Copyright © 2014 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

A New Computational Fluid Dynamics Method for In-Depth Investigation of Flow Dynamics in Roller Pump Systems *Xiaoming Zhou, †Xin M. Liang, †Gang Zhao, *Youchao Su, and *Yang Wang *School of Mechanical, Electronic, and Industrial Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan; and †Centers for Biomedical Engineering, Department of Electronic Science and Technology, University of Science and Technology of China, Hefei, Anhui, China

Abstract: Roller pumps are commonly used in circulatory assist devices to deliver blood, but the inherent high mechanical stresses (especially wall shear stress) may cause considerable damage to cells. Conventional experimental approaches to evaluate and reduce device-induced cell damage require considerable effort and resources. In this work, we describe the use of a new computational fluid dynamics method to more effectively study roller pump systems. A generalized parametric model for the fluid field in a typical roller pump system is presented first, and analytical formulations of the moving boundary are then derived. Based on the model and formulations, the dynamic geometry and mesh of the fluid field can be updated automatically according to the time-dependent roller positions. The described method successfully simulated the pulsing flow generated by the pump, offering a

convenient way to visualize the inherent flow pattern and to assess shear-induced cell damage. Moreover, the highly reconfigurable model and the semiautomated simulation process extend the usefulness of the presented method to a wider range of applications. Comparison studies were conducted, and valuable indications about the detailed effects of structural parameters and operational conditions on the produced wall shear stress were obtained. Given the good consistency between the simulated results and the existing experimental data, the presented method displays promising potential to more effectively guide the development of improved roller pump systems which produce less mechanical damage to cells. Key Words: Roller pump— Computational fluid dynamics—Wall shear stress—Cell damage.

Displacement (roller) and rotary (centrifugal) pumps have been developed extensively and are routinely used nowadays for treating patients with cardiac insufficiency as well as extracorporeal circulation for other purposes in various biomedical settings (1–13). Roller pumps have the advantages of simplicity of operation, cost-effectiveness, reliability of flow calculation, inherent immunity to fluid contamination, and the ability to pump against high resistance without reducing flow (1,2). With recent

independent studies failing to show any advantage in using centrifugal over roller pumps (3–6) in shortterm assistance applications (less than 8 h), roller pumps are still commonly used in circulatory assist devices. However, cell damage associated with roller pumps has long been noticed and is recognized as one of their fundamental problems (2–8). For example, during open-heart surgery, in which cardiopulmonary bypass is used to isolate the heart and lungs from the remainder of the circulation, pumpinduced cell damage is considered as a main cause of renal injury (14) and may prolong the patient’s recovery process (6,7,15–17). Furthermore, in a previously developed “dilution–filtration” system to remove cryoprotective agents from cryopreserved cells (11), roller pumps were utilized to drive cell suspensions; although the dilution–filtration process has already been proven to be safe and effective to a certain

doi:10.1111/aor.12319 Received October 2013; revised March 2014. Address correspondence and reprint requests to Dr. Xiaoming Zhou, School of Mechanical, Electronic, and Industrial Engineering, University of Electronic Science and Technology of China, Xiyuan Street #2006, Chengdu, Sichuan 611731, China. E-mail: [email protected]; Dr. Gang Zhao, Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230027, China. E-mail: [email protected] Artificial Organs 2014, 38(7):E106–E117

A NEW CFD METHOD FOR ROLLER PUMPS extent, a noticeable amount of cell lysis (up to 10%) was observed. One possible explanation for the cell loss is the mechanical stress produced by the roller pumps. It has been generally believed that the high shear stress generated during pumping is the primary cause of cell damage (7,15–17). As wall shear stress and other key fluid characteristics are closely related to pump geometry and operational conditions, much attention has been focused on the optimization of roller pumps based on intensive studies of the inherent fluid characteristics. Currently, in vitro hemolysis tests are commonly performed for evaluation of design modifications. These tests require a considerable amount of experimental effort and many repetitions due to large statistical variations. Furthermore, it is very difficult to attribute overall blood damage to a particular source, as many factors in experiments may influence the sensitivity of red blood cells (18). Today, computational methods are widely used as complementary tools for blood pump development in the early stages of the design process, as they offer convenient and efficient means for the analysis of flow patterns and pump efficiency. The majority of numerical simulations have focused on centrifugal pumps (10,17–20). Only a few studies investigating fluid characteristics in roller pumps using computational fluid dynamics (CFD) methods have been reported (7,21). Generally, two different approaches were utilized in these studies. The first approach used a two-dimensional CFD model to explore the blood flow and associated cell damage in a roller pump. The detailed flow patterns, as well as shear stress caused by the flow, were examined, and a theoretical blood damage prediction model was proposed (7). The study provided a visualized understanding of the detailed fluid dynamics inside the roller pump and raised the possibility of using CFD to further analyze and optimize the design of roller pumps. However, one of the basic assumptions used in the study, that the mass flow rate and velocity profile at the inlet were known and kept constant at all times, was obviously impossible in reality. Furthermore, the dynamic geometry used in the model was obtained by digitizing images of the roller pump boot taken at the various times. Such work is labor-intensive and time-consuming, to say nothing of the high possibility of artificial error during the process. Most importantly, as the study focused on a highly customized pump under very specific peristaltic modes, very limited insight could be obtained to guide the general optimization development of roller pumps.

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The second approach utilized the fluid–solid coupling calculation to simulate a roller pump system in Comsol, a commercial software package (21). Although the method was theoretically close to reality, the necessity of performing a large number of high-complexity calculations with a complicated model reduced its potential to be adapted in other applications. Furthermore, too many factors in the coupling calculation process have the possibility to influence the final simulation outcomes significantly, increasing the difficulty of interpolating the obtained results. These might be the reasons why only a few simple results were presented in the report without detailed discussion. Overcoming the current limitations in CFD-based numerical simulation to study flow characteristics inside roller pumps will lead to better-designed roller pump systems that will be beneficial for a wide range of biomedical applications. In this study, we present a new CFD-based simulation approach to conveniently study the flow characteristics of roller pump systems. A complete parametric model of the fluid field in the roller pump is presented, and analytical formulations of the moving boundary of the fluid field in the roller pump are derived. Based on the model and the formulations, the dynamic geometry can be generated and meshed automatically during the entire simulation process. By comparing the effects of different structural parameters and operation conditions on flow rate and shear stress, we aim to provide more comprehensive and in-depth insights to facilitate the design and applications of roller pump systems. MATERIALS AND METHODS CFD model Geometry As illustrated in Fig. 1, a two-dimensional model of a typical roller pump system was fully parameterized. The outline of the inner fluid field consists of the outer wall, the inner wall, and the inlet/outlet (Fig. 1a). The deformed inner wall near each of the rollers consists of several curves, which were modeled as arcs (Fig. 1b). The radius of the fillet curves (Fig. 1b), R, depends mainly on the roller size and the rigidity of the tubing. To reduce the complexity of the model, R was assumed to be constant for a given pump. Thus, the geometry of the inner fluid field depends only on the following parameters: (i) d, diameter of the tubing; (ii) L, length of the rolling arm; (iii) r and N, radius and number of the pump rollers, respectively; and (iv) D, inner diameter of the pump boot. Artif Organs, Vol. 38, No. 7, 2014

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y C

FIG. 1. A parametric model of a typical two-roller pump. (a) The geometry and boundary condition. (b) The modeled curves of the deformed inner wall near a roller.

E P

G

D

B

A

γ2

F

γ1 θ4 θ3 αi θ 1 θ 2

O

(a)

For a pump system with given structural dimensions, the time-dependent geometry of the tube and its inside fluid field can be considered as consequences of the positions of the rotating rollers. By establishing the analytical relationship between the geometry variations and the dynamic positions of the rollers, the dynamic geometry of the inner fluid field can be predicted. Given α1 and αi (1 < i ≤ N) are the angular positions of the leading roller and the trailing rollers, respectively, their values can be determined by

α 1 = ωt + α 0 and α i = α i −1 +

2π (1 < i ≤ N ) N

x

(b)

(1)

OB = OA cos γ 1 + AB2 − (OA sin γ 1 )

H = ( r + R) − ( D 2 + R − x A ) and h = 2

H

( D 2 + R) = L cos γ 1 + ( r + R)2 − ( L sin γ 1 )2

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(4)

Thus,

⎡ L2 + ( D 2 + R) − ( r + R) ⎤ γ 1 = γ 2 = arccos ⎢ ⎥ (5) 2 ( D 2 + R) L ⎣ ⎦ 2

(a)

(b)

y

G

(c)

2

y

E A

D F

G x

O

(2)

In case 1, yA > h. The roller is above the x-axis and induces deformation only in the elbow segment of the tubing, as shown in Fig. 2a. In case 2, |yA| ≤ h. The roller is in close proximity with the x-axis and induces deformation in both the elbow and the linear segments of the tubing, as shown in Fig. 2b. In case 3, yA < −h and H ≥ 0. The roller is below the x-axis and induces deformation in only one of the linear segments of the tubing, as shown in Fig. 2c. In case 4, yA < −h and H < 0. The roller is well below the x-axis and has no direct contact with the tubing, as shown in Fig. 2d. For each case, the values of θ1, θ2, θ3, and θ4 (Fig. 1b) are calculated accordingly. For example, in case 1, the calculation is performed as follows. Firstly, γ1 and γ2 (Fig. 1b) are determined by

(3)

That is,

where α0 is the initial position of the leading roller and ω is the rolling speed of the pump arm. Along with the moving roller, the induced deformation of the inner wall can be categorized into four cases, which can be specified by defining 2

2

y

G

O A

F

E D

x

A

O

(d)

E

F

D

x

y

x

O A

FIG. 2. Four typical cases of roller positions and the induced deformations of the tubing: (a) contact and deformation at the elbow segment; (b) contact and deformation at both the elbow and the linear segments; (c) contact and deformation at the linear segment; (d) no direct contact or deformation of tubing.

A NEW CFD METHOD FOR ROLLER PUMPS Subsequently, for a known position of a roller (αi) we have

θ1 = α i − γ 1 and θ 4 = α i + γ 2

(6)

In Cartesian coordinates, the position of node D (xD, yD) shown in Fig. 1b can be expressed as

xD =

Rx A + rxB RL cos α i + r ( D 2 + R) cos θ1 = AB R+r

(7)

yD =

RyA + ryB RL sin α i + r ( D 2 + R) sin θ1 = AB R+r

(8)

Then we have

θ 2 = arccos

xD

Based on the equations derived above, the geometric variation of the fluid field can be calculated given the structural parameters L, R, r, and D, together with the operational parameter ω, the rotation speed of the rollers with pump arms. Fluid Blood, the fluid typically delivered by roller pumps, was modeled as a Newtonian fluid with a constant density (ρ) of 1050 kg/m3 and a constant viscosity (μ) of 3.5 × 10−3 kg/m·s (7). According to its Casson plot, blood displays Newtonian properties at higher shear rates (higher than 100/s) (22,23). The assumption that blood behaves as a Newtonian fluid holds for the shear rates used in the presented simulation.

(9)

xD + yD2 2

Similarly,

xE =

Rx A + rxC RL cos α i + r ( D 2 + R) cos θ 4 = AC R+r

(10)

yE =

RyA + ryC RL sin α i + r ( D 2 + R) sin θ 4 = AC R+r

(11)

θ 3 = arccos

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xE

(12)

xE + yE 2 2

For the other cases, the values of θ1, θ2, θ3, and θ4 can be calculated similarly. As soon as the values are obtained, the deformation of the inner wall with respect to each roller can then be predicted. Given P(ρ,θ) denotes the position of an arbitrary node on the moving boundary before deformation, then the new position of the node when a roller is passing by, P′(ρ′,θ′), can be predicted as follows by assuming θ′ = θ. If θ2 > θ ≥ θ1, P′ is located on DF , and

[ρ′ cos θ − ( D 2 + R))cos θ1 ]2 + [ρ′ sin θ − ( D 2 + R) sin θ1 ] = R 2 2

(13)

If θ3 > θ ≥ θ2, P′ is located on ED, and

(ρ′ cos θ − L cos α i )2 + (ρ′ sin θ − L sin α i )2 = r 2

(14)

If θ4 > θ ≥ θ3, P′ is located on GE , and

[ρ′ cos θ − ( D 2 + R) cos θ4 ]2 + [ρ′ sin θ − ( D 2 + R) sin θ 4 ] = R 2 2

(15)

Otherwise, P is out of impact range of the roller.

Initial and boundary conditions The roller pump system was assumed to be at rest initially, with the velocity assumed to be 0 for the whole fluid field at t = 0. As soon as the simulation started, a certain rotational speed (ω = 2π rad/s) was imparted to the pump arm, and then the fluid began to flow. The boundaries of the fluid field consisted of an inlet, an outlet, a stationary wall boundary, and a moving boundary (Fig. 1a). Zero pressure was prespecified at the inlet, and the outlet pressure p was considered to be an operational condition varying among different applications. The velocities at the stationary and moving walls of the pump boot satisfied the no-slip condition. Simulation methods In this work, simulations were performed using a commercial software system, ANSYS Fluent v. 12.0 (ANSYS, Inc., Canonsburg, PA, USA). Detailed methods are described below. Dynamic updating and meshing of the fluid field The shape of the pump boot changes with time, which is associated with the periodic passes of the rollers. To describe the time-dependent boundary deformation, a user-defined function (UDF) file was compiled and loaded into the Fluent CFD project. At each time step, the function was activated to solve Eqs. 1–15, and the boundary was subsequently updated. The built-in dynamic mesh function of Fluent was utilized in this work. To create the dynamic mesh, the fluid field was split into a main fluid area and boundary layers. An unstructured mesh (edge size approximately 0.15 mm) was applied to the main fluid area, allowing it to be automatically remeshed Artif Organs, Vol. 38, No. 7, 2014

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and smoothed. For the boundary layers, fine quadrangular grids (thickness from 0.02 to 0.04 mm) were used to reflect the high-velocity gradients. At each time step, the dynamic positions of the nodes in the boundary layers near the inner wall were allocated automatically by the UDF functions to ensure high meshing quality. Solution To solve this time-dependent moving boundary problem, the interval between time steps was set as the time taken for the rollers to travel 0.1 degrees, and the model was set to automatically save the data file every five steps (0.5 degrees). The governing equations were solved using an implicit approach, requiring iterations at each time step, and the maximum number of iterations per time step was set to be 200. Convergence was achieved when the sum of the absolute values of normalized residuals was less than the predefined minimum residual sum, which was set to be 1 × 10−3. At each time step, the model was solved using a QUICK (Quadratic Upstream Interpolation for Convective Kinematics) discretization scheme, and a coupled solution scheme was applied to solve the velocity–pressure coupling problems. Unless otherwise stated, the results presented below were calculated for the defined pump system with the parameters shown in Table 1. The outlet pressure was set to be zero because such an operational condition can easily be realized in future experiments. The total number of cells was 314 380 initially for this pump and varied around 310 000 during the dynamic process. Test calculation for this pump indicated the average velocity at inlet was around 0.25 m/s, with a Reynolds number of 750. Existing studies indicate that stenotic arterial blood flow has a critical Reynolds number of around 300

TABLE 1. Parameter settings for the simulation D (mm) 120

d (mm)

r (mm)

L (mm)

N

ω (rad/s)

10

10

49

2

2π

(24); therefore, the flow in the defined system was assumed to be turbulent. In the presented simulation, the k–ω model was used to solve for the turbulent flow. RESULTS Geometry and mesh At t = 0, the pump arm was predefined to be at perfect vertical, and thus the angular position of the leading roller α1 was equal to 90°. The geometry and mesh of the fluid field are shown in Fig. 3. Occlusion of the roller pump, that is, the distance between the inner wall and the outer wall at the point of roller contact, was equal to 1 mm under the given structural parameters. The minimum and volume-average orthogonal qualities of the mesh were calculated to be 0.65 and 0.97, respectively. As soon as the simulation started, the geometry and mesh of the system were updated at each time step. The quality of the mesh was monitored and recorded throughout the entire simulation (Fig. 4). In general, the volume-average quality of the mesh decreased at the beginning and then leveled off at around 0.92. The minimum quality of the mesh was found to be around 0.6 in most cases, but several sudden decreases were observed. The minimum value was well over 0.4, suggesting the quality of the mesh was acceptable. Blood flow As soon as the rollers started to move and the geometry of the fluid field began to deform, the blood

FIG. 3. The initial geometry and mesh of the fluid field in the roller pump boot are shown.

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A NEW CFD METHOD FOR ROLLER PUMPS

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1

Orthogonal quality

0.8

Volume average Minimum value

0.6

FIG. 4. Monitored orthogonal quality of the dynamic mesh is shown.

0.4

0.2

0

0.5

1

1.5

Time (s)

flow in the tubing was gradually activated. The time variations of the velocity field, wall shear stress, mass flow rate at inlet/outlet, and all other flow parameters at different roller positions were simulated and recorded. As illustrated in Fig. 5, the flow requires a short, finite period of time to be fully mobilized; subsequently, the flow becomes stable periodically. The pulsatile flow feature demonstrates high consistency

Maximum wall shear stress (Pa) Maximum velocity magnitude (m/s) Mass flow rate at outlet (kg/s)

Activation stage

2

with experimental results (9). The cycle duration of the flow was calculated to be 0.5 s based on the number of rollers and their rolling speed:

T

= 2π ωN

(16)

Given that the activation stage was rather short and flow characteristics in the stable-flow stage would

Stable-flow stage

0.04 0.03 0.02 0.01

FTP1

0 2.5 2

FTP2 FIG. 5. Changes in the mass flow rate at outlet, the maximum velocity magnitude and the maximum wall shear stress with roller position are shown.

1.5 1

FTP3

0.5 0 150

FTP4

100

FTP5 50

0 0

0.5

1

1.5

Time (s)

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FIG. 6. Contours of velocity magnitude and static pressure plotted at several typical roller positions are shown.

offer more strategic insights for practical applications, attention was focused mainly on the stable-flow period. As shown in Fig. 5, the stable-flow period was divided into several substages by feature time points (FTPs), the flow characteristics of which were specified as follows. In substage 1 (between FTP1 and FTP2), only the leading roller moved along the arc section of the tube (Fig. 6a). Most of the fluid in front was forced to flow out through the outlet, while the rest flowed backward via the occlusion gap. At the narrowest part of the gap, the highest velocity and wall shear stress Artif Organs, Vol. 38, No. 7, 2014

were produced, although the amount of backward flow was very small. In this substage, the total volume of the fluid field and the gap size stayed constant, suggesting a rather steady blood flow. The maximum values for velocity and wall shear stress were determined to be around 0.68 m/s and 23.5 Pa, respectively. In substage 2 (between FTP2 and FTP3), the trailing roller started to come into contact with the tube (Fig. 6b), which induced a deformation of the tube that suppressed the backward flow near the leading roller, resulting in an increase in the outlet flow rate

A NEW CFD METHOD FOR ROLLER PUMPS as well as a sudden decrease in the maximum velocity magnitude and wall shear stress. In substage 3 (between FTP3 and FTP4), the leading roller moved to the left linear section of the tube and gradually left the tube, while the trailing roller moved from the right linear section into the arc section (Fig. 6c). These movements led to a volume excursion (shrinking followed by rapid expansion) of the fluid field, and the sizes of the two occlusion gaps changed inversely. As a result, the flow characteristics, such as the velocity magnitude and wall shear stress, were starting to show high complexity. In comparison, the variation in outlet mass flow rate exhibited a general decreasing trend because of the volume expansion near the outlet. In substage 4 (between FTP4 and FTP5), the leading roller was leaving the tube, and the moving trailing rollers started to be the dominant factor controlling the fluid field. Fluid was squeezed forward by the trailing rollers but was blocked at the gap near the leading roller. The pressure between the gaps was increasing rapidly (Fig. 6d). Consequently, the backward flow near the leading roller was completely suppressed and the outlet mass flow rate increased; at the same time, the backward flow near the trailing roller was increasing rapidly, leading to a sharp rise in velocity and wall shear stress. After FTP5, the leading roller was not in contact with the tube, and the flow cycle was over. For each cycle, the average mass flow rate was calculated to be 0.0312 kg/s, and the maximum velocity and wall shear stress were 0.896 m/s and 35.94 Pa, respectively. DISCUSSION CFD method Roller pump systems have not previously benefited from CFD-based simulation techniques because most of them were designed well before CFD became widely accessible. Most CFD modeling carried out in the blood pump field has focused on the centrifugal pump. Although no direct comparisons between in vitro hemolysis tests and visualization tests have actually been performed, recent evidence suggests CFD can be utilized as a valuable tool for studying and developing blood pumps (10,17–20). In this work, an analytical expression of the moving boundary was described specifically for roller pump systems. The inherent flow pattern was simulated and visualized using the built-in dynamic meshing function of Fluent. The initial geometry was generated at α = 90°, when the roller arm was vertical. The obtained mesh size was found to be very

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uniform. As soon as the rollers started moving, the geometry was updated, and the edges of the mesh near the moving boundary were either stretched or compressed. The system automatically divided the large grid into two sections or merged two small grids into a new one to maintain a good mesh quality, which caused a decrease-and-recover phenomenon in the mesh quality plot. Overall, a decent mesh quality was maintained throughout the entire simulation, suggesting the results obtained from the CFD process were accurate and reliable. The presented method can be easily extended to be three-dimensional; however, the complexity of the 3-D model and the amount of calculation associated with it will be significantly increased. In practice, the variation tendency of a flow parameter is more critical than the absolute value, especially when the goal is to optimize the roller pump performance. Therefore, a two-dimensional model is preferable, as it offers a balance between sufficiently accurate simulation results and a reasonable workload. The presented CFD method, adapted from a previously reported approach (7), offers exciting new features and superior capabilities, specifically more realistic inlet conditions and a less time-consuming and labor-intensive process for obtaining the dynamic geometry and mesh. By taking advantage of these features, we can easily predict the flow dynamics inside a pump more accurately. Most importantly, because of the parameterized model used in the presented approach, the results and conclusions obtained through this newly developed CFD method exhibit universality for general development and optimization of roller pump systems. Furthermore, by comparing the resulting flow characteristics (such as wall shear stress), valuable insights may be obtained for the development and optimization of pump systems. Wall shear stress Wall shear stress has been the most critical concern in studies of pump systems. In this study, the spatial maximum wall shear stress (τmax) at each time step was also monitored and presented. Based on the presented method, the detailed effects of all structural parameters and operation conditions in a roller pump system on the wall shear stress generated can be easily obtained through comparative simulations. A set of comparison studies was performed to evaluate the direct impact of various parameters on maximum wall shear stress and mass flow rate. The results were tabulated in Table 2. Each data point was obtained by assigning a different value (±25% variation from the former value, except for roller number and outlet Artif Organs, Vol. 38, No. 7, 2014

— — 6.6009 −3.1398 −43.9384 21.1183 3.7268 −14.2224 3.3822 −0.4423 −9.4145 73.2826 — — 21.1981 13.1549 23.3965 21.2586 12.3042 26.5827 22.7657 18.8262 22.6900 21.8506 19.8814 38.0315 25.9090 31.1763 — — 2.5728 −4.7178 −34.9601 5.6661 21.9807 −20.8674 −8.5055 −1.2299 0.07772 127.5979 — — Outlet pressure, p (Pa)

Rolling speed, ω (rad/s)

Tubing size, d (mm)

Occlusion, δ (mm)

Size of pump boot, D (mm)

Size of roller, r (mm)

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Note that pump boot size and rolling speed had the most significant effect on τmax.

28.3087 18.6092 36.8620 34.2419 23.3737 37.9736 43.8367 28.4382 32.8807 35.4954 35.9653 81.7928 41.3299 50.4093 — — 1.78194 −1.31243 −28.6404 32.4243 10.2453 −7.2798 −50.0070 62.0409 −17.7791 23.1110 — — Number of rollers, N

3 4 7.5 12.5 90 150 0.75 1.25 7.5 12.5 1.5 2.5 150 250

0.03074 0.02888 0.03171 0.03075 0.02223 0.04126 0.03435 0.02889 0.01558 0.05049 0.02562 0.03836 0.02933 0.02802

Percentage variation (%) Results (Pa) Percentage variation (%) Results (Pa)

Maximum value of τmax Mass flow rate

Percentage variation (%) Results (kg/s)

Average value of τmax

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Varied parameters

TABLE 2. Direct comparisons of the effects of structural parameters and operational conditions on the generated mass flow rate and maximum wall shear stress

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pressure) to one of the parameters in the modeling system while keeping the rest the same as those in Table 1. The previously mentioned results demonstrated that when the flow velocity increases, the wall shear stress increases accordingly. This regularity was confirmed again in the comparative study. Among the parameters, rolling speed and pump boot size (especially rolling speed) appear to have the most significant impact on τmax, because they determine the roller tangential velocity and the flow velocity inside the tubing. Therefore, to ensure cell safety in roller pumps, the rolling speed must be carefully regulated. Additionally, increasing the number and size of rollers also helps to reduce the maximum flow velocity, suggesting a reduction in τmax. Notably, in Table 2, the mass flow rate usually varies in the same direction (increasing or decreasing) as the wall shear stress. The only exception occurred when the tubing size changed. This finding suggests that larger diameter tubing may lead to a reduction in cell damage. Both in vitro and in vivo experiments have confirmed this result (8,25). However, larger tubing means a larger amount of blood outside the body, which in turn restricts the tubing size. For each set of comparisons shown in Table 2, a constant rolling speed was assumed. However, fixed mass flow rate, rather than fixed rolling speed, is usually preferred in practice. Therefore, another set of comparison studies, specifically a comparison at constant mass flow rate, was conducted by varying N, r, L, D, or d in conjunction with ω to maintain a constant mass flow rate of 0.0312 kg/s (the same as the basic design presented in Table 1) while keeping the other variables the same. It was found that some of the results, especially the effects of occlusion, were quite different from those in Table 2. Occlusion of the rollers has been considered as a potential factor in determining the degree of wall shear stress and cell damage; however, the literature reports contradictory conclusions regarding this. Noon et al. compared several different occlusive conditions and concluded that more severe hemolysis occurred when the rollers were more occlusive for long-term perfusion (8). However, Tayama et al. stated that there was no significant difference between nonocclusive conditions and normal occlusive conditions (26). Utilizing the newly developed CFD method, the time-varying τmax has been simulated for different occlusive conditions. As illustrated in Fig. 7, the maximum value of τmax in each cycle increased dramatically with decreasing occlusion, suggesting more occlusive conditions would cause more damage to cells. However, less occlusive con-

Average value 45

Maximum value

40 35 30 25 20 15 0.5

0.7

0.9 1.1 Occlusion (mm)

1.3

1.5

FIG. 7. Changes in maximum wall shear stress with occlusion under the constant mass flow rate condition. Data were obtained by changing L and ω together to maintain an equal mass flow rate. The other parameters were kept the same as those in Table 1.

ditions tended to result in a mild increase in the average value of τmax, implying the exposure time of cells in a relatively high-wall-shear-stress environment was prolonged, which might lead to additional cell loss. Our simulation findings support both published results. The shape of the pump boot may be another factor in wall shear stress. As illustrated in Fig. 5, when the leading roller is moving away from the straight section of the tube in substage 4, its velocity component along the tube axis is reduced and less than that of the trailing roller. In this case, the leading roller acts as an obstacle to the fluid flow behind it. Thus, the fluid pressure between the two rollers increases (Fig. 6d), and subsequently the maximum values of fluid velocity and wall shear stress increase sharply. From this point of view, the maximum wall shear stress may be reduced if the shape of the tubing is closer to that of the path of roller. Accordingly, a modified pump boot, using an O shape (Fig. 8)

FIG. 8. A computer-assisted design model of the proposed O-shaped pump system is shown.

instead of the conventional U shape, may be a better choice for the next generation of roller pumps. The simulated mass flow rate and maximum wall shear stress shown in Fig. 9 suggest that the O-shaped pump produces more uniform and steady flow with less shear stress for the same structural parameters and operational conditions. CONCLUSION Roller pumps are commonly used in clinical and scientific research to deliver blood as well as other cell suspensions. In this work, we presented a new CFD method for roller pumps. The CFD model is fully parametric and the simulation process is highly automated; therefore, the method can easily be adapted to various applications. The presented simulation results demonstrated high reliability and good correlation with both in vitro and in vivo experimental results. In conclusion, the presented approach

Mass flow rate produced by the O-shaped pump Maximum wall shear stress produced by the O-shaped pump Mass flow rate produced by the U-shaped pump Maximum wall shear stress produced by the U-shaped pump

3.5 Mass flow rate (kg/s)

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50

3

50

2.5

40

2

30

1.5 20 1 10

0.5 0

0.8

1

1.2

1.4

0

Maximum wall shear stress (Pa)

Maximum wall shear stress (Pa)

A NEW CFD METHOD FOR ROLLER PUMPS

FIG. 9. Comparisons of simulated mass flow rate and wall shear stress produced by a traditional U-shaped pump and the proposed O-shaped pump. The structural parameters and operational conditions are all the same as those in Table 1.

Time (s) Artif Organs, Vol. 38, No. 7, 2014

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enables convenient visualization of the inherent flow pattern and comprehensive assessment of shear-induced cell damage in roller pumps, not only providing a powerful technique to reinvestigate questionable experiment results toward reconciling conflicting conclusions, but also displaying potential to guide the development and optimization of new roller pump systems and other biomedical instruments whose operation involves the circulation of fluid. Some general conclusions and recommendations are summarized below: 1 Roller pumps generate pulsatile flow, and the period depends on the number of rollers and their rolling speed. Generally, multi-roller-pump systems tend to produce more uniform and steady flow with less shear stress. 2 Wall shear stress is closely related to flow velocity; hence, it is dangerous to utilize a roller pump overspeed to rapidly deliver a larger amount of cell suspension. 3 For certain pumps, use of larger-diameter tubing helps to achieve a desired flow rate at a lower rolling speed and, consequently, a reduced wall shear stress inside the pump. 4 The effect of occlusion on shear stress was not as significant as expected. Considering the higher risk of producing backflow, nonocclusive conditions should be applied cautiously. 5 A new style of pump boot, such as the proposed O-shaped pump boot, may significantly reduce the wall shear stress and thus be safer for delivering blood as well as other cell suspensions. Acknowledgments: The research work was supported by the National Natural Science Foundation of China (No. 51206019), the Doctoral Fund of the Ministry of Education of China (No. 20120185120024), and the Fundamental Research Funds for the Central Universities of China (No. ZYGX2012J103).

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