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Engineering microfluidic concentration gradient generators for biological applications

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Abstract

This paper reviews the latest developments in the design and fabrication of concentration gradient generators for microfluidics-based biological applications. New gradient generator designs and their underlying mass transport principles are discussed. The review provides a blueprint for design considerations of concentration gradients in different applications, specifically biological studies. The paper discusses the basic phenomena associated with microfluidic gradient generation and the different gradient generation modes used in static and dynamic biological assays. Finally, the paper summarizes all factors to consider when using concentration gradient generators and puts forward perspectives on the future development of these devices.

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References

  • Abhyankar VV, Toepke MW et al (2008) A platform for assessing chemotactic migration within a spatiotemporally defined 3D microenvironment. Lab Chip 8(9):1507–1515

    Google Scholar 

  • Ahmed T, Shimizu TS et al (2010) Bacterial chemotaxis in linear and nonlinear steady microfluidic gradients. Nano Lett 10(9):3379–3385

    Google Scholar 

  • Atencia J, Morrow J et al (2009) The microfluidic palette: a diffusive gradient generator with spatio-temporal control. Lab Chip 9:2707–2714

    Google Scholar 

  • Atencia J, Cooksey GA et al (2012) A robust diffusion-based gradient generator for dynamic cell assays. Lab Chip 12(2):309–316

    Google Scholar 

  • Bang H, Lim SH et al (2004) Serial dilution microchip for cytotoxicity test. J Micromech Microeng 14:1165–1170

    Google Scholar 

  • Berthier E, Surfus J et al (2010) An arrayed high-content chemotaxis assay for patient diagnosis. Integr Biol 2(11–12):630–638

    Google Scholar 

  • Beta C, Bodenschatz E (2011) Microfluidic tools for quantitative studies of eukaryotic chemotaxis. Eur J Cell Biol 90(10):811–816

    Google Scholar 

  • Boy DA, Gibou F et al (2008) Simulation tools for lab on a chip research: advantages, challenges, and thoughts for the future. Lab Chip 8(9):1424–1431

    Google Scholar 

  • Boyden S (1962) Chemotactic effect of mixtures of antibody and antigen on polymorphonuclear leucocytes. J Exp Med 115(3):453–466

    Google Scholar 

  • Brenner S (1974) The genetics of Caenorhabditis elegans. Genetics 77(1):71–94

    Google Scholar 

  • Brett M-E, DeFlorio R et al (2012) A microfluidic device that forms and redirects pheromone gradients to study chemotropism in yeast. Lab Chip 12(17):3127–3134

    Google Scholar 

  • Chau LT, Rolfe BE et al (2011) A microdevice for the creation of patent, three-dimensional endothelial cell-based microcirculatory networks. Biomicrofluidics 5(3):034115

    Google Scholar 

  • Chen C-Y, Wo AM et al (2012) A microfluidic concentration generator for dose-response assays on ion channel pharmacology. Lab Chip 12(4):794–801

    Google Scholar 

  • Cheng S-Y, Heilman S et al (2007) A hydrogel-based microfluidic device for the studies of directed cell migration. Lab Chip 7(6):763–769

    Google Scholar 

  • Cheng JY, Yen MH et al (2008) A transparent cell-culture microchamber with a variably controlled concentration gradient generator and flow field rectifier. Biomicrofluidics 2:024105

    Google Scholar 

  • Chung BG, Choo J (2010) Microfluidic gradient platforms for controlling cellular behavior. Electrophoresis 31(18):3014–3027

    Google Scholar 

  • Chung BG, Flanagan LA et al (2005) Human neural stem cell growth and differentiation in a gradient-generating microfluidic device. Lab Chip 5(4):401–406

    Google Scholar 

  • Chung K, Zhan M et al (2011) Microfluidic chamber arrays for whole-organism behavior-based chemical screening. Lab Chip 11(21):3689–3697

    Google Scholar 

  • Cimetta E, Cannizzaro C et al (2010) Microfluidic device generating stable concentration gradients for long term cell culture: application to Wnt3a regulation of [small beta]-catenin signaling. Lab Chip 10(23):3277–3283

    Google Scholar 

  • Connelly JT, Gautrot JE et al (2010) Actin and serum response factor transduce physical cues from the microenvironment to regulate epidermal stem cell fate decisions. Nat Cell Biol 12(7):711–718

    Google Scholar 

  • Crane MM, Chung K et al (2010) Microfluidics-enabled phenotyping, imaging, and screening of multicellular organisms. Lab Chip 10(12):1509–1517

    Google Scholar 

  • Dai W, Zheng Y et al (2010) A prototypic microfluidic platform generating stepwise concentration gradients for real-time study of cell apoptosis. Biomicrofluidics 4:024101

    Google Scholar 

  • Deen WM (1998) Analysis of transport phenomena. Oxford University Press, New York

    Google Scholar 

  • Dertinger SKW, Chiu DT et al (2001) Generation of gradients having complex shapes using microfluidic networks. Anal Chem 73:1240–1246

    Google Scholar 

  • Dirk AR, Cornelia BI (2011) High-content behavioral analysis of caenorhabditis elegans in precise spatiotemporal chemical environments. Nat Methods 8(7):599–605

    Google Scholar 

  • Discher DE, Janmey P et al (2005) Tissue cells feel and respond to the stiffness of their substrate. Science 310(5751):1139–1143

    Google Scholar 

  • Dishinger JF, Reid KR et al (2009) Quantitative monitoring of insulin secretion from single islets of langerhans in parallel on a microfluidic chip. Anal Chem 81(8):3119–3127

    Google Scholar 

  • Du Y, Shim J et al (2009) Rapid generation of spatially and temporally controllable long-range concentration gradients in a microfluidic device. Lab Chip 9(6):761–767

    Google Scholar 

  • El-Ali J, Sorger PK et al (2006) Cells chips. Nature 442(7101):403–411

    Google Scholar 

  • Englert DL, Manson MD et al (2009) Flow-based microfluidic device for quantifying bacterial chemotaxis in stable, competing gradients. App Environ Microbiol 75(13):4557–4564

    Google Scholar 

  • Englert DL, Manson MD et al (2010) Investigation of bacterial chemotaxis in flow-based microfluidic devices. Nat Protoc 5(5):864–872

    Google Scholar 

  • Esch MB, King TL et al (2011) The role of body-on-a-chip devices in drug and toxicity studies. Annual Rev Biomed Eng 13(1):55–72

    Google Scholar 

  • Francis K, Palsson BO (1997) Effective intercellular communication distances are determined by the relative time constants for cyto/chemokine secretion and diffusion. Proc Nat Acad Sci USA 94(23):12258–12262

    Google Scholar 

  • Frank T, Tay S (2013) Flow-switching allows independently programmable, extremely stable, high-throughput diffusion-based gradients. Lab Chip 13(7):1273–1281

    Google Scholar 

  • Glaser V (2011) Microfluidics making bigger impression-techniques evolve to focus on cells, tissues and whole organisms. Genet Eng Biotechnol News 31(20):1

    Google Scholar 

  • Gomez-Sjoberg R, Leyrat AA et al (2007) Versatile, fully automated, microfluidic cell culture system. Anal Chem 79:8557–8563

    Google Scholar 

  • Greiner AM, Richter B et al (2012) Micro-engineered 3D scaffolds for cell culture studies. Macromol Biosci 12(10):1301–1314

    Google Scholar 

  • Grossmann G, Guo W-J et al (2011) The RootChip: an integrated microfluidic chip for plant science. Plant Cell Online 23(12):4234–4240

    Google Scholar 

  • Guilak F, Cohen DM et al (2009) Control of stem cell fate by physical interactions with the extracellular matrix. Cell Stem Cell 5(1):17–26

    Google Scholar 

  • Gupta K, Kim DH et al (2010) Lab-on-a-chip devices as an emerging platform for stem cell biology. Lab Chip 10(16):2019–2031

    Google Scholar 

  • Haessler U, Kalinin Y et al (2009) An agarose-based microfluidic platform with a gradient buffer for 3D chemotaxis studies. Biomed Microdevices 11(4):827–835

    Google Scholar 

  • Haessler U, Pisano M et al (2011) Dendritic cell chemotaxis in 3D under defined chemokine gradients reveals differential response to ligands CCL21 and CCL19. Proc Natl Acad Sci USA 108(14):5614–5619

    Google Scholar 

  • Hamid ZAA, Blencowe A et al (2010) Epoxy-amine synthesised hydrogel scaffolds for soft-tissue engineering. Biomaterials 31(25):6454–6467

    Google Scholar 

  • Harting J, Kunert C et al (2010) Lattice Boltzmann simulations in microfluidics: probing the no-slip boundary condition in hydrophobic, rough, and surface nanobubble laden microchannels. Microfluid Nanofluid 8(1):1–10

    Google Scholar 

  • Heo YS, Cabrera LM et al (2010) Dynamic microfunnel culture enhances mouse embryo development and pregnancy rates. Hum Reprod 25(3):613–622

    Google Scholar 

  • Huh D, Hamilton GA et al (2011) From 3D cell culture to organs-on-chips. Trends Cell Biol 21(12):745–754

    Google Scholar 

  • Huh D, Leslie DC, et al. (2012) A human disease model of drug toxicity–induced pulmonary edema in a lung-on-a-chip microdevice. Sci Transl Med 4(159):159ra147

    Google Scholar 

  • Hulme SE, Shevkoplyas SS et al (2010) Lifespan-on-a-chip: microfluidic chambers for performing lifelong observation of C. elegans. Lab Chip 10(5):589–597

    Google Scholar 

  • Hung PJ, Lee PJ et al (2005) Continuous perfusion microfluidic cell culture array for high-throughput cell-based assays. Biotechnol Bioeng 89(1):1–8

    Google Scholar 

  • Incropera FP, DeWitt DP, et al. (2006). Fundamentals of heat and mass transfer. Wiley, New York

  • Irimia D, Geba DA et al (2006) Universal microfluidic gradient generator. Anal Chem 78:3472–3477

    Google Scholar 

  • Irimia D, Charras G et al (2007) Polar stimulation and constrained cell migration in microfluidic channels. Lab Chip 7(12):1783–1790

    Google Scholar 

  • Jeon NJ, Dertinger SKW et al (2000) Generation of solution and surface gradients using microfluidic systems. Langmuir 16:8311–8316

    Google Scholar 

  • Jeon NL, Baskaran H et al (2002) Neutrophil chemotaxis in linear and complex gradients of interleukin-8 formed in a microfabricated device. Nat Biotechnol 20:826–830

    Google Scholar 

  • Juncker D, Schmid H et al (2005) Multipurpose microfluidic probe. Nat Mater 4(8):622–628

    Google Scholar 

  • Keenan TM, Folch A (2008) Biomolecular gradients in cell culture systems. Lab Chip 8:34–57

    Google Scholar 

  • Keenan TM, Hsu CH et al (2006) Microfluidic “jets” for generating steady-state gradients of soluble molecules on open surfaces. Appl Phys Lett 89(11):114103

    Google Scholar 

  • Khetan S, Burdick JA (2011) Patterning hydrogels in three dimensions towards controlling cellular interactions. Soft Matter 7(3):830–838

    Google Scholar 

  • Kilian KA, Bugarija B et al (2010) Geometric cues for directing the differentiation of mesenchymal stem cells. Proc Natl Acad Sci 107(11):4872–4877

    Google Scholar 

  • Kim M, Kim T (2010) Diffusion-Based and Long-Range Concentration Gradients of Multiple Chemicals for Bacterial Chemotaxis Assays. Anal Chem 82(22):9401–9409

    Google Scholar 

  • Kim S, Kim HJ et al (2010) Biological applications of microfluidic gradient devices. Integr Biol 2(11–12):584–603

    Google Scholar 

  • Kirby B (2010) Micro- and nanoscale fluid mechanics: transport in microfluidic devices. Cambridge University Press, Leiden

    Google Scholar 

  • Kothapalli CR, van Veen E, et al. (2011) A high-throughput microfluidic assay to study neurite response to growth factor gradients. Lab Chip 11(3):497–507

    Google Scholar 

  • Lee PJ, Hung PJ et al (2006) Nanoliter scale microbioreactor array for quantitative cell biology. Biotechnol Bioeng 94(1):5–14

    Google Scholar 

  • Li GN, Liu J et al (2008) Multi-molecular gradients of permissive and inhibitory cues direct neurite outgrowth. Ann Biomed Eng 36(6):889–904

    Google Scholar 

  • Lin F (2009) A microfluidics-based method for analyzing leukocyte migration to chemoattractant gradients. Methods Enzymol 461:333–347

    Google Scholar 

  • Lin F, Nguyen CMC et al (2004) Effective neutrophil chemotaxis is strongly influenced by mean IL-8 concentration. Biochem Biophys Res Commun 319(2):576–581

    Google Scholar 

  • Liu V, Bhatia S (2002) Three-dimensional photopatterning of hydrogels containing living cells. Biomed Microdevices 4(4):257–266

    Google Scholar 

  • Long T, Ford RM (2009) Enhanced transverse migration of bacteria by chemotaxis in a porous T-Sensor. Environ Sci Technol 43(5):1546–1552

    Google Scholar 

  • Lucchetta EM, Lee JH et al (2005) Dynamics of Drosophila embryonic patterning network perturbed in space and time using microfluidics. Nature 434(7037):1134–1138

    Google Scholar 

  • Ma L, Zhou C et al (2010) A porous 3D cell culture micro device for cell migration study. Biomed Microdevices 12(4):753–760

    Google Scholar 

  • Maguire TJ, Novik E et al (2009) Design and application of microfluidic systems for in vitro pharmacokinetic evaluation of drug candidates. Curr Drug Metab 10:1192–1199

    Google Scholar 

  • Mark D, Haeberle S et al (2010) Microfluidic lab-on-a-chip platforms: requirements, characteristics and applications. Chem Soc Rev 39(3):1153–1182

    Google Scholar 

  • Meier M, Lucchetta EM et al (2010) Chemical stimulation of the Arabidopsis thaliana root using multi-laminar flow on a microfluidic chip. Lab Chip 10(16):2147–2153

    Google Scholar 

  • Moore TI, Chou CS et al (2008) Robust spatial sensing of mating pheromone gradients by yeast cells. PLoS ONE 3(12):e3865

    Google Scholar 

  • Morel M, Galas J-C et al (2012) Concentration landscape generators for shear free dynamic chemical stimulation. Lab Chip 12(7):1340–1346

    Google Scholar 

  • Mosadegh B, Saadi W et al (2008) Epidermal growth factor promotes breast cancer cell chemotaxis in CXCL12 gradients. Biotechnol Bioeng 100(6):1205–1213

    Google Scholar 

  • Nagai M, Ryu S et al (2010) Chemical control of Vorticella bioactuator using microfluidics. Lab Chip 10(12):1574–1578

    Google Scholar 

  • Nandagopal S, Wu D et al (2011) Combinatorial guidance by CCR7 ligands for T lymphocytes migration in co-existing chemokine fields. PLoS ONE 6(3):e18183

    Google Scholar 

  • Nguyen N-T (2012) Micromixers-fundamentals, design and fabrication. Elsevier, Amsterdam

    Google Scholar 

  • Nguyen NT, Wereley ST (2002) Fundamentals and applications of microfluidics. Artech House, Boston

    MATH  Google Scholar 

  • Oh KW, Lee K et al (2012) Design of pressure-driven microfluidic networks using electric circuit analogy. Lab Chip 12(3):515–545

    MathSciNet  Google Scholar 

  • Paguirigan AL, Beebe DJ (2008) Microfluidics meets cell biology: bridging the gap by validation and application of microscale techniques for cell biological assays. BioEssays 30(9):811

    Google Scholar 

  • Pampaloni F, Reynaud EG et al (2007) The third dimension bridges the gap between cell culture and live tissue. Nat Rev Mol Cell Biol 8(10):839–845

    Google Scholar 

  • Park JY, Hwang CM et al (2007) Gradient generation by an osmotic pump and the behavior of human mesenchymal stem cells under the fetal bovine serum concentration gradient. Lab Chip 7(12):1673–1680

    Google Scholar 

  • Park JY, Kim S-K et al (2009) Differentiation of neural progenitor cells in a microfluidic chip-generated cytokine gradient. Stem Cells 27(11):2646–2654

    Google Scholar 

  • Qasaimeh MA, Gervais T et al (2011) Microfluidic quadrupole and floating concentration gradient. Nat Commun 2:464

    Google Scholar 

  • Queval A, Ghattamaneni NR et al (2010) Chamber and microfluidic probe for microperfusion of organotypic brain slices. Lab Chip 10(3):326–334

    Google Scholar 

  • Ricart BG, John B et al (2011) Dendritic cells distinguish individual chemokine signals through CCR7 and CXCR4. J Immunol 186(1):53–61

    Google Scholar 

  • Rosa P, Tenreiro S et al (2012) High-throughput study of alpha-synuclein expression in yeast using microfluidics for control of local cellular microenvironment. Biomicrofluidics 6(1):014109

    Google Scholar 

  • Ruan J, Wang LH et al (2009) Fabrication of a microfluidic chip containing dam, weirs and gradient generator for studying cellular response to chemical modulation. Mater Sci Eng 29(3):674–679

    Google Scholar 

  • Russom A, Irimia D et al (2009) Chemical gradient-mediated melting curve analysis for genotyping of SNPs. Electrophoresis 30(14):2536–2543

    Google Scholar 

  • Saadi W, Wang SJ et al (2006) A parallel-gradient microfluidic chamber for quantitative analysis of breast cancer cell chemotaxis. Biomed Microdevices 8(2):109–118

    Google Scholar 

  • Sadava D, Heller C, et al. (2009). Life: the science of biology, Sinauer Associates Inc, Massachusetts

  • Squires TM, Quake SR (2005) Microfluidics: fluid physcis at the nanolitre scale. Rev Mod Phys 77(3):977–1026

    Google Scholar 

  • Sugiura S, Hattori K et al (2010) Microfluidic serial dilution cell-based assay for analyzing drug dose response over a wide concentration range. Anal Chem 82(19):8278–8282

    Google Scholar 

  • Sulston JE (2003) Caenorhabditis elegans: the cell lineage and beyond (Nobel Lecture). ChemBioChem 4(8):688–696

    Google Scholar 

  • Sung JH, Shuler ML (2010) In vitro microscale systems for systematic drug toxicity study. Bioprocess Biosys Eng 33:5–19

    Google Scholar 

  • Suri S, Schmidt CE (2010) Cell-laden hydrogel constructs of hyaluronic acid, collagen, and laminin for neural tissue engineering. Tissue Eng Part A 16(5):1703–1716

    Google Scholar 

  • Takayama S, Ostuni E et al (2003) Selective chemical treatment of cellular microdomains using multiple laminar streams. Chem Biol 10(2):123–130

    Google Scholar 

  • Toetsch S, Olwell P et al (2009) The evolution of chemotaxis assays from static models to physiologically relevant platforms. Integrat Biol 1(2):170–181

    Google Scholar 

  • Toh Y-C, Lim TC et al (2009) A microfluidic 3D hepatocyte chip for drug toxicity testing. Lab Chip 9(14):2026–2035

    Google Scholar 

  • Tong Z, Balzer EM et al (2012) Chemotaxis of cell populations through confined spaces at single-cell resolution. PLoS ONE 7(1):e29211

    Google Scholar 

  • Tripathi A, Kathuria N et al (2009) Elastic and macroporous agarose-gelatin cryogels with isotropic and anisotropic porosity for tissue engineering. J Biomed Mater Res, Part A 90A(3):680–694

    Google Scholar 

  • Van der Meer AD, Vermeul K et al (2010) A microfluidic wound-healing assay for quantifying endothelial cell migration. Am. J Physiol Heart Circ Physiol 298:H719–H725

    Google Scholar 

  • VanDersarl JJ, Xu AM et al (2011) Rapid spatial and temporal controlled signal delivery over large cell culture areas. Lab Chip 11(18):3057–3063

    Google Scholar 

  • Vazquez M, Paull B (2010) Review on recent and advanced applications of monoliths and related porous polymer gels in micro-fluidic devices. Anal Chim Acta 668(2):100–113

    Google Scholar 

  • Velve-Casquillas G, Le Berre M et al (2010) Microfluidic tools for cell biological research. Nano Today 5(1):28–47

    Google Scholar 

  • Walker GM, Zeringue HC et al (2004) Microenvironment design considerations for cellular scale studies. Lab Chip 4:91–97

    Google Scholar 

  • Walker GM, Sai J et al (2005) Effects of flow and diffusion on chemotaxis studies in a microfabricated gradient generator. Lab Chip 5(6):611–618

    Google Scholar 

  • Walsh CL, Babin BM et al (2009) A multipurpose microfluidic device designed to mimic microenvironment gradients and develop targeted cancer therapeutics. Lab Chip 9(4):545–554

    Google Scholar 

  • Wang SJ, Saadi W et al (2004) Differential effects of EGF gradient profiles on MDA-MB-231 breast cancer cell chemotaxis. Exp Cell Res 300(1):180–189

    Google Scholar 

  • Wang CJ, Li X et al (2008a) A microfluidics-based tuning assay reveals complex growth cone responses to integrated gradients of substrate-bound ECM molecules and diffusible guidance cues. Lab Chip 8:227–237

    Google Scholar 

  • Wang CJ, Li X et al (2008b) A microfluidics-based turning assay reveals complex growth cone responses to integrated gradients of substrate-bound ECM molecules and diffusible guidance cues. Lab Chip 8(2):227–237

    Google Scholar 

  • Wang SY, Yue F et al (2009) Application of microfluidic gradient chip in the analysis of lung cancer chemotherapy resistance. J Pharm Biomed Anal 49(3):806–810

    Google Scholar 

  • Weibel DB, Whitesides GM (2006) Applications of microfluidics in chemical biology. Curr Opin Chem Biol 10(6):584–591

    Google Scholar 

  • Wu MH, Huang SB et al (2010) Microfluidic cell culture systems for drug research. Lab Chip 10(8):939–956

    Google Scholar 

  • Zhang X, Grimley A et al (2010) Microfluidic system for generation of sinusoidal glucose waveforms for entrainment of islets of Langerhans. Anal Chem 85(15):6704–6711

    Google Scholar 

  • Zhang X, Daou A et al (2011) Synchronization of mouse islets of Langerhans by glucose waveforms. Am J Physiol Endocrinol Metab 301(4):E742–E747

    Google Scholar 

  • Zheng GX, Wang YH et al (2012) Microalgal motility measurement microfluidic chip for toxicity assessment of heavy metals. Anal Bioanal Chem 404(10):3061–3069

    MathSciNet  Google Scholar 

  • Zicha D, Dunn GA et al (1991) A new direct-viewing chemotaxis chamber. J Cell Sci 99:769–775

    Google Scholar 

  • Zigmond SH, Hirsch JG (1973) Leukocyte locomotion and chemotaxis New methods for evaluation and demostration of a cell-dervice chemotactic factor. J Exp Med 137(2):387–410

    Google Scholar 

  • Ziolkowska K, Jedrych E et al (2010) PDMS/glass microfluidic cell culture system for cytotoxicity tests and cells passage. Sens Actuators B Chem 145(1):533–542

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Alicia G. G. Toh & Chun Yang

  2. Singapore Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore, 63807, Singapore

    Alicia G. G. Toh & Z. P. Wang

  3. Queensland Micro and Nanotechnology Centre, Griffith University, Brisbane, 4111, Australia

    Nam-Trung Nguyen

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  1. Alicia G. G. Toh
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Toh, A.G.G., Wang, Z.P., Yang, C. et al. Engineering microfluidic concentration gradient generators for biological applications. Microfluid Nanofluid 16, 1–18 (2014). https://doi.org/10.1007/s10404-013-1236-3

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