Design of a Microfluidic System for Red Blood Cell Aggregation Investigation R. Mehri^ Department of Mechanical Engineering, University of Ottawa, Ottawa ON KIN 6N5, Canada e-mail; [email protected]
C. Mavriplis Department of Mechanical Engineering, University of Ottawa, Ottawa ON KIN 6N5, Canada
M. Fenech Department of Mechanical Engineering, University of Ottawa, Ottawa ON KIN 6N5, Canada
2
Materials and Methods
Two distinct techniques are used to design the apparatus for RBC aggregates analysis: numerical simulations and laboratory experiments.
The purpose of this paper is to design a microfluidic apparatus capable of providing controlled flow conditions suitable for red blood cell (RBC) aggregation analysis. The linear velocity engendered from the controlled flow provides constant shear rates used to qualitatively analyze RBC aggregates. The design of the apparatus is based on numerical and experimental work. The numerical work consists of 3D numerical simulations performed using a research computational fluid dynamics (CFD) solver, NekSOOO, while the experiments are conducted using a microparticle image velocimetry system. A Newtonian model is tested numerically and experimentally, then blood is tested experimentally under several conditions (hematocrit, shear rate, and fluid suspension) to be compared to the simulation results. We find that using a velocity ratio of 4 between the two Newtonian fluids, the layer corresponding to blood expands to fill 35% of the channel thickness where the constant shear rate is achieved. For blood experiments, the velocity profile in the blood layer is approximately linear, resulting in the desired controlled conditions for the study of RBC aggregation under several flow scenarios. [DOI: 10.1115/1.4027351]
1
there is no standard method to provide an estimation of aggregate size for prescribed fiow conditions. The existing methods, such as erythrocyte sedimentation rate [7-9], microscopic aggregation index [10,11] and syllectometry method [12,13] are only able to provide several aggregation indices to estimate the degree of aggregation in blood, which does not provide enough information to understand blood behavior in microcirculation. Therefore, a controlled experimental model is required for RBC aggregate analysis and size estimation. With such a model, we will investigate and define a relationship between aggregate size and constant shear rate applied. The subsequent findings could be implemented in numerical simulations or non-Newtonian models to better mimic blood behavior in microcirculation. This paper focuses mainly on the design of a microchannel configuration where controlled flow conditions can be obtained. The controlled fiow is generated using a two fluid flow in a F-microchannel configuration. Linear velocities engendered in the blood layer provide constant shear rates that are used to qualitatively analyze RBC aggregates.
Introduction
RBC or erythrocytes are the most abundant cells in blood. They have the ability to deform and adapt to the smallest vessels in the human body (capillaries) of 4—10 ^m diameter. RBC also aggregate at low appropriate shear rates and form aggregates, which are shown to greatly affect blood viscosity [1] thereby contributing to the non-Newtonian behavior of blood in vivo. The mechanism behind aggregate formation is not completely understood. Numerous studies have focused on understanding the mechanism behind aggregates leading to a better understanding of the microrheological behavior of blood. Viscometric studies [2-6] not only show that shear rate and aggregation force are inversely related to the aggregate size, but also that such aggregates are usually only seen for shear rates below 10s^'. Above this range, aggregates are shown to disaggregate causing RBC to flow separately. Therefore, aggregate size is crucial in defining a nonNewtonian model mimicking blood in microcirculation. However, measurement of RBC aggregates presents a challenge in the hemorheology field due to the lack of consistency between the tests performed and the blood samples used. In fact, to our knowledge.
2.1 Numerical Simulations. Three-dimensional numerical simulations are conducted using the computational fluid dynamics solver Nek5000 [14]. This high order incompressible direct numerical simulation solver is suitable for Stokes flows among other regimes. This solver uses the spectral element method in order to solve for velocity, pressure, temperature, and viscosity. This method is used to simulate the two fluid flow within the K-microcharmel configuration in order to determine the ideal "blood layer" thickness required to obtain a controlled shear rate for the study of RBC aggregates. The continuous domain of the K-microchannel configuration is discretized into small elements as shown in Fig. 1. The description of the numerical model is detailed in Ref. [15]. Two fluids A and B are used to simulate the required flow in the channel. Fluid B, entering via the top branch, is assumed to have the same viscosity as blood at high shear rates (kinematic viscosity value of fg = (3mm^/s)), while fluid A enters via the bottom branch with a kinematic viscosity of t'^ = (1 mm'^/s), the value for water at room temperature. The two fluids are assumed
> \
j
\.
y
/
150 pm
75 lim
2 mm
0.5 mm Corresponding author. Manuscript received July 15, 2013; final manuscript received April 1, 2014; accepted manuscript posted April 7, 2014; published online April 18, 2014. Assoc. Editor: Jeffrey Ruberti.
Journal of Biomechanical Engineering
Fig. 1 Mesh distribution and dimensions of the microchannei finai design using the spectral element method
Copyright © 2014 by ASME
JUNE2014, Vol. 136 / 064501-1
Table 1 Experimental (E) and numerical (S) shear rate comparison for 150x33/(m microchannel with Newtonian fluids (Re: Reynolds number based on the average velocity of the bottom layer of the channel). The interface location is measured from the bottom of the channel. Shear rate (s ') Velocity (mm/s) Interface {¡ira) Velocity ratio 1 2 4
DP Camera
Fig. 2
Micro PIV set up and light path within the system
to only mix by diffusion due to the very low Reynolds number at these microscales. Within the numerical solver, this is modeled by setting the value of fiuid diffusivity as low as possible (3.0710~*'(mm^/s)). The simulations performed consist of varying the velocity and viscosity ratios between the branches in order to visualize the location of the interface between the fluids. When steady state is reached, the location of the interface and the velocity profile in the channel are extracted from the numerical data. The goal is to determine the ideal "blood layer" thickness and ensure the linearity of the velocity profile within this layer in order to provide a suitable constant shear rate to qualitatively study RBC aggregates.
S
E
S
E
7.59 8.56 10.81
8.58 8.50 12.42
0.671 0.527 0.453
0.732 0.604 0.716
S
E
61.59 64.7 88.40 79.0 108.0 92.40
Re (10-^) 4.20 5.61 6.73
(H: volume of blood occupied by RBC) and RBC suspended in plasma at 20% hematocrit to study the effect of the velocity profile on aggregates. 3% particles are also added to each of the suspensions and the entraining fluid.
3 Results We first verify the microchannel design by comparing numerical simulations performed on a test channel to an exact solution, where the results can be found in Ref. [15]. We then validate the microfluidic apparatus by comparing numerical simulations performed with the y-microchannel configuration to ^PIV experiments performed with Newtonian fluids. Once the model is validated, RBC suspensions are tested to qualitatively analyze RBC aggregates.
3.1 Newtonian Fiuid. Numerical tests performed with the 150x33^m microchannel are compared to pP\N experiments 2.2.1 Experimental Set Up. The experimental setup, shown in with the same channel geometry. Three velocity ratios Fig. 2 comprises a /iPIV device (LaVision's MITAS) in order to (Vratio = V'bottom/Vtop = VA/VB = 1,2, and 4) are tested and previsualize the flow and estimate the velocity field within the area of sented to validate the microfiuidic apparatus, ensure the linearity interest. For this purpose, tracer particles diluted at 1% in water of the velocity profile and simultaneously determine the ideal («^particle = 0.86/xm, Aabs = 542nm, and Aemission = 612nm) are thickness of the "blood layer". For these tests, the flow rate in the introduced within the fluids, which illuminate when exposed to channel is ß = 10/iL/h and the viscosity ratio is ^'ratio = 3. Table the appropriate wavelength. Detailed description of this set up can 1 shows the shear rate, the velocity at the interface and its location be found in Ref. [15]. The fluids, contained into two 5 0 | Í L glass for the simulations (S) and the experiments (E) for the different syringes (Hamilton, USA), are pushed into a Polydimethylsilox- velocity ratios. One should note that the interface location is ane (PDMS) microchannel at different flow rates. In order to visu- measured from the bottom of the channel. Figure 3 presents the alize the motion of RBC in the microchannel, the LaVision device velocity profiles comparison between the simulation and experiis coupled with a high speed camera (Dalstar, USA). ment for Katio = 4. We conclude that the simulations agree well with the experimental results where we determined the ideal 2.2.2 Microchannels. The microchannel used consists of a "blood layer" thickness to occur when Vratio = 4 (35% of the 150 X 33 ßm PDMS channel fabricated in the laboratory following channel thickness). standard soft photolithography techniques. The PDMS channel is then bonded to a glass slide using the oxygen plasma bonding method. The bonding process is performed using the SPIOO ANA3.2 RBC Suspensions. RBC suspensions, in plasma or PBS, TECH, LTD-plasma series (ANATECH, USA). The depth of the are tested at 10% and 20% hematocrit with flow rates of ß = 5 mold created was measured using an Ambios XP200 profilometer and 10/iL/h to analyze RBC aggregates qualitatively. The follow(Ambios Technology, USA) with 10 angstroms sensitivity, while ing experiments are performed with the previously validated the thickness of the microchannel was verified under the micro- microchannel design: the 150x33/im microchannel with scope using a microscale with 10/im sensitivity. V • —4 2.2
Experiments
^ ratio — ^•
2.2.3 Fluids and Sample Preparation. The numerical model is replicated experimentally first with Newtonian fiuids to validate the simulations. Fluid B is represented by a diluted solution of glycerol at 36% (by weight) to obtain an average kinematic viscosity of vg = 3(mm^/s), while distilled water is used for fluid A. 3% of the tracer particles solution is added to both fluids. Once the tests with Newtonian fluids are performed and compared to the numerical simulations, RBC-suspensions (fluid B) are tested for RBC aggregation analysis. The fluid entraining blood (fluid A) is a solution of phosphate buffered saline (PBS). Porcine blood samples, treated with ethylenediaminetetraacetic acid, are centrifuged three times at 3000 rpm for 10 min to separate the RBC from all the constituents. From these samples, three different RBC-suspensions are used: RBC resuspended in PBS only (no aggregation), RBC suspended in plasma at 10% hematocrit 064501-2 / Vol. 136, JUNE 2014
3.2.1 Comparison of RBC-PBS and RBC-Plasma Suspensions at 10% H With Q = WßL/h. First, RBC-plasma suspension is compared to a RBC-PBS suspension with the same hematocrit and flowing at 10/iL/h. The results are presented for two different samples extracted from two different pigs termed S and T. The results for sample T, consisting of both experiments of RBC in PBS and RBC in plasma, are shown in Fig. 4. We can clearly see that the RBC cannot aggregate in PBS, while RBC suspended in plasma can form aggregates. The velocity profiles comparison for RBC-plasma and RBCPBS suspensions for blood sample T, shown in Fig. 5, show that within the blood layer, the velocity profile is almost linear for the two experimental curves, as desired. However, the velocity of RBC in PBS is slightly higher than the velocity of RBC in plasma within the blood layer, which is thicker for the RBC in plasma as Transactions of the ASME
Simulation: velocity profiie Experiment Simulation
Table 2 Experimental (E) and numerical (S) shear rate comparison for 150 X 33/
C. Mavriplis Department of Mechanical Engineering, University of Ottawa, Ottawa ON KIN 6N5, Canada
M. Fenech Department of Mechanical Engineering, University of Ottawa, Ottawa ON KIN 6N5, Canada
2
Materials and Methods
Two distinct techniques are used to design the apparatus for RBC aggregates analysis: numerical simulations and laboratory experiments.
The purpose of this paper is to design a microfluidic apparatus capable of providing controlled flow conditions suitable for red blood cell (RBC) aggregation analysis. The linear velocity engendered from the controlled flow provides constant shear rates used to qualitatively analyze RBC aggregates. The design of the apparatus is based on numerical and experimental work. The numerical work consists of 3D numerical simulations performed using a research computational fluid dynamics (CFD) solver, NekSOOO, while the experiments are conducted using a microparticle image velocimetry system. A Newtonian model is tested numerically and experimentally, then blood is tested experimentally under several conditions (hematocrit, shear rate, and fluid suspension) to be compared to the simulation results. We find that using a velocity ratio of 4 between the two Newtonian fluids, the layer corresponding to blood expands to fill 35% of the channel thickness where the constant shear rate is achieved. For blood experiments, the velocity profile in the blood layer is approximately linear, resulting in the desired controlled conditions for the study of RBC aggregation under several flow scenarios. [DOI: 10.1115/1.4027351]
1
there is no standard method to provide an estimation of aggregate size for prescribed fiow conditions. The existing methods, such as erythrocyte sedimentation rate [7-9], microscopic aggregation index [10,11] and syllectometry method [12,13] are only able to provide several aggregation indices to estimate the degree of aggregation in blood, which does not provide enough information to understand blood behavior in microcirculation. Therefore, a controlled experimental model is required for RBC aggregate analysis and size estimation. With such a model, we will investigate and define a relationship between aggregate size and constant shear rate applied. The subsequent findings could be implemented in numerical simulations or non-Newtonian models to better mimic blood behavior in microcirculation. This paper focuses mainly on the design of a microchannel configuration where controlled flow conditions can be obtained. The controlled fiow is generated using a two fluid flow in a F-microchannel configuration. Linear velocities engendered in the blood layer provide constant shear rates that are used to qualitatively analyze RBC aggregates.
Introduction
RBC or erythrocytes are the most abundant cells in blood. They have the ability to deform and adapt to the smallest vessels in the human body (capillaries) of 4—10 ^m diameter. RBC also aggregate at low appropriate shear rates and form aggregates, which are shown to greatly affect blood viscosity [1] thereby contributing to the non-Newtonian behavior of blood in vivo. The mechanism behind aggregate formation is not completely understood. Numerous studies have focused on understanding the mechanism behind aggregates leading to a better understanding of the microrheological behavior of blood. Viscometric studies [2-6] not only show that shear rate and aggregation force are inversely related to the aggregate size, but also that such aggregates are usually only seen for shear rates below 10s^'. Above this range, aggregates are shown to disaggregate causing RBC to flow separately. Therefore, aggregate size is crucial in defining a nonNewtonian model mimicking blood in microcirculation. However, measurement of RBC aggregates presents a challenge in the hemorheology field due to the lack of consistency between the tests performed and the blood samples used. In fact, to our knowledge.
2.1 Numerical Simulations. Three-dimensional numerical simulations are conducted using the computational fluid dynamics solver Nek5000 [14]. This high order incompressible direct numerical simulation solver is suitable for Stokes flows among other regimes. This solver uses the spectral element method in order to solve for velocity, pressure, temperature, and viscosity. This method is used to simulate the two fluid flow within the K-microcharmel configuration in order to determine the ideal "blood layer" thickness required to obtain a controlled shear rate for the study of RBC aggregates. The continuous domain of the K-microchannel configuration is discretized into small elements as shown in Fig. 1. The description of the numerical model is detailed in Ref. [15]. Two fluids A and B are used to simulate the required flow in the channel. Fluid B, entering via the top branch, is assumed to have the same viscosity as blood at high shear rates (kinematic viscosity value of fg = (3mm^/s)), while fluid A enters via the bottom branch with a kinematic viscosity of t'^ = (1 mm'^/s), the value for water at room temperature. The two fluids are assumed
> \
j
\.
y
/
150 pm
75 lim
2 mm
0.5 mm Corresponding author. Manuscript received July 15, 2013; final manuscript received April 1, 2014; accepted manuscript posted April 7, 2014; published online April 18, 2014. Assoc. Editor: Jeffrey Ruberti.
Journal of Biomechanical Engineering
Fig. 1 Mesh distribution and dimensions of the microchannei finai design using the spectral element method
Copyright © 2014 by ASME
JUNE2014, Vol. 136 / 064501-1
Table 1 Experimental (E) and numerical (S) shear rate comparison for 150x33/(m microchannel with Newtonian fluids (Re: Reynolds number based on the average velocity of the bottom layer of the channel). The interface location is measured from the bottom of the channel. Shear rate (s ') Velocity (mm/s) Interface {¡ira) Velocity ratio 1 2 4
DP Camera
Fig. 2
Micro PIV set up and light path within the system
to only mix by diffusion due to the very low Reynolds number at these microscales. Within the numerical solver, this is modeled by setting the value of fiuid diffusivity as low as possible (3.0710~*'(mm^/s)). The simulations performed consist of varying the velocity and viscosity ratios between the branches in order to visualize the location of the interface between the fluids. When steady state is reached, the location of the interface and the velocity profile in the channel are extracted from the numerical data. The goal is to determine the ideal "blood layer" thickness and ensure the linearity of the velocity profile within this layer in order to provide a suitable constant shear rate to qualitatively study RBC aggregates.
S
E
S
E
7.59 8.56 10.81
8.58 8.50 12.42
0.671 0.527 0.453
0.732 0.604 0.716
S
E
61.59 64.7 88.40 79.0 108.0 92.40
Re (10-^) 4.20 5.61 6.73
(H: volume of blood occupied by RBC) and RBC suspended in plasma at 20% hematocrit to study the effect of the velocity profile on aggregates. 3% particles are also added to each of the suspensions and the entraining fluid.
3 Results We first verify the microchannel design by comparing numerical simulations performed on a test channel to an exact solution, where the results can be found in Ref. [15]. We then validate the microfluidic apparatus by comparing numerical simulations performed with the y-microchannel configuration to ^PIV experiments performed with Newtonian fluids. Once the model is validated, RBC suspensions are tested to qualitatively analyze RBC aggregates.
3.1 Newtonian Fiuid. Numerical tests performed with the 150x33^m microchannel are compared to pP\N experiments 2.2.1 Experimental Set Up. The experimental setup, shown in with the same channel geometry. Three velocity ratios Fig. 2 comprises a /iPIV device (LaVision's MITAS) in order to (Vratio = V'bottom/Vtop = VA/VB = 1,2, and 4) are tested and previsualize the flow and estimate the velocity field within the area of sented to validate the microfiuidic apparatus, ensure the linearity interest. For this purpose, tracer particles diluted at 1% in water of the velocity profile and simultaneously determine the ideal («^particle = 0.86/xm, Aabs = 542nm, and Aemission = 612nm) are thickness of the "blood layer". For these tests, the flow rate in the introduced within the fluids, which illuminate when exposed to channel is ß = 10/iL/h and the viscosity ratio is ^'ratio = 3. Table the appropriate wavelength. Detailed description of this set up can 1 shows the shear rate, the velocity at the interface and its location be found in Ref. [15]. The fluids, contained into two 5 0 | Í L glass for the simulations (S) and the experiments (E) for the different syringes (Hamilton, USA), are pushed into a Polydimethylsilox- velocity ratios. One should note that the interface location is ane (PDMS) microchannel at different flow rates. In order to visu- measured from the bottom of the channel. Figure 3 presents the alize the motion of RBC in the microchannel, the LaVision device velocity profiles comparison between the simulation and experiis coupled with a high speed camera (Dalstar, USA). ment for Katio = 4. We conclude that the simulations agree well with the experimental results where we determined the ideal 2.2.2 Microchannels. The microchannel used consists of a "blood layer" thickness to occur when Vratio = 4 (35% of the 150 X 33 ßm PDMS channel fabricated in the laboratory following channel thickness). standard soft photolithography techniques. The PDMS channel is then bonded to a glass slide using the oxygen plasma bonding method. The bonding process is performed using the SPIOO ANA3.2 RBC Suspensions. RBC suspensions, in plasma or PBS, TECH, LTD-plasma series (ANATECH, USA). The depth of the are tested at 10% and 20% hematocrit with flow rates of ß = 5 mold created was measured using an Ambios XP200 profilometer and 10/iL/h to analyze RBC aggregates qualitatively. The follow(Ambios Technology, USA) with 10 angstroms sensitivity, while ing experiments are performed with the previously validated the thickness of the microchannel was verified under the micro- microchannel design: the 150x33/im microchannel with scope using a microscale with 10/im sensitivity. V • —4 2.2
Experiments
^ ratio — ^•
2.2.3 Fluids and Sample Preparation. The numerical model is replicated experimentally first with Newtonian fiuids to validate the simulations. Fluid B is represented by a diluted solution of glycerol at 36% (by weight) to obtain an average kinematic viscosity of vg = 3(mm^/s), while distilled water is used for fluid A. 3% of the tracer particles solution is added to both fluids. Once the tests with Newtonian fluids are performed and compared to the numerical simulations, RBC-suspensions (fluid B) are tested for RBC aggregation analysis. The fluid entraining blood (fluid A) is a solution of phosphate buffered saline (PBS). Porcine blood samples, treated with ethylenediaminetetraacetic acid, are centrifuged three times at 3000 rpm for 10 min to separate the RBC from all the constituents. From these samples, three different RBC-suspensions are used: RBC resuspended in PBS only (no aggregation), RBC suspended in plasma at 10% hematocrit 064501-2 / Vol. 136, JUNE 2014
3.2.1 Comparison of RBC-PBS and RBC-Plasma Suspensions at 10% H With Q = WßL/h. First, RBC-plasma suspension is compared to a RBC-PBS suspension with the same hematocrit and flowing at 10/iL/h. The results are presented for two different samples extracted from two different pigs termed S and T. The results for sample T, consisting of both experiments of RBC in PBS and RBC in plasma, are shown in Fig. 4. We can clearly see that the RBC cannot aggregate in PBS, while RBC suspended in plasma can form aggregates. The velocity profiles comparison for RBC-plasma and RBCPBS suspensions for blood sample T, shown in Fig. 5, show that within the blood layer, the velocity profile is almost linear for the two experimental curves, as desired. However, the velocity of RBC in PBS is slightly higher than the velocity of RBC in plasma within the blood layer, which is thicker for the RBC in plasma as Transactions of the ASME
Simulation: velocity profiie Experiment Simulation
Table 2 Experimental (E) and numerical (S) shear rate comparison for 150 X 33/
