Technical Note pubs.acs.org/ac
Easy Monitoring of Velocity Fields in Microfluidic Devices Using Spatiotemporal Image Correlation Spectroscopy Marco Travagliati,*,†,‡ Salvatore Girardo,§ Dario Pisignano,§,⊥ Fabio Beltram,†,‡ and Marco Cecchini*,† †
NEST, Scuola Normale Superiore and Istituto di Nanoscienze - CNR, Piazza San Silvestro 12, I-56127 Pisa, Italy Center for Nanotechnology Innovation @ NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, I-56127 Pisa, Italy § National Nanotechnology Laboratory of Istituto Nanoscienze-CNR, Universitá del Salento, via Arnesano, I-73100 Lecce, Italy ⊥ Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Universitá del Salento, via Arnesano, I-73100 Lecce, Italy ‡
S Supporting Information *
ABSTRACT: Spatiotemporal image correlation spectroscopy (STICS) is a simple and powerful technique, well established as a tool to probe protein dynamics in cells. Recently, its potential as a tool to map velocity fields in lab-on-a-chip systems was discussed. However, the lack of studies on its performance has prevented its use for microfluidics applications. Here, we systematically and quantitatively explore STICS microvelocimetry in microfluidic devices. We exploit a simple experimental setup, based on a standard bright-field inverted microscope (no fluorescence required) and a high-fps camera, and apply STICS to map liquid flow in polydimethylsiloxane (PDMS) microchannels. Our data demonstrates optimal 2D velocimetry up to 10 mm/s flow and spatial resolution down to 5 μm.
L
confocal microscope equipped with a photon-counting board, and in order to map the velocity over several micrometers, it requires rather long measurement times. Moreover, standard FCS (single focus FCS, 1f-FCS) can only measure the velocity magnitude, while more sophisticated set-ups (dual focus FCS, 2f-FCS, or fluorescence cross-correlation spectroscopy, FCCS) are required to measure velocity direction.19,20 Spatiotemporal image correlation spectroscopy (STICS) is an alternative correlation technique that was developed for measuring protein dynamics and interactions21,22 and can probe direction and magnitude of velocity fields. Recently, this technique was also applied to monitor the velocity field of a microfluidic device with an experimental setup that stands out for its simplicity: a simple bright-field microscope equipped with a fast camera.23 These authors demonstrated that STICS can measure the spatially averaged flow velocity in a straight rectangular microchannel at different applied flow velocity (up to 1 mm/s),23 but no discussion was reported about measurement accuracy or its dependence on experimental and computational parameters. Here, we systematically and quantitatively assess the performance of STICS microvelocimetry for microfluidic applications. Data were acquired by a simple experimental
ab-on-a-chip (LOC) technologies represent an advanced tool that can significantly impact several rather diverse research areas.1,2 Among these, biology is probably the field of choice for LOC applications: several traditional assays have already been miniaturized within micrototal analysis systems (μTAS);3 high-throughput devices were designed for parallel biomolecule screening,4 and a variety of biomimetic LOC devices were realized to study complex cellular cultures.5,6 At the heart of this success is the capability to control the properties of fluid-velocity fields at the microscale allowing a precise spatial and temporal modulation of chemical-concentration7,8 and shear-stress profiles.9−11 Hence, development of rapid and easy methods to measure fluid-velocity fields prior or during biological experiments is of paramount importance. Several techniques were developed in the past decade to measure the velocity field inside microfluidic devices for both fundamental fluid-dynamics studies and device testing. Among them, micro-particle image velocimetry (μPIV) represents the gold-standard technique,12−14 but unfortunately its implementation requires rather expensive fluorescence-based setups. Fluorescence correlation spectroscopy (FCS) is an established imaging technique15,16 that is commonly used in biology to investigate dynamics and interactions of intracellular and transmembrane proteins.17,18 FCS stands out for its spatial resolution, which is around 250 nm in the lateral direction and 1 μm along the vertical one, over velocity fields from ∼10 μm/s to ∼1 m/s, with sensitivity down to single fluorescent molecules. This performance relies on the availability of a © 2013 American Chemical Society
Received: July 1, 2013 Accepted: August 6, 2013 Published: August 6, 2013 8080
dx.doi.org/10.1021/ac4019796 | Anal. Chem. 2013, 85, 8080−8084
Analytical Chemistry
Technical Note
Figure 1. Schematic of the workflow for spatiotemporal image correlation spectroscopy (STICS) analysis. A 2D-image time stack represents the input raw data in the real space (x, y, t). The time stack is split into different interrogation areas, or regions of interest (ROI), over which the velocity is estimated separately to produce the final map. For different delay time τ, the frame t and the frame t + τ are spatially cross-correlated for every time point t. Finally, all the pair cross-correlations (t, t + τ) are averaged to obtain the final spatiotemporal correlation function (STCF).
compared to that of the suspension fluid.23 As in the case of μPIV,12−14 the diameter and density of the tracers must be chosen so that they can accurately follow fluid motion. Our experimental setup comprises a standard inverted transmission microscope (Olympus IX71) with a 40×, numerical aperture NA = 0.75, air objective and a Photron APX RS camera. The image time stacks were acquired at 3000 fps with texp =0.3 ms exposure time and 1024 × 1112 pixel resolution (pixel-size = 0.33 μm). Therefore, in our experiments, texp is equal to the time interval between two successive frames (Δtframes). The microfluidic apparatus consists of a syringe pump (Harvard Apparatus, Model 33) connected via Tygon tubings to a 216 μm-wide and 20 μm-high straight polydimethylsiloxane (PDMS) microchannel fabricated by replica molding from a silicon master realized by photolithography. The microchannel was covalently bonded to a glass coverslip by using oxygen plasma treatment. Unless otherwise stated, the experiments were performed using a suspension of water and 500 nm-latex beads (Sigma-Aldrich L3280) with 4 × 1010 particle/mL concentration. The tracer size is of the same order of the pixel-size for our optical setup (500 nm ∼ 1.5 pixels). In order to assess the actual performance of STICS velocity mapping, none of the outlier filters usually used in velocimetry was applied. Figure 2a shows a characteristic STICS velocity map obtained for a flow rate of 1.5 μL/min and for an image sequence of 200 frames. Calculations were carried out on a grid of points separated by 2.5 μm × 30 μm using 5 μm × 60 μm ROIs. This flow regime is described by the Hagen−Poiseuille equation for a rectangular channel,24
setup based on a standard bright-field inverted microscope (no fluorescence required) and a high-fps camera. We report how experimental conditions (such as exposure time, measurement time, particle concentration) and analysis parameters (such as interrogation area, time delay, peak and velocity calculation algorithm) determine measurement accuracy. Figure 1 illustrates the principle of STICS analysis. First, raw data, a time stack of 2D microscopy images, is preprocessed by normalizing the intensity of each frame (to remove light source fluctuations) and subtracting the time-averaged value of each pixel (to filter stationary objects). Then, the time stack is split into different interrogation areas, or regions of interest (ROI), over which the velocity is estimated separately to produce the final map. The spatiotemporal correlation function (STCF) is calculated for each ROI as:23 STCF(ξ , η , τ ) =
⟨δi(x , y , t )δi(x + ξ , y + η , t + τ )⟩x , y ⟨i(x , y , t )⟩x , y ⟨i(x , y , t + τ )⟩x , y
t
where i(x, y, t) is the intensity of the pixel at spatial coordinates x, y at the time t and the intensity fluctuation is defined as δi = i − ⟨i⟩x,y where ⟨...⟩ is the average operator. For a fixed delay time τ, the frame t and the frame t + τ are spatially crosscorrelated for every time point t. Finally, all the pair crosscorrelations (t, t + τ) are averaged to obtain the STCF. All intensity fluctuations that in real space have the same displacement Δx⃗ = (Δx, Δy) in the same time interval Δt contribute to generate a peak in the STCF(ξ,η,τ = Δt) located in ρ⃗ = (ξ = −Δx, η = −Δy). Thus, their velocity can be obtained as ν⃗ = −ρ⃗/τ. The resulting velocity map is therefore composed by vectors that result from averaging the velocity over the ROI and the total measurement time. This limits the technique to stationary fields over the measurement time with negligible variations over the ROI domains. Intensity fluctuations in the image real space can originate from a fluorescently labeled object21,22 or, in the case of bright-field microscopy, from tracers with different refractive index
vy(x , z) =
4h2Δp π 3μL
∑ n ,odd
cos h(nπx /h) ⎞ ⎛ nπz ⎞ 1⎛ ⎟ 1 − ⎜ ⎟sin⎜ cos h(nπw/2h) ⎠ ⎝ h ⎠ n3 ⎝ (1)
where w and h are, respectively, the channel height and width, Δp is the pressure drop between the ends of the channel separated by a distance L, and μ is the fluid dynamic viscosity. 8081
dx.doi.org/10.1021/ac4019796 | Anal. Chem. 2013, 85, 8080−8084
Analytical Chemistry
Technical Note
focus can be estimated using the formula developed by Olsen and Adrian for PIV,25 δ=2
(v − 0.9v)τ > σ
τ > τmin =
(5)
texp 0.1
∼ 9Δtframes
(6)
For time delays τ < τmin, the STICS velocity is underestimated owing to the broadening of the correlation peak caused by “outof-focus” slower particle dynamics, as shown in Figure S1, Supporting Information. In order to avoid underestimating the velocity, we modified the previously reported STICS algorithms.21,22 Usually, velocity is obtained by linear interpolation of the correlation peak position ρ⃗ versus τ, where the peak position is obtained by a Gaussian fit of the STCF at τ. Our algorithm calculates the velocity as ν⃗ = −ρ⃗/τ for the value of τ which is just below the delay time that the STCF maximum moves off the ROI or decreases to the camera noise value. Moreover, in order to avoid the contribution of secondary peaks related to slower particles and to decrease calculation time, we estimated the main peak position by a three-point Gaussian estimator of the STCF maximum. Using the time interval τmin of eq 6 in eq 2 and l = 60 μm, we obtain vmax ∼ 10 mm/s, in agreement with the data of Figure 2c. Equation 2 can also be rearranged to establish the maximum spatial resolution for a certain velocity:
−σ (2) τ where σ is the cross-correlation particle peak width given by 2
σ = d p + v ·texp
(4)
In the velocity range of our experiments, given our exposure time texp = Δtframes, eq 3 reduces to σ ∼ v·texp; therefore, from eq 5,
As demonstrated in Figure 2b, the measured STICS velocity profile agrees remarkably well with the theoretical prediction. According to eq 1, for our microchannel geometry, v does not vary significantly (less than 1%) in the region −60 μm < x < 60 μm. Figure 2c reports the measured velocity averaged within this region for 10 independent experiments as a function of the flow rate, calculated on a 12.5 μm × 30 μm grid with 25 μm × 60 μm ROIs. The expected linear relationship between the measured velocity and the applied flow rate is observed up to 3 μL/min (v ∼ 10 mm/s) for this spatial resolution. Indeed, STICS spatial resolution and maximum measurable velocity are not independent because the maximum displacement of the peak in the correlation space can be up to half the length of the ROI size l: l
2 2 ε ) ⎛⎜ n d p 5.95(M + 1)2 λ 2n 4 ⎞⎟ + ⎜ 4NA4 ⎟ ε 16M2 NA4 ⎝ ⎠
where NA and M are the numerical aperture and the magnification of the objective, respectively, n is the refractive index of its immersion medium, λ is the light wavelength, and ε ∼ 0.01 is the relative threshold below which defocused particles do not significantly contribute to the displacement-correlation peak.12 This means that the particles contributing to the displacement-correlation peak lie between the planes z = z0 ± δ/2, where z0 is the focal plane. In our case, z0 = 10 μm (in the center of the microchannel) and δ ∼ 4 μm; therefore, in the image sequence, we have particles with velocity, according to eq 1, between 0.9v and v, where v is the velocity calculated at z = 10 μm. In order to separate at least the contribution of the population with the largest velocity reduction (0.9v), the corresponding peak in the correlation space must be separated by more than σ from the peak originating from the population with velocity v:
Figure 2. Demonstration of dynamic range and spatial resolution of STICS measurements. (a) Representative velocity map on a 2.5 μm × 30 μm (5 μm × 60 μm ROIs). (b) Y-averaged velocity profile (black) calculated from data of panel (a) and its theoretical prediction (eq 1, red line). Curve fitting (reduced-χ2 = 3.02) has been performed assuming z = 10 μm and leaving only the prefactor 4h2Δp/(π3μL) and the center position of the microchannel x0 = (2.8 ± 0.1) μm as freeparameters. (c) Average velocity (−60 μm < X < 60 μm) over 10 experiments as a function of the flow rate. Data has been calculated on a 12.5 μm × 30 μm grid (25 μm × 60 μm ROIs). (d) Nondimensional analysis of the velocity estimated by STICS as a function of the ROI size for different flow rates (see text for details).
vmax ∼
(1 −
lmin = σ + 2vτmin
(3)
(7)
In Figure 2d, the velocity v(l) obtained by using different l values is plotted as a function of the dimensionless parameter l/ (Δt·vreal), where vreal = v(l ≫ lmin). In order to compare the results for different flow rates, velocity was normalized to vreal. We observe that velocity as a function of this dimensionless parameter follows a universal curve that does not depend on the applied flow rate and the velocity is underestimated for l/ (Δt·vreal) ≳ 20, in agreement with eqs 6 and 7. The universality of the curve stems from the independence of τmin on v. Table 1 reports the relative standard deviation (RSD), defined as the relative standard deviation of v for −60 μm < x
