Flow optimization study of a batch microfluidics PET tracer
synthesizing device
Arkadij M. Elizarov
&
Carl Meinhart
&
Reza Miraghaie
&
R. Michael van Dam
&
Jiang Huang
&
Antoine Daridon
&
James R. Heath
&
Hartmuth C. Kolb
Published online: 12 November 2010
#
The Author(s) 2010. This article is published with open access at Springerlink.com
Abstract
We present numerical modeling and experimen-
tal studies of flow optimization inside a batch microfluidic
micro-reactor used for synthesis of human-scale doses of
Positron Emission Tomography (PET) tracers. Novel
techniques are used for mixing within, and eluting liquid
out of, the coin-shaped reaction chamber. Numerical
solutions of the general incompressible Navier Stokes
equations along with time-dependent elution scalar field
equation for the three dimensional coin-shaped geometry
were obtained and validated using fluorescence imaging
analysis techniques. Utilizing the approach presented in this
work, we were able to identify optimized geometrical and
operational conditions for the micro-reactor in the absence
of radioactive material commonly used in PET related
tracer production platforms as well as evaluate the designed
and fabricated micro-reactor using numerical and experi-
mental validations.
Keywords
Flow optimization
.
Microfluidic
.
Positron
emission tomography
.
Fluorescence imaging
.
Microreactor
.
Numerical modeling
1 Introduction
The concept of individualized medicine and the use of
radiopharmaceuticals for early diagnostics and patient
treatment progress monitoring has drawn a lot of interest
in the field of healthcare and pharmaceutical research
(Pither
2003
; Eckelman et al.
2008
; Weber
2005
). One of
the emerging methods for reliable diagnostics and treatment
monitoring is Positron Emi
ssion Tomography (Phelps
2000
; Nutt
2002
; Czernin and Phelps
2002
) which is used
in a wide spectrum of fields including oncology (Dresel
2008
; Vallabhajosula
2007
; Shu et al.
2005
; Varagnolo et
al.
2000
), neurology (Mishina
2008
; Shoghi-Jadid et al.
2002
), cardiology (Knuuti and Bengel
2008
) and inflam-
mation (Laverman et al.
2008
; de Vries et al.
2008
).
Recently, there have been a lot of reports of studies related
to location and efficacy of targeted therapeutics using PET
imaging (Wang
2005
). The concept of PET relies on
incorporation of short-lived positron-emitting radioisotopes
(e.g.,
18
For
11
C) into small molecules thereby labeling
A. M. Elizarov
:
R. Miraghaie (
*
)
:
H. C. Kolb
Siemens Molecular Imaging, Biomarker Research,
6100 Bristol Parkway,
Culver City, CA 90230, USA
e-mail: reza.miraghaie@siemens.com
J. R. Heath
Caltech Division of Chemistry and Chemical Engineering and The
NanoSystems Biology Cancer Center,
MC 127-72, 1200 E. California Blvd,
Pasadena, CA 91125, USA
C. Meinhart
Department of Mechanical Engineering, University of California,
Santa Barbara,
Santa Barbara, CA 93106, USA
J. Huang
GN Biosystems Inc.,
2102 Walsh Ave., Ste D,
Santa Clara, CA 95050, USA
A. Daridon
Le Forestou Consulting,
Chemin du Rupalet 15,
CH-1185 Mont sur Rolle, Switzerland
Present Address:
R. M. van Dam
Crump Institute for Molecular Imaging, Department of Molecular
& Medical Pharmacology, University of California, Los Angeles,
Los Angeles, CA, USA
Biomed Microdevices (2011) 13:231
–
242
DOI 10.1007/s10544-010-9488-0
them as biomarkers or tracers capable of reaching within
specific target tissue. Numerous PET-probes have been
discovered and studied since the PET technology emerged
as an effective method of diagnostics with more under
development in both industry and academia. However, the
nature of short half-life isotopes and complexity of
synthesis of biomarkers have posed major problems in
development of these PET probes (Elizarov et al.
2010
).
Applying the concept of Lab-on-a-chip seems to be an
attractive solution (Huebner et al.
2008
; Hashimoto et al.
2006
; Hatakeyama et al.
2006
; Roberge et al.
2005
; Watts
and Haswell
2003
; Kawaguchi et al.
2005
; Liu et al.
2003
;
Chan et al.
2003
) as a) the amount of solvent and reagents
can be reduced substantially, b) higher concentration and
additional efficiency from rapid heat transfer and mass
transport can be achieved, c) easier modification of the
microfluidic reaction chamber (chip) for different types of
biomarkers can be obtained, and d) portability of the device
relative to conventional instruments can be enhanced.
Recently, several approaches to microfluidic methods of
production of the most common PET tracer, [
18
F] FDG
have been reported (Recent reviews include, Elizarov
2009
;
Miller
2009
; Lu and Pike
2007
). Many of those works rely
on reactions performed in moving solutions (Wester et al.
2009
; Gillies et al.
2006
; Yu et al.
2006
; Steel et al.
2007
)
while others have used batch CRC type devices (Lee et al.
2005
). The advantage of batch-type devices is that all
processes of the radiosynthesis are integrated into the chip,
including solvent evaporations and exchange that are not
possible in flow-through devices.
Recently, we reported a batch microfluidic device with
increased reactor capacity for production of larger amounts
of PET tracers (Elizarov et al.
2010
; van Dam et al.
2007
)
up to the clinical scale. A large size (5 mm diameter×250
micron deep) coin-shaped reactor was substituted for the
ring-shaped channel (100
μ
m wide) developed by Lee et al.
In the radiosynthesis of PET tracers, it is critical for the
incoming reagents to be thoroughly and rapidly mixed with
the contents of the reactor after the previous step. Because
of the large length-scale of the reactor, diffusion alone is
insufficient to achieve rapid mixing, and approaches based
on active circulation (van Dam et al.
2007
; Haeberle et al.
2005
) (e.g. with mechanical deformations, reciprocating
flows, centrifugal flow, or micro-stir bars) or passive flow
patterns (Yang et al.
2009
; Lin et al.
2007
; Chung et al.
2004
) (e.g. vortex mixers) are required. The advantage of
passive methods is simpler device fabrication, but studies
have typically assumed continuously flowing fluids rather
than the problem here of loading a reagent into a reactor
that is already partially-filled. Here we study the two
passive mixing approaches under the latter conditions: a
lamination approach based on a multi-input reagent
manifold and a high-velocity jet with inertia.
A second requirement for PET tracer synthesis chips is
that their contents must be eluted efficiently (without
significant dilution) after the synthesis in order to undergo
purification and quality control. In a ring-shaped reactor,
the contents can be readily eluted with air; but this is not
effective in the coin-shaped reactor; liquid must be
employed to help flush out the liquid contents of the
reactor. We investigate the effect of entrance angle and flow
rate of a single eluent input and product output channel in
order to achieve recovery of the product in minimal
volume.
These mixing and elution concepts are investigated via a
combination of fluorescence imaging and numerical modeling,
enabling optimization of operation parameters and geometry.
The combination of fluorescence studies and numerical
simulations addresses another important challenge facing
development and optimization of batch or flow-through PET
tracer reactors: working with radioactivity. Typically, one
requires protective radiation shielding and measurement
equipment, and the need to allow time for radioactive decay
after each experiment limits the throughput of studies.
Applying numerical methods (Ansari and Kim
2009
)and
experimental studies in the absence of radioactivity to better
understand the dynamics of flow and material transport inside
the reaction chamber are an attractive solution to overcome
some of those shortcomings.
The work here is generalizable to microfluidic devices
containing large-volume chambers in other application
areas.
1.1 Fabrication of microfluidic chip
The coin shaped microfluidic chip (Fig.
1
) was fabricated
using the soft lithography method (Erickson
2005
)ina
class 1000 clean room environment. The general procedure
for the fabrication of integrated, multilayer elastomeric
microfluidics chips has been described elsewhere (c.f. 11g).
Fully-cured chips were interfaced with reagents and control
pneumatics via steel tubes inserted into the punched chip
ports with the other end of the steel tubes connected to
flexible PTFE tubing leading to reagent vials or controlled
pressure sources.
2 Numerical modeling
To better understand the flow inside the reaction chamber, a
numerical model of the reaction chamber was developed.
The three-dimensional steady state incompressible Navier
Stokes equations along with time dependant elution scalar
field convection-diffusion equation were solved using
COMSOL Multiphysics (COMSOL Multiphysics User
’
s
Guide and Modeling Guide, Version 3.3, COMSOL,
232
Biomed Microdevices (2011) 13:231
–
242
Stockholm, Sweden). The numerical studies covered two
important aspects of the flow as primary focus. The first
aspect was the angle the flow enters the reaction chamber
and its effect on the quality of mixing inside the reactor.
The second aspect was the effect of different back pressures
imposed on the reactor inlet to induce optimal elution of the
product out of the reaction chamber.
A top view of the basic simulation geometry is shown in
Fig.
2
. The inlet and outlet of the reactor are simplified as
20
μ
m high 250
μ
m wide channels that intersect the
cylindrical cell reactor. The angle
α
depicts the angle
between the inlet/outlet to the normal of the reactor. The
angle
β
depicts the angle between the location of the inlet
and outlet. Both angles
α
and
β
were varied systematically.
The inlet flow rate was specified by a uniform velocity
boundary condition at the inlet. Zero pressure was specified
at the outlet boundary condition. The no-slip boundary
condition was specified for the remaining surfaces.
Figure
3
shows the 3-D meshed geometry. Approxi-
mately 26×10
3
three-dimensional tetrahedron elements
were used in a typical simulation. The mesh is more highly
resolved near the inlet because of the large velocity
gradients associate with the fluid jetting out of the inlet.
Simulations were conducted with higher resolution meshes
to ensure the solutions were grid independent.
3 Experimental studies
Mixing and elution optimization inside the fabricated
reaction chamber were studied using fluorescent imaging
techniques. For mixing quality evaluation testes, the reactor
was partially filled with an aqueous dye solution (Alexa
Fluor4 fluorophore dye; 0.1 mg/mL) followed by dead end
injection of pure water and monitoring the quality of
mixing over time. The gas permeable ceiling allowed dead
end filling of the reactor during various tests cases. A
Nikon Eclipse E800 microscope (equipped with Hama-
matsu ORCA-ER camera) was used to acquire images of
the reaction chamber. The efficiency of product elution was
also studied using fluorescent imaging method. The water
eluent was delivered from completely filled Tygon tubing
(ID 0.05 cm, 360 cm total length). Total fluorescence
emission within the reactor was monitored to record elution
Fig. 1
Complete design of the
“
coin-shaped reactor
”
chip. C1 is
the ion exchange column, and C2
is the product purification
column, both located off-chip.
Reagents are introduced or
removed through the indicated
channels, via open valves 1
–
11.
The radiator vent is shown in
yellow. The light green square
outlines the physical boundaries
of the chip
β
=180
°
Inlet
Outlet
(a)
Inlet
Outlet
α
=45
°
β
=60
°
(b)
Fig. 2
Top view of the simulation geometry for the cell reactor for two
baseline geometries considered in this study. The symbol
α
defines the
angle between the inlet/outlet to the normal of the reactor geometry. The
symbol
β
defines the angle between the location of the inlet and outlet.
(
a
) the straight through geometry is defined by
α
=0° and
β
=180°, (
b
)
the second baseline geometry is defined by
α
=45° and
β
=60°
Biomed Microdevices (2011) 13:231
–
242
233
efficiency. The elution process was considered complete
when the total reactor fluorescence measure had decreased
by 95% of the initial value.
4 Results and discussions
For the experimental studies of mixing optimization, water
entered the reactor partially filled with fluorescent water
through the single straight channel at a given back pressure.
When dye entered the reactor through the single straight
channel, the two liquids stayed virtually unmixed, the
incoming liquid merely filling the available space, up until
all the water had filled the reactor and motion had been
ceased as seen in Fig.
4(a)
.Mixingwasveryslow,
occurring only by diffusion at the boundary of the two
liquids. At water pressures of 1.7 bar or higher, when the
fluid
’
s flow rate (and inertia) was substantially increased, a
more complex jet-like stirring pattern of the two liquids was
achieved, somewhat increasing the interface area between
the two liquids and accelerating mixing. However at such
pressures, risk of valve failure was expected to increase and
therefore such high pressures were undesirable.
Next we evaluated the mixing characteristics of the 6-
inlet manifold (Fig.
4(b)
), based on the idea that simulta-
neous fluid entry from multiple ports could improve the
mixing as more layers of the fluid will be generated and
increasing the interfacial
area. Although diffusion-
dominated mixing was improved by utilizing multiple port
liquid entry, the inertia-driven aspect of mixing turned out
to be less pronounced than the case of single channel case.
This observation has two contributing factors: a) six jets of
water counteract each other in a symmetric fashion pushing
and containing all the initial reactor contents toward the
center of the reactor and b) the water inertia was reduced as
a single channel flow rate split between the six ports. The
overall impact of the loss of the jet-like stirring pattern
decreased mixing effectiveness, despite the increase in
interfacial area due to the six incoming streams.
We returned to the single straight channel tests with high
inertia which has been reported to contribute to the
enhanced mixing (Duffy et al.
1998
; Mautner
2004
). The
velocity of the fluid entrance jet could be further increased
by reducing the reactor pressure through the vacuum vent,
increasing the net pressure driving the fluid into the reactor
and thus increasing the total flow rate (Fig.
4(c)
). By
applying negative pressure to the vent line, gaseous
contents of the reactor were removed through the mem-
brane. This is observed by an absence of the initial air
bubble in Fig.
4(c)
compared to Fig.
4(a) and (b)
. In this
condition, the entry port to the reactor was opened by
actuating the valve and thereby filling the reactor using the
resulting higher pressure. The increased local pressure
gradient resulted in a greater inlet velocity to the reactor.
This
“
vacuum-assisted
”
method led to significant improve-
ment of mixing at 0.7 bar inlet pressure. With 1 bar of inlet
pressure, mixing was enhanced further by the formation of
pronounced vortex patterns as demonstrated in Fig.
4(c)
.
Lamination of the fluid stream into thin layers reduces the
diffusion length and improves the overall mixing. We
validated that such mixing was sufficient by driving the
reaction of mannose triflate with
18
F
−
resulting in comple-
tion of the reaction within 2.5 min.
We next investigated the efficiency of product elution
using fluorescent imaging. In the context of radiopharma-
ceutical synthesis, the reactor begins in a completely filled
state (reaction product), and this product must be eluted
such that recovery is high and volume is low. The coin-
shaped reactor was uniformly filled with Alexa Fluor 4
solution. Two channels were opened simultaneously
—
one
to deliver pressurized water eluent and the other which was
kept at atmospheric pressure to allow the contents to exit to
a collection vial. The water eluent was delivered from
completely filled Tygon tubing (ID 0.05 cm, 360 cm total
length). Total fluorescence emission within the reactor was
monitored to record elution efficiency, and elutions were
considered complete when the total reactor fluorescence has
decreased by 95%. The 95% elution volume (V
95
) was
Inlet
Outlet
Inlet
Outlet
(a) (b)
Fig. 3
Three-dimensional geometry of the reactor for two baseline
cases. Typically, the mesh consists of approximately 26×10
3
3-D
tetrahedron elements. Near the inlet, the elements are more refined to
better resolve the fluid jetting out of the inlet into the reaction
chamber: (
a
) straight through geometry defined by
α
=0° and
β
=180°,
(
b
) second baseline geometry defined by
α
=45° and
β
=60°
234
Biomed Microdevices (2011) 13:231
–
242
calculated from the filled exit tubing length. The 95%
elution time (t
95
) was another key value of interest due to
the importance of speed when working with short-lived
radioisotopes. Different elution conditions were compared
in terms of their
“
efficiency
”
defined as the product of V
95
and t
95
(Fig.
5
).
Two elution channel geometries were selected for the
tests. One geometry had entrance and exit channels
perpendicular to the reactor circumference (e.g., Fig.
1
,
port 5) located opposite to one another (Fig.
6(a)
) and the
other geometry utilized the tangential entrance (e.g., Fig.
1
,
ports 10 and 11) and exit channels (Fig.
6(b)
). Correlating
Figs.
5
and
6
, one can see that at certain flow rates, the
difference of elution efficiency value between the two
geometries is very significant while the same value being
similar at other flow rates. The tangential elutions were
always more efficient than perpendicular ones with the
optimum conditions being met at several local minima such
as those presented by T-II and T-IV where letter
“
T
”
corresponds to tangential entry/exit configuration as shown
in Fig.
5
. While pattern T-II, observed at these flow rates is
slightly less efficient than pattern T-IV, it only requires fluid
pressures of 0.5
–
0.8 bar, an advantage for reducing the risk
of valve failure during operation. The conditions of T-II
were chosen for the optimized radio-synthesis. Note that
pattern T-VI would not be a suitable choice due to increased
time of elution resulting in further decay of the radioactive
dose.
We next performed simulation on the modeled geometry
discussed earlier. Figure
7
shows the velocity magnitude
Fig. 4
Mixing study images
were recorded within 2 s subse-
quent to water delivery (before
any diffusion can take place).
Dark areas represent water and
light areas represent fluorescent
dye solution. Pattern of vertical
lines is due to the vent channel
above the reactor. Arrows rep-
resent location of reactor ports
Biomed Microdevices (2011) 13:231
–
242
235
and streamlines for flow rates
q
=1, 5, 10, 15
μ
l/s. As
observed in Fig.
7(a)
, the low flow rate
q
=1
μ
l/s has an
inlet Reynolds number Re=4. In this case, inertia does not
play an important role and the flow is distributed over the
entire reactor. For higher flow rates, inertia becomes more
dominant as a jet of the fluid enters the reactor. This is
clearly indicated by the recirculating vortices depicted by
the streamlines. These recirculating vortices can lower the
efficiency of the elution process. We will address this in
more details later.
The results of the scalar elution are shown in Fig.
8
with
the blue color corresponding to
c
=0 where there is no
elution fluid and red color representing
c
=1 with com-
pletely eluted fluid. The degree of elution is calculated by
averaging the concentration over the reactor volume shown
in Fig.
8
ranging from 6% to 69%.
Elution patterns observed with the straight channel
geometry change with increasing flow rate (Figs.
5
and
6
(a)
;patternsS-I
–
S-V). The slowest flow rates (0
–
2.5
μ
l/s,
Re=0
–
10; Pattern S-I) lead to most volume-efficient
elution that do not rely on inertia. As water enters the
reactor, it produces a liquid front that does not mix with
the reactor contents but forces undiluted contents through
the opposite side exit channel. The eluent stream will
eventually break through the original reactor content after
which the elution becomes less efficient. The lower the
flow rate, the more undiluted
“
product
”
can exit before
the eluent breaks through to the exit port and thus
at extremely low flow rates, elution efficiency is the
maximized.
The steep increase in elution volume is dominated by
Pattern S-II as inertia becomes significant and Reynolds
number rises above 10. The eluent enters rapidly and breaks
through to the opposite side of the reactor. Some eluent has
sufficient inertia to hit the farthest wall, change direction
and return along the two sides to join the entering jet.
Consequently, two fluorescent stagnating lobes which are
emptied primarily by diffusion into the surrounding moving
water that have little chance to be eluted are created. At
higher flow rates, these un-eluted
“
lobes
”
increase in size
and elution efficiency decreases. The peak of elution
inefficiency is characterized by a two-lobe pattern (S-max)
at a 12
μ
l/s flow rate (Re=60). At rates higher than 12
μ
l/s
inertial mixing becomes important and pattern S-III
dominates. In this case no bright and dark stagnant regions
are observed, but rather a gradual decline in reactor
fluorescence light intensity over time as the contents are
removed by dilution. The elution efficiency does not
change significantly between 23 and 36
μ
l/s flow rates.
At higher flow rates, (up to 46
μ
l/s, Re=240) elution
efficiency drops as some of the entering liquid pushes
directly to the exit channel (Pattern S-V).
Tangential elutions exhibit a more complex flow pattern
sequence with increasing flow rate (Figs.
5
and
6(b)
;
patterns T-I
–
T-VII). There are several local minima and
maxima in efficiency rather than a single peak. The
existence of these extrema is due to many qualitatively
different flow patterns observed as flow rate is changed.
There are three ranges (patterns) of flow rates that lead to
very efficient elutions, and those ranges alternate with
Fig. 5
Elution trends with per-
pendicular and tangential
patterns. Efficiency is a product
of time and elution volume
236
Biomed Microdevices (2011) 13:231
–
242
highly inefficient elutions. In Pattern T-I (0
–
1.5
μ
l/s, Re<
10) the eluent has little inertia and follows the path of least
resistance with little mixing, shortcutting from entrance to
the exit, leaving most of the original reactor contents
behind in the reactor. This inefficient pattern is determined
by the relative proximity of the ports, rather than their
tangential geometry.
As the flow rate increases and the incoming fluid gains
more inertia, the direction of the initial
“
jet
”
approaches
more closely the direction of the channel. However, the
entering inertia is insufficient for the fluid to cross the entire
layer of reactor content: the eluent gets turned around,
generating the
“
lobe
”
pattern (Pattern T-II). This more
efficient elution is followed through the first local minimum
(3
–
7
μ
l/s, Re=15
–
40) corresponding to V
95
.T
95
≈
500. Its
relative efficiency rises because the stream of eluent
extends further into the reactor to force more contents out.
Pattern T-III (7
–
9
μ
l/s, Re=40
–
50) requires the most
eluent. Stagnant lobes dominate this elution, similar to
Pattern S-II. However, compared to straight channel
elution, tangential channel elution required about ¼ the
amount of eluent at similar flow rates.
As the flow rate is increased (10
–
12
μ
l/s, Re=50
–
60)
Pattern T-IV is formed. A rapidly flowing jet of fluid
washes the far wall of the reactor first. No bright regions
are observed indicating the importance of dilution effects in
this pattern. This pattern co
nstitutes the second local
minimum.
Fig. 6
Patterns observed during
elution studies with various flow
rates perpendicular (
a
) and tan-
gential (
b
) inlet/outlet geometries
Biomed Microdevices (2011) 13:231
–
242
237
Pattern T-V (14
–
21
μ
l/s, Re=70
–
110) is characterized
by another loss of efficiency. The efficiency of this
structured pattern decreases because the entering jet of
fluid has sufficient inertia to follow the trajectory along the
far wall of the reactor to the exit. Some eluent makes a full
circle along the circumference, uniting with the incoming
jet. This pattern is then conceptually similar to one large
lobe which stays un-eluted for a long time as eluent moves
around it. Similar behavior can be seen in Fig.
6(b)
.
Further efficiency minima and maxima are observed at
higher flow rates. The optimal elution conditions are
created with tangential channels operated at flow rates in
the narrow range of 3
–
5
μ
l/s. While Pattern T-II, observed
at 5
μ
l/s flow rate is only slightly less efficient than patterns
T-IV and T-VI, it only requires fluid pressures of 0.5
–
0.8
bar, an advantage for reducing the risk of valve failure
during operation.
Comparing the plots for the tangential and perpendicular
elutions in Fig.
5
, the former are more efficient at all flow
rates except for the extremely slow ones which due to
decaying nature of radio isotopes and importance of timely
delivery of the dose are not attractive. Such flow rates are
very difficult to maintain pneumatically. Slight increase in
flow rate leads to an immediate loss of efficiency in the
(a)
(b)
(c)
30%
40%
50%
80%
(e)
(f)
(d)
70%
60%
Fig. 8
Scalar fields during elution for the baseline case where
α
=0,
β
=180 with an inlet flow rate
q
=15 uL/s. The blue color indicates no elution
fluid, while the red color indicates elution fluid. The percent of elution shown are: (
a
) 30%, (
b
) 40%, (
c
) 50%, (
d
) 60%, (
e
) 70%, (
f
) 80%
(a)
(c)
(b)
q
= 1uL/s
q
= 5uL/s
q
= 10uL/s
q
= 15uL/s
(d)
Fig. 7
Flow patterns for the
baseline case where
α
=0,
β
=
180 with varying inlet flow
rates. The blue color represents
low fluid velocity magnitude,
while the orange color repre-
sents high fluid velocity magni-
tude. Streamlines of the fluid are
indicated in red. (
a
)
q
=1 uL/s,
(
b
)
q
=5 uL/s, (
c
)
q
=10 uL/s, (
d
)
q
=15 uL/s
238
Biomed Microdevices (2011) 13:231
–
242
straight elution case. Therefore, a tangential elution
exhibiting similar efficiency at a higher flow rate was
considered to be a more robust choice.
Further observations can be made from the two baseline
geometry simulations resembling the location of the inlet and
exit ports in the actual reactor. For
α
=0 and
β
=180
representing perpendicular elution case were inlet and outlet
ports are located on a straight line and
α
=45,
β
=60represent
tangential elutions where inlet and outlet ports were located in
an angle facing the center of the reactor two distinct behaviors
of the flow can be distinguished. The instantaneous elution
scalar fields for
α
=0 and
β
=180 case in Fig.
8
correspond to
the different stages of completion. The effects of the
recirculating vortices are apparent as stirring imposed by
the vortices better helps with the completion of the elution.
These results are consistent with the data obtained from the
(a)
(b)
(c)
30%
40%
50%
80%
(e)
(f)
(d)
70%
60%
Fig. 10
Scalar fields during elution for the baseline case where
α
=45,
β
=60 with an inlet flow rate
q
=15 uL/s. The blue color indicates no
elution fluid, while the red color indicates elution fluid. The percent of elution shown are: (
a
) 30%, (
b
) 40%, (
c
) 50%, (
d
) 60%, (
e
) 70%, (
f
) 80%
(a) (b)
(c) (d)
q
=1 uL/s
q
=10 uL/s
q
=5 uL/s
q
=15 uL/s
Fig. 9
Flow patterns for the
baseline case where
α
=45,
β
=
60 with varying inlet flow rates.
The blue color represents low
fluid velocity magnitude, while
the orange color represents high
fluid velocity magnitude.
Streamlines of the fluid are
indicated in red. (
a
)
q
=1 uL/s,
(
b
)
q
=5 uL/s, (
c
)
q
=10 uL/s, (
d
)
q
=15 uL/s
Biomed Microdevices (2011) 13:231
–
242
239
perpendicular elution experiments discussed earlier. The
vortices (
“
lobes
”
)appearathigherflowratesandincrease
in size as the flow rate increases. Close correlation can be
observed between patterns in Fig.
8
, those resulting from
fluorescence experiments in Fig.
5
and velocity profiles of
Fig.
7
.
Similarly, the results of the tangential elution simulation,
presented in Fig.
9
, indicate the onset of elution inside the
reactor due to existence of the recirculating regions. It is
seen that at low inlet flow rate of 1
μ
l/s corresponding to
Reynolds number of Re=4, there is very little inertia to
induce mixing in the reactor. Note that empirical results of
(a)
(b)
(c)
(d)
(e)
(f)
β
=30
β
=180
β
=150
β
=120
β
=90
β
=60
Fig. 12
Flow patterns with an inlet flow rate of
q
=15 uL/s for various
angles
β
. Inertial effects cause the fluid to jet out of the inlet into the
cell reactor creating counter rotating vortices. The blue color
represents low fluid velocity magnitude, while the orange color
represents high fluid velocity magnitude. Streamlines of the fluid are
indicated in red. (
a
)
β
=30, (
b
)
β
=60, (
c
)
β
=90, (
d
)
β
=120, (
e
)
β
=
150, (
f
)
β
=180
(a)
(d)
(c)
(b)
α
= 0
α
= 45
α
= 30
α
= 15
Fig. 11
Flow patterns with an
inlet flow rate of
q
=15 uL/s for
various angles
α
. Inertial effects
cause the fluid to jet out of the
inlet into the cell reactor creat-
ing counter rotating vortices.
The blue color represents low
fluid velocity magnitude, while
the orange color represents high
fluid velocity magnitude.
Streamlines of the fluid are
indicated in red. (
a
)
α
=0, (
b
)
α
=15, (
c
)
α
=30, (
d
)
α
=45
240
Biomed Microdevices (2011) 13:231
–
242
Fig.
6(b)
show the same behavior in the actual flow which
further validates computational results. As the flow rate is
increased to 5
μ
l/s, the Reynolds number is increased to 20
and inertial effects become more pronounced. At the
highest flow rate of 15
μ
l/s corresponding to Re=60, the
jet of the incoming eluent cuts all the way across the reactor
and two counter rotating vortices dominate the flow field.
These results once more confirm the explanations of the
empirical data obtained with fluorescent tangential elutions
presented in Fig.
4(b)
. Both the jet along the far wall at high
flow rates and the shortcut at the low flow rates have been
explained in Fig.
9
and confirmed in Fig.
11
.
Distribution of the scalar elut
ion concentration inside the
reactor in Fig.
10
shows the effect of the jet extending out from
the inlet and impinging on the back wall of the reactor
chamber and redirecting the jet towards the exit port. This
creates a large-scale circulation in the reactor, which helps
elute the fluid. At flow rates equal or higher than 5
μ
l/s, inertial
effects cause the fluid to jet from the inlet into the reaction
chamber. This is especially signi
ficant comparing the straight
and tangential elution at the highest flow rate of 15
μ
l/s, where
inlet Reynolds numbers approach Re=60. For perpendicular
elution, the jet at the inlet port creates two counter-rotating
vortices that produce substantial re-circulation in the chamber
and away from the exit port, and can reduce elution efficiency
(see Fig.
8(f)
). On the other hand, with tangential elution the
jet and the bigger vortex are directed towards the exit port
resulting in more efficient elution (see Fig.
10(f)
).
The effects of the angles
α
and
β
were studied further
for the high flow rate case of
q
=15
μ
l/s, by first
systematically varying
α
, with
β
=60. The resulting velocity
magnitude and streamlines are shown in Fig.
11
, for
α
=0,
15, 30, 45. The angle of the outlet does not appear to have
any significant effect on the flow pattern. However, the
angle of the inlet significantly affects the location of the jet
emanating from the inlet. The
α
=45 case (Fig.
11(d)
),
directs the jet (and recirculating vortices) to the upper
portion of the reaction chamber. This creates large-scale
clockwise circulation, which helps elute the fluid from the
chamber. As a result, the elution time is lower for
α
=45, as
compared to the other angles studied.
The effect of the angle
β
on the elution times was
examined by fixing
α
=0, and varying
β
=30, 60, 90, 120,
150, and 180. The resulting velocity magnitude and
streamlines are shown in Fig.
12
. When then angle
β
is
small, there is a weak large-scale circulation that helps to
elute fluid from the reactor. When
β
=180 (corresponding
to straight through elution), there is no large-scale clock-
wise or counterclockwise circulation, and the elution
efficiency is reduced. Typically, the smaller
β
allows for
more efficient elution than the larger
β
. It was found that the
most efficient elution occurs for large angles of
α
and small
angles of
β
. An optimal configuration for short elution times
and low elution volumes determined based on the above
simulations is with tangential elution at
α
=45,
β
=60, and
flow rate of
q
=15
μ
l/s. These parameters are consistent with
the existing design of the microfluidic radio-synthesizer of
PET probes, suggesting that intuitive design of geometry
has already resulted in optimal elution efficiency and
consequently higher yields.
5 Conclusion
As length scales in microfluidics devices become smaller
resulting in limited Reynolds numbers and less efficient
elution and mixing compared
to macro-scale fluidics,
utilizing flow and geometry to enhance active mixing and
more efficient elution becomes of paramount importance.
Through experimental and numerical studies, we have
shown the optimal design criteria from the standpoint of
mixing and efficient elution of the product for the coin-
shaped microfluidic radio-synthesis reaction chamber for
PET radiosynthesis. The numerical model used in this work
was a simplified model of a more complex system which
can be studied using more advanced methods of Compu-
tational Fluid Dynamics. The close agreement between
numerical and experimental results suggests that computa-
tional modeling can serve as a powerful tool for optimizing
both chip design and operating parameters, exploring new
chip designs without fabricating new chips, and even
gleaning insights without complicated measurement equip-
ment. Additionally, the decaying nature of radio-isotopes
and radiation safety limitations better justify acquiring a
platform such as the one discussed in this work to optimize
on-chip radiochemistry processes reducing user exposure.
Acknowledgements
This work was funded by Siemens Molecular
Imaging, Biomarker Research, Culver City, CA and by the Institute
for Collaborative Biotechnologies throughcontract no. W911NF-09-
D-0001 from the U.S. Army Research Office. The content of the
information herein does not necessarily reflect the position or
policy of the Government and no official endorsement should be
inferred.
Open Access
This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which per-
mits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.
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