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OPTICS LETTERS / Vol. 32, No. 17 / September 1, 2007
Three-dimensional chemical concentration maps
in a microfluidic device using two-photon
absorption fluorescence imaging
Dawn Schafer,1,* Emily A. Gibson,2 Wafa Amir,1 Rebecca Erikson,1 Jodi Lawrence,1 Tor Vestad,3
Jeff Squier,1 Ralph Jimenez,2 and David W. M. Marr3
1
Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
Department of Chemistry and Biochemistry and National Institute of Standards and Technology,
University of Colorado, Boulder, Colorado 80309, USA
3
Department of Chemical Engineering, Colorado School of Mines, Golden, Colorado 80401, USA
*Corresponding author: dschafer@mines.edu
2
Received June 25, 2007; accepted July 16, 2007;
posted August 6, 2007 (Doc. ID 84458); published August 22, 2007
Two-photon absorption fluorescence is employed within a microfluidic device to create a three-dimensional
chemical concentration map for mixing uniformity characterization. This multiphoton technique images
fluorescence intensity directly and provides a simple, rapid, and readily employed route to composition characterization within microfluidic systems. © 2007 Optical Society of America
OCIS codes: 190.4180, 180.2520.
Microfluidics have been successfully utilized to study
reaction kinetics over time scales from microseconds
to minutes [1,2]. Though microfluidic environments
provide extreme sample confinement and precise
mixing control, each microfluidic design has a characteristic mixing time (or dead time) corresponding
to the minimum resolvable reaction time. In addition,
the detection volume typically overlaps many
streamlines within the channel in which significant
mixing variations may exist. The resulting incoherent summation of signals sets a limit on the temporal
resolution. Therefore it is necessary to characterize
variations in reaction extent due to nonuniform mixing before accurately quantifying uncertainty in measured reaction kinetics [3–5].
In an attempt to study variation problems in dynamic systems, significant work has been done to
characterize three-dimensional (3D) fluid flow in microfluidics including particle image velocimetry and
scalar fluorescence studies [6–9], each a method that
visualizes flow fields. However, when studying reaction kinetics, it is also critical to monitor concentration directly because reactions are typically initiated
by changes in chemical concentration rather than by
changes in velocity. Unlike velocity, chemical concentration differences between streamlines diminish as
the molecules flow downstream due to mass diffusion. A number of detection methods have therefore
been employed to assess mixing uniformity including
light microscopy [4], confocal fluorescence microscopy
[10], optical coherence tomography (OCT) [11], and
fluorescence lifetime imaging [12]. Compared with
other published 3D imaging techniques, studies
based on fluorescence intensity have reduced complexity in optical detection and in data analysis. Twophoton absorption fluorescence, for example, is well
suited for mixing characterization because it provides full depth 3D imaging and often has greater
resolution than OCT when the numerical aperture is
tailored to match the aspect ratio of the channels.
0146-9592/07/172568-3/$15.00
Furthermore, the systematic error associated with
fluorescence measurements in microchannels, due to
position-dependent refractive losses caused by indexmismatched interfaces, is removed by taking the ratio of two intensity values rather than the absolute
value of the intensity. Conversion between fluorescence intensity and chemical concentration is
straightforward for a first-order quenching reaction.
In this Letter the concentration of potassium iodide,
a quickly diffusing quencher (diffusivity 2
⫻ 10−9 m2 / s), was mapped in 3D by monitoring the
fluorescence emission of rhodamine 6G conjugated to
dextran (MW 70,000), a slow diffuser. This is, to our
knowledge, the first demonstration of two-photon absorption fluorescence imaging for 3D mixing characterization in a microfluidic.
The multiphoton microscope setup is illustrated in
Fig. 1(a). The excitation light was generated by a
home-built Nd:glass laser delivering 50 mW, 150 fs
Fig. 1. (Color online) (a) Schematic of two-photon absorption fluorescence microscope setup and (b) optical detection
geometry.
© 2007 Optical Society of America
September 1, 2007 / Vol. 32, No. 17 / OPTICS LETTERS
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pulses centered at 1064 nm. Lenses L1 and L2 reduced the beam diameter to underfill the 0.65 NA objective while lenses L3 and L4 imaged the beam from
scanning mirrors to the back of the objective. These
scanning mirrors rastered the beam across the
sample in x and y in full field of view of the objective
while an automated z-stage positioned the sample for
imaging at different depths. Figure 1(b) illustrates
the microfluidic geometry and defines the axes referenced throughout the paper. Channel cross-section
dimensions are 19 ␮m wide (y axis) and 37 ␮m deep
(z axis). We determined the confocal parameter of the
imaging system to be 8 ␮m by measuring the fluorescence change upon scanning the laser focus axially
across the interface between the sample and glass
coverslip. The calculated focal spot size is 1.6 ␮m,
providing a 0.79 ␮m lateral resolution for two-photon
imaging. A BG39 filter blocked the transmitted
1064 nm excitation light, and a photomultiplier
(PMT) collected the fluorescence in transmission. The
optical signal was integrated for 30 ms at each data
point, providing a 20:1 signal to noise ratio.
We constructed microfluidic devices using softlithography techniques [13,14], fabricating the template in SU-8 2050 photoresist on a silicon wafer.
Polydimethylsiloxane (PDMS) was poured onto the
template, heat cured, removed, and then chemically
bonded to a fused-silica microscope slide after exposure to oxygen plasma. High-pressure silicone tubing
was cured into the PDMS to connect the pressurized
sample reservoirs to the microfluidic for pumping
fluid. A pressure controller (Marsh-Bellofram) applied 17.5± 0.15 psi to the sample reservoirs.
For quantitative measurements of the mixing dynamics, we mixed a fluorescent dye with a quenching
species and measured the change in intensity. A
100 ␮M solution of dextran-conjugated rhodamine
6G (chosen for its large absorption cross section at
the two-photon wavelength [15]) in a 100 mM phosphate buffer (pH 7) was sent down the center channel
and hydrodynamically focused with either buffer only
or with a 500 mM potassium iodide (KI) solution.
Three-dimensional images were collected for the two
separate cases of mixing with and without the KI
quencher as shown in Fig. 2.
The relative fluorescence intensity change upon
mixing was related to KI concentration using the
Stern–Volmer model, 关Q兴KSV = q0 / q − 1, where Q is the
concentration of the quencher, KSV is the Stern–
Volmer constant, and q0 and q are the unquenched
and quenched fluorescence intensities [16]. KSV was
found experimentally by measuring the fluorescence
of the dye as a function of KI concentration and applying a least-squares fit 共KSV = 4.8± 0.26 M−1兲. The
KI concentration determined from experimental fluorescence measurements for a two-dimensional slice
in x and z at the center width of the channel is shown
in Fig. 3(a), while Fig. 3(b) shows the prediction from
fluid dynamics modeling. The simulated data were
subject to the same data averaging as the experiment, namely, convolution with our axial spot shape
and nearest-neighbor data averaging. Computational
models were made using COMSOL multiphysics finiteelement analysis software. Within the chemical engineering module, steady-state incompressible Navier–
Stokes and convection and diffusion partial
differential equations were solved uncoupled. To take
advantage of the rectangular channel cross sections,
we used mapped meshes of element size 24 ␮m3.
When experiment is compared with model, the
same trends are noted; however, measured KI concentration does not rise to as high of a value as the
simulated data does uniformly. The scan length of
114 ␮m is the full field of view of our system. Experimentally the scan area could be increased along the x
direction to view the complete mixing dynamics by
stepping the device in x and combining the data sequentially. There is an asymmetry in the experimental data, which may be a result of imperfections in
the microfluidic device. This type of measurement,
therefore, demonstrates the need for experimental
characterization of each microfluidic device before
Fig. 2. Three-dimensional fluorescence images showing
(a) unquenched and (b) quenched cross sections across the
channel width and (c) unquenched and (d) quenched cross
sections across the channel depth. Channel outlines are superimposed on the figures. Fluorescence intensity is
normalized.
Fig. 3. Distribution of KI concentration as a function of x
and z at the center width of the channel 共y = 0兲 (a) measured
experimentally and (b) calculated from 3D modeling. The
zero position along the x axis corresponds to the beginning
of the mixing junction.
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OPTICS LETTERS / Vol. 32, No. 17 / September 1, 2007
making quantitative measurements of reaction dynamics.
The accuracy of the simulated data is dependent
upon the validity of simplifying assumptions, specifically, constant diffusivity, density, and viscosity, as
well as perfect channel walls with no slip. The next
steps for improving the simulation may be an evaluation of slip at PDMS and glass interfaces [7] and an
investigation of the concentration dependence of potassium iodide’s diffusivity [17]. Errors in measured
experimental parameters used in the model must
also be taken into account, including measured KSV,
channel dimensions, initial concentration, and bulk
flow rate. By first-order error analysis, uncertainty in
each measured experimental parameter was related
to uncertainty in predicted KI concentration. Since
predicted KI concentration has a different value for
each spatial point, the following are the maximum
uncertainty values in the measured region: ±12 mM
for a 0.26 M−1 uncertainty in KSV, ±10 mM for a 3
⫻ 10−6 cm3 / s uncertainty in the bulk flow rate, and
±25 mM for a 4 ␮m uncertainty in the channel width.
This channel width uncertainty is equivalent to a 5%
slope in the sidewalls over the channel height. A sloping to the channel walls is the most likely source of
disagreement between measured and predicted KI
concentration and is a common artifact of softlithography fabrication. Models made with these assumptions and experimental parameters can project
expected mixing variations, but they cannot compensate for the entirety of the complex mixing environment elucidated by experiment.
Significant mixing variation exists in the axial dimension in this microfluidic device. Although mixing
uniformity was not achieved within the imaged region, the predicted mixing time at center width and
depth 共y = z = 0兲 is 3.6 ms (defining the mixing time as
the time to pass between 10% and 90% of equilibrium
concentration). The variation in mixing times between streamlines encompassed by the FWHM of our
axial spot size is 0.12 ms. Mixing variations play a
role in linear measurements such as absorption and
even in nonlinear measurements since the detection
volume can cover a significant portion of the channel
depth. For full depth imaging, we employed a slowly
focusing beam. However, in microfluidics that employ
hydrodynamic focusing, 3D imaging in narrow channels could be improved by using a line focus. If the
line focus was oriented perpendicular to the direction
of flow, the effective working distance would increase
without compromising the temporal resolution.
Three-dimensional mixing characterization provides an estimate of the temporal variation in reac-
tion progress between streamlines that limits the
ability of a mixer to resolve reaction kinetics. Some
approaches to dealing with mixing nonuniformity
may include an appropriately scaled detection volume or numerical deconvolution of the reaction kinetics using the measured mixing distribution. Twophoton absorption fluorescence imaging of a firstorder quenching reaction is a direct and
straightforward method for measurement of chemical
concentration in 3D.
The National Science Foundation under grant
DBI-0454686 supported this work. E. A. Gibson acknowledges support from the National Research
Council Postdoctoral Fellowship program. R. Jimenez is a staff member in the Quantum Physics division of NIST.
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