Patent Application
20110300570
Not Applicable
1. Technical Field of the Invention
The present invention is directed to methods and systems for rapidly generating concentration gradients of diffusible molecules, polymers, beads and cells. Further, the invention is directed to methods and systems for rapidly generating spatially and temporally controllable concentration gradients of these gradient materials in a portable microfluidic device.
2. Description of the Prior Art
Natural materials exhibit anisotropy with variations in soluble factors, cell distribution, and matrix properties. The ability to recreate the heterogeneity of the natural materials is a major challenge for investigating cell-material interactions and for developing biomimetic materials.
Anisotropic materials are highly important for many natural and engineered systems. Examples of anisotropic materials in nature include marbles, tree trunks and squid beaks. Examples of engineered anisotropic materials include the birefringent crystals of prisms, the metal wood head of golf clubs and the aluminum alloys used in aircraft and rockets. Spatial anisotropy in materials is especially prominent in cellular microenvironments in vivo where heterogeneous distributions of cells and molecules exist within spatially varying extracellular matrices (ECM). Molecular concentration gradients play an important role in biological phenomena such as chemotaxis, morphogenesis and wound healing. Meanwhile, the graded variations of ECM and cell concentration at the tissue interface (e.g. bone-cartilage interface, dentino-enamel junctions) are nature's solution for connecting mechanically mismatched tissues. Creating chemical and material gradients to mimic the heterogeneity of cellular environments is important for investigating cell-matrix interaction and for developing biomimetic materials for tissue engineering.
Concentration gradients of diffusible molecules (chemical compounds or biomolecules) play an important role in many chemical processes (e.g. crystal growth) as well as biological phenomena (e.g., chemotaxis, morphogenesis and wound healing). A variety of approaches have been developed for generating gradients of diffusible molecules driven either purely by diffusion or by a balance of convection and diffusion. Most of the existing approaches for gradient generation are diffusion-driven, which can be generally categorized into: (1) forming gradients perpendicular to parallel laminar flows of varying concentrations and (2) forming gradients along a channel by free-diffusion between a source and a sink. The first method is advantageous for producing stable complex gradients, but the experiments are not compatible with non-adherent and weakly adherent cells and the shear/drag force generated by the flow may alter the intercellular signaling pathways. Moreover, to generate the laminar flows, pumping systems with external connections (i.e. tubing and valves) are often used, which limit the portability and ease of use of the device 16. To maintain a continuous flow, relatively large volumes of fluid containing the materials of interests are consumed, which constrain their applications for precious materials (i.e. growth factors, drugs).
The second approach normally requires larger gradient generation times and the gradient produced is unstable and hard to maintain over long time periods. Gradients have also been formed parallel to the direction of flow. Goulpeau et al. built up longitudinal concentration gradients along their ancrochannel by using transient dispersion along the flow. Kang et al. developed a device that generated concentration gradients parallel to the direction of flow by using a convective-diffusive balance in a counter-flow configuration. Although these approaches could be used to rapidly generate concentration gradients in less than one minute, they still required external components i.e. hydrostatic pumps or valves to introduce and control the flows within the channels.
The ability to build pumpless fluidic devices that generate controllable gradients while maintaining the portability and scalability of microfluidic systems is of significant benefit for field testing and high-throughput studies. Furthermore, the ability to generate longer gradients cart be used to test the effects of molecular dose responses on cell behaviors. One approach to eliminate the use of external pumps is by using a passive-pump technology, which was first developed by G. M. Walker et al. as a semi-autonomous method for pumping fluid. Passive-pump technology only requires a device capable of producing small drops of liquid, such as a pipette. The surface tension difference between the larger drop of solution at the outlet and smaller drop of solution at the inlet was used to pump the small drop of liquid through the micro-channel, which has been shown to be a powerful high-throughput microfluidic tool for cell culturing. Evaporation has also been used as driving force in pump-less' microfluidic devices. Evaporation is a well-known issue when handling small liquid volumes, especially in microfluidic devices. While the loss of volume due to evaporation may cause unwanted effects such as the change of concentrations or osmolarity of the fluid solution; evaporation in microfluidic devices has proven to be a useful tool in several applications, including generating slow, steady flows in microchannels used for chromatography, DNA analysis devices, and sample concentration.
Various methods exist to generate molecular and material gradients. Diffusion-based approaches for gradient generation are limited to diffusible molecules and require long times to create millimeter length gradients, since the timescale for pure diffusion scales as length squared. Dispersion-based approaches, which combine primary stretching by flow shear and secondary spreading by diffusion, have been used to generate centimeter long molecular gradients in seconds to minutes. However, so far no generic platform employing dispersion to generate stable material gradients of single or multiple components over long distances have been developed.
The present invention is directed methods and systems for rapidly generating concentration gradients of diffusible materials (including chemical compounds and biologic molecules), polymers, beads, particles and cells in the channel of a microfluidic device. In accordance with the invention, alternating flows are induced in the channel to produce multi-centimeter long concentration gradients. Methods and systems according to the invention use alternating flows and hydrodynamic stretching to rapidly generate long gradients of these gradient materials and long cross-gradients of two species of gradient materials in a simple microchannel. In accordance with the invention, the length of the concentration gradient can be predetermined for wide range of material properties. For example, a polyethylene-glycol) hydrogel gradient, a porous collagen gradient and a composite material with a hyaluronic acid/gelatin cross-gradient can be generated with continuous variations in material properties and in their ability to regulate cellular response. The present invention can be useful for creating anisotropic biomimetic materials and high-throughput platforms for investigating cell-microenvironment interaction.
In one embodiment of the invention, methods and systems according to this embodiment utilize a forward flow induced by the passive-pumping and a reversed flow induced by evaporation to rapidly establish centimeter-length concentration gradients of molecules along the channel of a simple and portable microfluidic device. Passive-pumping is used to generate a forward flow from the inlet to the outlet of the channel, which introduced the gradient material (molecules of interest) into the microfluidic device in a rapid and simple manner and initiated a concentration gradient profile of the molecules due to the parabolic shape of the front flow. An evaporation-induced backward flow from the outlet to the inlet of the channel followed the forward flow resulting in the formation of dynamic concentration gradients of the molecule. The gradient profile can be stabilized by stopping the flow. The centimeter-length concentration gradients were in parallel with the flow direction along the microfluidic channel and can be spatially and temporally controlled.
In an alternative embodiment of the invention, methods and systems according to this embodiment utilize a pumping mechanism that produce fast alternating flows, which continually lengthen the gradient. In addition, the methods and systems according to this embodiment utilize the pumping mechanism to produce fast alternating flows of a second gradient material to generate a cross gradient.
In accordance with an alternative embodiment, a non-viscous solution, such as a buffered solution is input into the channel of the microfluidic device and the gradient material is pumped into in one or more cycles of alternating forward and backward flows. Each cycle can be defined to include injecting into the inlet a predefined volume of gradient material at a predefined flow rate, imparting a predefined forward flow velocity on the gradient material, waiting a predefined period of time to allow for diffusion and withdrawing a predefined volume of gradient material from the inlet at a predefined flow rate, imparting a predefined backward flow velocity on the gradient material. Optionally, a predefined waiting period to allow for diffusion between cycles can be provided. In accordance with the invention, the length of the gradient in the channel can determined as function of the flow velocity and the amount of time that the gradient material flows.
The present invention provides methods and systems for simple and rapid generation of relatively long concentration gradients in portable microfluidic devices. The present invention can provide that: 1) the concentration gradient is generated by dispersion, the combined effect of convection and molecular diffusion, and flow reversal, which changes the direction of the parabolic flow; 2) due to the convection-driven nature, the process of gradient generation was rapid (within several minutes), highly dynamic (throughout the backward flow stage) and spatially/temporally controllable (by controlling the evaporation-induced backflow); 3) the gradient can be formed by consuming low amounts of the gradient material (particles, cells, or molecules, etc.) of interest; 4) centimeter-length concentration gradients can be generated parallel to the flow direction along the channel; and 5) the process is simple and highly reproducible in a portable microfluidic device, requiring only a pipette for implementation.
The present invention is directed to a versatile platform for generating centimeter scale gradients of a broad range of gradient materials, from molecular to micron scale, in seconds to minutes. Particle and cell concentration gradients can be produced by high-speed alternating fluidic shear in a simple microfluidic channel. For diffusible gradient materials, flow sequences according to the invention can be used to generate long and laterally uniform gradients, including 2-3 cm gradients of fluorescent dyes. The same flow sequences can also be used to create gradients of hydrogels and cross gradients composite materials (such as, HA-gelatin, which possessed a gradient in cell-attachment). In accordance with the invention, gradient generation can be controlled using a formula for estimating gradient growth which is useful over a wide range of Péclet numbers and channel geometries.
It is an object of the invention to generate a concentration gradient of a gradient material over a predefined length of a microfluidic channel.
It is another object of the invention to rapidly generate a concentration gradient of a gradient material over a predefined length of a microfluidic channel.
It is an object of the invention to rapidly generate a stable concentration gradient of a gradient material over a predefined length of a microfluidic channel.
It is an object of the invention to rapidly generate a stable concentration gradient of a gradient material over a predefined length of a microfluidic channel, where the gradient material cart include biomolecules, cells, particles, polymers, and beads.
It is an object of the invention to generate a stable cross-concentration gradient of two gradient materials over a predefined length of a microfluidic channel.
It is an object of the invention to generate a concentration gradient of a gradient material by causing a sequence of forward flows and backward flows in a microfluidic channel.
These and other capabilities of the invention, along with the invention itself, will be more fully understood after a review of the following figures, detailed description, and claims.
The present invention is directed methods and systems for rapidly generating concentration gradients and cross-gradients of gradient materials (e.g., diffusible molecules, chemical compounds, biologic molecules, polymers, beads, particles, and cells) in the channel of a microfluidic device. In accordance with the invention, alternating flows are introduced in the channel of the microfluidic device to produce multi-centimeter long concentration gradients.
Methods and systems according to one embodiment of the invention utilize a forward flow induced by the passive-pumping and a reversed flow induced by evaporation to rapidly establish centimeter-length concentration gradients of molecules along the channel of a simple and portable microfluidic device. Passive-pumping is used to generate a forward flow from the inlet to the outlet of the channel, which introduced the molecules of interest (with volume less than 10 μL) into the microfluidic device in a rapid and simple manner and initiated a concentration gradient profile of the molecules due to the parabolic shape of the front flow. Passive-pumping includes applying one or more droplets to the inlet port of the microfluidic channel. An evaporation-induced backward flow from the outlet to the inlet of the channel followed the forward flow resulting in the formation of dynamic concentration gradients of the molecule. The gradient profile can be stabilized by stopping the flow. The centimeter-length concentration gradients were in parallel with the flow direction along the microfluidic channel and can be spatially and temporally controlled.
In accordance with the invention, one methodology used to generate the concentration gradient relies on the flow properties and the combined effect of convection and diffusion of the gradient materials into the base solution in the microfluidic channel. Throughout the channel, the flow is essentially fully-developed laminar Poiseuille flow in a rectangular channel, a textbook example where the Navier-Stokes equations admit an exact solution. The Peclet numbers for the forward and backward flows are approximately 1000 and 10, respectively. In the axial direction, the chemical transport is mainly due to convection; since the flow is essentially axial, the transport in the transverse direction is mainly due to molecular diffusion. This type of chemical spreading, involving both axial convection and transverse molecular diffusion, is called Taylor dispersion. Theoretical descriptions of dispersion in microchannels are well developed. Much of the existing theory for dispersion assumes steady flow. While the flows due to the passive-pump and evaporation stages are approximately steady, the transition between the two (flow reversal) is not but we can solve numerically to determine the flow and chemical concentration parameters.
Computational simulations of the gradient generation and stabilization agree well with the experimental data, which show that the concentration gradients are mainly generated and controlled by a combined effect of convection (forward and backward flow) and molecular diffusion. In one example, the portable microfluidic device according to the invention was used to rapidly generate a stabilized concentration gradient of a cardiac toxin used for conducting a cytotoxicity test. The stabilized concentration gradient of a cardiac toxin was used to test the toxicity response of HL-1 cardiac cells seeded within the channel. The present invention provides for ease of use, portability, low consumption and scalability and can be useful for various biological and chemical processes where rapid generation of long-range concentration gradients can be used.
The microfluidic device can be fabricated by using standard soft-lithography methods. Photomasks with channel patterns were designed using AutoCAD and printed on transparencies with 20,000 dpi resolution (CAD/Art Services, Inc., Bandon, Oreg.). Master molds patterned with 100 μm thick resist were made by patterning a negative photoresist (SU-8 2050, Microchem, MA) on a silicon wafer. PDMS molds were fabricated by curing prepolymer (Sylgard 184, Essex Chemical, Midland, Mich.) on silicon masters patterned with SU-8 photoresist. Briefly, PDMS molds were generated by mixing silicone elastomer and curing agent (10:1 ratio). The PDMS prepolymer was poured on the silicon master that was patterned with photoresist and cured at 70° C. for 2 h. PDMS molds were then peeled off from the silicon wafer. The inlet and outlet of the microchannel were created by a sharp punch (hole radius: 0.4 mm) for medium perfusion and cell seeding. The microfluidic device consisted of a top PDMS fluidic channel and a bottom glass slide. The top fluidic channel was 100 μm (height)×50 mm (length)×1.6 mm (width), which was bonded to the bottom glass slide after treatment by oxygen plasma (Hayrick Scientific, Pleasantville, N.Y.).
The size of the large drop 134 can determined as a function of the desired passive-pumping action to induce the desired flow, given the materials used. For example, the large drop 134 cart range from 100 μL to 500 μL. Similarly, the small drop 132 can be determined as a function of the desired flow. For example, the small drop can be a small droplet and can range from 1 μL to 5 μL. Evaporation at the inlet port can be naturally induced, such as the result of ambient environmental conditions or can be actively induced by subjecting the environment adjacent to the inlet port to decreasing pressure or increasing temperature. The length of time that the evaporation-driven backflow is allowed to continue can be determined by the desired length of the concentration gradient. In one example, the time ranged from 10 minutes to 50 minutes and the time of the backflow can be longer than 50 minutes depending on the characteristics of the system and the desired length of the concentration gradient.
Depending on the intended use of the concentration gradient, the microfluidic device can be cooled, frozen, freeze-dried, exposed to UV energy or otherwise processed further to cause the solution in which the gradient was generated to solidify allowing the top portion of the microfluidic device to be removed so that the concentration gradient can be exposed and/or harvested.
In one example according to the invention, the channel was initially filled with Dulbecco's Phosphate Buffered Saline (DPBS, Gibco, Carlsbad, Calif.). A 200 μL drop of DPBS was pipetted onto the outlet opening and a 2 μL drop of DPBS containing the molecule of interest was dropped onto the inlet opening and subsequently entered the channel automatically. After the small drop entered the channel completely, a second drop containing 2 μL was pipetted onto the inlet to continue the forward flow. When the inlet was not refilled, the forward flow would stop and a backflow occurred due to evaporation at the room humidity (˜65%). To visualize the dynamic process of the concentration gradient generation, fluorescein isothiocyanate-dextran (FITC-Dextran, molecular weight (MW): 10 kD) was used as the model molecule, and the fluorescence image series was captured using a Kodak Gel Logic 100 Imaging System, shown in
Computational fluid dynamics was used to simulate the dynamic process of concentration gradient generation using the finite element method (COMSOL Multiphysics v3.2, Burlington, Mass.). Unstructured mesh generation method was performed and 5420 elements were used for constructing the 3D mesh domain. The concentration gradient generation driven by the passive pump and evaporation fluid model was based on the following three equations, including the 3D incompressible Navier-Stokes equations (i.e. the momentum and continuity equations):
and the convection-diffusion transport equation:
where ρ, u, and p are the density, flow velocity and pressure of the liquid, and C and D are the concentration and diffusivity of the molecules in the liquid. At each time step, the flow u is first found independently of the concentration, which is then found using the computed flow. The boundary conditions are as follows. At the inlet, the flow velocity was set to 0.08 cm/s for the forward flow and 10.1 μm/s for the backward flow. These values agree with the average flow rates produced by the passive pump and by evaporation, experimentally observed and analytically calculated (see Appendix A). At the outlet we imposed zero normal stress, and at the channel walls we imposed the no-slip conditions (u=0). For the convection-diffusion equation, constant concentration was set at the channel inlet and zero concentration at the channel outlet. No-flux conditions were imposed at all, channel walls
Table 1 in Appendix A summarizes the input parameters used for the numerical simulations. The channel geometry was set as 5 cm×1600 μm×100 μm and FITC-Dextran was used as the model dye molecules. To quantify the simulation results with time, the concentrations were extracted from the centerline along the channel and normalized with the maximum concentration at the inlet of the channel.
HL-1 cells (Cardiac muscle cell line) were cultured with medium containing 87% Claycomb Medium, 10% Fetal Bovine Serum (FBS), 1% Penicillin/Streptomycin, 1% Norepinephrine, and 1% L-Glutamine at 37° C. in a humidified 5% CO2/95% air incubator. To enhance the cell adhesion, the bottom glass slide was coated with a mixture of extracellular matrix (0.02% gelatin (w/w) and 5 μg/mL fibronectin) after the top channel was bonded to the bottom glass slide. To seed the cells into the microfluidic device, the cells were trypsinized and seeded through the outlet port using dynamic seeding at a cell density of 2×106 cells mL-1 that allowed uniform cell distribution. Cells were cultured for 2 h to ensure attachment. The medium was then changed and 3 drops of 2 μL medium containing 20 mM Alpha-cypermethrin were introduced by passive pumping and a concentration gradient was established by leaving the microfluidic device in the hood for 5 min to allow for evaporation-induced backflow. The microfluidic device was then transferred to a humidified incubator where the concentration gradient of the toxin was stabilized and the cells were treated for 4 h. Cell morphology and viability was characterized by peeling off the top channel and incubating the cells with live/dead dyes (2 μL Calcein AM and 0.5 μL Ethidium homodimer-1, Molecular Probes, California) in 1 mL DPBS for 10 min. ImageJ was used to quantify the fluorescence images of live-dead staining of the cells. At least three images were used for quantification of the cell viability.
In another example, a stable concentration gradient was produced using the process shown in
In this example, the microfluidic channel was initially filled with DPBS, and a 200 μL drop of DPBS was pipetted onto the outlet. A small drop of 2 μL DPBS containing FITC-Dextran was then dropped onto the inlet (
The gradient is generated by dispersion, the combined effect of convection and molecular diffusion, and flow reversal, which changes the direction of the parabolic flow shown in
The timescale for molecular diffusion across a distance L is L2/(π2D), where D is the molecular diffusivity. The timescales for vertical and horizontal mixing of FITC-Dextran across the 100 μm height and 1.6 mm width of the channel are therefore 6 seconds and 25 minutes, respectively. Thus, the chemical concentration is essentially uniform vertically across the microchannel, and it suffices to consider only its horizontal variation, as we have done. The timescale for molecular diffusion across the width of the channel is significantly greater than the duration of the forward flow and commensurate with the timescale of the backward flow. It is therefore instructive to consider the role of the backward flow on gradient generation. After a concentration profile was produced by the forward flow, we compared the concentration profiles obtained after a given duration of backward flow with those obtained instead from the same duration of pure diffusion. The results indicate that the main role of backward flow is to spatially place the gradient. Moreover, the backward flow slightly elongates the gradient by 1%-10%.
To achieve the spatial and temporal control of the dynamic concentration gradients, a particular concentration gradient was stabilized using two methods to stop the flow. As shown in
By preventing evaporation, the flow is stopped and spreading is due purely to (passive) molecular diffusion. The evolution of the concentration profile due only to molecular diffusion is shown over one day in
Estimates can be made of the timescale over which the gradient is maintained, since exact analytical solutions are known for the diffusion equation for any initial concentration gradient. The exact solutions decay exponentially with rate constants approximately equal to π2D/L2, where L is the length scale of the concentration gradient and D is the molecular diffusivity. The concentration gradient is maintained to within 10% of its initial state over a time interval of 0.1L2/(π2D). Centimeter-long concentration gradients of chemicals with molecular diffusivities of 10−7 cm2/s and 10−6 cm2/s remain within 10% of their initial states over time intervals of approximately 28 h and 2.8 h, respectively. These results indicate that stable concentration gradients can be maintained for molecules over a wide range of diffusion coefficients for several hours.
In this example, the stabilized, spatially and temporally controllable concentration gradient technique is utilized for cytotoxicity testing. A cardiac muscle cell line (HL-1) is used to investigate the cytotoxicity of Alpha-cypermethrin, a cardiac toxin. Three drops of 2 μL medium containing 20 mM Alpha-cypermethrin were loaded consecutively into the micro-devices with HL-1 cells seeded along the channel. A concentration gradient of the toxin was established by evaporation when the micro device was left at ambient conditions for 5 min (5 min exposure does not cause severe damage to cell viability) and the gradient was stabilized when the micro device was transferred to the humidified incubator. HL-1 cells exposed to the toxin concentration gradient for 4 h exhibited distinguishable morphologies along the channel, with more severe effects observed in the regions containing higher concentrations of toxin. The drastic morphological change of HL-1 cells exposed to various concentrations of toxin was also observed when the cytotoxicity testing was conducted with HL-1 cells seeded in a 96-well plate. The cytotoxicity of the toxin gradient was further tested on the HL-1 cells by conducting a live-dead assay. A correlation of cell viability was found with the toxin concentration gradient along the channel. According to the correlation between cell viability and morphology changes with respect to Alpha-cypermethrin concentration obtained from the toxicity testing on HL-1 cells seeded in 96-well plates, the experimental conditions used in this example established a concentration gradient of the toxin from 12.5 mM to 0 mM along the 5 cm-length channel based on the assay conducted in this example.
According to the invention, the gradient generation process is highly reproducible at ambient conditions (i.e. 22 C, 30% relative humidity). Variations in temperature and humidity in the laboratory mainly affect the gradient generation process by slightly altering the backward flow rate induced by evaporation; their effects on the forward flow and the diffusion of the molecular are generally considered negligible.
The flow is essentially fully developed Poiseuille flow throughout the rectangular channel. Regions of adjustment to the fully developed flow exist at the ends of the channel. However, based on the Reynolds numbers (0.1 and 0.001) of the forward and backward flows, the extent of these adjustment regions is short: approximately the channel height. Thus, throughout the channel the flow is essentially fully-developed Poiseuille flow.
The concentration gradient profile according to the present invention can be easily altered and controlled by choosing the initial analyte concentration in the applied drops and by manipulating the timing of the forward and backward flow. The factors affecting the flow properties, such as the fluid viscosity, the pressure difference between the inlet and outlet, the rate of evaporation and the geometry of the microfluidic channel affect the gradient generation.
Methods and systems according to an alternative embodiment of the invention utilize a pumping device, such a syringe pump, to drive fast alternating flows which continually lengthen the concentration gradient in the channel. This embodiment of the invention provides for rapidly generating multi-centimeter long concentration gradients along the channel in a simple and portable microfluidic device. Active pumping is provided to drive forward and backward flows in the channel. In addition, active pumping can be used to rapidly generate long cross gradients of two gradient materials in the channel of a simple and portable microfluidic device.
In accordance with this embodiment, fluidic shear-driven stretching, also known as hydrodynamic stretching, is the primary mode of gradient generation. A particle in the center of the channel moves faster than one at the wall and the two spread apart at a rate proportional to the maximum channel velocity. As shown in
The spreading of gradient material in a microfluidic channel involves both hydrodynamic stretching (advection) and diffusion, a combined process known as dispersion as shown in
In a channel of uniform cross-section characterized by a height scale H and width scale W, where we assume without loss of generality that H≦W, three different regimes of dispersion exist: a short time regime t<<H2/D where diffusion is not important, molecules follow the streamlines, and gradient growth is linear; an intermediate time interval H2/D<<t<<W2/D over which the molecules spread over the channel height; and a long time regime t>>W2/D, called Taylor-Aris dispersion, over which molecules have sampled the entire channel cross-section. In one example, the channels are rectangular with a height H=100 μm and width W=2 mm, with molecules of diffusivity D ˜10−7 to 10−6 cm2 s−1. Thus H2/D is seconds to minutes and W2/D is hours to days. Since the concentration gradients are generated in seconds to minutes, their evolution falls in the early to intermediate dispersion regime. Approximate theoretical descriptions valid for early, intermediate, and late times exist for many geometries, including rectangular channels, cylindrical tubes, and channels with smooth cross-sections. In these approximate theories, the cross-sectionally averaged concentration has the classic erfc profile (Appendix B, II.3c) with a dispersivity {tilde over (D)}, which plays the role of an effective diffusivity, though orders of magnitude larger than the molecular diffusivity. The theories listed above give different forms for the dispersivity depending on the time regime and the geometry. All theories listed are for uni-directional flow; the effects of flow reversal can be computed numerically.
To rationalize the experimental findings and to provide general experimental design criteria, a computational model was developed for the advection and diffusion of a diffusible species in sequences of forward and backward flow segments across a wide range of channel geometries and Pe'clet numbers (Appendix B, II.3d). Dimensional analysis reduces the parameter space to four dimensionless parameters: W/H, Pe, Re, L/H (Appendix B, II.1). In accordance with the invention, the Reynolds number Re=UH/v which quantifies the relative magnitudes of fluid inertia and viscosity, is 0.1 or less. Thus, throughout the rectangular channel the flow is essentially fully developed laminar Poiseuille flow, a textbook exact solution to the Navier-Stokes equations governing the fluid flow (Appendix B,
), 0.62 (+), 0.58 (∘) mm/s from left to right) and corresponding simulations (W/H=20, Pe=1889, 1457, 1333, 884, 734, 476, 450 from left to right); iv) gradient length along centerline of channel after fluid travels x=2.34 cm for experiments (∘), simulation (
vertically averaged centerline concentration, - - cross-sectionally averaged concentration), and fitting formula (-•-);
In order to facilitate rapid gradient growth, higher flow rates dominate diffusion to generate longer gradients, even if the total distance the fluid moves along the channel is kept constant. This was quantified experimentally by producing gradients of FITC-Dextran with different flow rates, and theoretically with numerical simulations. Fluorescent images of the microchannel were captured at 5 s intervals (
For diffusible gradient materials in a finite channel, additional gradient growth can be obtained by subsequence backward and forward flow segments (
By combining material engineering technologies, the high-speed gradient generation method according to the invention was used to create material gradients of synthetic and natural polymers with controlled property variations. In each example, a concentration gradient of precursor solution of a material was first generated in accordance with one embodiment of the invention and then polymerized by the appropriate cross-linking method.
The gradient platform according to the present invention can also be used to produce material gradients of various microparticles. Using high flow speeds (mm/s), gradients of endothelial cells and 5 μm and 10 μm microbeads were generated along the channel (
The gradient platform according to the present invention allows cross-gradients to be formed by loading one species in one port, creating a single gradient on the forward flow, loading a second species in the opposite port and reversing the flow to create crossing gradients.
In one example, this method was used with four flow cycles to generate a 2 cm cross-gradient of the fluorescent dyes FITC-Dextran (mw 10 KDa) and Rhodamine-Dextran (mw 10 KDa) (
To facilitate the design of gradient devices, the following approximate formula can be used to estimate gradient length, Δ(t)/H=3.6√{square root over ({tilde over (D)}τ)}, where τ=tD/H2 is the dimensionless diffusive time and the dimensionless dispersivity is
(see Supp. II.2c for details). The formula for D was originally found to be an excellent approximation for the dispersion between parallel plates, uniformly valid in time. An example of a table of the added fitting coefficients a and b is provided in Appendix C. For each W/H and Pe, values that best fit our numerical simulation of Δ(t) were chosen (Appendix B,
While hydrodynamic stretching creates long gradients in seconds, the gradients produced may not be perfectly laterally uniform. The lateral (cross-sectional) non-uniformity is quantified by the distance σ between the x-locations of concentration c=0.5 at the channel centre and at the wall. Appendix B,
In accordance with the invention, the channel size can affect the time required to generate a gradient of a given length Δ. In the absence of diffusion, the gradient length evolves as 1.2Ut, given above, which is independent of the channel dimensions provided the average flow speed U is kept constant. Generating a gradient of length Δ requires Δ/1.2U time. For non-diffusible species, a uniform gradient is formed once the particles settle to the channel bottom, and hence the settling time scales as the channel height. For diffusible species, increasing the smallest dimension of the channel, defined here as the height H, while keeping U constant increases the Péclet number and enhances hydrodynamic stretching. However, achieving a uniform gradient requires lateral diffusive mixing. While flow reversal may be used to render the gradient uniform across the largest lateral dimension of the channel, defined here as the width, to avoid collapsing the gradient diffusive mixing must first complete across the height, which requires a time H2/(π2D). Thus while scaling up may enhance the hydrodynamic stretching, the total time to generate a uniform gradient scales as the channel height H for non-diffusible species and as H2 for diffusible species, where H is the smallest dimension of the channel.
For completeness, we comment on the effects of other parameters on gradient evolution. The Reynolds number Re=UH/v and the scaled channel length L/H do not directly affect the concentration profile and gradient evolution. The analytic solution for the fully developed flow profile has the special property that the convective derivatives in the Navier-Stokes equation vanish and hence so does the dependence on the Reynolds number. Moreover, since the flow solution is independent of the longitudinal coordinate x, the role of the channel length is merely to provide a stopping point once the gradient reaches the end of the channel. Thus while the channel length L/H affects the choice of time sequence, it does not directly affect the concentration profile. Lastly, temperature affects gradient formation through its effect on the diffusion coefficient.
Poly(ethelyene glycol-diacrylate) with Molecular Weight 4000 is available from Monomer-Polymer & Dajac Labs. The photo-initiator (PI), 2-hydroxy-1-[4-(hydroxyethoxy)phenyl]-2-methyl-1-propanone (Irgacure D2959), is available from Ciba Geigy (Dover, N.J.). Polyethylene microtubing (I.D. 0.38 mm, O.D. 1.09 mm) is available from Intramedic Clay Adams (Becton Dickinson & Co, MD). Green Fluorescent FITC-microbead and non-fluorescent microbead solutions are available from Polysciences (Warrington, Pa.). Human Umbilical Vein Endothelial cells (HUVECs) and endothelial cell basal medium (EBM-2, Clonetics) supplemented with 0.5 mL vascular endothelial growth factor (VEGF), 0.2 ML hydrocortisone, 0.5 ML epidermal growth factor (rhEGF), 0.5 ML ascorbic acid, 2.0 ML r-human fibroblast growth factor-B (rhFGF-B), 0.5 ML heparin, 0.5 ML recomb long R insulin-like growth factor (R3-IGF-1) and 0.5 ML gentamicin sulfate amphotericin-B (GA-1000) are available from Lanza (Basel, Switzerland). All other reagents are available from Sigma-Aldrich (St. Louis, Mo.) unless specifically mentioned.
In accordance with one embodiment of the invention, the microfluidic device includes a microchannel was fabricated by standard soft lithography methods as described above. It includes a top Polydimethylsiloxane (PDMS) fluidic channel that was plasma bonded to a bottom glass slide. Preferably, the rectangular channel dimensions were 100 μm (height)×2 mm (width)×50 mm (length), although other channel dimensions can be used.
In accordance with one embodiment of the invention, the microchannel was pre-filled with 1× Dulbecco's Phosphate Buffered Saline (DPBS) solution. 1% wt fluorescein isothiocyanate-dextran (FITC-dextran) solution was introduced into the channel in one or more a cycle. Each cycle can include a forward flow, a delay, and a backward flow pumping sequence, for example: 4.67 μl of the solution was pumped in (inducing forward flow) at 0.009 ml/min flow rate, wait 30 s of down time, and 2 μl of the solution was withdrawn (inducing backward flow) at 0.022 ml/min flow rate. The cycle can be repeated as needed to increase the length of the concentration gradient, however, for this example, it was not needed. After the last cycle, there was a wait of 30 s for down time, and 1.34 μl of the solution was pumped in (inducing forward flow) at 0.035 ml/min flow rate. The solution was pumped in and withdrawn using a syringe pump (World Precision Instruments Aladdin 1000, WPI, FL) and the flow rates were calibrated with a flow meter (from Gilmont Instrument, IL). The inlet and outlet ports can then be covered with oil or exposed to a 100% humidity environment to preserve the concentration gradient.
In accordance with one embodiment of the invention, microbead stock solutions containing microbeads with diameters in 5.0 and 9.91 μm (with a solid fraction of 0.1% w/w) were diluted 10 times in DPBS. The microfluidic device was the same as described above, a PDMS top portion bonded to a glass slide bottom portion. A syringe pump and flow meter were used to pump and withdraw the gradient material solution and measure the flow rates. In this embodiment, 6 μL of the microbead solution was pumped into the channel at a rate of 0.035 ml/min, followed by a 30 s downtime before 4 μL of the solution was withdrawn back into the tubing. 4 μL of the fluid was pumped, then withdrawn, and finally pumped again into the channel with a 30 s downtime between flow cycles.
In an alternative embodiment of the invention, HUVECs were cultured in endothelial cell basal medium at 37° C. in a humidified incubator. The protocol for generating cell gradients was similar to microbead gradients. The HUVEC medium was used in place of DPBS as the background solution and a medium containing HUVECs (5×106/ml) after trypsinization was used as the gradient material.
In accordance with one embodiment of the present invention, a concentration gradient of hydrogel precursor solution (with high concentration of 40 wt % PEG-DA in DPBS and 1% PI) was first generated at 0.022 ml/min using the above-mentioned flow sequences for FITC-Dextran. To ensure the integrity of gradient in the hydrogel, 5 wt % PEG-DA solutions were pre-filled in the channel. Upon photo-polymerization (UV exposure: 10 mW/cm2 for 20 s), the hydrogel precursor concentration gradient was cross-linked. For characterization, the resultant hydrogel was air-dried, cut with a scalpel blade to obtain a cross section, sputter-coated with gold and imaged using SEM (ULTRA 55, ZEISS). The thickness of the hydrogel was quantified relatively to the scale bar in the SEM image using ImageJ.
In accordance with one embodiment of the present invention, the flow condition for generating PEG-DA hydrogel gradient was used to generate collagen concentration gradient (from 0.5 mg/ml to 3.8 mg/ml). Collagen fibers were formed upon gelation for 30 min in the incubator (37 C). The device containing the collagen gradient was then pre-frozen at −20 C for 10 min and demoulded, exposing the collagen gradient. The collagen gradient was further frozen at −80 C for 2 hr and then freeze-dried in a lyophilizer. The morphology of the collagen gradient was visualized by SEM.
In accordance with one embodiment of the present invention, a concentration gradient was generated from a solution containing 1 wt % FITC dextran (MW: 10 KDa) gradient material as described above. In accordance with the invention, the second gradient material, Rhodamine-Dextran (MW: 10 KDa) is introduced at the outlet port by withdrawing a predefined quantity of solution from the inlet port. In this embodiment, 200 μL Rhodamine-Dextran (MW: 10 KDa) solution (1 wt %) was pipetted onto the outlet port of the channel and 6 μL Rhodamine-Dextran solution was withdrawn into the channel from the outlet at a flow rate of 0.022 ml/min with a syringe pump which was connected to the inlet of the channel. The solution (6 μL) withdrawn into the tube was pumped back into the channel substantially immediately. This cycle of backward and forward flow induced by the pumping process was conducted for three times. The channel containing the cross-gradient of the double dyes was stabilized at least 30 s before visualization. A series of continuous fluorescent images along the channel were taken using the green filter and red filter of the fluorescent microscope respectively and then were stitched together using Photoshop. The merged double dye cross-gradient was further quantified using ImageJ. To create the cross gradient of microbeads, 5 μm diameter FITC-microbeads and non-fluorescent beads were diluted 20 times. The similar protocol as for creating FITC-dextran/Rhodamine-Dextran was followed except that a higher flow rate of 0.035 ml/min was used and only one flow cycle was conducted.
Generation of Composite Materials with Cross-Gradient of HA and Gelatine.
In one embodiment of the present invention, Hyaluronic acid and gelatin were methacrylated to be photo-crosslinkable as described previously. 2 wt % methacrylated HA solution (containing 1 wt % PI) was pre-filled into the channel and 2 wt % methacrylated gelatin (1 wt % PI) was added onto the outlet of the channel. HA and gelatin cross gradient was formed as mentioned above for FITC-dextran/Rhodamine-Dextran cross-gradient and stabilized upon photo-polymerization (UV exposure: 10 mW/cm2 for 60 s). Smooth muscle cells (SMC) were cultured in SMC basal medium (RPIM 1640, Gibco) at 37° C. in a humidified incubator. Upon trypsinization, the cells were seeded in a density of 1×104 cells/cm2 on the surface of HA-gelatin composite hydrogels. After 24 h of incubation, the hydrogels were rinsed with sterile PBS for three times to wash away unattached cells and then fixed with 3.7% formaldehyde solution. A series of continuous phase contrast images along the channel were taken using microscope and then were stitched together. Cells were quantified by counting attached cell number using ImageJ.
In accordance with the invention, the pump can be controlled by a controller, such as a computer, and the flow cycles can be programmed such that the flow cycles are completed automatically. Other types of pumps can be used.
Other embodiments are within the scope and spirit of the invention. Features implementing functions may also be physically located at various positions, including being distributed such that portions of functions are implemented at different physical locations.
Further, while the description above refers to the invention, the description may include more than one invention.
This application claims any and all benefits as provided by law of U.S. Provisional Application No. 61/114,539 filed Nov. 14, 2008, the entire contents of which are hereby incorporated by reference in its entirety.
This invention was made with government support under Grant Nos. 103577, HL092836, DE019024, and EB007249 awarded by the National Institutes of Health. The US Government has certain rights in this invention.
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/US09/64555 | 11/16/2009 | WO | 00 | 8/4/2011 |
| Number | Date | Country | |
|---|---|---|---|
| 61114539 | Nov 2008 | US |
