The Scientific World Journal

The Scientific World Journal / 2014 / Article

Research Article | Open Access

Volume 2014 |Article ID 929163 |

B. Deng, X. F. Li, D. Y. Chen, L. D. You, J. B. Wang, J. Chen, "Parameter Screening in Microfluidics Based Hydrodynamic Single-Cell Trapping", The Scientific World Journal, vol. 2014, Article ID 929163, 8 pages, 2014.

Parameter Screening in Microfluidics Based Hydrodynamic Single-Cell Trapping

Academic Editor: Ya Cheng
Received11 Mar 2014
Accepted04 May 2014
Published09 Jun 2014


Microfluidic cell-based arraying technology is widely used in the field of single-cell analysis. However, among developed devices, there is a compromise between cellular loading efficiencies and trapped cell densities, which deserves further analysis and optimization. To address this issue, the cell trapping efficiency of a microfluidic device with two parallel micro channels interconnected with cellular trapping sites was studied in this paper. By regulating channel inlet and outlet status, the microfluidic trapping structure can mimic key functioning units of previously reported devices. Numerical simulations were used to model this cellular trapping structure, quantifying the effects of channel on/off status and trapping structure geometries on the cellular trapping efficiency. Furthermore, the microfluidic device was fabricated based on conventional microfabrication and the cellular trapping efficiency was quantified in experiments. Experimental results showed that, besides geometry parameters, cellular travelling velocities and sizes also affected the single-cell trapping efficiency. By fine tuning parameters, more than 95% of trapping sites were taken by individual cells. This study may lay foundation in further studies of single-cell positioning in microfluidics and push forward the study of single-cell analysis.

1. Introduction

The goal of current cellular biology studies is to understand the molecular mechanisms underlying cellular functions [1]. Most cell-based assays (e.g., western blot and bulk PCR) collect data averaged across large cell populations and thus overlook rich information available when single cells are studied. Meanwhile, it has been known that individual cells with identical appearances differ in biological properties as cellular heterogeneity. Due to this heterogeneity, much effort has been devoted over the past few years in technical developments to study cells in the single-cell level [2, 3].

Among these developed methods, flow cytometry is the most commonly used method for single-cell analysis, enabling simultaneous multiparametric analysis of the biophysical/biochemical properties of single cells in a high-throughput manner [4]. Although powerful, flow cytometry cannot monitor temporal changes of single cells under stimulation and thus its functionality in understanding cellular molecular mechanisms is limited [5].

Quantitative microscopy enables single-cell monitoring in a time-lapse manner where both biophysical (e.g., cellular morphology) and biochemical information (e.g., calcium concentration) can be obtained [1]. However, in conventional culture flasks, uniform environments of single cells cannot be guaranteed due to nonuniform distributions of biochemical and biophysical cues (e.g., glucose, oxygen, and local fluid flow). Thus, microscopy based single-cell analysis using conventional culture flaks leads to compromised results [5].

Recently, microfluidics is under intensive research, which is the science and technology of manipulation and processing of small amounts of fluids [6, 7]. Since its critical dimension is in the microscale, microfluidics has been used to capture, culture, stimulate, and retrieve single biological cells [810]. In the field of single-cell capture, both active and passive trapping principles were proposed to enable large-array single-cell positioning in a uniform environment [1113].

Among active single-cell trapping schemes, dielectrophoresis is the most commonly used method, which confines cells via their inducible electric dipoles in an electric field gradient, featured with selective cellular capture and release [1416]. However, dielectrophoresis requests fine tuning of the applied electrical parameters, which may lead to trapping of multiple cells due to inappropriate control of the dielectrophoretic forces. In addition, the trapping method is not suitable for long-term cell culture due to potentially cytotoxic low-conductivity buffers and/or high temperatures induced by Joule heating [17].

As to passive methodologies for single-cell trapping, flow-based single-cell positioning has been developed, which can be divided into two categories. In the first strategy, single cells are loaded into individual wells patterned on silicon or polymeric materials due to gravity where the single-cell trapping efficiency is dominated by geometrical parameters of trapping wells and cellular diameters [18, 19]. Although this trapping method is featured with simplicity, its nature of static cell culture limits its possibilities to actively manipulate the trapped cells and conduct temporal stimuli.

In the second strategy, arrays of weirs or dams are used to trap cells as they move through a fluidic device under hydrodynamic forces. Di Carlo et al. firstly presented a hydrodynamic trapping array with U-shaped barriers, where the trapping of one single cell increases the flow resistance significantly and thus following cells travel around the trapping spot [20, 21]. Furthermore, Takeuchi et al. proposed a serpentine design in which single cells were trapped in the trapping sites in sequence [22, 23], which was then scaled up in the design proposed by Lu et al. [24]. Although lots of efforts were devoted in this area, further parameter investigation and optimization on cellular trapping efficiencies are still requested [25].

To address this issue, in this study, we proposed a microfluidic device including two parallel microchannels (main channel and buffer channel) interconnected with cellular trapping sites with a decrease in the cross-sectional area (see Figure 1). By choosing the on/off status of the inlets and outlets of these two channels, this design can represent previous trapping structures where Figure 1(c) represents the structure proposed by Shoji et al. [26, 27] and Figure 1(d) presents the trapping structure put forward by Lu et al. [24]. Numerical simulations were conducted to evaluate the cellular trapping efficiencies for a variety combination of inlets and outlets as well as geometry parameters. In addition, experimental results were conducted to further screen parameters including cellular fluid velocities and sizes for high-efficiency cellular positioning.

2. Materials and Methods

2.1. Materials and Cell Culture

Unless otherwise indicated, all cell-culture reagents were purchased from Life Technologies Corporation (Van Allen Way Carlsbad, CA, USA). Materials required for device fabrication included SU-8 photoresist (MicroChem Corp., Newton, MA, USA) and 184 silicone elastomer (Dow Corning Corporation, Midland, MI, USA).

A non-small-cell lung cancer cell line A549 was cultured at 37°C in 5% CO2 in RPMI 1640 medium supplemented with 10% heat-inactivated fetal bovine serum, 100 units/mL penicillin, and 100 μg/mL streptomycin.

2.2. Numerical Simulation

Extensive simulations were conducted using the finite element analysis package COMSOL 4.3 (Burlington, MA, USA) to quantify the effects of channel inlet/outlet status and geometry parameters on the cellular trapping efficiency. In this study, the incompressible Navier-Stokes module (element type: tetrahedral element and element number: 6787192) was used to simulate fluid flow velocity distributions in the microfluidic device. The trapping site flow ratio was defined as the ratio of the fluid volume flow rate through the trapping site and the volume flow rate at the main channel after the cellular trapping site. This parameter was used in previous studies to indicate the possibility of cellular trapping and it was speculated that should be higher than 1, which may enable sequential trapping of single cells [22, 25].

In this simulation, the effect of inlet and outlet status on was investigated. There are 6 status combinations for ports A, B, C, and D under study which are IOOO, IOWO, IWOO, IOOW, IWOW, and IWWO. Note that “I” represents the channel inlet with a defined fluid flow rate, “O” represents the channel outlet with a zero pressure, and “” represents the channel outlet with a zero flow rate. Four key geometry parameters (, , , and , see Figure 1(b)) with adjustable valuables were listed in Table 1 and their effects on were quantified using numerical simulations.

20/30/40  m5/10  m20/40/10  m10/5  m

2.3. Device Fabrication

The PDMS device with two different channel heights was fabricated based on conventional microfabrication techniques, including two-layer SU-8 mold fabrication, PDMS molding, and sealing with glass substrates.

The SU-8 mold starts with glass substrate cleaning where glass slides were soaked in the glass cleaning solution (H2SO4 : K2Cr2O7 = 10 : 1, 8 hours) and then rinsed in DI-water (three times). A heating step on a hotplate (150°C, 30 min) was used to drive away water residuals on top of glass slides, which were then coated with Cr based on sputtering (200 nm). The deposited Cr was then spin-coated with positive photoresist of AZ1500 (1000 rpm, 1 min), prebaked (100°C, 90 sec), exposed in a mask aligner (15 mw/cm2, 4 sec), developed (AZ1500 developer, 50 sec), and patterned in a Cr etchant (NaOH : KMnO4 : H2O = 1 : 3 : 100, 10 min) to form alignment marks for the following two-step lithography of SU-8 (see Figure 2(a)).

For better adhesion of SU-8 structures to the patterned glass substrate, a seed layer of SU-8 was formed. More specifically, SU-8 5 was spin-coated on glass slides patterned by Cr (500 rpm, 10 sec; 2500 rpm, 35 sec), prebaked (65°C, 1 min; 95°C, 3 min), flood-exposed in the mask aligner (6 sec, 15 mw/cm2), postexposure-baked (65°C, 1 min; 95°C, 1 min), and hard-baked (175°C, 2 hours) (see Figure 2(a)).

Then SU-8 5 was spin-coated again to form a 5 μm thick layer enabling cellular trapping, following the previously described methodology of SU-8 spin coating and prebake. Exposure at a series of exposure time (2.5 sec, 3 sec, and 3.5 sec) with mask alignment was conducted, followed by postexposure bake (65°C, 1 min; 95°C, 1 min), without development and hard bake (see Figure 2(b)). Then, the second layer of SU-8 5 was spin-coated on top of the first layer of SU-8 (500 rpm, 10 sec; 900 rpm, 35 sec), prebaked (65°C, 2 min; 95°C, 5 min), exposed with alignment (4 sec, 15 mw/cm2), postexposure-baked (65°C, 1 min; 95°C, 3 min), developed (SU-8 developer, 90 sec), and hard-baked (175°C, 2 hours) (see Figure 2(b)).

The PDMS molding procedure was described as follows: 75 g PDMS base and 7.5 g curing agent were mixed together at the mixing ratio of 10 : 1 and poured onto molds in a Petri dish (10 cm × 10 cm). The degassing step was then performed, followed by the curing process in an oven (80°C, 6 hours). The cured PDMS layer was then peeled away from the SU-8 mold and the through holes were punched by a hollow needle of 2 mm in diameter. Plasma oxidation (30 w, 2 min) was used to activate the surfaces of PDMS and glass slides, which were then gently put together on top of the hotplate for PDMS-glass sealing (120°C, overnight) (Figure 2(c)).

2.4. Device Operation

In experiments, the microfluidic devices were filled with culture medium to remove air bubbles properly. A cell suspension solution (1 million cells per mL) was injected into the main channel while the cellular trapping process was monitored by an inverted microscope (IX 71, Olympus China).

In these experiments, A549 cells were tested in experiments and their internal size distributions were used to address the effect of cellular diameters on the cellular trapping efficiency. As to the choice of pressure sources for cell injection, syringe pumping (PHD 2000, Harvard Apparatus) and gravity based pumping were used and compared, representing fluid flow at higher and lower flow rates, respectively.

3. Results and Discussion

Microfluidics based hydrodynamic single-cell trapping has been used to quantify cellular responses at the single-cell level, which can be classified into three stages from the perspective of technical development. In stage I, Di Carlo et al. trapped single cells based on large-array U-shape trapping weirs [20, 21] and Shoji et al. trapped single cells based on flow rate differences between two fluid channels [26, 27]. In these reported mechanisms, the trapped single cells have negligible effects on other trapping positions, and thus these trapping spots are taken randomly without a specific order. This issue leads to low trapping efficiencies in the large-array single-cell positioning [25].

To address this issue, Takeuchi et al. proposed the sequential trapping concept where the trapping sites were taken by single cells in sequence [22, 23]. In this design, for each trapping site, a bypass channel was designed to divert upcoming single cells after cellular trapping. The trapping efficiency was optimized by Lutolf et al. where the key parameter was optimized to values much higher than 1.00 [25]. Although a trapping efficiency higher than 97% was claimed by Lutolf et al., the proposed structure cannot realize high-density single-cell positioning.

In the third stage, Lu et al. [24] and Lee et al. [28, 29] modified the design of Takeuchi and realized high-density single-cell positioning where multiple trapping sites were placed in a sequential order together with one bypassing channel. Although a trapping efficiency of 95% was claimed, this study has a much lower (no higher than 0.5) and thus whether these trapping sites can be taken by cells in a sequential order is questionable, which needs further optimization.

To address this issue, in this study, we proposed a microfluidic structure including two parallel channels interconnected with cell trapping sites. By choosing inlet/outlet status, the design can be used to mimic previous designs. If the outlets of the main channel and the buffer channel are left open, the device functions as a duplicate of Shoji’s design while if the outlets of the main channel and the buffer channel are left closed, the device works as a single-column counterpart of the design proposed by Lu et al.

3.1. Device Fabrication Characterization

The proposed SU-8 mold master contained two layers, which are 5 μm and 15 μm, respectively. The exact thickness was realized by regulating the spin rate of SU-8 5. After a careful parameter screening, the spin rates of 2500 rpm and 900 rpm were chosen in this study with characterized thickness of fabricated SU-8 layers shown in Table 2. It is interesting to note that the thickness of the SU-8 layer in corner areas was slightly higher than the values in the middle areas.

( m)C1M1M2C2Ave. ± std.

Device 416.
Device 514.414.515.416.4
Device 615.515.315.017.5

Besides channel thickness optimization, exposure time was fine-tuned to fabricate the cell trapping channel with the height of 5 μm. In the exposure time of 2.5 sec, channel distortion was located as a sign of underexposure (see Figure 3(a)) while, for the exposure time of 3.5 sec, overexposure was noticed by the channel width enlargement (see Figure 3(b)). Thus, exposure time of 3.0 sec was chosen as the optimized parameter for further device fabrication (see Figure 3(c)). Figure 3(d) shows the fabricated prototype device for single-cell trapping.

3.2. Numerical Simulation Results

The of the first cellular trapping site for six inlet/outlet combinations was shown in Figure 4(a) where geometry parameters were listed as follows: μm, μm, μm, and μm. For the case of IWOW, the setup was consistent with the device structure described in Lu’s design and the was the highest among all the combinations (63.32%), indicating the optimal trapping efficiency. It is worth noting that since this value is much lower than 1.00, the sequential trapping of single cells along the trapping sites cannot be guaranteed.

Three setups including IOOW, IWOO, and IOOO produced comparable of roughly 40% and two setups of IOWO and IWWO lead to the lowest values in (roughly 20%). These results indicate that, for the first cellular trapping site, the status of the inlet buffer channel has a key role in determining . As the inlet of the buffer channel was changed from the status of open “O” to wall “W”, a significant decrease in was recorded. Furthermore, the status of the outlets of the main channel and the buffer channel has negligible effects on . It is worth noting that, for the case of IOOO, the channel setup was comparable to the design proposed by Shoji et al. and it has a lower compared to the design proposed by Lu et al.

The effect of channel geometry parameters on was also investigated based on numerical simulations for the case of IWOW (see Figure 4(b)). Among four parameters, was shown to play a key role. As it was decreased from 10 μm to 5 μm, was decreased from 63.32% to 30.01%. For other parameters including , , and , the effect on is less significant. More specifically, the increase in from 20 μm to 40 μm leads to a decrease in from 63.32% to 49.75% and the increase in from 10 μm to 40 μm resulted in a decrease in from 66.33% to 60.80%.

3.3. Cellular Trapping Results

Figure 5 summarizes single-cell trapping results in case of IWOW with detailed geometry parameters as μm, μm, μm, and μm. Figure 5(a) shows the cellular trapping images without proper cellular positioning when gravity was used to drive cells into the main channel. These results show that when gravity was used as the driving force to push cells into the channel at a relatively low flow rate, no cellular trapping was noticed. At relatively high flow rates based on syringe pumps, cellular trapping was noticed (see Figure 5(c)). These results indicate that, in case of single-cell trapping, the fluid flow velocity is a key parameter and it was speculated that, at low flow velocities, the fluid drag forces exerted on cells were quite limited, which may not be capable of driving cells into the cellular trapping sites.

Figure 5(b) shows the effect of cellular sizes on the trapping efficiency where a larger cell was noticed to travel along the main channel without being trapped in the trapping spots. This result suggests that the cellular trapping spots are size selective and the proposed device has difficulties in trapping larger cells. After parameter optimization, trapped single cells were shown in Figure 5(c), which indicates that although this microfluidic structure was capable of single-cell trapping, it has quite strict requirement on trapping parameters. Note that, in this cellular trapping process, trapping spots were not taken in sequence which may result from the fact that was much lower than 1.00.

4. Conclusion

In this study, both numerical simulations and experimental results were conducted to investigate the effect of capture site geometries, cellular flow velocities, and sizes on the cellular trapping efficiency. Numerical simulations confirmed that the design proposed by Lu et al. was capable of producing a higher than the design proposed by Shoji et al. Experimental results suggested that higher flow rates were capable of capturing single cells more easily than the lower flow rate counterpart. After fine-tuning the relevant parameters, the cellular trapping efficiency higher than 90% was realized, which may further push the development of single-cell positioning.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Authors’ Contribution

B. Deng and X. F. Li are co-first authors to this paper.


The authors would like to acknowledge financial support from Natural Science Foundation of China (Grants nos. 81261120561 and 61201077), National Basic Research Program of China (973 Program, Grant no. 2014CB744602), National High Technology Research and Development Program of China (863 Program, Grant no. 2014AA093408), and Beijing NOVA Program and FP7 with Grant no. PIRSES-GA-2009-247641.


  1. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell, Garland Science, New York, NY, USA, 2007.
  2. D. G. Spiller, C. D. Wood, D. A. Rand, and M. R. H. White, “Measurement of single-cell dynamics,” Nature, vol. 465, no. 7299, pp. 736–745, 2010. View at: Publisher Site | Google Scholar
  3. D. Ryan, K. Ren, and H. Wu, “Single-cell assays,” Biomicrofluidics, vol. 5, no. 2, Article ID 021501, 2011. View at: Publisher Site | Google Scholar
  4. D. A. Ateya, J. S. Erickson, P. B. Howell Jr., L. R. Hilliard, J. P. Golden, and F. S. Ligler, “The good, the bad, and the tiny: a review of microflow cytometry,” Analytical and Bioanalytical Chemistry, vol. 391, no. 5, pp. 1485–1498, 2008. View at: Publisher Site | Google Scholar
  5. C. E. Sims and N. L. Allbritton, “Analysis of single mammalian cells on-chip,” Lab on a Chip—Miniaturisation for Chemistry and Biology, vol. 7, no. 4, pp. 423–440, 2007. View at: Publisher Site | Google Scholar
  6. R. C. R. Wootton and A. J. Demello, “Microfluidics: exploiting elephants in the room,” Nature, vol. 464, no. 7290, pp. 839–840, 2010. View at: Publisher Site | Google Scholar
  7. G. M. Whitesides, “The origins and the future of microfluidics,” Nature, vol. 442, no. 7101, pp. 368–373, 2006. View at: Publisher Site | Google Scholar
  8. H. Yin and D. Marshall, “Microfluidics for single cell analysis,” Current Opinion in Biotechnology, vol. 23, no. 1, pp. 110–119, 2012. View at: Publisher Site | Google Scholar
  9. R. N. Zare and S. Kim, “Microfluidic platforms for single-cell analysis,” Annual Review of Biomedical Engineering, vol. 12, pp. 187–201, 2010. View at: Publisher Site | Google Scholar
  10. J. El-Ali, P. K. Sorger, and K. F. Jensen, “Cells on chips,” Nature, vol. 442, no. 7101, pp. 403–411, 2006. View at: Publisher Site | Google Scholar
  11. G. T. Roman, Y. Chen, P. Viberg, A. H. Culbertson, and C. T. Culbertson, “Single-cell manipulation and analysis using microfluidic devices,” Analytical and Bioanalytical Chemistry, vol. 387, no. 1, pp. 9–12, 2007. View at: Publisher Site | Google Scholar
  12. J. Nilsson, M. Evander, B. Hammarström, and T. Laurell, “Review of cell and particle trapping in microfluidic systems,” Analytica Chimica Acta, vol. 649, no. 2, pp. 141–157, 2009. View at: Publisher Site | Google Scholar
  13. S. Lindström and H. Andersson-Svahn, “Overview of single-cell analyses: microdevices and applications,” Lab on a Chip—Miniaturisation for Chemistry and Biology, vol. 10, no. 24, pp. 3363–3372, 2010. View at: Publisher Site | Google Scholar
  14. J. Voldman, M. L. Gray, M. Toner, and M. A. Schmidt, “A microfabrication-based dynamic array cytometer,” Analytical Chemistry, vol. 74, no. 16, pp. 3984–3990, 2002. View at: Publisher Site | Google Scholar
  15. B. M. Taff and J. Voldman, “A scalable addressable positive-dielectrophoretic cell-sorting array,” Analytical Chemistry, vol. 77, no. 24, pp. 7976–7983, 2005. View at: Publisher Site | Google Scholar
  16. B. M. Taff, S. P. Desai, and J. Voldman, “Electroactive hydrodynamic weirs for microparticle manipulation and patterning,” Applied Physics Letters, vol. 94, no. 8, Article ID 084102, 2009. View at: Publisher Site | Google Scholar
  17. J. Voldman, “Electrical forces for microscale cell manipulation,” Annual Review of Biomedical Engineering, vol. 8, pp. 425–454, 2006. View at: Publisher Site | Google Scholar
  18. J. C. Love, J. L. Ronan, G. M. Grotenbreg, A. G. Van Der Veen, and H. L. Ploegh, “A microengraving method for rapid selection of single cells producing antigen-specific antibodies,” Nature Biotechnology, vol. 24, no. 6, pp. 703–707, 2006. View at: Publisher Site | Google Scholar
  19. J. R. Rettig and A. Folch, “Large-scale single-cell trapping and imaging using microwell arrays,” Analytical Chemistry, vol. 77, no. 17, pp. 5628–5634, 2005. View at: Publisher Site | Google Scholar
  20. D. Di Carlo, N. Aghdam, and L. P. Lee, “Single-cell enzyme concentrations, kinetics, and inhibition analysis using high-density hydrodynamic cell isolation arrays,” Analytical Chemistry, vol. 78, no. 14, pp. 4925–4930, 2006. View at: Publisher Site | Google Scholar
  21. D. D. Carlo, L. Y. Wu, and L. P. Lee, “Dynamic single cell culture array,” Lab on a Chip—Miniaturisation for Chemistry and Biology, vol. 6, no. 11, pp. 1445–1449, 2006. View at: Publisher Site | Google Scholar
  22. W.-H. Tan and S. Takeuchi, “A trap-and-release integrated microfluidic system for dynamic microarray applications,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 4, pp. 1146–1151, 2007. View at: Publisher Site | Google Scholar
  23. W.-H. Tan and S. Takeuchi, “Dynamic microarray system with gentle retrieval mechanism for cell-encapsulating hydrogel beads,” Lab on a Chip—Miniaturisation for Chemistry and Biology, vol. 8, no. 2, pp. 259–266, 2008. View at: Publisher Site | Google Scholar
  24. K. Chung, C. A. Rivet, M. L. Kemp, and H. Lu, “Imaging single-cell signaling dynamics with a deterministic high-density single-cell trap array,” Analytical Chemistry, vol. 83, no. 18, pp. 7044–7052, 2011. View at: Publisher Site | Google Scholar
  25. S. Kobel, A. Valero, J. Latt, P. Renaud, and M. Lutolf, “Optimization of microfluidic single cell trapping for long-term on-chip culture,” Lab on a Chip—Miniaturisation for Chemistry and Biology, vol. 10, no. 7, pp. 857–863, 2010. View at: Publisher Site | Google Scholar
  26. Y. Yamaguchi, T. Arakawa, N. Takeda, Y. Edagawa, and S. Shoji, “Development of a poly-dimethylsiloxane microfluidic device for single cell isolation and incubation,” Sensors and Actuators B: Chemical, vol. 136, no. 2, pp. 555–561, 2009. View at: Publisher Site | Google Scholar
  27. T. Arakawa, M. Noguchi, K. Sumitomo, Y. Yamaguchi, and S. Shoji, “High-throughput single-cell manipulation system for a large number of target cells,” Biomicrofluidics, vol. 5, no. 1, Article ID 014114, 2011. View at: Publisher Site | Google Scholar
  28. R. D. Sochol, B. P. Casavant, M. E. Dueck, L. P. Lee, and L. Lin, “A dynamic bead-based microarray for parallel DNA detection,” Journal of Micromechanics and Microengineering, vol. 21, no. 5, Article ID 054019, 2011. View at: Publisher Site | Google Scholar
  29. R. D. Sochol, M. E. Dueck, S. Li, L. P. Lee, and L. Lin, “Hydrodynamic resettability for a microfluidic particulate-based arraying system,” Lab on a Chip—Miniaturisation for Chemistry and Biology, vol. 12, no. 23, pp. 5051–5056, 2012. View at: Publisher Site | Google Scholar

Copyright © 2014 B. Deng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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