\partial p}{\partial x}+{\upsilon}\left(\frac{\partial ^{2}{\upsilon}_{x}}{\partial x^{2}}+\frac{\partial ^{2}{\upsilon}_{x}}{\partial y^{2}}+\frac{\partial ^{2}{\upsilon}_{x}}{\partial z^{2}}\right)+f_{x}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \displaystyle \frac{\partial {\upsilon}_{y}}{\partial t}+{\upsilon}_{x}\frac{\partial {\upsilon}_{y}}{\partial x}+{\upsilon}_{y}\frac{\partial {\upsilon}_{y}}{\partial y}+{\upsilon}_{z}\frac{\partial {\upsilon}_{y}}{\partial z}=-\frac{1}{{\rho}}\frac{\partial p}{\partial y}+{\upsilon}\left(\frac{\partial ^{2}{\upsilon}_{y}}{\partial x^{2}}+\frac{\partial ^{2}{\upsilon}_{y}}{\partial y^{2}}+\frac{\partial ^{2}{\upsilon}_{y}}{\partial z^{2}}\right)+f_{y}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \displaystyle \frac{\partial {\upsilon}_{z}}{\partial t}+{\upsilon}_{x}\frac{\partial {\upsilon}_{z}}{\partial x}+{\upsilon}_{y}\frac{\partial {\upsilon}_{z}}{\partial y}+{\upsilon}_{z}\frac{\partial {\upsilon}_{z}}{\partial z}=-\frac{1}{{\rho}}\frac{\partial p}{\partial z}+{\upsilon}\left(\frac{\partial ^{2}{\upsilon}_{z}}{\partial x^{2}}+\frac{\partial ^{2}{\upsilon}_{z}}{\partial y^{2}}+\frac{\partial ^{2}{\upsilon}_{z}}{\partial z^{2}}\right)+f_{z}.\nonumber\end{eqnarray}$

Blood was modeled as a Newtonian fluid with a density of 1050 kg/m³ and dynamic viscosity of 0.0035 Pa.s. The boundary conditions were chosen to mimic a critical heart condition. For this, a value of static pressure of 80 mmHg with high turbulence intensity (10%) was set at the inlet. Flow rates ranging between 3 l/min and 12 l/min were used at the outlet. Assuming that the fluid velocity near the walls is null, a no-slip condition was placed on the inner walls of the housing. The flow was calculated using a standard k–𝜀 model.

Following the original designs, except for the domain motion related to the rotors designated as rotating domains with angular velocities ranging between 7000 rpm and 15000 rpm, the other parts’ domains motion were designated as stationary. As for the convergence criteria, the Root Mean Square (RMS) was chosen as the residual criterion with a residual target of 10⁻⁵. The maximum number of iterations was fixed at 1500 iterations.

2.4. Shear stress

The three-dimensional numerical prediction model proposed by Bludszuweit [15] was used to calculate the mechanical load applied to red blood cells accurately: $\begin{eqnarray}\displaystyle {\sigma}=\left[{\textstyle \frac{1}{3}}({\sigma}_{ii}^{2}+{\sigma}_{jj}^{2}+{\sigma}_{kk}^{2})-{\textstyle \frac{1}{3}}({\sigma}_{ii}{\sigma}_{jj}+{\sigma}_{jj}{\sigma}_{kk}+{\sigma}_{kk}{\sigma}_{ii})+({\sigma}_{ij}^{2}+{\sigma}_{jk}^{2}+{\sigma}_{ki}^{2})\right]^{1/2}. & & \displaystyle \nonumber\end{eqnarray}$

Implementing this equation and using it along the red blood cells trajectories allowed us to monitor each cell’s movement and estimate the load variations applied to it at each point.

2.5. Hemolysis

To calculate the hemolysis index, we used the mathematical model developed by Giersiepen et al. [16]. The proposed model was initially developed to predict hemolysis in mechanical heart valves. However, some researchers have proven that it is also valid for studying hemolysis in ventricular assist devices [17,18].

According to Giersiepen [16], hemolysis is related to many factors. Some of the factors he was interested in and included in his model were shear stress 𝜎 and exposure time t. $\begin{eqnarray}\displaystyle \mathit{HI}(\%)=\frac{{\Delta}\mathit{Hb}}{\mathit{Hb}}\times 100=C\times t^{{\alpha}}\times {\sigma}^{{\beta}}. & & \displaystyle \nonumber\end{eqnarray}$

C, 𝛼, and 𝛽 are constants determined by regression of experimental data. At the same time, 𝛥Hb represents plasma-free hemoglobin, and Hb represents total blood hemoglobin.

Some researchers found that the constants C, 𝛼, and 𝛽 proposed by Giersiepen [16] led to overestimating hemolysis. Therefore, they proposed alternatives to the original constants to recalibrate the model. Table 1 presents the researchers and their proposed constants.

Table 1
Constant 𝛼, 𝛽, and C of the power-low equation

C 𝛼 𝛽

Heuser [19] 1.800 × 10⁻⁶ 0.7650 1.9910

Giersiepen [16] 3.620 × 10⁻⁵ 0.7850 2.4160

Zhang [20] 1.228 × 10⁻⁵ 0.6606 1.9918

Sheriff [21] 1.470 × 10⁻⁶ 1.3000 1.0400

Ding [22] 4.080 × 10⁻⁵ 0.8000 1.5600

	C	𝛼	𝛽
Heuser [19]	1.800 × 10⁻⁶	0.7650	1.9910
Giersiepen [16]	3.620 × 10⁻⁵	0.7850	2.4160
Zhang [20]	1.228 × 10⁻⁵	0.6606	1.9918
Sheriff [21]	1.470 × 10⁻⁶	1.3000	1.0400
Ding [22]	4.080 × 10⁻⁵	0.8000	1.5600

3. Results

3.1. Flow field

The two models were simulated under different conditions. Figures 3 and 4 show the simulation results under a rotation speed of 15000 rpm and a flow rate of 5 l/min. The blood flow field is represented by velocity contours, streamlines showing the paths of the red blood cells, and a pressure contour illustrating the pressure changes in the simulation domain.

3.2. Model A

In Fig. 3, the velocity contours show the formation of stagnation regions in the impeller, the inducer, and the diffuser, where the flow velocity is almost zero, which means the possibility of thrombus formation. The streamlines show the formation of some small recirculation regions in the inducer and impeller. The recirculation regions are much more prominent in the diffuser. There are also significant flow turbulences after the blood exits the diffuser. In contrast, the pressure contour shows no abnormalities.

Fig. 3.

Model A flow field represented as velocity contour on a turbo surface of 0.5 span, streamlines, and pressure contour.

3.3. Model B

In Fig. 4, the most remarkable thing about the velocity contour is the stagnation regions covering a large area, implying a greater possibility of thrombus formation. On the other hand, the streamlines show a smooth blood flow passing through the inducer and the impeller. However, recirculation areas begin to form as it passes through the diffuser. Fortunately, the straightener fixed these turbulences, providing a smooth flow at the outlet. As with Model A, the pressure contour of Model B shows no abnormalities.

Fig. 4.

Model B flow field represented as velocity contour on a turbo surface of 0.5 span, streamlines, and pressure contour.

The pressure contours of the two models in Figs 3 and 4 do not show any abnormalities. However, after analyzing the static pressure rise curves (𝛥p) shown in Fig. 5 and comparing the characteristics of the ventricular assist devices under the same operating conditions, it can be seen that the static pressure rise provided by Model B is higher than that provided by Model A. This means that the same static pressure rise and flow rate can be obtained using Model B at a lower rotation speed than Model A.

Fig. 5.

VAD’s performance curves at nine different rotation speeds, Model A (top), Model B (bottom).

3.4. Shear stress

As mentioned previously, the shear stress was calculated at all points belonging to the streamlines using the three-dimensional numerical prediction model proposed by Bludszuweit. Figure 6 shows the evolution of the shear stress over time on two randomly selected streamlines.

Fig. 6.

Shear stress history in a randomly chosen streamlines from Model A (top), Model B (bottom).

A large number of streamlines and the large number of points belonging to them made it difficult to represent all the result data in a single figure. Therefore, the mass distribution of shear stress was calculated at all points belonging to all streamlines.

The results depicted in Fig. 7 show that the magnitude of shear stress in both ventricular assist devices ranges from 0 to 400 Pa. In Model A, among the total studied points, 82.77% are subjected to shear stress magnitudes below or equal to 10 Pa. The percentage of points subjected to shear stress magnitudes below or equal 150 Pa is approximately 99.98%. In Model B, 69.61% of the studied points in the model are subjected to shear stress magnitudes below or equal to 10 Pa, while 99.97% are subjected to shear stress magnitudes below or equal to 150 Pa.

Fig. 7.

Shear stress distribution in Model A (top) and Model B (bottom) at the optimal operating conditions.

3.5. Exposure time

Figure 8 shows the variation in the average exposure time in Model A and Model B under different rotation speeds and flow rates. For both models, at the same flow rate, the average exposure time was longer at lower rotation speeds than at higher rotation speeds. This difference in average exposure time gradually decreases as the flow rate increases. At the same rotation speed, the average exposure time was longer at lower flow rates. The average exposure time drops significantly when the flow rate is raised from 3 l/min to 5 l/min. This intensity decreases between 5 L/min and 12 L/min. Compared with other axial flow ventricular assist devices, the performance of both models in terms of average exposure time was significantly better [23].

Fig. 8.

Average exposure time in Model A (top) and Model B (bottom) at different operating conditions.

3.6. Hemolysis

To cover the largest possible area of the simulation domain, about 500 streamlines were used. The streamlines were used as references for calculating shear stress and hemolysis index. Figure 9 shows the variation of the hemolysis index over time along a randomly selected streamline. Each of the five curves shown in Fig. 9 corresponds to one of the five sets of constants C, 𝛼, and 𝛽 mentioned in Table 1. There is a difference in the results obtained by each set of constants, with the highest estimate of the hemolysis index obtained using the constants suggested by Giersiepen [16] and the lowest estimate obtained using the constants suggested by Sheriff [21].

Fig. 9.

Hemolysis index variation in randomly chosen streamlines from Model A (top) and Model B (bottom).

Due to the large number of streamlines used in calculating the hemolysis index and the fact that each streamline contained many points, it was difficult to plot the results separately.

Because the equation used was a cumulative one and to present the results without too many figures, the average hemolysis index was used to evaluate the performance of the two ventricular assist devices. The average hemolysis index was calculated at the ventricular assist devices outlet, where the hemolysis reaches its maximum value.

Figures 10 and 11 show the change in average hemolysis index in the two ventricular assist devices at different rotation speeds and flow rates. Both figures include curves obtained using the constants C, 𝛼, and 𝛽 proposed by Heuser [19], Giersiepen [16], Zhang [20], Sheriff [21], and Ding [22]. After analyzing the curves, we found that the average hemolysis index decreases with decreasing rotation speed. However, the opposite happens with decreasing flow rate, so the average hemolysis index increases with decreasing flow rate.

Fig. 10.

Average hemolysis index in Model A using different sets of constants C, 𝛼 and 𝛽.

Fig. 11.

Average hemolysis index in Model B using different sets of constants C, 𝛼 and 𝛽.

4. Discussion

When comparing the velocity domain of the two models, it is clear that the performance of Model A was better than Model B. This conclusion can be explained by the fact that the stagnation regions of Model B cover a larger area in the whole simulation domain compared to Model A. This is very obvious in the velocity contours in Figs 3 and 4. On the other hand, the streamlines structure enhances Model B’s preferability. The smoothness of the flow and the reduced recirculation and turbulence areas are required features in a ventricular assist device.

In terms of hydraulic performance, despite the decrease in static pressure rise across the ventricular assist device as the flow rate at the outlet increases, there is still a clear difference in performance between the two models. As an interpretation of what is shown in Fig. 5, it can be said that if a constant flow rate and a specific pressure head are required, they can be obtained by using a lower rotational speed if Model B is used than if Model A is used.

The performance of the two models in terms of induced shear stress was relatively converged. For low-level shear stress magnitudes (≤10 Pa), the difference between the percentage of points exposed to this level of shear stress is significant (Model A: 82.77%, Model B: 69.61%). However, the difference is insignificant for shear stress magnitude below or equal 150 Pa (Model A: 99.98%, Model B: 99.97%). Moreover, suppose the obtained results are compared with what has been reported in other studies [23]. In that case, it can be said that the performance of both models was very satisfactory.

When analyzing the exposure time, both models showed remarkable performance compared with other ventricular assist devices of the same type. However, by comparing the two models under the same operating conditions, it can be seen that in most cases, the average exposure time of Model B is shorter than that of Model A.

In the final part of this investigation, hemolysis was calculated using the hemolysis prediction model proposed by Giersiepen [16]. Comparing the obtained results either using the original constants suggested by Giersiepen [16] or using the constants suggested by Heuser [19], Zhang [20], Sheriff [21], and Ding [22], it can be seen that the performance of Model A was slightly better than that of Model B. However, compared to what has been reported in other investigations [23,24], the hemolysis index results obtained in this investigation remain within the acceptable range.

5. Conclusion

The main objective of this article was to investigate the performance of two new ventricular assist device models. These models were selected from dozens of models that have been proposed. This study included investigating hydraulic properties, induced shear stress, exposure time, and hemolysis.

This study highlighted many points of difference between the two models. Figures 3 and 4 show that the stagnation region in Model B covers a large area compared to Model A. On the other hand, the streamlines in Model A have a lot of turbulence and vortices, while the streamlines in Model B are much smoother. The difference in the percentage of points subjected to low shear stress magnitude was relatively insignificant, especially for shear stress magnitudes below 150 Pa (Fig. 7). Although Model A has a long average exposure time (Fig. 8), the hemolysis index of Model A is significantly lower than that of Model B (Figs 10 and 11). As a result of this investigation, Model B was selected as a test subject for further investigation.

Ethical approval

Not required.

Conflict of interest

None declared.

Funding

None declared.

Author contributions

Concept/design: MB, HB; Data analysis: MT, MB, WM; Manuscript writing: MB; Critical revision: MT; Approval of article: MT; Statistics: MB; Data collection: HB, MB; Extra coding: HB.

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Analysis of shear stress related hemolysis in a ventricular assist device

Abstract

BACKGROUND:

OBJECTIVE:

METHOD:

RESULTS:

CONCLUSION:

Keywords

1. Introduction

2. Methods

2.1. Geometry

2.4. Shear stress

2.5. Hemolysis

Table 1 Constant 𝛼, 𝛽, and C of the power-low equation C 𝛼 𝛽 Heuser [19] 1.800 × 10−6 0.7650 1.9910 Giersiepen [16] 3.620 × 10−5 0.7850 2.4160 Zhang [20] 1.228 × 10−5 0.6606 1.9918 Sheriff [21] 1.470 × 10−6 1.3000 1.0400 Ding [22] 4.080 × 10−5 0.8000 1.5600

3.1. Flow field

3.2. Model A

5. Conclusion

Ethical approval

Conflict of interest

Funding

Author contributions

References