Using a micro-device with a deformable ceiling to probe stiffness heterogeneities within 3D cell aggregates

The micro-device is fabricated as a monolithic piece of PDMS, which is cast onto a 3D-printed mould, then bonded to a coverslip or glass slide. It is composed of two main components, as shown in figure 1(a): two observation chambers that are surrounded by two air cavities each. The observation chambers contain the spheroids and are fluidically independent of the air cavities (see cross-section in figure 1(b)). Each of the two observation chambers is a disc of diameter 2.5 mm and height 100 µm. They are connected to each other and to the channel inlets with a 500 µm high channel, as shown in the cross-section of figure 1(c) and the full scan of the device in figure 1(e). Two air cavities surround each observation chamber. They are rectangular in the x–y plane and have a right-trapezoidal cross-section, with one rounded corner, in the x–z plane (figure 1(b)). Applying a negative pressure inside the air cavities deforms the PDMS and decreases the ceiling height in the observation chamber, allowing for the compression of the spheroids.

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A typical experiment begins with filling the observation chamber with the culture medium. Then preformed hepatoma and/or fibroblast spheroids ($130 \pm 20\,\mu$m in diameter) are introduced at the inlet, using a hand-held pipette. The high ceiling of the channel allows them to flow freely at first. Once they reach the observation chamber they are slightly compressed, so that they become trapped by the low ceiling (figure 1(c)). The spheroids can then be deformed by the moving ceiling, while their geometrical and functional responses are observed with a microscope (figure 1(e)).

Applying a negative pressure inside the air cavities deforms the device and decreases the ceiling height in the observation chamber. This deformation depends on the geometry and inner pressure of the air cavities. To control the strain applied to the spheroids, the device deformation is calibrated for different inlet pressures, as shown in figure 2.

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First, the device deformation was simulated using Autodesk Fusion 360 for different geometries of the air cavities and observation chambers (figures 2(a)–(c) and SI movie 1 for an animation). A rounded trapezoidal cross-section of the air cavities was found to induce an efficient vertical displacement of the ceiling of the observation channel, for the range of negative pressures available. In particular, the protrusion of the overhanging part above the channel could be modulated to enhance the deformation of the observation chamber. The amount of protrusion was then chosen through a compromise between increasing the deformation while maintaining the ease of microfabrication, particularly when peeling the PDMS off the 3D-printed mould.

The simulation results were then tested experimentally by injecting a suspension of fluorescent microspheres into a device and letting the solvent dry. This led the PDMS and glass surfaces inside the chip to be non-specifically coated with a layer of fluorescent particles that could be tracked by performing confocal z-stacks for different air cavity pressures, as shown in the orthogonal views along y–y' in figure 2(d) (SI movie 2). They show that the whole ceiling indeed goes down as negative pressures are applied in the air cavities. It is important to notice that the axes in these images are scaled unequally, as is apparent from the scale bars. The ceiling is, therefore, essentially flat and curves slowly around the edges. The ceiling position is then estimated by fitting a quartic function (in white) to the positions of the fluorescent particles. Then by subtracting the fit at zero applied pressure, the vertical displacement of the ceiling could be measured at each pressure.

The experimental measurements show that the vertical displacement of the ceiling increases linearly as a function of the negative pressure, independently of the position within the chamber figure 2(e). To compare simulation and experiments, the displacement of the chamber centre is shown for each case. The simulation also predicts a linear displacement of the chamber centre but underestimates its value by ${\approx}1/3$.

The profiles of the ceiling along x–x' and y–y' are shown in figures 2(f) and (g), for a moderate range of pressures. Over this range, the variability in the ceiling displacement over its surface is $\approx \pm10\%$ around the mean value. Note that it is possible to entirely collapse the ceiling by extending the pressure range.

By following the protocols above, multiple spheroids can be injected into the observation chamber with a pipette. They can then be deformed in parallel while being observed with brightfield microscopy, as shown in figures 3(a) and (d) and supplementary movie 3 for spheroids formed from a hepatoma cell line (H4-II-EC3). Since the pressure in the air cavities is computer-controlled, it is possible to program the spheroids to be compressed either statically, see figures 3(a)–(c), or dynamically, see figures 3(d–f). As the spheroids are compressed vertically and observed from the bottom, their area increases in the brightfield images. The spheroids are segmented automatically (figure 3(e)) and the change in their equatorial area is monitored.

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In the static compression mode, the ceiling is lowered stepwise, and we wait 5–10 s for the spheroids to reach a steady state at each step before taking an image (see movie 4). The observed area of the spheroids increases as a convex function of the applied pressure, independently of the initial undeformed area within the range tested here (see figures 3(b) and (c)). Moreover, by normalising the deformed area by its value at zero deformation, the curves are found to nearly collapse on a single master curve, where the ${\approx}10\%$ variability between spheroids can be attributed to differences in position within the chamber (figure 3(c)).

In addition to the static compression, the pressure in the air cavities can be programmed to follow a sinusoidal pattern. This in turn leads to oscillations of the chamber ceiling and of the observed area of the spheroids, as shown in figures 3(d)–(f) (SI movie 3). Here oscillations in the range 0, −300 mbar, corresponding to a 25% deformation of the chamber, are applied at a frequency of 0.5 Hz. Again, the different spheroids follow the forcing frequency in synchrony, and they can be observed individually or together.

Co-culture spheroids were made by mixing H4-II-EC3 cells with fibroblasts (NIH-3T3). The result was reproducible core–shell structures where the fibroblasts formed a compact core, and the hepatoma cells formed a shell, as shown in figure 4(a). The core size was controlled with the initial number of seeded cells: NIH-3T3 cells do not proliferate in 3D while H4-II-EC3 cells do. The number of fibroblasts was therefore chosen to reach the desired core size and the number of hepatoma cells was chosen to reach a total diameter of $130 \pm 20\,\mu$m.

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Given the different phenotypes of these cell types, we expect their mechanical properties to be different. To investigate this, we look at the structure of the cocultures by staining their nuclei and F-actin. An early indication of the mechanical contrast between the two cell types can be found by the F-actin signal, which is much brighter in the fibroblasts than in the hepatoma cells (figure 4(b)) [22]. Moreover, the nuclear staining also displays a flattening of the fibroblast nuclei at the edge of the NIH-3T3 region, also suggesting that internal stresses are compressing these cells together.

To confirm that the core and shell have different elastic moduli, we made mono-culture spheroids with the two cell types and measured their elastic response in a cantilever experiment: a micro-cantilever of known stiffness was used to press the spheroid against a 3D-printed trap while observing the spheroid in bright-field (see figure 4(c)). The difference between the imposed displacement on the root of the cantilever and the observed displacement of its tip was used to measure the deflection. The stress is $f/A$ with $f$ the applied force and $A$ the contact area of the spheroid and the cantilever which we approximate $A = 40\times 40\,\mu$m². An ellipse was fit to the spheroid in each frame to measure the strain: the change of the length of the semi-axis along the direction of the compression (for more detail, see 5.6). This allowed us to acquire the stress–strain plots of figure 4(d), which yield average apparent Young's moduli of $E_\mathrm{H4} = 2.14 \pm 0.69$ kPa and $E_\mathrm{3T3} = 31.8 \pm 9.08$ kPa, for the hepatomas and fibroblasts respectively.

The deformation of the monoculture and co-culture spheroids was imaged using the micro-device while applying air cavity pressures from 0 to −300 mbar, with steps of −50 mbar. Brightfield images were taken while statically compressing mono-culture hepatoma spheroids and co-cultures with different fibroblast core sizes (figure 5 and SI movie 4). Consecutive images were compared together by applying a local image correlation algorithm, using a library for particle image velocimetry (PIV, see Methods section). This analysis provided a local displacement field on the spheroids, as shown in figure 5(i) for the transition from −100 to −150 mbar for three co-culture configurations.

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The norm of the velocity vectors from this vector field can then be averaged azimuthally to obtain a one-dimensional representation of the displacement as a function of the distance from the centre of each spheroid. This is shown in figure 5(iii) for the three spheroids in part (ii). A strong contrast is observed between the displacement field of the monoculture spheroid and the co-culture spheroids: in the first case, the displacement is continuous from the centre to the edge of the spheroid, while the co-culture cases display a flat region, with very little displacement. The undeformed region matches the observed fibroblast core for different core sizes.

Finite element simulations were used to better understand how differences between the mechanical responses of the core and the shell would influence the deformations of the whole co-cultures. Here the spheroids were modelled as nearly incompressible (Poisson ratio 0.49) elastic balls, deformed between two plane surfaces considered rigid, since the PDMS Young's modulus is 100–1000 times higher than the values measured for our cell aggregates [23]. Contact between the spheroids and the substrate and ceiling surfaces is considered purely frictionless. Because of invariance properties, the problem depends only on one spatial variable, here we choose the spheroid initial radius R, which we set to 1, and normalise all other quantities with respect to it. By using the problem symmetries, this could be reduced to simulating an axisymmetric 2D section of a half hemisphere (figure 6(a)). In the simulated spheroid, the core and the shell were allowed to have different Young's moduli $E_\mathrm{core}$ and $E_\mathrm{shell}$. Simulations were performed while varying $E_\mathrm{r} = E_\mathrm{core}/E_\mathrm{shell}$ and simulating the mesh's compression along $z_\mathrm{s}$ (figure 6(b)). Again, because of invariance properties, the problem only depends on this ratio, so we fix $E_\mathrm{core}$ to an arbitrary value and vary $E_\mathrm{shell}$.

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The displacement of the nodes along the $x_\mathrm{s}$ axis is plotted in figure 6(c) for a compressive strain of 0.1R. This strain is comparable with the data of figure 5, where the deformation due to a 50 mbar pressure change is equivalent to approximately 5 µm out of a channel height of 100 µm (figure 5(iii)). The simulations produced a family of curves for different ratios $E_\mathrm{r}$ of the core to shell moduli, as shown in figure 6(c).

Comparison between the experimental and simulated displacement curves display semi-quantitative agreement for the monoculture spheroids, where the curve for $E_\mathrm{r} = 1$ presents a concave shape that reaches a displacement at the edge of around $1.2\%\cdot R$, in agreement with the experimental measurements of figure 5(a). In the case of the co-cultures however, the agreement is merely qualitative, with a factor of about 3 separating the values of the edge displacement between the experiments and simulations. Nevertheless the shape of the experimental displacement curve is consistent with a large heterogeneity in stiffness between the core and shell ($E_\mathrm{r}\gt10$), which is in agreement with the independent measurements using the cantilever that give $E_\mathrm{r,exp} \approx 15$.

The moulds to fabricate the chips were designed using Fusion 360 (Autodesk) and 3D printed using an SLA-FORM3 printer and ClearV4 resin (Formlabs). The moulds were filled with a mixture of PDMS (SYLGARD, Dow) base and a curing agent at a ratio of 1:10. The PDMS was cured at 80 ^∘C for 2 h. Then, it was separated from the moulds and then plasma treated (Cute, Femto Science Inc.) for 40 s. It was then bonded to a $24 \times 65$ mm (#1.5) coverslip (Menzel–Gläser). The device was connected to Fluigent's Flow EZ pressure controller (LU-FEZ-N800), fed by a supply line of −800 mbar. The pressure cycles were controlled using Fluigent's OxyGEN software

H4-II-EC3 (CRL-1600, American Type Culture Collection) and NIH-3T3 cells (CRL-1658, American Type Culture Collection) between Passage 10 and Passage 20 were maintained on T-25 cm² flasks (Corning, France) in a standard CO₂ incubator (Thermo Fisher Scientific), following the instructions provided by the manufacturer (ATCC). The culture medium was composed of Dulbecco's Modified Eagle's medium (DMEM) containing high glucose (Gibco, Life Technologies) supplemented with 10% (v/v) fetal bovine serum (Gibco) and 1% (v/v) penicillin-streptomycin (Gibco). The cells were seeded at $5 \times 10^4$ cells·cm⁻² and sub-cultivated every three days.

The spheroids were fabricated using ultra-low adhesion U-bottom 96 well plates (Corning). Monoculture of 300 H4-II-EC3 cells or 500 NIH-3T3 cells were seeded into the wells in order to form spheroids of about 130 ± 20 µm in diameter after 24 h. To fabricate co-culture spheroids, the two cell types were mixed at different ratios to generate various sizes of fibroblast cores. 100 H4-II-EC3 and 400 NIH-3T3 cells resulted in large cores, while 200 cells of each cell type gave small cores. Co-cultures were grown for 72 h to ensure their proper core-shell arrangement by cellular self-organization.

All the images were taken using a motorized inverted microscope (Ti2, Eclipse, Nikon), equipped with either a spinning disc module (W1, Yokogawa) or an epifluorescence setup (Lumencor). Brightfield and fluorescent images were taken with a 20x objective with a 1.8 mm working distance (long working distance) and a 0.70 numerical aperture (NA) (CFI S Plan Fluor LWD, Nikon). The fluorescence images of figure 7 were taken with a 60x oil immersion objective with a 1.40 NA (Plan Apo VC, Nikon).

All the following reagents were introduced simply by placing a filled pipette tip at an inlet and letting the solution flow by gravity. No pressure is applied through the pipette, allowing the spheroids to stay in place. For F-actin staining, the cells were first fixed with a 4% (w/v) PFA (Alpha Aesar) for 30 min and permeabilized with 0.2 to 0.5% (v/v) Triton X-100 (Sigma-Aldrich) for 5 min. The samples were then blocked with a 5% (v/v) FBS solution and incubated for 90 min in a 1:200 phalloidin–Alexa Fluor 594 (Life Technologies) diluted in a 1% (v/v) FBS solution. The cytoplasmic membranes were stained with the CellBrite® Steady 650, following the manufacturer's protocol. The nuclei were labelled using the NucBlue^TM Live ReadyProbes^TM Reagent for live cells and NucBlue^TM Fixed Cell ReadyProbes^TM Reagent for PFA fixed cells, following the manufacturer's instructions.

The spheroids were segmented using a custom-made FIJI macro [33]. For each pressure value, the total area, perimeter, and major and minor axes of the spheroids are measured and recorded. To quantify radial displacement within spheroids upon compression, Particle Image Velocimetry (PIV) was performed using the open-source MatPIV toolbox in Matlab (2019b) [34], with a chosen window size $32\times 32$ px and overlap 75%. A displacement field was obtained for every deformation step applied to the spheroid by integrating the velocity data. Note that Digital Image Correlation (DIC) [35, 36] could have been used as an alternative to PIV to directly extract displacement data from the images.

5.6.1. Cantilever fabrication and calibration

5.6.2. Fabrication of traps for the spheroids

5.6.3. Spheroid compression

5.6.4. Spheroid elasticity measurement

5.7.1. Modeling device deformation

5.7.2. Modeling the mechanical response of hetero-spheroid compression