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Antibody consumption reduction in lateral flow immunoassays within porous media
Chemical Engineering & Processing: Process Intensification xxx (xxxx) xxxx
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Antibody consumption reduction in lateral flow immunoassays within porous media Abbas Gholami, Amir Shamloo* Department of Mechanical Engineering, Sharif University of Technology, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords: Lateral flow immunoassays Human chorionic gonadotropin (hCG) Nitrocellulose membrane Porous media flow Lattice-Boltzmann modeling
In this study, the effect of the geometrical parameters of the Lateral Flow Immunoassay (LFI) membrane on the performance of the pregnancy kits is investigated. Consequently, a new geometry for LFI membrane is proposed based on some theoretical, numerical and experimental observations in order to improve the performance of the related kits. A pregnancy kit (for the detection of hCG in urine samples) is developed and the effect of the relocation of the test and the control lines over the membrane was studied based on the variation of the sample fluid velocity. Using Lattice-Boltzmann simulation of the lateral flow within the porous media and the experimental results, the fluid flow within the kit membrane was fully analyzed. Finally, by focusing on the Washburn model, a modified geometry for the kit’s membrane was suggested while the flow characteristics were studied by using numerical and experimental methods. It is concluded from the observations that in our proposed geometry, the color intensity in the reaction zone of the kit is improved by 9.4 percent that can result in the reduction of antibody consumption in the kit’s membrane that could be a considerable saving during the production process of LFI.
1. Introduction Lateral Flow Immunoassay (LFI) is an applicable instrument for rapid and low-cost diagnosis of disease markers. By using LFIs, many target analytes including whole blood, serum, plasma, urine, saliva etc. can be analyzed. A variety of applications for LFIs have been reported in the last decade that can be categorized into clinical application [1–6], toxins and pathogens recognition [7,8], pesticides diagnosis [9–11], metal ions recognition [12–15], and pharmaceuticals and drugs identification [16–18]. One of the most common tests by LFIs is the pregnancy test in which Human Chorionic Gonadotropin (hCG) is the target analyte. Pregnancy tests, which need to be cheap, trustworthy, straightforward, and simple to use, were significantly improved in the 1970s as a result of antibody generation technologies introduced by Vaitukaitis et al. [19]. LFIs generally consist of four main parts including sample, conjugate, absorbent pads and nitrocellulose membrane. In a standard LFI, detecting antibodies are conjugated with labels and are dispensed on the conjugate pad while capture antibodies and secondary antibodies are fixed on the nitrocellulose membrane as the test and the control lines respectively. By immersing LFIs into the sample liquid (urine in pregnancy case), the fluid flows within the sample pad and propagates into the conjugate pad. The possible hCG hormones within the sample ⁎
will physically bind to the anti-hCG beta antibodies conjugated with gold nanoparticles. The hCG-labeled antibody complex in the sample fluid gradually moves forward into the nitrocellulose membrane by adhesive forces. The hCG-labeled antibody set will bind to the fixed anti-hCG alpha antibodies on the test line, and consequently, the test line would appear due to the existence of gold nanoparticles. The remained anti-hCG beta antibodies will bind to the fixed sheep anti mouse IgG antibodies on the control line, so the control line would appear too. Finally, the extra fluid would accumulate in the wicking pad at the end of the assay (Fig. 1). Physical characteristics of LFIs (or specifically nitrocellulose membrane) like material, porosity, and geometry can affect their performance significantly [20]. The sample fluid flow velocity has a significant influence on the test sensitivity and the effective concentration of the analyte is inversely proportional to the squared fluid velocity in the membrane. In low fluid velocities, antibodies have sufficient time for binding; therefore, more effective bindings will be formed [20,21]. The sample fluid, gradually flows in the assay’s membrane by capillary forces while its movement depends on the geometrical parameters of the membrane which means that the fluid velocity in the strip can be controlled by changing membrane’s geometry. Many experimental and theoretical studies have investigated one or two-dimensional capillary flows within paper-based microfluidics
Corresponding author at: Department of Mechanical Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran. E-mail address: [email protected] (A. Shamloo).
https://doi.org/10.1016/j.cep.2019.107773 Received 5 July 2019; Received in revised form 4 October 2019; Accepted 3 December 2019 0255-2701/ © 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Abbas Gholami and Amir Shamloo, Chemical Engineering & Processing: Process Intensification, https://doi.org/10.1016/j.cep.2019.107773
Chemical Engineering & Processing: Process Intensification xxx (xxxx) xxxx
A. Gholami and A. Shamloo
fa (x + ea Δt, t+ Δt) = fa (x,t) −
fa (x,t) − f aeq (x, t) τ
(1)
In which τ is the relaxation time, and equilibrium distribution function f eq is defined as below:,
e .u 9 (ea . u)2 3 u2 ⎤ f aeq (x) = wa ρ(x) ⎡1 + 3 a 2 + − 4 ⎢ c 2 c 2 c2 ⎥ ⎦ ⎣
(2)
Where c is the basic speed on the lattice, wa is the directions’ weight, ρ is the macroscopic density, and u is the macroscopic velocity. 8
ρ=
∑ fa ,
8
u=
a= 0
1 ∑ f a ea ρ a= 0
(3)
To apply adhesive forces in fluid-fluid and fluid-solid interactions, the velocity of particles must be updated in each time step for computing equilibrium distribution functions. Fig. 1. Lateral Flow Immunoassays’ function.
ueq = u +
devices. Mendez et al. investigated imbibition in porous membranes of a complex shape and showed that the fluid flow in the straight segment of the paper follows the Washburn flow equation and it follows the quasi-steady state flow principles in the two-dimensional part [22]. Fluid flow within two-dimensional paper networks (2DPNs) were thoroughly examined by Fu et al. using analytical Washburn model and experimental methods [23]. Park et al. meticulously explored the effects of the porosity and permeability of the pressed papers on fluid capillary flow by using experiment and analytical Darcy’s law [24]. Lattice Boltzmann method (LBM) is a method based on the Boltzmann’s kinetic equation for fluid simulation to simulate fluid density on a lattice with streaming and collision steps instead of solving Navier-Stokes equations directly. It is more straightforward to simulate fluid flow within complex environments (like porous medium) with complex boundaries using this method [25–28]. In recent years, LBM has been used in various studies including microscopic gaseous flows, multiphase flows, droplet deformation, electrokinetic and magnetohydrodynamic flows, biological microfluidics and porous media Microflows [29–35]. Simulation of flow within complex environments like porous materials in which the microscopic porous structure and surface wettability is important, is relatively easier by LBM due to its particulate features [33]. Considering this advantage of LBM for modelling flow within porous medium (and especially microporous materials), many applications of LBM for Darcy and non-Darcy flows in microreactors, fuel cells, underground water resources, fabric materials and biological/biomedical materials have been reported [36–39]. In this paper, fluid flow within nitrocellulose membrane of LFIs has been studied by theoretical Washburn model and LBM method to propose a new geometry for nitrocellulose membrane in order to improve the color intensity in the reaction zone. In the following, fluid flow, especially the fluid velocity has been investigated in nitrocellulose membrane by using Lattice-Boltzmann method and experimental observations. Finally, according to the analytical, numerical, and experimental results, an assay has been developed and by quantifying the color intensity in the reaction zone, the expectations which are acquired from the analysis was verified.
τF ρ
(4)
Where the external force F can be classified as, 8 fluid-fluid: F (x,t) = −Gψ(x,t) ∑a= 1 wa ψ(x + ea Δt,t) ea (5) 8
fluid-solid: Fads (x,t) = −Gads ψ(x,t) ∑a= 1 wa S(x + ea Δt,t) ea (6) Where G is the interaction strength, Gads is the adsorption coefficient which varies with the fluid-solid contact angle, S function value is 1 if x + ea Δt is a solid node and is 0 otherwise. Ψ is the interaction potential and can be defined as below [40]:
ρ ψ(ρ) = ψ0exp ⎜⎛− 0 ⎞⎟ ⎝ ρ⎠
(7)
ψ0 and ρ0 are arbitrary constants which are assumed to be 4 and 200 respectively in this study [41]. 3. Materials and methods 3.1. Materials Mouse polyclonal anti- α hCG antibodies, mouse monoclonal anti- β hCG antibodies (conjugated with gold nanoparticles), and sheep antimouse IgG secondary antibodies were purchased from Abcam (Shanghai, China). Nitrocellulose membrane (Hi-Flow Plus #HF12004S30), glass fiber conjugate pad (G041 Glass Fiber Conjugate Pad Rolls # GFCP001000), absorbent pad, and cellulose fiber sample pad (C083 Cellulose Fiber Sample Pad Strip #CFSP203000) were purchased from Millipore (Guangzhou, China). Bovine serum albumin (BSA #A1933), Tween-20 (#P9416), Trehalose (#PHR1344) and all the chemical reagents that have been used in the experiments (NaCl, KCl, Na2HPO4, Na2HPO4, KH2PO4, Sodium perborate, Sucrose) were purchased from Sigma-Aldrich (Shanghai, China). Ultrapure water has been used in the laboratory for preparation of buffers and solutions. 3.2. Preparation of antibodies Anti-hCG alpha and sheep antimouse IgG should be dispensed on the test and control lines respectively. These antibodies should be diluted to 1 mg/ml for dispensing purpose, and Anti-hCG beta conjugated antibodies should be diluted similarly. For diluting antibodies, phosphate buffered saline (PBS) –consists of NaCl 137 mM, KCl 27 mM, Na2HPO4 10 mM and KH2PO4 2 mM in PH 7.4 - is used.
2. Lattice-Boltzmann approaches for porous media flow Lattice-Boltzmann modelling is a proper and time saving method for simulating fluid flow within porous media in small scale. LatticeBoltzmann equation is a simplified form of Boltzmann kinetic equation which assumes only 9 directions (a = 0… 8) for particles to move (D2Q9 model). Distribution functions of particles is updated in each time step as below,
3.3. Preparation of sample and conjugate pads Sample and conjugate pads must have suitable performances during the release of analytes and they must be treated before being used in LFIs. Sample and conjugate pads are soaked in the sample buffer (Boric acid 0.003 mM, Sodium perborate 0.004 mM, NaCl 0.5 %w/v, BSA 0.5 2
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concentrations of hCG in sample liquid (15, 25, and 40 mIU/ml) and different concentrations of the conjugated antibodies (1 and 2 mg/ml) were employed to ensure the reproducibility and repeatability of the experiments and the reported results are an average of 10 series of experiments. In Fig. 4, the sample fluid front velocity variation within nitrocellulose membrane is shown. While the sample fluid passes along nitrocellulose membrane, its velocity decreases because of the contrast between the adhesive forces and the viscose forces of the porous media. Diluted anti-hCG alpha is dispensed on different positions (by 5 mm space) over the nitrocellulose membrane by the same mentioned rate and tested by positive samples. Resulted lines are shown in Fig. 5 in which the color intensity has been quantified. In order to quantify the color intensity at the reaction zone, image processing toolbox within MATLAB software was employed to analyze the pictures. It is necessary to mention that for measuring the color intensity of these lines, 10 series of experimental data were gathered and analyzed and an average over all measurements was obtained. By reducing the sample fluid velocity along the nitrocellulose membrane and considering the point that antibodies have sufficient time to capture the analytes in low fluid velocities, the lines that are placed in the tail-end of the membrane have a better quality for visualization as can be seen in Fig. 5. Keeping in mind that some of the target analytes would be captured by the first line and some of them would be captured by the second line and etc., there would be a lower amount of target analyte at the last line compared to the case that each line is located in a separate strip. This observation makes one sure that the location of the last line is the best position for the test line, however it obtains the lowest amount of target analytes among all the lines. Therefore, the tail-end of the membrane is the best place for setting the reaction lines.
%w/v, and Tween-20 20 %v/v) and the conjugate buffer (Boric acid 0.003 mM, Sodium perborate 0.004 mM, Sucrose 10 %w/v, Trehalose 2 %w/v and Tween-20 0.05 %v/v) respectively for 30 min and then dried for 3 h in 37 ℃. 3.4. Preparation of LFI for hCG detection After preparing and drying all pads and antibody solutions, antibodies should be dispensed on the nitrocellulose membrane and the conjugate pad. Diluted anti-hCG alpha monoclonal and sheep antimouse IgG secondary antibodies are dispensed on the nitrocellulose membrane as the test and control lines respectively with a rate of 1 μl/cm by using a lateral flow linear dispenser purchased from Kinbio (Shanghai, China). There are two methods for dispensing conjugated antibodies on the conjugate pad. The first method is to dispense antibodies on the pad by using a dispenser, and the second method is to soak the pads into the antibody solution. In this study, the conjugate pad was soaked into the conjugated antibody solution and then dried at the room temperature and stored in low humidity within an environment with temperature of 4 ℃. Afterward, sample, conjugate, nitrocellulose membrane and wicking pads are assembled respectively by a 2 mm overlap on a plastic with an adhesive backing that has the dimension of 6 cm × 30 cm and then are cut into a number of strips with 5 mm width. 3.5. Detection of hCG by LFI After cutting pads into strips, one can use it for the detection of hCG in urine by immersing strips into the urine sample. For a positive sample, both the test and the control lines would appear, but if hCG hormones does not exist within the urine sample, just the control line would be visible. In Fig. 2, the results of the developed assay versus positive and negative samples is shown.
4.2. Proposing modified geometry for nitrocellulose membrane Fluid flow transportation in one-dimensional porous media like a nitrocellulose membrane in LFIs which are fed by a non-limiting fluid reservoir follows the Washburn equation [43],
4. Results and discussion 4.1. Displacement of reaction line over the nitrocellulose membrane
L2 =
At first, the effect of the reaction zone position over LFI’s membrane on the detection performance was investigated. In this regard, by simulating the fluid flow within the porous media using LatticeBoltzmann method, it was observed that by progressing the fluid (by capillary forces) within the porous network (nitrocellulose membrane), the fluid front velocity will be reduced that is in a very good agreement with the study of Elizalde et al. [42] (Fig. 3). Then, the sample fluid velocity is measured in the nitrocellulose membrane by tracking its front position, frame by frame, using a highspeed camera with 1000 fps. It is necessary to mention that different instruments and measurement procedures including different dispensers with different dispensing rates (1 and 2 1μl/cm ), different
γDt 4μ
(8)
in this equation, L is the transport length of the fluid front in the porous matrix, γ is the effective surface tension, D is the average pore diameter, t represents time, and μ is the fluid viscosity [44,45]. As can be seen by Eq. (8), the transported length of the fluid front depends on time like L∼ t which means that the fluid front velocity in the nitrocellulose strips would decrease by time (by progressing the fluid in the nitrocellulose membrane). In Fig. 6, fluid front velocity in the experiments (resulted by obtaining fluid front position, frame by frame, using a high-speed camera with 1000 fps) has been compared with Washburn equation for a strip that is fed by a non-limiting reservoir. According to Fig. 6, Washburn equation can properly predict
Fig. 2. Developed LFI for hCG detection in human urine sample by assembling all pads on a plastic with adhesive backing. 3
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Fig. 3. (Left) sample flow simulation through membrane. red and purple represent a velocity of 1.62 mm/s and zero respectively. (right) flow velocity over the membrane according to LBM. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 4. Sample fluid velocity within the nitrocellulose membrane based on experimental measurements. Fig. 7. Three strips fed in a non-limiting reservoir in order to investigate by Washburn equation.
the fluid flow behavior within the nitrocellulose membrane of LFI. In the following, fluid flow characteristics, especially fluid velocity has been studied in three different geometries, in which the first one is a simple strip (A), the second one is a strip with a contracted segment (B) and the last one is a strip with an expanded segment (C). It is necessary to mention that all the strips are supposed to be fed by a non-limiting reservoir since Washburn equation requires this condition. As shown in Fig. 7, all the strips have the same width in the end-tail segment because this zone is appropriate for dispensing antibodies according to the discussion in the previous section. In strip A, the fluid front displacement follows the Washburn equation and as mentioned before, the fluid velocity would decrease with time. In the first segment of strip B, Washburn equation can be used and for the second part can be used similarly since one can suppose that the first segment plays the role of an unlimited reservoir for the second segment but it should be noted that for the second segment, the time (t in Washburn equation) is relative to the time when the fluid front reaches the position of the cross-section variation, so accordingly, the fluid front velocity magnitude will increase abruptly. In the last strip, in which the cross section expansion occurs, the fluid displacement in the first part follows the Washburn equation; however, for the second segment it cannot be used owing the fact that this part of the strip is not fed by a non-limiting reservoir. According to the assumption of the incompressibility of the fluid, the velocity of the fluid front would decrease as it transported from the thinner segment to the wider one. In Fig. 8, the fluid front velocity for these three strips has been compared. Fluid front velocity was measured along the nitrocellulose membrane for these three membranes by using Lattice-Boltzmann simulation. Results of the simulation have been presented in Fig. 9 and it can be seen that the fluid velocity within the porous membrane follows the mentioned trend by Washburn equation and the results are in good agreement with the aforementioned assumptions. As mentioned before, the fluid velocity has a great influence on the binding of antibody and as a result on the color intensity in test zone.
Fig. 5. Color intensity of reaction lines placed on different positions over the membrane which shows that the tail-end of membrane has the best color intensity due to the lower flow velocity.
Fig. 6. Flow velocity within nitrocellulose membrane by Washburn equation and experimental observations.
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Fig. 8. Prospect of sample fluid velocity within nitrocellulose membrane for three presented strips by Washburn equation.
Fig. 11. Comparison of the color intensity of the reaction lines for simple and modified strips.
between these two series of data for simple and modified assays is significant.
Fig. 9. Lattice-Boltzmann modelling results for fluid front velocity for tree strips introduced in Fig. 7.
5. Conclusion In our previous studies, the fluid movement within different types of devices was analyzed by employing various numerical techniques [46–50]. In this study, LBM method was employed to investigate the effect of some geometrical parameters on the performance of the lateral flow immunoassays which was verified by experimental studies. It was shown that for low sample fluid flow velocities, antibodies have sufficient time for binding, so by increasing the capture rate, the color intensity of the reaction lines would be increased. Due to the reduction of the fluid velocity within the nitrocellulose membrane, the effect of the reaction line position on the color intensity was also investigated by using experimental and Lattice-Boltzmann simulation. It was observed that the tail-end of the membrane is the best place for dispensing the test and the control antibodies. A modified geometry was also proposed by predicting the fluid flow velocity within the nitrocellulose membrane according to the Washburn equation that was proved by Lattice-Boltzmann simulation. Then, the lateral flow assays were developed accordingly and by testing immunoassays in the same conditions (the same dispensing rate of antibodies, the same width of strips and the same concentration of hCG in urine sample), it was observed that the color intensity has been improved by ∼ 10 percent. Studying of capillary flow behavior within paper-based biosensors and presenting a new modified geometry for their membrane could be used for not only the related immunoassays and their performance improvement but also for lab-on-chip applications with paper-based substrates.
Fig. 10. Experimental results for typical and modified membranes.
So, this parameter has a significant impact on the visualization of LFIs for household use. In low fluid velocities, antibodies have more time for binding and in the geometries with lower fluid velocity, one may expect a higher color intensity in the reaction zone. In this regard, the lateral flow strips with geometries like strip C are developed because of their low fluid front velocity in the reaction zone (tail-end of the nitrocellulose membrane). To confirm the mentioned idea, the lateral fluid velocity in the membrane of strip C and a typical strip for LFIs (strip A) has been measured and compared experimentally (Fig. 10). Diluted anti-hCG alpha was dispensed on both simple and modified (strip C) nitrocellulose membrane geometries by the same mentioned rate. By testing intended lateral flow strips with positive hCG samples, the color intensity of the appeared lines are compared by image processing tool as shown in Fig. 11. According to Fig. 11, color intensity of the reaction line in the nitrocellulose membrane has increased due to the low flow velocity of sample fluid within the modified geometry of the nitrocellulose membrane by 9.4 percent. It is worth noting that these data are the average of seven series of experimental data for both simple and modified assays which t-test analysis has been done for them. The t-value for these data was -1.957 which according to the corresponding p-value (0.037), the difference
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Contents lists available at ScienceDirect
Chemical Engineering & Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Antibody consumption reduction in lateral flow immunoassays within porous media Abbas Gholami, Amir Shamloo* Department of Mechanical Engineering, Sharif University of Technology, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords: Lateral flow immunoassays Human chorionic gonadotropin (hCG) Nitrocellulose membrane Porous media flow Lattice-Boltzmann modeling
In this study, the effect of the geometrical parameters of the Lateral Flow Immunoassay (LFI) membrane on the performance of the pregnancy kits is investigated. Consequently, a new geometry for LFI membrane is proposed based on some theoretical, numerical and experimental observations in order to improve the performance of the related kits. A pregnancy kit (for the detection of hCG in urine samples) is developed and the effect of the relocation of the test and the control lines over the membrane was studied based on the variation of the sample fluid velocity. Using Lattice-Boltzmann simulation of the lateral flow within the porous media and the experimental results, the fluid flow within the kit membrane was fully analyzed. Finally, by focusing on the Washburn model, a modified geometry for the kit’s membrane was suggested while the flow characteristics were studied by using numerical and experimental methods. It is concluded from the observations that in our proposed geometry, the color intensity in the reaction zone of the kit is improved by 9.4 percent that can result in the reduction of antibody consumption in the kit’s membrane that could be a considerable saving during the production process of LFI.
1. Introduction Lateral Flow Immunoassay (LFI) is an applicable instrument for rapid and low-cost diagnosis of disease markers. By using LFIs, many target analytes including whole blood, serum, plasma, urine, saliva etc. can be analyzed. A variety of applications for LFIs have been reported in the last decade that can be categorized into clinical application [1–6], toxins and pathogens recognition [7,8], pesticides diagnosis [9–11], metal ions recognition [12–15], and pharmaceuticals and drugs identification [16–18]. One of the most common tests by LFIs is the pregnancy test in which Human Chorionic Gonadotropin (hCG) is the target analyte. Pregnancy tests, which need to be cheap, trustworthy, straightforward, and simple to use, were significantly improved in the 1970s as a result of antibody generation technologies introduced by Vaitukaitis et al. [19]. LFIs generally consist of four main parts including sample, conjugate, absorbent pads and nitrocellulose membrane. In a standard LFI, detecting antibodies are conjugated with labels and are dispensed on the conjugate pad while capture antibodies and secondary antibodies are fixed on the nitrocellulose membrane as the test and the control lines respectively. By immersing LFIs into the sample liquid (urine in pregnancy case), the fluid flows within the sample pad and propagates into the conjugate pad. The possible hCG hormones within the sample ⁎
will physically bind to the anti-hCG beta antibodies conjugated with gold nanoparticles. The hCG-labeled antibody complex in the sample fluid gradually moves forward into the nitrocellulose membrane by adhesive forces. The hCG-labeled antibody set will bind to the fixed anti-hCG alpha antibodies on the test line, and consequently, the test line would appear due to the existence of gold nanoparticles. The remained anti-hCG beta antibodies will bind to the fixed sheep anti mouse IgG antibodies on the control line, so the control line would appear too. Finally, the extra fluid would accumulate in the wicking pad at the end of the assay (Fig. 1). Physical characteristics of LFIs (or specifically nitrocellulose membrane) like material, porosity, and geometry can affect their performance significantly [20]. The sample fluid flow velocity has a significant influence on the test sensitivity and the effective concentration of the analyte is inversely proportional to the squared fluid velocity in the membrane. In low fluid velocities, antibodies have sufficient time for binding; therefore, more effective bindings will be formed [20,21]. The sample fluid, gradually flows in the assay’s membrane by capillary forces while its movement depends on the geometrical parameters of the membrane which means that the fluid velocity in the strip can be controlled by changing membrane’s geometry. Many experimental and theoretical studies have investigated one or two-dimensional capillary flows within paper-based microfluidics
Corresponding author at: Department of Mechanical Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran. E-mail address: [email protected] (A. Shamloo).
https://doi.org/10.1016/j.cep.2019.107773 Received 5 July 2019; Received in revised form 4 October 2019; Accepted 3 December 2019 0255-2701/ © 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Abbas Gholami and Amir Shamloo, Chemical Engineering & Processing: Process Intensification, https://doi.org/10.1016/j.cep.2019.107773
Chemical Engineering & Processing: Process Intensification xxx (xxxx) xxxx
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fa (x + ea Δt, t+ Δt) = fa (x,t) −
fa (x,t) − f aeq (x, t) τ
(1)
In which τ is the relaxation time, and equilibrium distribution function f eq is defined as below:,
e .u 9 (ea . u)2 3 u2 ⎤ f aeq (x) = wa ρ(x) ⎡1 + 3 a 2 + − 4 ⎢ c 2 c 2 c2 ⎥ ⎦ ⎣
(2)
Where c is the basic speed on the lattice, wa is the directions’ weight, ρ is the macroscopic density, and u is the macroscopic velocity. 8
ρ=
∑ fa ,
8
u=
a= 0
1 ∑ f a ea ρ a= 0
(3)
To apply adhesive forces in fluid-fluid and fluid-solid interactions, the velocity of particles must be updated in each time step for computing equilibrium distribution functions. Fig. 1. Lateral Flow Immunoassays’ function.
ueq = u +
devices. Mendez et al. investigated imbibition in porous membranes of a complex shape and showed that the fluid flow in the straight segment of the paper follows the Washburn flow equation and it follows the quasi-steady state flow principles in the two-dimensional part [22]. Fluid flow within two-dimensional paper networks (2DPNs) were thoroughly examined by Fu et al. using analytical Washburn model and experimental methods [23]. Park et al. meticulously explored the effects of the porosity and permeability of the pressed papers on fluid capillary flow by using experiment and analytical Darcy’s law [24]. Lattice Boltzmann method (LBM) is a method based on the Boltzmann’s kinetic equation for fluid simulation to simulate fluid density on a lattice with streaming and collision steps instead of solving Navier-Stokes equations directly. It is more straightforward to simulate fluid flow within complex environments (like porous medium) with complex boundaries using this method [25–28]. In recent years, LBM has been used in various studies including microscopic gaseous flows, multiphase flows, droplet deformation, electrokinetic and magnetohydrodynamic flows, biological microfluidics and porous media Microflows [29–35]. Simulation of flow within complex environments like porous materials in which the microscopic porous structure and surface wettability is important, is relatively easier by LBM due to its particulate features [33]. Considering this advantage of LBM for modelling flow within porous medium (and especially microporous materials), many applications of LBM for Darcy and non-Darcy flows in microreactors, fuel cells, underground water resources, fabric materials and biological/biomedical materials have been reported [36–39]. In this paper, fluid flow within nitrocellulose membrane of LFIs has been studied by theoretical Washburn model and LBM method to propose a new geometry for nitrocellulose membrane in order to improve the color intensity in the reaction zone. In the following, fluid flow, especially the fluid velocity has been investigated in nitrocellulose membrane by using Lattice-Boltzmann method and experimental observations. Finally, according to the analytical, numerical, and experimental results, an assay has been developed and by quantifying the color intensity in the reaction zone, the expectations which are acquired from the analysis was verified.
τF ρ
(4)
Where the external force F can be classified as, 8 fluid-fluid: F (x,t) = −Gψ(x,t) ∑a= 1 wa ψ(x + ea Δt,t) ea (5) 8
fluid-solid: Fads (x,t) = −Gads ψ(x,t) ∑a= 1 wa S(x + ea Δt,t) ea (6) Where G is the interaction strength, Gads is the adsorption coefficient which varies with the fluid-solid contact angle, S function value is 1 if x + ea Δt is a solid node and is 0 otherwise. Ψ is the interaction potential and can be defined as below [40]:
ρ ψ(ρ) = ψ0exp ⎜⎛− 0 ⎞⎟ ⎝ ρ⎠
(7)
ψ0 and ρ0 are arbitrary constants which are assumed to be 4 and 200 respectively in this study [41]. 3. Materials and methods 3.1. Materials Mouse polyclonal anti- α hCG antibodies, mouse monoclonal anti- β hCG antibodies (conjugated with gold nanoparticles), and sheep antimouse IgG secondary antibodies were purchased from Abcam (Shanghai, China). Nitrocellulose membrane (Hi-Flow Plus #HF12004S30), glass fiber conjugate pad (G041 Glass Fiber Conjugate Pad Rolls # GFCP001000), absorbent pad, and cellulose fiber sample pad (C083 Cellulose Fiber Sample Pad Strip #CFSP203000) were purchased from Millipore (Guangzhou, China). Bovine serum albumin (BSA #A1933), Tween-20 (#P9416), Trehalose (#PHR1344) and all the chemical reagents that have been used in the experiments (NaCl, KCl, Na2HPO4, Na2HPO4, KH2PO4, Sodium perborate, Sucrose) were purchased from Sigma-Aldrich (Shanghai, China). Ultrapure water has been used in the laboratory for preparation of buffers and solutions. 3.2. Preparation of antibodies Anti-hCG alpha and sheep antimouse IgG should be dispensed on the test and control lines respectively. These antibodies should be diluted to 1 mg/ml for dispensing purpose, and Anti-hCG beta conjugated antibodies should be diluted similarly. For diluting antibodies, phosphate buffered saline (PBS) –consists of NaCl 137 mM, KCl 27 mM, Na2HPO4 10 mM and KH2PO4 2 mM in PH 7.4 - is used.
2. Lattice-Boltzmann approaches for porous media flow Lattice-Boltzmann modelling is a proper and time saving method for simulating fluid flow within porous media in small scale. LatticeBoltzmann equation is a simplified form of Boltzmann kinetic equation which assumes only 9 directions (a = 0… 8) for particles to move (D2Q9 model). Distribution functions of particles is updated in each time step as below,
3.3. Preparation of sample and conjugate pads Sample and conjugate pads must have suitable performances during the release of analytes and they must be treated before being used in LFIs. Sample and conjugate pads are soaked in the sample buffer (Boric acid 0.003 mM, Sodium perborate 0.004 mM, NaCl 0.5 %w/v, BSA 0.5 2
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concentrations of hCG in sample liquid (15, 25, and 40 mIU/ml) and different concentrations of the conjugated antibodies (1 and 2 mg/ml) were employed to ensure the reproducibility and repeatability of the experiments and the reported results are an average of 10 series of experiments. In Fig. 4, the sample fluid front velocity variation within nitrocellulose membrane is shown. While the sample fluid passes along nitrocellulose membrane, its velocity decreases because of the contrast between the adhesive forces and the viscose forces of the porous media. Diluted anti-hCG alpha is dispensed on different positions (by 5 mm space) over the nitrocellulose membrane by the same mentioned rate and tested by positive samples. Resulted lines are shown in Fig. 5 in which the color intensity has been quantified. In order to quantify the color intensity at the reaction zone, image processing toolbox within MATLAB software was employed to analyze the pictures. It is necessary to mention that for measuring the color intensity of these lines, 10 series of experimental data were gathered and analyzed and an average over all measurements was obtained. By reducing the sample fluid velocity along the nitrocellulose membrane and considering the point that antibodies have sufficient time to capture the analytes in low fluid velocities, the lines that are placed in the tail-end of the membrane have a better quality for visualization as can be seen in Fig. 5. Keeping in mind that some of the target analytes would be captured by the first line and some of them would be captured by the second line and etc., there would be a lower amount of target analyte at the last line compared to the case that each line is located in a separate strip. This observation makes one sure that the location of the last line is the best position for the test line, however it obtains the lowest amount of target analytes among all the lines. Therefore, the tail-end of the membrane is the best place for setting the reaction lines.
%w/v, and Tween-20 20 %v/v) and the conjugate buffer (Boric acid 0.003 mM, Sodium perborate 0.004 mM, Sucrose 10 %w/v, Trehalose 2 %w/v and Tween-20 0.05 %v/v) respectively for 30 min and then dried for 3 h in 37 ℃. 3.4. Preparation of LFI for hCG detection After preparing and drying all pads and antibody solutions, antibodies should be dispensed on the nitrocellulose membrane and the conjugate pad. Diluted anti-hCG alpha monoclonal and sheep antimouse IgG secondary antibodies are dispensed on the nitrocellulose membrane as the test and control lines respectively with a rate of 1 μl/cm by using a lateral flow linear dispenser purchased from Kinbio (Shanghai, China). There are two methods for dispensing conjugated antibodies on the conjugate pad. The first method is to dispense antibodies on the pad by using a dispenser, and the second method is to soak the pads into the antibody solution. In this study, the conjugate pad was soaked into the conjugated antibody solution and then dried at the room temperature and stored in low humidity within an environment with temperature of 4 ℃. Afterward, sample, conjugate, nitrocellulose membrane and wicking pads are assembled respectively by a 2 mm overlap on a plastic with an adhesive backing that has the dimension of 6 cm × 30 cm and then are cut into a number of strips with 5 mm width. 3.5. Detection of hCG by LFI After cutting pads into strips, one can use it for the detection of hCG in urine by immersing strips into the urine sample. For a positive sample, both the test and the control lines would appear, but if hCG hormones does not exist within the urine sample, just the control line would be visible. In Fig. 2, the results of the developed assay versus positive and negative samples is shown.
4.2. Proposing modified geometry for nitrocellulose membrane Fluid flow transportation in one-dimensional porous media like a nitrocellulose membrane in LFIs which are fed by a non-limiting fluid reservoir follows the Washburn equation [43],
4. Results and discussion 4.1. Displacement of reaction line over the nitrocellulose membrane
L2 =
At first, the effect of the reaction zone position over LFI’s membrane on the detection performance was investigated. In this regard, by simulating the fluid flow within the porous media using LatticeBoltzmann method, it was observed that by progressing the fluid (by capillary forces) within the porous network (nitrocellulose membrane), the fluid front velocity will be reduced that is in a very good agreement with the study of Elizalde et al. [42] (Fig. 3). Then, the sample fluid velocity is measured in the nitrocellulose membrane by tracking its front position, frame by frame, using a highspeed camera with 1000 fps. It is necessary to mention that different instruments and measurement procedures including different dispensers with different dispensing rates (1 and 2 1μl/cm ), different
γDt 4μ
(8)
in this equation, L is the transport length of the fluid front in the porous matrix, γ is the effective surface tension, D is the average pore diameter, t represents time, and μ is the fluid viscosity [44,45]. As can be seen by Eq. (8), the transported length of the fluid front depends on time like L∼ t which means that the fluid front velocity in the nitrocellulose strips would decrease by time (by progressing the fluid in the nitrocellulose membrane). In Fig. 6, fluid front velocity in the experiments (resulted by obtaining fluid front position, frame by frame, using a high-speed camera with 1000 fps) has been compared with Washburn equation for a strip that is fed by a non-limiting reservoir. According to Fig. 6, Washburn equation can properly predict
Fig. 2. Developed LFI for hCG detection in human urine sample by assembling all pads on a plastic with adhesive backing. 3
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Fig. 3. (Left) sample flow simulation through membrane. red and purple represent a velocity of 1.62 mm/s and zero respectively. (right) flow velocity over the membrane according to LBM. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 4. Sample fluid velocity within the nitrocellulose membrane based on experimental measurements. Fig. 7. Three strips fed in a non-limiting reservoir in order to investigate by Washburn equation.
the fluid flow behavior within the nitrocellulose membrane of LFI. In the following, fluid flow characteristics, especially fluid velocity has been studied in three different geometries, in which the first one is a simple strip (A), the second one is a strip with a contracted segment (B) and the last one is a strip with an expanded segment (C). It is necessary to mention that all the strips are supposed to be fed by a non-limiting reservoir since Washburn equation requires this condition. As shown in Fig. 7, all the strips have the same width in the end-tail segment because this zone is appropriate for dispensing antibodies according to the discussion in the previous section. In strip A, the fluid front displacement follows the Washburn equation and as mentioned before, the fluid velocity would decrease with time. In the first segment of strip B, Washburn equation can be used and for the second part can be used similarly since one can suppose that the first segment plays the role of an unlimited reservoir for the second segment but it should be noted that for the second segment, the time (t in Washburn equation) is relative to the time when the fluid front reaches the position of the cross-section variation, so accordingly, the fluid front velocity magnitude will increase abruptly. In the last strip, in which the cross section expansion occurs, the fluid displacement in the first part follows the Washburn equation; however, for the second segment it cannot be used owing the fact that this part of the strip is not fed by a non-limiting reservoir. According to the assumption of the incompressibility of the fluid, the velocity of the fluid front would decrease as it transported from the thinner segment to the wider one. In Fig. 8, the fluid front velocity for these three strips has been compared. Fluid front velocity was measured along the nitrocellulose membrane for these three membranes by using Lattice-Boltzmann simulation. Results of the simulation have been presented in Fig. 9 and it can be seen that the fluid velocity within the porous membrane follows the mentioned trend by Washburn equation and the results are in good agreement with the aforementioned assumptions. As mentioned before, the fluid velocity has a great influence on the binding of antibody and as a result on the color intensity in test zone.
Fig. 5. Color intensity of reaction lines placed on different positions over the membrane which shows that the tail-end of membrane has the best color intensity due to the lower flow velocity.
Fig. 6. Flow velocity within nitrocellulose membrane by Washburn equation and experimental observations.
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Fig. 8. Prospect of sample fluid velocity within nitrocellulose membrane for three presented strips by Washburn equation.
Fig. 11. Comparison of the color intensity of the reaction lines for simple and modified strips.
between these two series of data for simple and modified assays is significant.
Fig. 9. Lattice-Boltzmann modelling results for fluid front velocity for tree strips introduced in Fig. 7.
5. Conclusion In our previous studies, the fluid movement within different types of devices was analyzed by employing various numerical techniques [46–50]. In this study, LBM method was employed to investigate the effect of some geometrical parameters on the performance of the lateral flow immunoassays which was verified by experimental studies. It was shown that for low sample fluid flow velocities, antibodies have sufficient time for binding, so by increasing the capture rate, the color intensity of the reaction lines would be increased. Due to the reduction of the fluid velocity within the nitrocellulose membrane, the effect of the reaction line position on the color intensity was also investigated by using experimental and Lattice-Boltzmann simulation. It was observed that the tail-end of the membrane is the best place for dispensing the test and the control antibodies. A modified geometry was also proposed by predicting the fluid flow velocity within the nitrocellulose membrane according to the Washburn equation that was proved by Lattice-Boltzmann simulation. Then, the lateral flow assays were developed accordingly and by testing immunoassays in the same conditions (the same dispensing rate of antibodies, the same width of strips and the same concentration of hCG in urine sample), it was observed that the color intensity has been improved by ∼ 10 percent. Studying of capillary flow behavior within paper-based biosensors and presenting a new modified geometry for their membrane could be used for not only the related immunoassays and their performance improvement but also for lab-on-chip applications with paper-based substrates.
Fig. 10. Experimental results for typical and modified membranes.
So, this parameter has a significant impact on the visualization of LFIs for household use. In low fluid velocities, antibodies have more time for binding and in the geometries with lower fluid velocity, one may expect a higher color intensity in the reaction zone. In this regard, the lateral flow strips with geometries like strip C are developed because of their low fluid front velocity in the reaction zone (tail-end of the nitrocellulose membrane). To confirm the mentioned idea, the lateral fluid velocity in the membrane of strip C and a typical strip for LFIs (strip A) has been measured and compared experimentally (Fig. 10). Diluted anti-hCG alpha was dispensed on both simple and modified (strip C) nitrocellulose membrane geometries by the same mentioned rate. By testing intended lateral flow strips with positive hCG samples, the color intensity of the appeared lines are compared by image processing tool as shown in Fig. 11. According to Fig. 11, color intensity of the reaction line in the nitrocellulose membrane has increased due to the low flow velocity of sample fluid within the modified geometry of the nitrocellulose membrane by 9.4 percent. It is worth noting that these data are the average of seven series of experimental data for both simple and modified assays which t-test analysis has been done for them. The t-value for these data was -1.957 which according to the corresponding p-value (0.037), the difference
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