High-Speed Microfluidic Differential Manometer for Cellular-Scale Hydrodynamics

Division of Engineering and Applied Sciences, Harvard University, Pierce Hall, Cambridge, MA 02138, USA.
Proceedings of the National Academy of Sciences (Impact Factor: 9.67). 02/2006; 103(3):538-42. DOI: 10.1073/pnas.0507171102
Source: PubMed


We propose a broadly applicable high-speed microfluidic approach for measuring dynamical pressure-drop variations along a micrometer-sized channel and illustrate the potential of the technique by presenting measurements of the additional pressure drop produced at the scale of individual flowing cells. The influence of drug-modified mechanical properties of the cell membrane is shown. Finally, single hemolysis events during flow are recorded simultaneously with the critical pressure drop for the rupture of the membrane. This scale-independent measurement approach can be applied to any dynamical process or event that changes the hydrodynamic resistance of micro- or nanochannels.


Available from: Magalie M. Faivre
High-speed microfluidic differential manometer
for cellular-scale hydrodynamics
Manouk Abkarian, Magalie Faivre, and Howard A. Stone*
Division of Engineering and Applied Sciences, Harvard University, Pierce Hall, Cambridge, MA 02138
Edited by Harden M. McConnell, Stanford University, Stanford, CA, and approved November 8, 2005 (received for review August 17, 2005)
We propose a broadly applicable high-speed microfluidic approach
for measuring dynamical pressure-drop variations along a micro-
meter-sized channel and illustrate the potential of the technique
by presenting measurements of the additional pressure drop
produced at the scale of individual flowing cells. The influence of
drug-modified mechanical properties of the cell membrane is
shown. Finally, single hemolysis events during flow are recorded
simultaneously with the critical pressure drop for the rupture of
the membrane. This scale-independent measurement approach can
be applied to any dynamical process or event that changes the
hydrodynamic resistance of micro- or nanochannels.
pressure measurement microcirculation hemolysis red blood cell
membrane properties
luid motions at the micrometer scale are at the heart of many
recent developments in microfabrication (1), separation pro-
cesses (2), cellular-scale identifications (3), DNA sequencing (4),
protein cryst allization (5) and many basic transport pathways in
plants (6), in the microcirculation (7), and specific to industrial
processes. The main characteristics of these advances lie in the
man ipulation and understanding of the dynamics of ‘‘sof t’’
objects such as polymers (8) (e.g., DNA), drops (9, 10), micro-
emulsions (11), microfoams (12), cells (13), vesicles and micro-
capsules (14). In fact, the interaction of the flow with these
defor mable entities is a tool to further investigate the details of
their mechanical properties and their str uctural features (e.g.,
the entropic elasticit y of a polymer, the viscoelastic properties of
a capsule, or the rheology of the liquid film between micro-
bubbles in a foam). For the case of strong confinement offered
by microchannels, the flow and shape of any close-fitting soft
object is controlled by a competition among the properties of the
objects, the fluid pressure, and the viscous stresses acting on the
boundaries that resist the motion. The hydrodynamic resistance
resulting from this fluid–structure interaction is reflected in a
dynamical variation of the pressure drop along the channel
during the flow and hence represents a crucial parameter to be
Nevertheless, rapid variations of pressure are very dif ficult to
measure at the micrometer scale and below. Indeed, the diffi-
culties do not originate f rom the lack of precision sensors
c ommercially available or those described in the research liter-
ature (15). The problem is a subtle mix of pragmatism and
technological limits. In addition to issues of dead volumes in
st andard pressure-measurement techniques (16–18) and those
associated w ith interfacing microelectromechanical system de-
vices to st andard pressure gauges (19), existing techniques are
simply difficult to implement [lasers, quadrant diodes, deform-
able membranes, multistep process of production (16–18)] and
are unable to measure at millisecond rates the pressure changes
in micrometer-scale flows. For instance, when a single red blood
cell (RBC) enters a channel of 5 5
m, the volume variation
produced by a flow at physiological speeds of a few millimeters
per second is 100 fL in a few milliseconds, which represents a
t ypical pressure-drop variation of tens to hundreds of pascals.
Such rapid pressure measurements at the cellular scale, crucial
to future dev ice and microcirculatory advances, are not available
at this time. Here we report a technique that overcomes these
limit ations and demonstrate the ability to measure rapid varia-
tions of pressure drop between two points in a microfluidic
device. The techn ique needs no external elements and is easy to
implement with soft lithography. The basic principle should
naturally allow similar measurements of pressure variations in
We chose to illustrate the flexibility of our approach by focusing
on blood cells, which allows us to provide insights into outstanding
problems in hemodynamics. Indeed, there is a long history of the
study of cells at the micrometer scale for assessing mechanical
properties (20) and cell shape (21) and for applying these ideas for
understanding microcirculatory diseases (22, 23). In fact, the main
approach for characterizing the influence of possible diseases on a
suspension of cells is the filtration technique (23–25). Briefly, the
cells flow through a multipore polycarbonate membrane, and the
measured pressure-drop versus flow-rate relation (or the mean
passage time of the cells) serves as an index of the deformability
state in a population of healthy or sick cells (23, 26). Even if the
potential of this technique is for the analysis of large samples, the
resultant data reflect only the average properties: the technique is
not able to resolve information at the scale of a particular pore or
a single cell. Recent advances in microsystems technology allow
direct observation of the flow of cells in microchannel arrays similar
to the filtration geometry (27, 28); for example, area and volume
measurements for cell populations have been reported. However,
the fact remains that the most basic mechanical measurements that
are characteristic of the physical state of individual cells in physi-
ological flow conditions have not been accomplished.
We propose several illustrations of our dif ferential microma-
nometer that address these issues and indicate further avenues
for studies of dynamics and hemorheology. We measure (i) the
pressure-drop variation associated with the motion of single and
multiple RBCs and white blood cells (WBCs) in a microchannel,
(ii) the additional pressure drop associated with the flow of
dr ug-treated cells, and (iii) single hemolysis events.
Measurement Principle
To measure simultaneously the dynamical deformation of the cells
and the variation of the pressure drop produced by their motion in
the channel, we developed a device with twin channels: a test
channel (Fig. 1A Upper) and an identical control, or ‘‘comparator,’’
channel (Fig. 1A Lower), both of which produce downstream two
parallel and adjacent streams of fluid. To maintain a stable inter-
face, the two fluids are miscible, and the liquid flowing through the
control channel is dyed to visualize the interface downstream.
Hence, the principle of the measurement lies in the use of the
second control channel to detect any variation of pressure in the te st
channel when a cell, or another object, is flowing through it. In
effect, for a given applied pressure difference across the device, the
Conflict of interest statement: No conflicts declared.
This paper was submitted directly (Track II) to the PNAS office.
Abbreviations: RBC, red blood cell; WBC, white blood cell; PDMS, poly(dimethylsiloxane).
*To whom correspondence should be addressed. E-mail:
© 2006 by The National Academy of Sciences of the USA
January 17, 2006
vol. 103
no. 3 www.pnas.orgcgidoi10.1073pnas.0507171102
Page 1
placement of an object in the channel decreases the flow rate and
consequently increases the pressure drop that occurs in the narrow
test section. A change in the pressure drop along the channel alters
the position of the interface downstream. The measurement of this
deflection allows the pressure to be determined after a basic
calibration procedure (see next paragraph), and consequently we
are able to monitor the time-dependent dynamical changes in the
pressure drop in the test channel. In the particular case of steady
channel flow, Groisman et al. (29) used a similar approach of
comparator channels for static measurements of pressure drop in a
microfluidic ‘‘diode’’ (i.e., a device in which the pressure varies
nonlinearly with flow rate and the direction of flow). We note that
for the experiment reported here by directly imaging the two-
channel system, it is possible to obtain simultaneously the sequence
of deformation of suspended particle s and the dynamical variations
of the pressure drop. Finally, we emphasize that our measurement
technique is general and can be applied to any dynamical proce ss
by changing the hydrodynamic resistance of the test channel relative
to the control channel (chemical reactions, changing viscosity, etc).
Device, Calibration, and Cells
The microfluidic device was manufactured by using principles of
sof t lithography (30, †). The typical dimensions of the device are
shown in Fig. 1 A. The dimensions are fixed by the size of the
object chosen for study. In the case of blood cells, we produced
the test and comparator channels at 5 5
m in cross section
so as to deform the cells significantly. We mount our microfluidic
device onto an inverted Leica (Deerfield, IL) DM IRB micro-
sc ope coupled w ith a Leica 100 objective (NPlan) for bright-
field imaging (numerical aperture, 1.25) to observe the motion
of the cells. A high-speed camera (Phantom V5, Vision Re-
search, Inc., Wayne, NJ) is used to follow the motion and the
defor mation of the cells through the capillaries; typically, we use
an imaging rate of a few thousands frame per second. The field
of v iew of the camera (1024 1024) allows simultaneous
observation of the cells and the deflection of the interface.
It first is necessary to calibrate the deflection of the interface
as a function of the pressure drop. The flow is produced by
pressurizing the fluids in the syringes connected to the two inlets
of the microfluidic device. With no RBCs in the solution, the
pressure P
applied in the test channel and the pressure P
in the
c ontrol channel are fixed so that the fluid–fluid interface
downstream is centered in the main exit channel (Fig. 1 A). We
change the pressure P
in small increments P without changing
the pressure P
in the c ontrol channel and follow the displace-
ment of the interface in the Y direction by performing image
analysis with
MATLAB software (Fig. 1B). The variation Y is
linear in P for the two initial working pressures applied: P
5 psi, and P
10 psi (Fig. 1C). A lso, the slope of Y(P)at
5 psi is tw ice as large as the slope at P
10 psi (in absolute
value); both responses are ex pected for small variations of this
viscously driven flow.
The RBCs used during the experiment are extracted from a
droplet of blood obtained by pricking a finger of a healthy donor.
The blood sample is diluted and washed tw ice with a solution of
PBS at an osmolarity of 300 mOs (physiological value). All of the
solutions are made with dextran of molecular weight 2 10
a concentration of 9% (wtw t). The viscosity of the solutions is
47 centipoise. All of the solutions are at a pH of 7.4. The viscosity
Briefly, a negative mask is placed on a silicon wafer that is spin-coated with a 5-
layer of photoresist polymer (SU-8) and exposed to UV light. The cross-linked design then
is developed to obtain a positive mold, and liquid poly(dimethylsiloxane) (PDMS) (Dow-
Corning) is poured over the mold. The PDMS is cured and peeled from the mold, and two
inlet holes are punched with custom-prepared 20-gauge needles. The PDMS negative
mold is bonded irreversibly to a glass slide to produce the device. The suspension of cells
is loaded in a gas-tight syringe (Hamilton) and connected to a compressed air tank through
custom adapters. Polyethylene (PE 20) tubes are connected from the syringe needle to the
inlet hole of the control channel of the device. A similar setup is used with the dyed
solution without the suspension and is connected to the inlet hole of the control channel
of the device. Pressure applied to the needles is independently controlled by a regulator
(Bellofram, St. Louis, MO) with a precision of 0.001 psi (1 psi 6.89 kPa).
Fig. 1. The height of the channels measured by a profilometer is the same in all of the devices and is equal to 4.7
m. (A) Calibration of the excess pressure
drop in the upper channel. The pressures P
and P
are fixed when no RBCs are flowing so that the fluid–fluid interface is centered in the exit channel. (B) Image
analysis determines the variation Y of the position of the co-flowing line that marks the interface. (C) Variation of Y as a function of the change in pressure,
P, in the upper channel for two different upstream pressures P
at 5 psi (
) and 10 psi (
). The slope YP at 5 psi is twice the slope at 10 psi in absolute value.
(D) Variation of the relative position Y of the interface as a function of time when cells enter the channel (Inset). The dashed vertical line separates the plot
into two regions. (Left) Valid points for the pressure-drop measurement. (Right) Points caused by the exiting cells passing close to, and thus disturbing, the
co-flowing line that marks the interface.
Abkarian et al. PNAS
January 17, 2006
vol. 103
no. 3
Page 2
of the ink solution has been measured to be 1.07 centipoise, i.e.,
approximately the viscosity of water.
To obtain rigidified RBCs, which allows characterization of
the changes in pressure drop caused by mechanical changes in
the cell membrane, an extra step is added in the process of
dilution. The RBCs are maintained in PBS solution containing
a given c oncentration of glutaraldehyde [0.001–0.01% (volvol)]
at 25°C for 4 min. The rigidified cells then are dispersed in the
PBS solution with the same osmolarity, pH, and viscosity as
described previously. In the process of blood separation, a few
WBCs are separated with the RBCs, which allows the study of
their motion in the microchannels as well.
Pressure-Drop Change due to Blood Cells. After calibration of the
interface deflection as a function of the change in pressure drop,
the dilute suspension of RBCs is introduced in the device. Each
time a cell enters the test channel (Fig. 1D Inset), we record a
movie of the whole field of view, which allows us to follow the
position of the interface (Fig. 1B ) and the deformation of the
cell. Each event is analyzed with
MATLAB software to measure
the dynamical variations of the interface position (i.e., the
pressure drop) as a function of time and the deformation of the
cell. An example of the measured pressure-drop variations after
the entry of a cell into a channel and continuing until after the
cell has exited the channel is shown in Fig. 1 D . The second bump
in Fig. 1D corresponds to the exit of the cell near the co-flow line,
which directly disturbs the position of the interface, but does not
have any physical significance in terms of the global pressure-
drop variations.
Two comments about details of the measurement approach
are in order. First, PDMS channels are known to be deformable
under pressure-driven flow. Thus, it is necessary to estimate the
maximum deformation produced by the passage of a cell, which
causes a pressure drop P. The additional strain in the walls of
the PDMS channel is estimated by the ratio of P (of the order
700 Pa) to the Young modulus of PDMS (5 10
Pa), which
is 10
. Hence, any such defor mation is negligible. Second, the
time response of our system is related to the pressure-driven flow
characteristics. There are three different time scales relevant to
describe the time resolution of the device: (i) the time scale
related to the propagation of sound waves (speed c) along the
channel (length L and height H), which controls the axial
development of the velocity profile and is estimated to be
Lc 10
to 10
s; (ii) the time scale associated with the
dif fusion of vorticity across the channel, which controls the
evolution of the nearly parabolic velocit y profile and is estimated
to be H
, where
is the kinematic viscosity of the
fluid); and (iii) the time scale associated with the fluid rear-
rangement because of the pressure changes, which is the longest
time scale in the problem. This last time scale is of the order of
U, where is the length on which the velocit y of the fluid is
disturbed (typically the cell size). With the estimates 10
and the mean velocit y of the fluid passing in the channels U
1cms, this time scale is of the order of a few milliseconds. This
time can be even shorter for higher mean speeds U, which
suggests a way to reduce and tune the time response of the dev ice
by working at higher injection pressures (i.e., higher flow mean
speeds). Finally, we note that experimentally we visually observe
on the high-speed movie the link between the motion (and
inst antaneous position) of the cell and the deformation of the
The next illustration of our technique consists in the mea-
surement of the complete sequence of the deformation and the
time evolution of the excess pressure drop when the cells flow in
the channel as shown in Fig. 2. A n RBC enters the channel,
followed shortly thereafter by a larger (and stiffer) WBC. The
time trace of the pressure-drop variations can be compared with
the images of the sequence of deformations represented in the
figure. The time evolution of the pressure drop while the same
cell is in the channel, and away from either the entrance or exit,
is a consequence of the deformation of the cell. This example
illustrates the ability to monitor dynamically pressure drop and
mechan ical processes comparable to in vivo conditions that
oc cur in the microcirculation.
Recent advances in computational mechanics have treated cell
entry and translation in cylindrical geometries with models for
the mechanical response of the cell. In one study (14), the RBC
is treated as a viscous droplet surrounded by a thin elastic
Fig. 2. Sequence showing the deformation first of an RBC and then a WBC,
which pass successively through the upper channel. A plot of the variation of
the pressure drop is shown as a function of time (in milliseconds). The corre-
sponding position and shape of the cells are represented on the plot by the
numbering of the sequence.
Fig. 3. Pressure drop versus time for different conditions characterizing the
state of the RBCs; the driving pressure is 5 psi. , healthy RBC; open symbols,
RBCs treated with 0.001% glutaraldehyde;
, one RBC;
, a train of two RBCs;
, a train of five RBCs.
www.pnas.orgcgidoi10.1073pnas.0507171102 Abkarian et al.
Page 3
membrane of two-dimensional modulus E
. The dynamical
response of these systems depends on the capillary number,
which is a dimensionless parameter
, where
is the
viscosity of the outer fluid and V
is the mean velocity of the fluid
in the channel. For example, the maximum additional pressure
drop P
during the flow is calculated to be P
for 10
0.05, where R
is the radius of the
circular capillary (see figure 14 in ref. 14). Using the measure-
ments shown in Fig. 3, our results give P
, which
is in good agreement with the order of magnitude from the
c omputational model. Finally, we note that the computational
models provide P
as a function of the position along the
channel, and our results are in qualitative agreement. A detailed
c omparison of simulation and ex periment would require the
same geometry and should, in principle, allow extraction of the
mechan ical properties.
The interactions of cells, and their number density, in the
microcirculation impact the overall pressure drop in a tissue
and is still not well understood (31). Next, we report in Fig. 3
results that suggest a way to study these hydrodynamic inter-
actions of cells through the measurement of the pressure drop
for the flow of one, two, and five cells translating through a
microchannel (cells are closely spaced, similar to a rouleaux).
The pressure drop systematically increases as the number of
cells increases, but the results are not simply proportional to
the number of cells. This qualit ative response is t ypical of
c onfined geometries w ith suspended particles spaced closer
than the microchannel width.
Pressure-Drop Change due to Membrane-Modified Cells. Next, we
c onsider the change in the hydrodynamic resistance that occurs
when the mechanical properties of the cells are modified. In Fig.
3, we compare a single healthy cell with a glutaraldehyde-treated
cell, which is k nown to be stiffer (25): the pressure drop is
enhanced after treatment with glutaraldehyde, and the station-
ary shape of the cell is obtained at later times. Thus, we conclude
that our approach allows differentiation of cells with different
mechan ical properties or geometrical features, which may pro-
vide a simple biomedical tool for clinical hemorheology and
phar maceutical testing.
Hemolysis. As a final example that illustrates the insights that can
be obtained with our microfluidic differential manometer in Fig.
4, we visualize a cell blocking the entrance to a channel (Fig.
4A2) and the subsequent hemolysis event (the cell membrane
r uptures) (Fig. 4 A4A6). When the blockage event begins, the
pressure drop increases linearly over 10 ms and reaches a
maximum value of 1.1 psi when hemolysis happens. We then
see the ghost of the RBC (Fig. 4 A4A6) as well as the
hemoglobin solution, which follows the parabolic velocity dis-
tribution. This critical value of stress that is necessary for
hemolysis is in good agreement with the approx imate value of
4,000 Pa 0.6 psi found with static micropipette experiment on
preswollen RBCs (32). It is interesting to note also that malaria-
infected RBCs have increased rigidity, which is associated with
organ failure. Microfluidic approaches have been used recently
to examine qualitatively the flow-induced hemolysis (or ‘‘pit-
ting’’) of malaria-infected cells (7), and our methodolog y pro-
vides a quantit ative approach for more in-depth studies of these
In summary, we have prov ided an approach for time-
dependent pressure-drop measurements at the micrometer scale
with millisecond resolution. We have shown how insights into
mechan ical processes can be obtained at the scale of individual
cells. These ideas naturally apply to other soft objects and to
nanoscale flows.
We acknowledge V. Studer for inspiring discussions on the device and
G. Cristobal-Azkarate for sharing his experience w ith the soft-
lithography techn ique. We thank G.M. Whitesides for helpful feedback.
We acknowledge L. Courbin for his help measuring viscosities. We also
thank the Harvard Nanoscale Science and Engineering Center for
support of this research.
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    • "Instantaneous Young's moduli were quantified as 3.48 ˘ 0.86 kPa for A549 cells and 2.99 ˘ 0.38 kPa for 95C cells [47] Meanwhile, the microfluidic constriction channel is used to quantify the cellular entry and transition process through a micro channel with a cross-sectional area smaller than the dimensions of a single cell, enabling high-throughput single-cell mechanical property characterization23242526 (seeTable 1). This technique was first used to evaluate the mechanical properties of RBCs [23,2728293031323334353637383940, which was then expanded to study the deformability of WBCs [24,41,42] and tumor cells [25,434445. "
    [Show abstract] [Hide abstract] ABSTRACT: This mini-review presents recent progress in the development of microfluidic constriction channels enabling high-throughput mechanical property characterization of single cells. We first summarized the applications of the constriction channel design in quantifying mechanical properties of various types of cells including red blood cells, white blood cells and tumor cells. Then we highlighted the efforts in modeling the cellular entry process into the constriction channel, enabling the translation of raw mechanical data (e.g., cellular entry time into the constriction channel) into intrinsic cellular mechanical properties such as cortical tension or Young’s modulus. In the end, current limitations and future research opportunities of the microfluidic constriction channels were discussed.
    Full-text · Article · Nov 2015 · Micromachines
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    • "CTA has detected differences in deformability of RBCs from healthy and diseased individuals (Baskurt et al., 1996; Koutsouris et al., 1989; Scott et al., 1993, 1992). Adaptations of this approach measure RBC deformation in capillary obstructions and tapered constrictions (Shelby et al., 2003), transit through constrictions (Gifford et al., 2006, 2003; Herricks et al., 2009a, 2009b), pressure drop while transiting constrictions (Abkarian et al., 2006), and elongation via fluid shear stress (Forsyth et al., 2010; Katsumoto et al., 2010; Lee et al., 2009). Some common limitations of these approaches are that their measures of RBC deformability do not account for variation in cell size, nor do they account for friction between the cell surface and the vessel walls (Zheng et al., 2012). "
    [Show abstract] [Hide abstract] ABSTRACT: A common indicator of rheological dysfunction is a measurable decrease in the deformability of red blood cells (RBCs). Decreased RBC deformability is associated with cellular stress or pathology and can impede the transit of these cells through the microvasculature, where RBCs play a central role in the oxygenation of tissues. Therefore, RBC deformability has been recognized as a sensitive biomarker for rheological disease. In the current study, we present a strategy to measure RBC cortical tension as an indicator of RBC deformability based on the critical pressure required for RBC transit through microscale funnel constrictions. By modeling RBCs as a Newtonian liquid drop, we were able to discriminate cells fixed with glutaraldehyde concentrations that vary as little as 0.001%. When RBCs were sampled from healthy donors on different days, the RBC cortical tension was found to be highly reproducible. Inter-individual variability was similarly reproducible, showing only slightly greater variability, which might reflect biological differences between normal individuals. Both the sensitivity and reproducibility of cortical tension, as an indicator of RBC deformability, make it well-suited for biological and clinical analysis of RBC microrheology.
    Full-text · Article · Apr 2014 · Journal of Biomechanics
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    • "Among those, the devices made from PDMS soft lithography are cost-efficient, oxygen-permeable and non-cytotoxic. Moreover, the capability to duplicate intricate geometries of the micro-cardiovascular system and to accurately adjust the proportions of microchannels has made the microfabrication technique exceptionally favorable for cell studies [11]. Definitely, the data on blood flow in microchannel is relevant for improving our understanding of microcirculation in the human body. "
    [Show abstract] [Hide abstract] ABSTRACT: With the advent of point-of-care diagnostics systems, investigation into properties of blood at micron scales is gaining fundamental importance. Past research has shown that blood displays significantly different properties at small scales than at conventional scales. This study investigates properties of blood flow in small non-circular passages (hydraulic di-ameter: 95-960 mm) under pulsatile condition. The observations are compared with flow of water under otherwise similar conditions. Prominent observation includes a more stable response to abrupt mass flow rate fluctuations as compared to water, which is attributed to the presence of deformable cells in blood. The study also reveals that, the pressure drop for blood flow with pulsations is less than for steady condition with the difference increas-ing with a reduction in microchannel size and flow rate. Such a comparative study facili-tates development of models for blood flow at micro-scales, and will eventually aid in the design of future micro-Total Analysis Systems.
    Full-text · Article · Mar 2013
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