investigation on mechanical and bio-mechanical … · 2015-07-29 · 88 / j. comput. fluids eng....

88 / J. Comput. Fluids Eng. Vol.20, No.2, pp.88-95, 2015. 6

1. Introduction

Centrifugal blood pumps are crucial devices for cardiopulmonary bypass and circulatory assistance. Therefore, in addition to their mechanical efficiency, bio-mechanical factors have to be considered. One of these bio-mechanical factors is hemolysis, which is the release of hemoglobin from the red blood cells into the plasma. Hemolysis is also important due to the fact that high level

of free hemoglobin is a toxin for the kidneys and can lead to organ failure[1]. During a blood pump operation, the main reason for the hemolysis is the shear stress generated by rotation of the rotating parts[2,3]. Due to the limitation of experiment and complexities in flow characteristics, especially inside the pump, there are obstacles for investigating the details in a real case(in vivo condition). Hence, numerical simulations are used to evaluate mechanical and bio-mechanical performances of blood pumps. Generally, there are two approaches, Eulerian and Lagrangian[4-8], to evaluate hemolysis in numerical simulations. Since the results of Lagrangian-based approaches are usually controversial and time consuming[9], an Eulerian approaches could be more appropriate.

INVESTIGATION ON MECHANICAL AND BIO-MECHANICAL PERFORMANCE

OF A CENTRIFUGAL BLOOD PUMP

M. Chang,1 M. Moshfeghi,2 N. Hur,*2,3 S. Kang,2,3 W. Kim2,3 and S.H. Kang4

1Dept. of Mechanical Engineering, Graduate School, Sogang Univ.2Multi-Phenomena CFD Engineering Research Center(ERC), Sogang Univ.

3Dept. of Mechanical Engineering, Sogang Univ.4Dept. of Mechanical and Aerospace Engineering, Seoul National Univ.

혈액 펌프의 기계적 성능과 생체 역학적 성능에 대한 연구

장 민 욱,1 M. Moshfeghi,2 허 남 건,*2,3 강 성 원,2,3 김 원 정,2,3 강 신 형4

1서강대학교 대학원 기계공학과2서강대학교 다중현상 CFD 연구센터(ERC)

3서강대학교 기계공학과4서울대학교 기계항공공학부

Blood pump analysis process includes both mechanical and bio-mechanical aspects. Since a blood pump is a mechanical device, it has to be mechanically efficient. On the other hand, blood pumps function is sensitively related to the blood recirculation; hence, bio-factors such as hemolysis and thrombosis become important. This paper numerically investigates the mechanical and bio-mechanical performances of the Rotaflow in the extracorporeal membrane oxygenation(ECMO), Ventricular Assist Device(VAD), and full-load conditions. The operational conditions are defined as(400[mmHg], 5[L/min.]), (100[mmHg], 3[L/min.]), and (600[mmHg], 10[L/min.]) for ECMO, VAD, and full-load conditions, respectively. The results are presented and analyzed from the mechanical aspect via performance curves, and from bio-mechanical aspect via focusing on hemolytic characteristics. Regions of top and bottom cavities show recirculation in both ECMO and VAD condtions. In addition, Eulerian-based calculation of modified index of hemolysis(MIH) has been investigated. The results demonstrate that the VAD condition has the least risk of hemolysis among the others, while the full-load condition has the highest risk.

Key Words : Centrifugal Blood Pump, CFD, Mechanical Performance, ECMO, VAD, MIH

Received: May 20, 2015, Revised: June 29, 2015,Accepted: June 29, 2015.* Corresponding author, E-mail: [email protected] http://dx.doi.org/10.6112/kscfe.2015.20.2.088Ⓒ KSCFE 2015

INVESTIGATION ON MECHANICAL AND BIO-MECHANICAL PERFORMANCE… Vol.20, No.2, 2015. 6 / 89

This paper aims to investigate the mechanical performance of a commercial model(Rotaflow) and its modified index of hemolysis(MIH) in the three predefined conditions, Extracorporeal Membrane Oxygenation(ECMO), Ventricular Assist Device(VAD), and full-load conditions.

2. Geometry of Model and Mesh Arrangement

The pump is composed of a four-bladed-impeller, in which the blades have an airfoil section, and a casing (shroud). In addition, there exists a volute which is connected to the impeller housing through a diffuser. Fig. 1(a)-(d) show the schematic geometry of the pump. The impeller radius and the pump volume are 25 mm and 32 mL[10], respectively. Owing to the importance of first grid spacing in shear stress calculation, a mesh sensitivity analysis has been conducted on the first prism layer thickness. As shown in Fig. 2, a value of first grid spacing between 0.02 mm and 0.04 mm shows acceptable convergence of MIH value; hence, a value of 0.024 mm and six prism layers are chosen for the final model. The final mesh has been generated using polyhedral option in Star-CCM+ Ver. 9.06 with the minimum and maximum surface sizes of 0.25 mm and 1.0 mm, respectively, as shown in Fig. 3.

Fig. 2 Mesh sensitivity analysis

3. Physics of Problem and Numerical Method

The simulation of the blood flow has been conducted assuming incompressible flow assumptions. In addition, because the average characteristics are investigated, the steady-state condition is assumed, which eliminates the time dependency of the flow parameters. The governing equations include the mass conservation and the

(a) (b)

(c) (d)

Fig. 1 (a) Top view; (b) front view; (c) side view ; (d) isometric view of the pump

90 / J. Comput. Fluids Eng. M. Chang ․ M. Moshfeghi ․ N. Hur ․ S. Kang ․ W. Kim ․ S.H. Kang

Fig. 3 Mesh arrangement

Navier-Stokes momentum conservation. These equations in the Cartesian coordinate system are given as:

0 u (1)

t

u Pu u u (2)

where u denotes the velocity vector and P represents the pressure.

Since the centrifugal blood pump rotates at high rpm (2000-5000 rpm), the flow are considered as turbulent (Reynolds number based on the impeller diameter: 1.6×105 ~ 6.0×105). Hence, in order to capture the turbulence effects caused by the rotation of the pump impeller, the standard k-epsilon model is adopted. The standard k-epsilon model is a two-equation model which uses transport equation for the turbulence kinetic energy and turbulence eddy dissipation. Although k-epsilon model assumes isotropic turbulence, since the present research does not deal with the flow details inside the boundary layer, it can be considered as an appropriate choice.

In addition, the steady-state result of the rotating impeller is simulated using the multiple reference frame (MRF) method. The simulations start with the initial velocity and pressure values of zero at the whole domain. The inlet part is defined as mass flow inlet condition and the outlet part is set as outlet condition. The walls are assumed to have no-slip condition.

To fulfill the non-Newtonian properties of the blood, the Carreau model is chosen for the blood viscosity. The equation for the Carreau model is:

1 22

0 1n

(3)

where λ = 3.313 s, n = 0.3568, μ0 = 0.056 Pa-s and μ = 0.00345 Pa-s[11,12].

4. MIH Concept and Formulation

Because there is no conventional method for hemolysis index evaluation at in vivo condition, the ASTM F1841-97 standard[13] proposes three numerically-calculated indices for blood damage caused at in vitro condition by a medical device. These indices are: (a) normalized index of hemolysis(NIH); (b) normalized milligram index of hemolysis(mgNIH) and (c) modified index of hemolysis (MIH). Among them, the present research considers the MIH, which measures the increase in plasma-free hemoglobin normalized by the total quantity of hemoglobin in the volume of blood pumped in a closed circuit.

On the basis of the experimental data, Wurzinger et al. [14] and Giersiepen et al.[15] developed a power-law- based model for steady-shear hemolysis analysis. The formulation of damage fraction is given as:

D C t (4)

where C, α, β are constant determined by regression analysis of the experimental data by Wurzinger et al.[14](C = 3.62×10-7, α = 2.416, β = 0.785), τ is shear stress and t represents time of exposure.

The main advantage of using this power-law-based assumption is the simplicity of application in numerical calculation. After choosing Eq. (4), the von Mises stress derived from six components of the derivatives of stress tensor is used for the τ[16]. It is noteworthy to mention that since the values of Reynolds shear stress (turbulent stress) do not have significant effect on the blood damage and hemolysis[17,18], the von Mises stresses are calculated solely based on the laminar stress values. The formulation of the von Mises stress, which calculates a scalar shear stress value, is given by the following equation.

vm 1

22 2 2 2 2 216

2 xx yy yy zz zz xx xy yz zx

(5)

In order to predict the MIH, the numerical method proposed by Farinas et al.[5] and Garon and Farinas[8], replacing the computation of blood damage along the


Fig. 4 Schematics of cannulae sizes[15,16]

streamline by a volume integration of a damage function over the computational domain, is applied. Since this method is based on steady-state condition, the time derivatives of the changes are zero. The above assumptions lead to:

1/0.785 7 1/0.785 2.416/0.785(3.62 10 )lD D t (6)

where Dl is linear damage, τ is scalar shear stress, and t is time of exposure.

Assuming that the shear stress stays constant throughout the material volume, the time derivative of the linear damage function becomes:

7 1/0.785 2.416/0.785(3.62 10 )ld

Ddt

(7)

Finally, these assumptions together with relationship between concept of Eulerian and Lagrangian approaches result in calculation of average linear damage as:

7 1/0.785 2.416/0.7851(3.62 10 )l

V

D dVQ

(8)

where Q is the flow rate passing through the outlets. And finally the MIH can be calculated using the relations in Eq. (6):

0.785( , ) ( )lD t D (9)6( , ) 10MIH D t (10)

In order to validate the aforementioned equations, and prior to implement the above method for the MIH

Fig. 5 Computation of the MIH for different cannulae with experimental data

calculation, two cannulae are simulated, and as the results show the MIH values are comparable with experimental results of Wachter and Verdonck[19] and Wachter et al.[20]. Schematic of the cannulae is shown in Fig. 4 and the dimensions are listed in Table 1. The MIH values presented in Fig. 5 show the competence and the accuracy of this Eulerian MIH formulae.

5. Results and Discussions

As an investigation for the mechanical aspect, analyses at different ranges of rotation speed(2000-5000 rpm) and flow rate(2-10 L/min.) are conducted. In addition, three predefined conditions(ECMO, VAD and full-load) are investigated for the MIH analysis(Table 2).

For mechanical evaluation, non-dimensional values such as the head coefficient(ψ), flow coefficient(φ) and hydraulic efficiency(η) of the pump are used. Classically, by defining ρ, Q and D as the flow density, flow rate and impeller diameter, we have:

A[mm] B[mm] α[deg.]13G 2.21 1.6 714G 1.91 1.3 7

Table 1 Dimensions of the cannulae[15,16]

ECMO VAD Full-loadΔP[mmHg] 400 100 600Q[L/min.] 5 3 10

Table 2 Operating conditions for ECMO, VAD and full-load


2 20

u VH

g (11a)

impimp

PH

g

(11b)

PH

g

(11c)

where H0 is head of the ideal pump, Himp represents head of the impeller and H denotes the head of the whole pump. In addition, u2(u2 = r2ω) and Vθ2 are the tangential velocities at the impeller outlet based on the theory and CFD results; ΔPimp and ΔP represent total pressure difference between the inlet of the pump and the outlet of the impeller and the pump.

Furthermore, the head coefficient and the flow coefficient are defined as:

22

H

u

(12)

22

Q

D u (13)

Also, the efficiency factors corresponding to the impeller and the whole pump are calculated as:

0

impimp

H

H (14a)

0

H

H (14b)

Fig. 6(a) shows variation of the head coefficient and Fig. 6(b) presents the variation of hydraulic efficiency of the pump with respect to the flow coefficient. Overall, the plots clearly show that the results are acceptably close to each other and follow the same trend, regardless of different rotational speeds. As it can be seen in Fig 6(a), as flow coefficient increases, the head coefficient decreases. In addition, the whole pump head coefficient (blue lines) declines with a higher rate than the ideal pump head coefficient(black lines) and the impeller head coefficient(red lines). Furthermore, as it is shown in Fig. 6(b), both impeller(black lines) and pump(red lines) hydraulic efficiencies decrease gradually as flow coefficient increases. Also, hydraulic efficiency loss at the volute is approximately 20-30%, due to the average difference between two lines.

In addition to the performance curves, the streamlines, contours of pressure and von Mises stress are presented in Figs. 7, 8 at ECMO and VAD conditions. A region of high velocity can be observed between the case and the volute as shown in Fig. 7(a) and Fig. 8(a), which corresponds to high scalar stress in Fig. 7(c) and Fig. 8(c). Since ECMO condition requires higher pressure and flow rate than VAD condition, it has higher pressure and velocity values. Also recirculations are observed between the impeller and the casing at top and bottom cavities, as shown in Fig. 7(a) and Fig. 8(a). Center of impeller shows complex streamline due to the rotational motion. In addition, as shown in Fig. 7(c) and Fig. 8(c), high von Mises stresses appear in vicinity of the case wall top and bottom cavities and also areas of recirculation, which have higher level of contribution to the blood damage.

From bio-mechanical aspect, all of the predefined

(a) (b)

Fig. 6 Numerical results at different operational conditions: (a) head coefficient vs. flow coefficient; (b) pump efficiency vs. flow coefficient


conditions listed in the Table 2 are investigated. The rotational speeds, at which the pump generates each condition, are determined as 4159 rpm, 2100 rpm, 5134 rpm through conducting a set of simulations at different rpm(s) and measuring the pressure increase generated at the outlet. The MIH values for these three conditions are calculated based on the CFD results as 1170, 7570, 9140 for the VAD, ECMO, and full-load conditions. As seen, the full-load condition has the highest MIH value which

represents highest blood damage risk. Also, VAD condition shows the lowest MIH value. In addition, no direct connection between pressure distribution and the areas with high risk of hemolysis has been found.

6. Concluding Remarks

In this paper, investigation of a centrifugal blood pump

(a) Streamlines and velocity magnitude[m/s]

(b) Pressure[Pa]

(c) Von Mises stress[Pa]

Fig. 7 Numerical results at ECMO condition: (a) streamlines and velocity magnitude [m/s]; (b) pressure contour [Pa]; (c) von Mises stress contour [Pa]


(Rotaflow) is conducted at different operational conditions. The results are analyzed from both mechanical and bio-mechanical aspects. From the point of view of mechanical engineering, performance and efficiency of the Rotaflow are calculated. As it is observed, the pressure loss in the volute is higher than the impeller. Also, the pump efficiency decreases 20-30%, when the inlet flow rate increases from 2 L/min. to 10 L/min. Some areas of recirculation are observed near the center of the impeller and on the suction surface of the airfoil-shaped impeller

blades. From the point of view of bio-mechanics, the MIH value has been calculated based on an Eulerian approach for three predefined conditions of ECMO, VAD and full-load. The regions with the higher risk of the blood damage have been found at the casing walls around the impeller as high scalar shear stress appears. This may be due to the high velocity variation caused by the rotational motion of the impeller and also due to the flow recirculation. Between three conditions VAD shows the lowest MIH value, while the full-load condition has the highest.

(a) Streamlines and velocity magnitude[m/s]

(b) Pressure[Pa]

(c) Von Mises stress[Pa]

Fig. 8 Numerical results at VAD condition: (a) streamlines and velocity magnitude [m/s]; (b) pressure contour [Pa]; (c) von Mises stress contour [Pa]


Acknowledgments

This research was supported by a grant of the Korea Health Technology R&D Project through the Korea Health Industry Development Institute(KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea(grant number : HI14C0746).

Note

This paper is a revised and extended version of the paper presented at the KSCFE 2015 Spring Annual meeting, Jeju KAL Hotel, Jeju, May 14-15, 2015.

References

[1] 2004, Marsden, A.L., Bazilevs, Y., Long, C.C. and Behr, M., "Recent Advances in Computational Methodology for Simulation of Mechanical Circulatory Assist Devices," WIREs Syst Biol Med 2014, Vol.6, No.2, pp.169-188.

[2] 2004, Goubergrits, L. and Affeld, K., "Numerical Estimation of Blood Damage in Artificial Organs," Artificial Organs, Vol.28, No.5, pp.499-507.

[3] 2005, Day, S.W. and McDaniel, J.C., "PIV Measurements of Flow in a Centrifugal Blood Pump: Steady Flow," Journal of Biomechanical Engineering, Vol.127, No.2, pp.244-253.

[4] 2004, Arora, D., Behr, M. and Pasquali, M., "A Tensor-based Measure for Estimating Blood Damage," Artificial Organs, Vol.28, No.11, pp.1002-1015.

[5] 2006, Farinas, M.I., Garon, A., Lacasse, D. and N’dri, D., "Asymptotically Consistent Numerical Approximation of Hemolysis," Journal of Biomechanical Engineering, Vol.128, No.5, pp.688-696.

[6] 2005, Arvand, A., Hormes, M. and Reul, H., "A Validated Computational Fluid Dynamics Model to Estimate Hemolysis in a Rotary Blood Pump," Artificial Organs, Vol.29, No.7, pp.531-540.

[7] 2012, Fraser, K.H., Zhang, T., Taskin, M.E., Griffith, B.P. and Wu, Z.J., "A Quantitative Comparison of Mechanical Blood Damage Parameters in Rotary Ventricular Assist Devices: Shear Stress, Exposure Time and Hemolysis Index," Journal of Biomechanical Engineering, Vol.134, No.8, 081002.

[8] 2004, Garon, A. and Farinas, M.I., "Fast Three- dimensional Numerical Hemolysis Approximation," Artificial Organs, Vol.28, No.11, pp.1016-1025.

[9] 2012, Taksin, M.E., Fraser, K.H., Zhang, T., Wu, C., Griffith, B.P. and Wu, Z.J., "Evaluation of Eulerian and Lagrangian Models for Hemolysis Estimation," ASAIO Journal, Vol.58, No.4, pp.363-372.

[10] 1996, Naito, K., Suenaga, E., Cao, Z.L., Suda, H., Ueno. T., Natsuaki, M. and Itoh, T., "Comparative Hemolysis Study of Clinically Available Centrifugal Pumps," Artificial Organs, Vol.20, No.6, pp.560-563.

[11] 2004, Johnston, B.M., Johnston, P.R., Corney, S. and Kilpatrick, D., "Non-Newtonian blood flow in human right coronary arteries:steady state simulations," Journal of Biomechanics, 37, pp.709-720.

[12] 1991, Cho, Y.I. and Kensey, K.R., "Effects of the nonb-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: steady flows," Biorheology, 28, pp.241-262.

[13] 1997, ASTM Committee, Standard Practice for Assessment of Hemolysis in Continuous Flow Blood Pumps, Annual Book of ASTM Standards, F1841-97, Vol.13.01.

[14] 1986, Wurzinger, L.J., Opitz, R., Eckstein, H., "Mechanical Bloodtrauma. An overview," Angeiologie, Vol.38, No.3, pp.81-97.

[15] 1990, Giersiepen, M., Wurzinger, L.J., Opitz, R., Reul, H., "Estimation of Shear Stress-related Blood Damage in Heart Valve Prosteses-In Vitro Comparison of 25 Aortic Valves," Artificial Organs, Vol.13, No.5, pp.300-306.

[16] 1994, Bludszuweit, C., "A Theoretical Approach to the Prediction of Haemolysis in Centrifugal Blood Pumps," Ph.D. thesis, University of Strathclyde Glasgow, Scotland.

[17] 1995, Jones, S.A., "A Relationship Between Reynolds Stresses and Viscous Dissipation: Implications to Red Cell Damage," Annals of Biomedical Engineering, Vol. 23, pp.21-28.

[18] 2007, Ge, L., Dasi, L.P., Sotiropoulos, F. and Yoganathan, A.P., "Characterization of Hemodynamic Forces Induced by Mechanical Heart Valves: Reynolds vs. Viscous Stresses," Annals of Biomedical Engineering, Vol. 36, No.2, pp.276-297.

[19] 2002, De Wachter, D. and Verdonck, P., "Numerical Calculation of Hemolysis Levels in Peripheral Hemodialysis Cannulas," Artificial Organs, Vol.26, No.7, pp.576-582.

[20] 1997, De Wachter, D.S., Verdonck, P.R., De Vos, J.Y. and Hombrouckx, R.O., "Blood Trauma in Plastic Haemodialysis Cannulae," Artificial Organs, Vol.20, No.7, pp.366-270.

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