|  High-throughput mechanophenotyping of multicellular spheroids using a
microfluidic micropipette aspiration chip†
---|---
|  Ruben C. Boot,a Alessio Roscani,a Lennard van Buren,b Samadarshi Maity,a
Gijsje H. Koenderinkb and Pouyan E. Boukanya
|  Cell spheroids are in vitro multicellular model systems that mimic the
crowded micro-environment of biological tissues. Their mechanical
characterization can provide valuable insights in how single-cell mechanics
and cell-cell interactions control tissue mechanics and self-organization.
However, most measurement techniques are limited to probing one spheroid at a
time, require specialized equipment and are difficult to handle. Here, we
developed a microfluidic chip that follows the concept of glass capillary
micropipette aspiration in order to quantify the viscoelastic behavior of
spheroids in an easy-to-handle, high-throughput manner. Spheroids are loaded
in parallel pockets via a gentle flow, after which spheroid tongues are
aspirated into adjacent aspiration channels using hydrostatic pressure. After
each experiment, the spheroids are easily removed from the chip by reversing
the pressure and new spheroids can be injected. The presence of multiple
pockets with a uniform aspiration pressure, combined with the ease to conduct
successive experiments, allows for a high throughput of tens of spheroids per
day. We demonstrate that the chip provides accurate deformation data when
working at different aspiration pressures. Lastly, we measure the viscoelastic
properties of spheroids made of different cell lines and show how these are
consistent with previous studies using established experimental techniques. In
summary, our chip provides a high-throughput way to measure the viscoelastic
deformation behavior of cell spheroids, in order to mechanophenotype different
tissue types and examine the link between cell-intrinsic properties and
overall tissue behavior.

##

††footnotetext: a Department of Chemical Engineering, Delft University of
Technology, Delft, The Netherlands. E-mail:
<EMAIL_ADDRESS>b Department of Bionanoscience, Kavli
Institute of Nanoscience Delft, Delft University of Technology, Delft, The
Netherlands ††footnotetext: † Electronic Supplementary Information (ESI)
available: [details of any supplementary information available should be
included here]. See DOI: 00.0000/00000000.

## Introduction

Physical properties like cellular mechanics are of undeniable importance in
physiological processes such as morphogenesis1, tissue remodeling2, wound-
healing3 and cancer growth4, 5. During these events, cells are collectively
confined, squeezed, pushed or pulled upon, affecting their self-organization
in time and space. The overall mechanical response to these forces, termed
tissue mechanics, will shape the resulting tissue morphology. This response
depends on the properties of the single cells alongside the interplay between
cells across multiple length scales. 6, 7 While the mechanical deformation of
single cells mostly depends on their cytoskeleton, plasma membrane and nuclear
stiffness, tissue mechanics are defined through the linkage between cell
adhesion molecules, the cytoskeleton and the extracellular environment. 8, 9

Cell spheroids have become a popular in vitro model to study tissue mechanics,
as they replicate both the multicellular nature and three-dimensional (3D)
micro-environment of in vivo tissues. 10 These spherical aggregates are made
from immortalized cell lines or primary cells that adhere to each other and
collectively round up. The resulting spheroid morphology and internal cell
arrangement is defined by the interplay between cell-cell adhesion and
cortical tension. 11, 7, 12 Probing spheroids with relevant physical forces
therefore increases insight in how tissue composition and resulting mechanics
relate to tissue sorting, cellular mechanosensing and cell invasion. 6, 13, 14

Spheroid mechanics have been quantified using various techniques, probing
either from within or without. 15 For example, hydrogel mechanosensors give
information on the spatial distribution of mechanical stress within spheroids.
16, 17 Cavitation rheology probes the internal elasticity and tissue
interfacial tension by inducing a spherical cavity in the spheroid with a
needle. 18 From without, the elastic modulus has been quantified by squeezing
the spheroid between two "chopsticks" termed microtweezers. 19 Atomic force
microscopy (AFM) determines the viscoelastic response of a spheroid by
indenting the surface with a nano-probe 20, 21, while tissue surface
tensiometry (TST) squeezes the spheroid between two plates 11, 7, 22, 23, 24
and micropipette aspiration (MPA) aspirates a spheroid tongue in a glass
capillary to look at the viscoelastic creep response. 13, 25, 26, 27
Additionally, TST and MPA quantify a tissue surface tension, for which the
analogy is made between round spheroids and liquid droplets. 11, 28, 13 This
surface tension is directly related to tissue sorting, tissue spreading and
energetic constraints on the size of spheroids. 7, 29, 26

However, available techniques to quantify spheroid mechanical parameters such
as the elastic modulus $E$, viscosity $\eta$ and surface tension $\gamma$ have
a limited throughput. First, techniques such as AFM, microtweezers, TST or MPA
only probe one spheroid at a time. Second, the handling of nano-cantilevers,
small tweezers or glass microcapillaries is a delicate, difficult and time-
consuming task. The resulting low throughput is found in the previously
mentioned studies probing spheroid mechanics, as these usually report a data
set that ranges between a total number of $\sim$5 to 30 probed spheroids. As
the technical challenges form a bottleneck on the size of data sets, it is
difficult to quantify differences between various spheroid models using
present techniques. Given the fact that biological variability tends to be
rather large, mechanical phenotyping, for instance to compare different cancer
types, or in-depth studies of the role of cytoskeletal components or specific
(cancer) biomarkers in overall tissue behavior require an assay with higher
throughput than what is currently available.

Microfluidic devices are widely used to measure the mechanical properties of
single cells at high throughput. 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
Here, cell deformability is examined by letting large numbers of cells flow or
migrate through narrow channels or micro-pillars. The chip’s defined
geometries are easily replicated into new chips, making this a highly
reproducible set-up. Besides overall cell deformability, these devices are
able to quantify more specific mechanical parameters such as both the cell’s
and nuclear elastic modulus and viscosity. For example, the design of a
microfluidic array where single cells land in individual pockets and are
aspirated via a pressure gradient enables high-throughput micropipette
aspiration. 34, 35 However, applying the same principles to study mechanics of
spheroids or tissues, which requires microfluidic chips with larger channel
dimensions, has remained unaddressed. While microfluidic devices exist to
examine spheroid growth and for functional assessment of drugs41, 42, a high-
throughput microfluidic chip to study spheroid mechanics in parallel and with
high reproducibility does not exist to date.

Inspired by the microfluidic micropipette array for single cells 34, 35, we
have designed a microfluidic device to perform MPA on multiple spheroids in
parallel, thereby drastically increasing the throughput. After each
measurement, spheroids can be easily removed from the device by reversing the
flow and aspirating them at the inlet, allowing for multiple experiments per
chip. As the device is made from a mold, each chip has the exact same
dimensions for the micropipette channels, which is much harder to obtain when
pulling glass micropipettes for traditional MPA. The aspiration pressure is
precise and easily controlled for each measurement by using hydrostatic
pressure. With a custom-made Python script for automated image analysis, the
creep length of aspirated spheroid tongues can be analyzed to derive the
viscoelastic response of the spheroids. Our device can aspirate 8 spheroids in
parallel per measurement for multiple runs per day, allowing for much larger
data sets while providing the same information as traditional glass
micropipette aspiration. Additionally, we show that our microfluidic device is
sensitive enough to pick up mechanical differences between different spheroid
models, making it a suitable device to mechanically phenotype different
cellular systems.

## Materials and methods

### Cell culture

Human embryonic kidney 293 (HEK293T) cells were generously provided by the
group of Dimphna Meijer (Department of Bionanoscience, Delft University of
Technology). They were kept in Dulbecco’s Modified Eagle Medium High Glucose
(DMEM, Sigma) containing 4.5 g/L glucose, L-glutamine but without sodium
pyruvate, and supplemented with 10% Fetal Bovine Serum (FBS, Sigma) and 1%
Antibiotic-Antimycotic solution (Gibco).

NIH3T3 embryonic mouse fibroblasts (ATCC CRL-1658) were kept in Dulbecco’s
Modified Eagle Medium High Glucose (DMEM, Sigma) containing 4.5 g/L glucose,
L-glutamine but without sodium pyruvate, and supplemented with 10% Newborn
Calf Serum (NCS, Sigma) and 1% Antibiotic-Antimycotic solution (Gibco).

Human mammary MCF10A cells (ATCC CRL-10317) were cultured in DMEM/F12 1:1
medium (Gibco) supplemented with 5% horse serum (Gibco), 0.5 µg/mL
hydrocortisone (Sigma), 20 ng/mL human epidermal growth factor (hEGF)
(Peprotech), 100 ng/mL cholera toxin (Sigma), 10 µg/mL insulin (Human
Recombinant Zinc, Gibco) and 1% Penicillin-Streptomycin 100x solution (VWR
Life Science).

All cells were incubated at 37 °C with 5% CO2 and subcultured at least twice a
week.

### Spheroid fabrication

Spheroids were generated using a custom-designed microfabricated microwell
array platform (which is available at:
https://github.com/RubenBoot/HighThroughput_Spheroid_MPA
/blob/main/SpheroidMicrowellArray.dwg), inspired by work from Minglin Ma’s
lab.43 Following their protocol, two microwell array platforms were created
using standard soft lithography at the Kavli Nanolab Delft to allow for the
creation of spheroids with different diameters. Using SU-8 2150 photoresist
(Kayaku Advanced Materials) and a µMLA laserwriter (Heidelberg Instruments),
the master wafers were designed to have an array of circular microposts. The
first wafer had posts with a diameter of 200 µm and height of 220±20 µm, while
the second wafer had posts with a diameter of 280 µm and a height of 300±30
µm. The master wafers were coated with
trichloro(1H,1H,2H,2H-perfluorooctyl)silane (Sigma-Aldrich) to allow for easy
demolding. Microwell arrays were molded from the wafers using
polydimethylsiloxane (PDMS) (Sylgard 184, Dow Corning) and curing agent at a
mixing ratio of 10:1 (w/w). The arrays were placed in a 12-well cell culture
plate (Thermo Fisher Scientific) using rubber glue (Reprorubber), and then
sterilized by thoroughly washing with ethanol and leaving under UV light
overnight.

Before seeding cells, the arrays were coated with 1% (w/v) Pluronic® F127
(Sigma-Aldrich) solution to prevent cell adhesion to the PDMS. The pluronic
solution was removed from the well after 45 minutes of incubating. A cell
suspension with a concentration of ±1 x 106 cells in matching cell media,
obtained through trypsinization, was deposited in the well with the coated
array in order to form spheroids. It is important to note that the resulting
spheroid dimensions not only depend on the chosen cell concentration but also
on the duration of culture, cell adhesion and the cell type-specific
proliferation rate. After deposition, cells divide over the microwells and
settle at the bottom due to gravity, where they aggregate into spheroids
overnight (Fig. S1†). The spheroids were cultured in the wells for either 2 or
3 days before aspiration experiments, changing the media every day. On the day
of the experiment, spheroids were gently washed out of the microwells using
the same media and brought into suspension.

### Design and fabrication of the microfluidic chip

The master wafer was created using standard soft lithography at the Kavli
Nanolab Delft. The design is available at
https://github.com/RubenBoot/HighThroughput_Spheroid_MPA. The multi-layer
design contains features with different heights, so had to be created in two
separate photolithography steps using a µMLA laserwriter (Heidelberg
Instruments). The final chip was designed as a combination of two slabs of
PDMS, one slab with the aspiration channels 50 µm in height plus the top half
of the aspiration pockets ±150 µm in height (see Fig. 1A, PDMS slab 1), and
the other slab containing the bottom half of the aspiration pockets (PDMS slab
2). The molds for both these slabs were fabricated together on one silicon
wafer. To obtain this, the first step of the design was created by spinning
SU-8 3050 to an average thickness of 50 µm and soft baking it at 95 °C for 15
minutes, after which the laserwriter wrote the first layer. The wafer was post
baked at 65 °C for 1 minute, then at 95 °C for 5 minutes and developed in SU-8
developer. The second layer was created with SU-8 2050 and spun to an average
thickness of 150 µm. It is important to note that the thickness was not equal
over the whole wafer, as the resist covered both the first half of the design
(consisting of the micropipette channel and part of the aspiration pocket) and
the empty place where the second half of the aspiration pockets will be
written. Therefore, one half of the aspiration pockets (see Fig. 1A, PDMS slab
2) resulted in a thickness of 150±2 µm, while the other half containing half
of the pocket plus the aspiration channel (PDMS slab 1) had a different
thickness of 175±25 µm. After spinning, the wafer was soft baked at 65 °C for
5 minutes and then at 95 °C for 30 minutes. The laserwriter wrote the second
part of the design, after which the wafer was post baked at 65 °C for 5
minutes, at 95 °C for 12 minutes and then developed. The master wafer was
coated with trichloro(1H,1H,2H,2H-perfluorooctyl)silane to allow for easy
demolding. PDMS chips were created using Sylgard 184 at a curing agent ratio
of 10:1. Individual chips were cut and holes were punched in only one slab of
the design for the later introduction of tubing. Both halves of the design
were plasma cleaned (Harrick Plasma) for two and a half minutes to facilitate
bonding, after which one half was slightly wetted with a droplet of distilled
water to allow for better alignment. The two halves were put together and
aligned using the alignment arrows at the border of the design and an optical
microscope (ZEISS Primovert) to check the alignment (Fig. S2†). Finally, the
chip was kept in the oven at 65 °C to bond overnight. Afterwards, chips could
be stored indefinitely and used on the desired day for the experiment.

Fig. 1:  Overview of the microfluidic chip. (A) 3D schematic showing (left)
the top view of the design and a close-up on the pockets and aspiration
channels, and (right) a tilted side view showing the heights of the two
separate PDMS slabs and the resulting height when bonded together. (B)
Photograph of two actual devices, filled with red dye for visualization and a
EU 1 cent coin for scale. (C) Schematic of the experimental set-up. Spheroids
enter the PDMS chip at the inlet reservoir, which is a pipette cone, after
which they are aspirated with hydrostatic pressure by changing the height
$\Delta h$ of the outlet vial that is mounted to a vertical rod. The
experiment is captured with an inverted microscope using a 5x objective. (D)
Brightfield top view image of the aspiration pockets loaded with aspirated
spheroids, scale bar 200 µm.

### Data acquisition

Before each experiment, the chip was filled with 1% Pluronic® F127 (Sigma)
solution and left at room temperature to prevent cell adhesion to the PDMS
walls. After 45 minutes, the pluronic solution was flushed from the chip using
the culture media that matched the cell line used in the experiment. For this,
vials with cell-free culture media were connected to the inlet and outlet of
the microfluidic chip with PTFE 008T16-030-200 tubing (Diba Industries, inner
diameter 0.3 mm, outer diameter 1.6 mm) and a pressure was applied to the
media using an MFCS-EZ pressure controller (Fluigent). Once all the pluronic
solution, PDMS debris particles and possible air bubbles were flushed out, the
tube connected to the inlet was gently unplugged from the chip and a loading
reservoir, being a shortened 1 ml pipette tip cut with a scalpel, was plugged
into the inlet. Then, the vial connected to the outlet was disconnected from
the pressure controller and mounted to a vertical rod, to be able to exert a
precise hydrostatic aspiration pressure when lowering the vial compared to the
height of the reservoir. Slightly lowering the vial induced a minor flow in
the chip towards the aspiration pockets, after which 20 µl of spheroid
suspension was pipetted into the reservoir. Spheroids were guided by the flow
and entered the aspiration pockets, after which the outlet tube was brought
back to the height where no flow is present. For loading, the inlet hole
needed to be punched close enough to the aspiration pockets. Otherwise, the
volume of space in the loading bay of the chip would be too large and could
not induce a high enough flow velocity to sweep the spheroids into the
pockets. Spheroids then sedimented to the bottom instead and remained
immobile. Once ready to perform the experiment, the vial was manually lowered
to the chosen aspiration pressure, thereby inducing spheroid tongue
aspiration.

Brightfield images of spheroid tongues entering the aspiration channels were
captured on an inverted fluorescence microscope (Zeiss Axio-Observer) every 5
seconds for a total of 5 minutes using a 5x/NA 0.16 air objective and ORCA
Flash 4.0 V2 (Hamamatsu) digital camera with a resolution of 2048x2048 px2. We
ensured that the full aspiration curve of the tongue was captured by starting
the image acquisition before lowering the outlet tube (Movie S1†). At the end
of the experiment, spheroids were pushed out of the pockets and flown back
towards the inlet by raising the outlet vial above the reservoir. There, they
were removed from the chip by pipetting them up through the reservoir. This
way, new spheroids could be inserted and a new measurement started with the
same chip. All experiments were conducted at 37 $\degree$C and 5$\%$ CO2 using
a stage top incubator (ibidi). Chips were used for 4-5 successive experiments
on average, and were always discarded after the final experiment of the day.

### COMSOL simulations on pressure distribution in the chip

The design of the device contains 8 parallel pockets, and thus pressure will
redistribute once spheroids start clogging the flow in pockets. To examine the
influence of this effect, the pressure distribution was computationally
modeled in the 3D design of the device using the finite elements modeling
software COMSOL Multiphysics 5.6. Considering the fluid flow to be laminar and
following the Navier-Stokes equation,44 the pressure distribution was modeled
for two different cases: (1) all pockets are open, or (2) all pockets are
clogged, except for one where fluid still flows through the aspiration
channel.

The Hagen-Poiseuille equation tells us that the pressure drop over a tubular
channel with laminar flow scales with the length of the channel and the
inverse of the channel radius to the fourth power.45 As the design of our
device has much larger dimensions than typical microfluidic chips, the cross-
sectional area of the tubing connected to the chip now has the same order of
magnitude as the cross-sectional area of the device. Therefore, the
hydrodynamic resistance across the tubing is considerable and non-negligible
as long as a flow is present in the device. It is therefore important to
realize that the device is only able to accurately perform spheroid aspiration
at a single defined step pressure once all pockets are filled with a spheroid,
thus blocking the flow.

To examine what pressure spheroids experience in pockets when not all are
filled yet, case (1) and (2) were modeled for the design of the device
including a 60 cm long rectangular channel with a 300x300 µm cross section
that mimics the outlet tube and corresponding pressure drop. The same average
length of tubing was used during our experiments. Boundary conditions of 700
Pa at the inlet and 0 Pa at the outlet were installed, similar to lowering the
outlet tube with 7 cmH2O. These simulations generated the pressure
distribution and corresponding fluid flow profile in the device.

### High-throughput analysis of spheroid tongue aspiration

The creep length of the spheroid tongues into the aspiration channels over
time was extracted from the experimental images using Fiji
(https://imagej.net/software/fiji/) and a custom-written Python script (which
is available at: https://github.com/RubenBoot/HighThroughput_Spheroid_MPA
/blob/main/SpheroidAspiration_AnalysisScript.py). First, the brightfield
aspiration time-lapse images were rotated to make the aspiration channels
vertically oriented (with the tongue creeping upward over time), and then
cropped using ZEN software (Zeiss). The cropped region captured the whole
aspirated spheroid tongue and aligned the beginning of the channels with the
bottom of the cropped images. The cropped time-lapse was saved as a JPEG
stack, and converted to binary images using a threshold in Fiji (see bottom
two frames in Fig. 2A). The threshold value was chosen manually to obtain a
clear contrast between the aspirated tongue edge and the surrounding empty
channel. This binary stack was then imported in the Python script. Using the
Fiji interface, the x-coordinates of pixels along the horizontal line were
manually inserted in the Python script to indicate where the middle of all 8
aspiration channels was located. The script was set up to find the edge of the
aspiration tongue by checking the binary value of every pixel on the vertical
line along these coordinates (from top to bottom) and recording the
y-coordinate corresponding to the tongue edge. This analyses was repeated for
all images in the stack, returning the set of y-coordinates for all 8 channels
and for each time step.

Fig. 2:  Automated data analysis using a custom-written Python script. (A)
Preparation workflow before running the script. First, the 8 pocket-time
series (scale bar 200 µm) is cropped to the constrictions with spheroid
tongues, where the bottom of the cropped images is aligned with the precise
start of the aspiration channels. Next, the cropped time series is converted
to binary images by setting a threshold using ImageJ. Tongues are analyzed if
they have a smooth thresholded edge and belong to spheroids that remain round
and retain a constant volume before and during aspiration, here indicated by a
red star. (B) Plot of the creep length of the 5 selected spheroids (pocket
numbers, see (A)) as a function of time. The inset shows how the tongue length
is calculated by subtracting the distance from the top of the cropped image to
the tongue edge from the total image height.

Y-coordinates (pixels) were converted into creep lengths (µm) by subtracting
the y-coordinate (which is the distance from the top of the image to the
tongue edge) from the total height of the image and multiplying this result
with the pixel distance. All results were collected in a Microsoft Excel file
alongside the time step per image.

### Statistical analysis

Statistical analysis was performed using Python and Microsoft Excel. Student
t-tests were executed using the TTEST function in Excel and p values below
0.05 were considered to be significant. Python was used to do standard error
propagation calculations on the fitting parameters to obtain error values. The
average human error in the aspiration pressure when manually lowering the
outlet vial is estimated to be 20 Pa ($\sim$ 0.2 cmH2O), and the error in
dimensions of the aspiration channel is around 5 µm (measured with a Dektak
stylus profiler). The error bars in the figures display the standard error of
the mean unless indicated otherwise, and are always based on at least two
independent experiments with separately prepared chips.

## Results and discussion

### High-throughput data extraction

In order to measure mechanics of cell spheroids in a high-throughput manner,
we designed a microfluidic device to parallelize micropipette aspiration. The
design consists of 8 parallel aspiration pockets that are 250 µm wide and
325±27 µm tall, in order to be able to contain a single spheroid with a
maximum diameter of 250 µm. Each pocket connects to an aspiration channel that
is 50 µm wide and 50±2.5 µm tall, chosen to be similar in size to pipette
diameters used in previous glass micropipette spheroid aspiration studies
(Fig. 1A-B) .13, 26 We decided to implement 8 pockets as it was the maximum
number of pockets that fit in the field of view of the 5x microscope
objective. To mimic traditional micropipette aspiration as accurately as
possible, the multilayer wafer mold was designed to create symmetric
aspiration pockets with aspiration channels positioned at the centerline of
the pockets. This way, spheroids were raised from the device bottom during
aspiration (similar to the single cell aspiration device created by Lee et
al.).35 Two PDMS halves from the device mold, one side with half the pocket
and the other with the other half of the pocket plus the aspiration channel,
were aligned under a microscope using alignment arrows incorporated in the
design (see ESI† Fig. S2) and bonded in the oven overnight.

The chip was flushed with media before starting an experiment. Then, a small
volume of spheroid suspension ($\sim$ 20 µL) was added to the inlet reservoir.
The spheroids were moved into the pockets through the flow induced by lowering
a media reservoir connected to the outlet and mounted to a vertical rod,
thereby exerting a precise hydrostatic pressure gradient (Fig. 1C). Once a
spheroid arrived in the pocket, it blocked the flow through the aspiration
channel, thus preventing other spheroids from entering the same pocket.
Induced pressure gradients, by lowering the outlet media reservoir, were at
first kept low enough to ensure that spheroids did not deform in the
aspiration channels yet. Only when all pockets were loaded with spheroids was
the outlet reservoir lowered to a level that induced the chosen step pressure
for aspiration. Spheroid tongues started creeping in the aspiration channels
as they were subjected to the pressure difference between the atmospheric
pressure at the inlet reservoir and the hydrostatic pressure exerted by the
outlet media tube (Fig. 1D). In this way, spheroids experienced the aspiration
force in a similar manner as for traditional micropipette aspiration, where
spheroids are kept at atmospheric pressure and aspirated by applying an
underpressure in a glass capillary.

We developed a custom-made Python script to analyze the spheroid tongue
deformations in an efficient and fast manner. Before running the script,
brightfield time-lapse image series were rotated, cropped and changed into
binary images to focus on the creeping tongues in the channels (Fig. 2A). To
determine the creep length $L(t)$, the script derived the distance from the
top of the binarized image to the spheroid tongue edge, and subtracted this
value from the total image height. The Python script thus extracted the creep
lengths for the 8 aspiration channels and each step in time (Fig. 2B). We
excluded spheroids that were not round before- or did not remain constant in
volume during aspiration.

### Pressure distribution in the chip

In contrast to microfluidic single cell aspiration chips, where channels have
smaller dimensions than the used tubing,34, 35 the required cross-section for
channels to flow undeformed spheroids in is as large as the tubing (with a
diameter of 300 µm).

Fig. 3:  Pressure distribution across aspiration pockets. (A) A 3D numerical
simulation of the pressure distribution assuming the device is connected to a
60 cm long straight rectangular channel mimicking the outlet tube. A pressure
gradient of 700 Pa is simulated for two different configurations: all pockets
are open (left), and all pockets but one are clogged by spheroids (right). (B)
Brightfield images from an HEK cell spheroid aspiration experiment,
demonstrating how simultaneous aspiration starts as soon as all channels are
clogged. At first (a), no pressure gradient is present yet and three pockets
remain open, indicated by red arrows. Five seconds later (b), a pressure
gradient has been induced and spheroids flow into the pockets but do not clog
everything yet. After five more seconds (c), all spheroids have clogged the
pockets, thereby blocking further flow and ramping up the pressure. Spheroids
now experience the full induced hydrostatic pressure gradient as evident from
the tongues all creeping simultaneously into the aspiration channels. Scale
bar 200 µm.

Therefore, the pressure drop over the tubing is non-negligible in comparison
to the pressure drop across the chip. This is a considerable problem, as
slight changes in the length of the tubing may cause significant changes in
the experienced pressure drop in the microfluidic device. To avoid these
pressure drop effects, we designed the device in such a way that the entire
flow is stopped once all pockets are filled with spheroids and the pressure
gradient is fully defined by the hydrostatic pressure. However, spheroids that
are loaded into the device and swept along by the induced flow will reach the
aspiration pockets one at a time. Therefore, pressures will redistribute in
the device for each spheroid that clogs an aspiration pocket and stops the
flow through the adjacent aspiration channel. This might cause a problem, as
the spheroids that already arrived in the pockets may experience an aspiration
pressure that increases over time when additional pockets fill up with
spheroids. Instead, all spheroids should experience a single step pressure to
allow correct data analysis.

To examine the effect of pressure redistribution, we performed 3D COMSOL
simulations for two different cases: (1) all pockets are open, and (2) all
pockets are clogged by spheroids except for one. A 60 cm long rectangular
channel with a 300x300 µm cross section was incorporated into the 3D design to
mimic the outlet tube, as it induces a considerable pressure drop, and a
pressure gradient of 700 Pa was simulated across this total geometry. The
model showed how the pressure gradient over the aspiration channel increases
from $\sim$50 Pa when all pockets are open to $\sim$300 Pa when all but one
are clogged (Fig. 3A). It is important to note that these values are dependent
on the chosen boundary conditions, and in this context simply serve to
estimate the extent of this effect.

We concluded from these simulations that it is important to ensure that
spheroids arrive at the pockets at approximately the same moment in time.
Otherwise, spheroids might experience a pressure that starts aspiration when
almost all pockets are clogged but jumps once the final pocket clogs. In
experiments, we discovered that spheroids all start aspirating at the same
time as long as we punch the inlet hole close to the pockets and add
sufficient spheroids to the inlet reservoir (Fig. 3B). To circumvent the
effect of pressure redistribution, spheroids were slowly flown towards the
pockets by inducing a minor pressure gradient ($\sim$150 Pa) and were halted
before the pockets by bringing the height of the outlet vial back to the
starting point with no flow. Then, the final pressure gradient was induced by
lowering the outlet vial again, and all spheroids that were floating near the
pockets experienced the flow and filled up the remaining unclogged pockets at
the same time. This ramped up the pressure, and the spheroids experienced the
full pressure gradient, thus starting the measurement at the same time for all
pockets.

Fig. 4:  Validation of sensitivity of the device to determine spheroid
mechanical properties. (A) Comparison plot of the creep length versus time for
one HEK cell spheroid aspirated at 700 Pa (orange) and another at 500 Pa
(blue). The creep curves are fitted with the modified Maxwell model (black
dashed lines), which is explained in the inset. The fast elastic deformation
$\delta$ equals the intercept of the linear viscous flow with the y-axis, and
is shown to be larger when aspirating spheroids at larger pressures. (B)
Brightfield images of two separate aspiration experiments for HEK cell
spheroids, showing the creep length L(t) after 23 s of aspiration at 500 Pa
(top) or 700 Pa (bottom), with snapshots focusing on the aspiration pocket
(left, scale bar 50 µm) and zoomed in on the aspiration channel (right, scale
bar 20 µm). (C) Histograms comparing the average elastic deformation $\delta$
for HEK cell spheroids aspirated at different pressures (500 Pa and 700 Pa).
***, p < 0.001 with n = 56 and 24 for 500 Pa and 700 Pa respectively. Error
bars are SEM.

### Validation of sensitivity and reproducibility when working at different
aspiration pressures

To confirm the sensitivity and reproducibility of our device, we measured the
deformability of HEK293T spheroids at two slightly different aspiration
pressures of 500 and 700 Pa. The obtained creep data alongside visual
confirmation showed that the aspirated spheroids displayed an initial elastic
deformation followed by a viscous response (Fig. 4A). The tissue relaxation
time $\tau$ demarcates these two regimes and is given by $\tau$ = $\eta$/$E$,
with $\eta$ being the viscosity and $E$ the elastic modulus of the spheroid.
We fitted this viscoelastic response to the modified Maxwell model, following
previous studies on spheroid micropipette aspiration.13, 26, 25 The model
consists of four elements (shown in the inset of Fig. 4A): a dashpot $\xi_{t}$
in series with a modified Kelvin-Voigt element, which consists of a spring
$k_{1}$ in parallel with a dashpot $\xi_{c}$ and spring $k_{2}$ in series. The
creep length $L(t)$ in the context of this model is given by:

$L(t)=\frac{f}{k_{1}}(1-\frac{k_{2}}{k_{1}+k_{2}}e^{\frac{-t}{\tau_{c}}})+\frac{f}{\xi_{t}}t$
(1)

where $f$ is the aspiration force, $k_{1}$ is the spring constant for the
elasticity of the spheroid, $k_{2}$ relates to the initial increase in $L(t)$,
$\xi_{t}$ represents the viscous dissipation of the flowing tongue and
$\tau_{c}$ is the rising time of the elastic deformation $\delta$. Here,
$\tau_{c}$ = $\frac{\xi_{c}(k_{1}+k_{2})}{k_{1}k_{2}}$ with $\xi_{c}$ being a
friction coefficient related to the rising time. Hence, the modified Maxwell
model has four fitting parameters: $\delta$ = $f$/$k_{1}$, $\dot{L_{\infty}}$
= $f$/$\xi_{t}$ (being the flow velocity at long timescales), $\beta$ =
$k_{2}$/($k_{1}$ \+ $k_{2}$) and $\tau_{c}$.

As shown in Fig. 4B, the creep length $L(t)$ of the spheroid tongue was
smaller for measurements at 500 Pa in comparison to 700 Pa, demonstrating the
sensitivity of our device. However, creep length can only be compared for a
precise point in time. To quantify differences between the entire
measurements, we compared the average elastic deformation $\delta$ by fitting
Eq. (1) to the creep data. The average deformation $\delta$ was significantly
smaller for measurements performed at 500 Pa ($\delta$ = 70 $\pm$ 2 µm) in
comparison to 700 Pa ($\delta$ = 90 $\pm$ 4 µm), as one would expect when
exerting a smaller force (Fig. 4C). This demonstrates how the device is
sensitive enough to work at small differences in pressure and create
reproducible deformations in agreement with theoretical expectations.

### Measurements on spheroids with known mechanical properties

To demonstrate the high-throughput mechanical phenotyping capabilities of our
device, we measured the mechanical properties of three different cell spheroid
models that have been probed in previous studies.46 In addition to our
measurements performed with HEK293T cell spheroids, we studied two stiffer
spheroid models made of either NIH3T3 fibroblasts or MCF10A cells. While the
HEK293T cell spheroids were probed at 500 and 700 Pa, the two stiffer spheroid
models were aspirated at a higher pressure of 1500 Pa as lower pressures would
induce a slower deformation and require a longer time scale to analyze the
full viscoelastic response (Fig. 5A).

In traditional micropipette aspiration, the aspiration force $f$ of the
pipette when considering spheroid volume conservation is given by:

$f=\pi R_{p}^{2}\Delta P,$ (2)

where $R_{p}$ is the radius of the pipette and $\Delta P$ the applied
underpressure in the pipette.47 Previous studies on micropipette aspiration of
spheroids have pointed out that the actual pressure exerted on the spheroid
equals the applied underpressure $\Delta P$ minus a critical pressure $\Delta
P_{c}$ at which aspiration of the spheroid occurs. When aspirating at a
pressure lower than $\Delta P_{c}$, the spheroid will not deform due to its
inherent tissue surface tension $\gamma$.13, 26

To calculate this critical pressure, separate measurements of the retraction
of the spheroid tongues are required when the pressure is brought back to zero
(see ESI†). In contrast with traditional glass micropipette aspiration, where
spheroids remain stuck in the pipette and the tongue slowly retracts, on our
device spheroid tongues retracted so fast that it was impossible to measure a
retraction curve when the pressure was brought back to zero (see Movie S2†).
This effect was consistent for all three cell lines. We therefore investigated
the effect of accounting for $\Delta P_{c}$ through traditional micropipette
measurements on HEK293T spheroids (measuring both aspiration and retraction,
see ESI†). We found that $\Delta P_{c}$ ranged between 50 and 150 Pa (when
aspirating at 500 Pa), which changes parameter values obtained by fitting
aspiration curves by maximally 10-30 % (Fig. S3 and Table S1†). Additionally,
we saw that the spheroids deformed differently in the glass micropipettes in
comparison to our device, displaying a lower elastic deformation $\delta$ and
flow velocity $\dot{L_{\infty}}$. One possible explanation for the discrepancy
between our device and traditional MPA is that the chip has square aspiration
channels instead of round capillaries, potentially influencing the creep of
the tongue due to the different geometry or due to wall friction (PDMS instead
of glass). Moreover, the pockets on our chip have rounded walls which the
spheroids potentially push back on during relaxation, making them move
slightly backwards in the pocket during retraction. We conclude that
measurements with our microfluidic device slightly deviate from glass
micropipette aspiration measurements. However, our device has the unique
benefit of providing measurements at high throughput, thus allowing systematic
comparisons between different cell types.

The creep curves showed that the two stiffer spheroid models made of NIH3T3 or
MCF10A cells had a lower initial elastic deformation $\delta$ and slower
viscous flow $\dot{L_{\infty}}$ than the more deformable HEK293T spheroids
(Fig. 5B). All curves were fitted with the modified Maxwell model to extract
the relevant mechanical parameters. The first term in Eq. (1) characterizes
the elastic regime, with $k_{1}$ = $\pi$$R_{p}$$E$, while the second term
represents the flow at constant velocity $\dot{L_{\infty}}$ for longer
timescales, with $\xi_{t}$ = 3$\pi^{2}\eta R_{p}$. As our microfluidic device,
unlike traditional glass micropipettes, does not present cylindrical
constrictions, a correction for rectangular constrictions needs to be
implemented in regards to $R_{p}$.48, 34

Fig. 5:  High-throughput comparison of spheroid mechanics for different cell
lines. (A) Brightfield snapshots after 23 s of aspiration at 1500 Pa of a
NIH3T3 (left) and MCF10A (right) spheroid, scale bars 50 µm. (B) Comparison
plot of creep length versus time for a HEK293T spheroid (purple) aspirated at
700 Pa, and a NIH3T3 (green) and MCF10A (orange) spheroid aspirated at 1500
Pa. The creep curves are fitted with the modified Maxwell model (black dashed
lines). (C) Average elastic moduli and (D) average viscosity measured for the
three different cell lines. ***, p < 0.001 and ns is nonsignificant with n =
80, 75 and 34 for HEK293T, NIH3T3 and MCF10A respectively. Error bars are SEM.

The effective channel radius $R_{eff}$ is now given by:

$R_{eff}^{4}=\frac{2}{3\pi}\frac{W\times H^{3}}{(1+\frac{H}{W})^{2}\times
f^{*}},$ (3)

with $W$ and $H$ being the width and height of the rectangular constriction
and $f^{*}$ being a function of the aspect ratio ($H$/$W$), given by Son.48

When fitting obtained creep data with Eq. (1) and plugging in Eq. (2, the
elastic modulus $E$ is derived as:

$E=\frac{R_{eff}\Delta P}{\delta},$ (4)

and the viscosity $\eta$ as:

$\eta=\frac{1}{3\pi\dot{L_{\infty}}}R_{eff}\Delta P.$ (5)

The average elastic moduli were almost four times as large for both NIH3T3 and
MCF10A cell spheroids in comparison to the softer HEK293T cell spheroids, but
were not significantly different from each other (Fig. 5C). Similarly, both
models had a viscosity almost six times larger than for HEK293T spheroids but
again were not significantly different from each other (Fig. 5D).

These obtained values are consistent with values measured in previous studies
(Table 1). For HEK293T cell spheroids, we measured an average elastic modulus
of $\sim$210 Pa which agrees with parallel-plate compression on HEK293 cell
spheroids measuring a range of 200-400 Pa.49 Our NIH3T3 spheroids had an
average modulus of $\sim$780 Pa, which falls within the range of 500-3500 Pa
measured with colloidal probe AFM.50 However, the MCF10A spheroids displayed
an average modulus of $\sim$770 Pa which is just below the range of
1250$\pm$320 Pa measured by squeezing MCF10A spheroids with microtweezers.19
This discrepancy could be explained by the fact that this range was determined
for only 6 spheroids in the microtweezer study, or potentially squeezing might
induce different deformation behavior compared to aspiration. Altogether,
these results demonstrate that our device is well capable

Table 1:  Spheroid mechanical parameters for different cell lines, derived using the modified Maxwell model and performing a least squares regression of the experimental creep curves Cell line |  E (Pa) |  $\eta$ (kPa s) | n
---|---|---|---
HEK293T | 210 (±5) | 12 (±1) | 80
NIH3T3 | 780 (±30) | 67 (±3) | 75
MCF10A | 770 (±30) | 67 (±5) | 34

to measure the viscoelastic behavior of multicellular spheroids and determine
their mechanical properties in agreement with other experimental techniques.

## Outlook and conclusions

We have developed a microfluidic chip that follows the principles of
traditional micropipette aspiration to quantify the viscoelastic response of
cell spheroids in a high-throughput manner, making it possible to make
statistically meaningful comparisons between different experimental
conditions. The chip performs viscoelastic creep measurements as soon as
spheroids fill up the 8 parallel aspiration pockets and block further fluid
flow. The design of the chip can in principle be adapted to obtain smaller or
larger aspiration channels, but this will influence the overall volumetric
flow rate through the chip and thus the ease of loading spheroids. Similarly,
the number of pockets could be increased, though this would make it more
difficult to load them. With the current geometry, our chip is able to obtain
reproducible and accurate results and to detect differences upon small changes
in pressure. Our results are in agreement with values from previous studies
and demonstrate the high-throughput aspect of the chip: it is efficient and
easy to use in comparison to traditional micropipette aspiration and other
experimental techniques, and provides large amounts of data in a smaller
amount of time. Therefore, the microfluidic device presented here is a
suitable technique to investigate the mechanics of a wide range of tissues,
from embryonic to tumor, to provide mechanistic insights in important
physiological processes such as tissue remodeling and cancer metastasis.

## Conflicts of interest

There are no conflicts to declare.

## Acknowledgements

R.C.B. and P.E.B. gratefully acknowledge funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
program (grant agreement no. 819424). A.R. was supported by an Erasmus+
Traineeship. G.H.K. gratefully acknowledges funding from the VICI project How
cytoskeletal teamwork makes cells strong (project number VI.C.182.004) which
is financed by the Dutch Research Council (NWO). The authors thank Dimphna
Meijer for the HEK293T cells, and thank Timon Idema for helpful discussions.

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## Supplementary Information

### Glass capillary micropipette aspiration

HEK293T spheroids were aspirated using pipettes with a diameter of 65$\pm$5
µm, fabricated by pulling borosilicate glass pipettes (Harvard Apparatus, 1 mm
OD, 0.5 mm ID) with a laser-based puller (Sutter Instruments Co Mode P-2000)
and cutting them with a quartz tile. Cell adhesion to the pipette walls was
prevented by incubating the pipettes in 2 mg/mL PolyEthyleneGlycol-PolyLysine
(PLL(20)-g[3.5]-PEG(2)/PEG(3.4)-Biotin(20%), SuSos AG, Dubendorf, Switzerland)
in MRB80 solution (80 mM piperazine-N,N’-bis(2-ethanesulfonic acid) (Pipes),
pH 6.8, 4 mM MgCl2, 1 mM EGTA [Sigma]) for 30 minutes. Spheroids were
suspended in CO2-equilibrated medium and kept in an experimental chamber
consisting out of microscopic slides. For this, slides were stuck to a custom-
made aluminum spacer of 3 mm thickness using vacuum grease (Beckman Coulter).
The pipette was introduced into the chamber, aligned with a spheroid and an
aspiration pressure was attained by vertically displacing a water reservoir
connected to the pipette using a vertical translational stage (LTS300,
Thorlabs). Spheroids were aspirated using a pressure $\Delta P$ = 5 cmH2O and
visualized on an inverted microscope (Nikon Eclipse TI) with a 10x air
objective. After aspiration, the pressure gradient was removed and the
retraction of the tongue was recorded. The creep advancement of the tongue was
recorded with an ORCA Flash 4.0 digital camera using a 1s interval for a total
of 10 minutes, of which 5 minutes corresponded to aspiration and the next 5
minutes to retraction. Data was obtained for two independent experiments,
which were performed at room temperature. As the experimental set-up did not
include a heating stage to keep the experimental chambers at the physiological
temperature of 37 °C, aspiration of spheroids was only performed in the first
hour after they came out of the incubator. The critical pressure $\Delta
P_{c}$ to aspirate the spheroids was derived from

$\Delta P_{c}=\Delta P\frac{\dot{L_{R}}}{\dot{L_{R}}+\dot{L_{A}}},$ (S1)

where $\dot{L_{R}}$ and $\dot{L_{A}}$ are the retraction and aspiration flow
rates respectively 13, 26.

## Supplementary Movies

Movie 1: Microfluidic multi-channel aspiration experiment to determine
spheroid mechanics. A brightfield video of HEK293T spheroids being aspirated
into the aspiration channels under an applied hydrostatic pressure of $\Delta
P$ = 700 Pa for a total duration of 5 minutes. Scale bar is 200 µm.

Movie 2: Spheroids move out of pockets during retraction measurement. A
brightfield video of NIH3T3 spheroids being aspirated under a hydrostatic
pressure of $\Delta P$ = 1500 Pa for the first 10 minutes, after which the
pressure gradient is removed and spheroid tongues start retracting. The
tongues retract within seconds, making it impossible to record a retraction
curve and extract a retraction rate $\dot{L_{R}}$ to derive a critical
pressure $\Delta P_{c}$. Scale bar is 200 µm.

Movies are available upon request to the corresponding author.

## Supplementary Figures

See below.

Fig. S1: Close-up of the microwell array with HEK293T cell spheroids after 3
days of culture. After depositing the cell suspension in the microwell array,
cells divide over the wells and aggregate into spheroids to reach a final size
that depends on the culturing time, original cell number, and cell type. Here,
cells are stained with Calcein AM (AAT Bioquest) for visualization and
confirmation of cell viability. The image is an overlay of a brightfield image
and a fluorescence image, cropped from an original image taken with an
inverted fluorescence microscope (Zeiss Axio-Observer) using a 5x/NA 0.16 air
objective. Scale bar 200 µm. Fig. S2: Alignment of PDMS slabs using alignment
arrows in the design. (A-D) AutoCAD screenshots of the full design that was
printed on the silicon wafer using soft lithography. (A) First layer, which
was printed to a height of $\pm$50 µm, with the design enframed with alignment
arrows. For slab 1, the alignment arrows are written by the laserwriter as
pillars, while for slab 2 an entire rectangular surface is written except for
empty wells complementary to the arrows of slab 1. Alignment crosses are
written to facilitate the alignment of layer 2 with layer 1 in the next step
of the writing process. (B) Final developed design, where the second written
layer is indicated in green. (C) Zoomed-in section of layer 1, clarifying the
placement of alignment arrows. (D) Zoomed-in section of layer 2 (with the
middle part cut out) to demonstrate how the right part of the wafer design is
mirrored to the left part. This is necessary to create the correct final
design, as PDMS slab 2 is turned over when aligning it with PDMS slab 1. (E)
Side view of the final developed design on the silicon wafer, which is used
for PDMS casting. Slab 1 contains arrow pillars and slab 2 complementary arrow
wells (both indicated in red) to facilitate easy alignment before bonding the
two slabs in order to create the final device. Fig. S3: Glass micropipette
aspiration experiment. (A) Brightfield images of the micropipette aspiration
of an HEK293T cell spheroid using a glass micropipette with a radius $R_{p}$ =
32.5 µm. Left and middle panels: images taken during aspiration at a
hydrostatic underpressure of $\Delta$P = 500 Pa, at the beginning of the
experiment at $t_{A}$ = 0 s (left) and after $t_{A}$ = 2 minutes (middle).
Right image: After 5 minutes, the pressure gradient is removed and the
retraction is measured, here shown after $t_{R}$ = 2 minutes (right). Scale
bar 100 µm. (B) Creep curve (yellow) of the aspiration of the tongue over
time, and (C) creep curve (yellow) for the retraction of the tongue, both
fitted with the Modified Maxwell model (black dashed lines).

## Supplementary Tables

See below.

Table S1:  Mechanical characteristics of spheroids with different radii $R_{0}$ measured by glass micropipette aspiration. The elastic modulus $E$ and viscosity $\eta$ were derived from creep curves fitted to the Modified Maxwell Model, either using just the applied aspiration pressure $\Delta P$ or taking the aspiration pressure corrected for the critical pressure $\Delta P_{c}$ (from Eq. (S1) in the Supplementary Information), $\Delta P$ – $\Delta P_{c}$ Nr. |  $R_{0}$ (µm) |  $E_{\Delta P-\Delta Pc}$ (Pa) |  $\eta_{\Delta P-\Delta Pc}$ (kPa s) |  $E_{\Delta P}$ (Pa) |  $\eta_{\Delta P}$ (kPa s) |  $\Delta P_{c}$ (Pa)
---|---|---|---|---|---|---
$1$ | $92$ | $317$ | $30$ | $383$ | $36$ | $86$
$2$ | $76$ | $237$ | $21$ | $345$ | $31$ | $156$
$3$ | $99$ | $328$ | $22$ | $419$ | $28$ | $109$
$4$ | $101$ | $276$ | $18$ | $319$ | $21$ | $68$
$5$ | $84$ | $281$ | $23$ | $364$ | $30$ | $113$
$6$ | $87$ | $270$ | $26$ | $374$ | $37$ | $138$