Deciphering the mechanics of cancer spheroid growth in 3D environments through microfluidics driven mechanical actuation

Abstract

Uncontrolled growth of tumor cells is a key contributor to cancer associated mortalities. Tumor growth is a biomechanical process whereby the cancer cells displace the surrounding matrix that provides mechanical resistance to the growing cells. The process of tumor growth and remodeling is regulated by material properties of both the cancer cells and their surrounding matrix, yet the mechanical interdependency between the two entities is not well understood. Herein, we developed a microfluidic platform that precisely positions tumor spheroids within a hydrogel and mechanically probes the growing spheroids and surrounding matrix simultaneously. By using hydrostatic pressure to deform the spheroid-laden hydrogel along with confocal imaging and finite element analysis, we deduced the material properties of the spheroid and the matrix in situ. For spheroids embedded within soft hydrogels, we detected decreases in the Young’s modulus of the matrix at discrete locations accompanied by localized tumor growth. Contrastingly, spheroids within stiff hydrogels did not significantly decrease the Young’s modulus of the surrounding matrix, despite exhibiting growth. Spheroids in stiff matrices leveraged their high bulk modulus to grow and displayed a uniform volumetric expansion. Collectively, we established a quantitative platform and provided new insights into tumor growth within a stiff 3D environment.

Graphical Abstract

Cancer spheroids are precisely positioned in a degradable hydrogel by photopatterning within a microfluidic device. Using a combination of both experiments and modeling, the changes in material properties of spheroid and matrix are estimated in situ. Rapid spheroid growth in soft matrices is observed following local matrix breakdown while in stiff matrices, spheroids grow slowly via uniform expansion.

Introduction

Solid cancer progression is characterized by different stages such as dysregulated cell growth, invasion into adjacent tissues, and metastasis to secondary sites. At its core, tumor growth is a biochemical and mechanical process whereby cancer cells release enzymes to soften surrounding tissue and generate forces to displace the extracellular matrix (ECM) [1–3]. The ability of the cancer cells to manipulate their surrounding ECM is of upmost importance since it governs the ability of the tumors to grow. This process has to account for stiffness of the tumor relative to that of its surrounding [4].

Cancer spheroids have been widely used as a model system to study tumor growth in vitro, yet a detailed understanding of the physical mechanism of cell growth within a 3D matrix remains elusive. While cancer cell proliferation within a degradable matrix relies on the use of matrix metalloproteinases (MMP) [5, 6], cancer cell proliferation is also reported in non-degradable matrices, such as alginate and agarose hydrogels, with a wide range of elastic moduli, ranging from 0.5 to 50 kPa [7, 8]. For a cancer spheroid within a 3D matrix, the spheroid will generate and experience forces from its surrounding matrix. For tumor growth to occur, the surrounding matrix must sufficiently deform and/or breakdown to make space for the growing cells. Current studies assessing the interplay between the cells and the ECM primarily focus on Young’s moduli [4, 9–12]. The Young’s moduli of free-floating spheroids and spheroids extracted from 3D matrices are reported to be ~1 kPa [9, 11], which is significantly lower than that of most matrices used to grow cancer spheroids. The use of Young’s moduli, associated with uniaxial loading, is insufficient to explain the growth of tumor spheroids within a 3D matrix wherein the spheroids experience multidirectional loading. To this end, the relative bulk moduli differences between the spheroid and the surrounding matrix need to be considered to understand spheroid growth in 3D matrices.

To elucidate the impact of the relative differences in material properties between the cancer spheroid and its surrounding matrix, we developed a microfluidic platform that confines individual MCF7 spheroids within a degradable gelatin-based hydrogel embedded with fluorescent particles[13]. MCF7 cells are less invasive and readily form compact spheroids in vitro, which makes the cell line a suitable source to study cancer cell growth in 3D environment [14]. The gelatin hydrogel (GelMA) was chemically tethered to the top and bottom surfaces of a deformable flow chamber. Hydrostatic pressure was utilized to mechanically load individual spheroid-laden hydrogels, and the resulting spheroid and hydrogel deformation combined with computational analysis was used in tandem to deduce spatial changes in material properties. Employing this platform, we have identified two distinct modes of cell growth depending on the Young’s modulus of the surrounding hydrogel. Hydrogels with low Young’s modulus showed localized regions of matrix softening accompanied by spheroid growth protruding into the softened matrix. In contrast, spheroids in stiff hydrogels with significantly higher Young’s modulus showed minimal softening of the surrounding material; the spheroids were found to uniformly expand during growth. A detailed analysis of these two growth modes suggested that the growth of tumor cells within the stiffer matrices mostly relied on bulk modulus while those within the soft matrices leveraged localized matrix breakdown.

Materials and Methods

Gelatin Methacrylate Synthesis and Purification

Gelatin methacrylate was synthesized using the previously described method [15]. Briefly, 10% w/v gelatin in PBS was reacted with 8mL of methacrylic anhydride at 50°C with continuous stirring. The reacted solution was filtered and dialyzed at 40°C using dialysis tubes with cutoffs of 12–14kDa. Lithium phenyl-2,4,6-trimethylbenzoylphosphinate (LAP) was used as photoinitiator.

Cell Culture and Spheroid Formation

MCF-7 cells were cultured in growth media (GM) of the following composition: 88% DMEM, 10% fetal bovine serum, 1% L-glutamine, and 1% penicillin/streptomycin. For spheroid formation, MCF-7 cells were trypsinized, centrifuged, and resuspended in 5 mL of the aforementioned GM at a concentration of 50,000 cells/mL. The cell suspension was placed in a 65 mm diameter petri dish and kept on an orbital shaker at an RPM of 60 at 37°C and 5% CO2. Spheroid formation was observed within 48 hours.

Fabrication of microfluidic device containing spheroid-laden GelMA

Fluidic chip design

The microfluidic chip was designed to selectively encapsulate individual cancer spheroids within cylindrical hydrogels via photopolymerization and support their growth. To select spheroids of 50 μm diameter, the microfluidic device was designed to have a disc shaped chamber (12 mm diameter) at the center of the device, which provides a window view for selection and positioning of the targeted spheroids. Capturing of the spheroids following the perfusion of the device with photopolymerizable GelMA solution containing spheroids and their confinement within the disc chamber was achieved by using a photomask and collimated UV light. Multiple, branched flow channels entering and exiting the chamber were designed to efficiently and homogenously supply fresh media to the spheroid-laden hydrogel throughout the chamber (Fig. S1A).

Activation of glass surfaces and subsequent tethering of polyacrylamide (PAm) hydrogels

The microfluidics device was designed to prevent the adhesion of cancer cells within the central cylindrical chamber by tethering a thin layer of bioinert PAm hydrogel onto the glass surfaces [16]. Circular coverslips of 12 mm diameter and rectangular glass coverslips of 24 mm x 50 mm were cleaned in pure ethanol for 15 minutes under gentle agitation, rinsed in DI water, and air-dried. To methacrylate the cover slips, they were exposed to a solution containing 60 μl of 10% glacial acetic acid in DI water, 40 μl of 3-(trimethoxysilyl) propylmethacrylate and 1.9 ml of pure ethanol. After 15 minutes of reaction, the coverslips were rinsed with ethanol and air-dried.

To form thin layers of polyacrylamide (PAm) hydrogels conjugated to the coverslips, a precursor solution containing 8% wt/v acrylamide, 0.4% wt/v Bis-acrylamide, 0.1% wt/v ammonium persulfate, and 0.01% wt/v N,N,N′,N′-tetramethylethylenediamine was used. 3 μl droplet of this solution was added to the center of each methacrylated rectangular coverslip and covered with a non-treated 12mm diameter circular coverslip. Conversely, 3 μl droplet of this solution was added to non-treated 1 mm square coverslips and covered with a methacrylated 12 mm diameter circular coverslip. The solution was allowed to polymerize for 30 minutes at room temperature after which the hydrogels were submerged in DI water; the non-treated coverslips detached while the PAm gels remained conjugated to the methacrylated coverslips.

Incorporation of PAm tethered glass coverslips into the microfluidic device

Within the central disc shaped cavity of the microfluidic chip, the top and bottom surfaces were comprised of thin PAm hydrogel layers (~ 5 μm). These hydrogels facilitate tethering of the GelMA hydrogels by allowing the precursors to diffuse into the PAm network prior to creating an entangled network between GelMA and PAm and thereby an integrated interface between the hydrogels layers. Moreover, the anti-fouling properties of the PAm hydrogel prevents the adhesion of spheroids that were flushed into the device thereby minimizing artifacts associated rampant growth of spheroids outside of the spheroid laden GelMA hydrogel.

The silicon wafer containing the microfluidic channel were fabricated as previously described (Fig. S1A). The etched flow channels on the silicon wafer were ~ 75 μm high. To create the top portion of the microfluidic device, a 10:1 weight ratio of PDMS to curing agent was mixed and degassed. A 3 μl water droplet was added over the circular section of the silicon wafer chip design. A 12mm coverslip tethered with PAm gel was then placed on the droplet such that the gel was in contact with the water. The volume of the water droplet ultimately determines the height of the microfluidic chamber, where a volume of 3 μl resulted in a height of ~100 μm. For taller flow channels needed to measure bulk moduli change, a 6 μl water droplet was used to achieve a chamber height of ~150 μm. The PDMS mixture was then poured over the wafer and cured at 60°C for 3 hours. Post curing, the polymerized mold was detached from the silicon wafer, and the surface with the adhered PAm hydrogel was treated with UV-Ozone along with a rectangular coverslip containing a PAm hydrogel. The UV-Ozone exposed surfaces were pressed in contact while maintaining the alignment between the PAm hydrogels on the circular and rectangular coverslips, and was bonded overnight at 60°C. Prior to use, these devices were perfused with PBS and UV sterilized for 45 minutes.

Encapsulation of MCF7 spheroids in GelMA hydrogels within the microfluidic device

GelMA powder was weighed and dissolved in PBS to create a 6.5% or 10% w/v solution at 60°C for 20 minutes. This mixture was filter sterilized (0.22 um pore size) and maintained at 37°C. MCF7 spheroids in GM were centrifuged at 800 RCF for 5 minutes, and the medium aspirated. The cell spheroid pellet was re-suspended in 100 μl of GelMA solution containing 1% far-red fluorescent particles (Thermofisher Scientific, 200 nm diameter Fluospheres), 0.01% ascorbic acid, and 2 μM LAP. This spheroid-GelMA mixture was perfused into the sterilized microfluidic device using a syringe and was briefly maintained without any flow. Under this static condition, the spheroid encapsulation was initiated by mounting a transparency based binary mask onto the microscope stage such that a single circular pattern (320 μm diameter) can be observed at the center of the field of view of a 10x objective lens. The microfluidic chip, containing spheroids and GelMA precursor solution, was placed on top of the photomask and held using a slide holder. The slide holder was used to maneuver the device and identify individual spheroids and precisely position them at the center of the circular pattern of the photomask. The system was then exposed to UV light for 30s and photopolymerized to generate spheroid-laden GelMA structures within the microfluidic device. This process was performed multiple times to generate approximately 4–7 hydrogels embedded with MCF7 spheroids within the same device. Unpolymerized GelMA was removed by perfusing with PBS containing 6.5% penicillin and streptomycin. Using 30-gauge Teflon tubing, a 10 mL syringe, containing a GM reservoir, and a stop cock with a Leur lock connection was respectively attached to the inlet and outlet of the microfluidic device. For acellular hydrogels, a GelMA precursor solution, devoid of any spheroids was used. The devices were maintained at 37°C and 5% CO₂ under a media perfusion rate of 50 μL/hr.

Applying hydrostatic pressure to the flow device and quantification of hydrogel deformation

Using the microfluidic device to apply hydrostatic pressure to the spheroid-laden hydrogels, the flow outlet valve was closed and the GM reservoir syringe at the inlet was replaced with an empty 10 mL syringe with no plunger. 8 mL of PBS, supplemented with 6.5% penicillin/streptomycin, was added to the empty syringe and the nozzle was gently agitated to remove any air bubbles. Afterwards a sterilized cotton swab was fitted into the syringe opening to prevent debris and contaminants entering the PBS solution. The microfluidic device was mounted onto the confocal stage, and the syringe loaded with PBS was positioned such that the top of the fluid column was at the same height as the microscope stage. The cancer spheroids were allowed to equilibrate at this 0 pressure difference for 20 minutes prior to obtaining z-stack images of the cancer spheroid and the surrounding GelMA hydrogel. To apply hydrostatic pressure, the syringe was elevated and maintained at ~11.25 inches above the microscope stage and maintained for 20 minutes prior to re-imaging the spheroid and the surrounding GelMA hydrogel. The cell-laden hydrogels were imaged one at a time at 0 and 2.8 kPa hydrostatic pressures prior to relocating to a different sample site. To continue the culture of the encapsulated spheroids, the PBS containing syringe was replaced with a GM reservoir syringe and transferred back into 37°C incubator with 5% CO₂. For compression of free-floating spheroids, the cancer cells were injected into the microfluidic device prior to closing the flow outlet valve, and the hydrostatic pressure was applied as previously described.

Deformation of the GelMA hydrogel was quantified via particle image velocimetry (PIV) by tracking the displacement of embedded fluorescent particles before and after hydrostatic pressure application. Here, a 3D interrogation window (size) of 14×14×4 μm along with 3.5 μm and 4 μm spacing in XY, and Z directions, respectively, were used to generate a Cartesian displacement field. Additionally, the accuracy of the cross-correlation process was monitored by quantifying the signal-to-noise ratio, defined as the peak divided by the mean correlation value within each interrogation window.

Finite element modeling (FEM)

COMSOL V.07 was used for the finite element modeling where the analysis was carried out under elastostatic conditions, and the materials were assumed to be isotropic and linearly elastic. For all cases, the finite element domain was designated to be circumferentially homogeneous and meshed with 2D tetrahedral elements.

Fabrication of bi-layer GelMA hydrogel

To validate that the radial strain ratio, λ, can be used to detect relative differences in the elastic moduli of different regions of the hydrogel, we fabricated a bi-layer hydrogel with a stiff exterior and soft interior and vice-versa. Firstly, a 6.5% GelMA solution, mixed with 1% green fluorescent particles, and 2 μM LAP was perfused into the microfluidics device. To initiate polymerization, this solution was exposed to UV light using a dark photomask containing a 100 μm diameter clear circle pattern for 20 seconds. The unreacted GelMA solution was flushed out using PBS prior to the addition of 10% GelMA solution containing 1% red fluorescent particles and 2 μM LAP for the generation of outer layer. A dark photomask containing a 320 μm diameter clear circle pattern was mounted onto a microscope stage, and the polymerized GelMA hydrogels containing the green particles were located. This pre-existing hydrogel was placed at the center of the circular pattern and exposed to UV light for 30 seconds to polymerize the exterior layer of the bi-layer hydrogel. The device was rinsed with PBS to remove all unreacted solution. A similar approach was used to form a bi-layered hydrogel with a soft interior and stiff exterior by switching the concentration of the GelMA solution used to form each layer.

Calculation of λ value

Mathematically, the parameter λ is defined as ${ϵ}_r^{LocalECM}/{ϵ}_r^{Spheroid}$, where ${ϵ}_r^{LocalECM}$ and ${ϵ}_r^{Spheroid}$ are the average radial strains within the local matrix and spheroid, respectively. To determine λ, we first converted the PIV generated 2D Cartesian displacements to radial displacements with origin of the polar coordinates located at the center of the spheroid-laden hydrogel. Focusing primarily on the mid-transverse plane of the cylindrical hydrogel, we evaluated ${ϵ}_r^{LocalECM}$ and ${ϵ}_r^{Spheroid}$. To quantify ${ϵ}_r^{Spheroid}$ at a specific angle, θ, the radial displacement at a point along the edge of the spheroid was divided by its distance to center of the hydrogel. Moreover, ${ϵ}_r^{LocalECM}$ was also evaluated at the same angle by taking the difference in displacement at the same point on the edge of the spheroid and 20 μm in the radial direction before dividing by 20 μm. With these two parameters, λ was determined and averaged along the entire circumference to calculate the mean radial strain ratio or divided into ± 5° bins that were centered at the following angular positions: 5, 45, 90, 135, 180, 225, 270 and 315° (see Figure 2G and 2H).

Figure 2: Changes in materials properties with cancer spheroid growth.

(A) Schematic illustrating the spatial model of the spheroid-laden hydrogel used for FE analyses and the applied boundary conditions (red) used to simulate the hydrostatic pressure. The local matrix is defined as a region within 20 μm distance away from the periphery of the spheroid. (B) The effect of local matrix Young’s moduli on the radial strain profiles (ε_r) within the mid-transverse plane of the spheroid-laden hydrogels under hydrostatic pressure. The strain profiles is shown as a function of normalized radial position, r’, which is the radial position (r) divided by the radius of the cylinder, 160 μm. The Young’s Modulus of the spheroid was kept at 10 kPa while that of the local matrix was varied. The Poisson’s ratios of the spheroid and hydrogel were ~0.5 and 0.45, respectively. (C) Radial strain ratio (λ) as a function of the Young’s moduli of the cancer spheroid and hydrogel. At a modulus ratio of 10, the Young’s moduli of the spheroid and hydrogel are 1.25 and 12.5 kPa, respectively. (D) Fluorescence images of the cancer spheroid (green) embedded within the soft or stiff GelMA hydrogels (magenta) at day 0 and day 6 culture time. Scale bar: 50 μm. (E) Quantification of the spheroid growth within the soft or stiff hydrogels by normalizing the area of encapsulated spheroid at day 6 to day 0. (n = 4–5 spheroids/group for D-E; Student T-test comparison between Soft and Stiff). (F) Circumferentially averaged λ values as a function of culture time in soft and stiff GelMA hydrogels containing cancer spheroids. (G-H) Representative polar plots of binned λ values at different angles for spheroids grown within a soft (G) and stiff (H) hydrogel. (I) The ratio of peak to the mean circumferential λ value of spheroids within the soft and stiff hydrogels as a function of culture time. (n = 5 spheroids/group for F-I; Student T-test comparison between Soft and Stiff at each time point). (J-K) XY confocal sections showing images of the embedded fluorescent particles (magenta) within soft (J) and stiff (K) GelMA hydrogels containing cancer spheroids at day 0 and day 3 of culture time. White dashed lines show the contour of the cancer spheroid within the hydrogels. Insets show day 0 images of the cancer spheroid-laden GelMA hydrogels. Magnified images of the regions within the dashed blue squares are shown to the right of the images. For soft hydrogels (J), the magnified images show the presence of internalized fluorescent particles within the spheroid. For stiff hydrogels (K), the magnified images show fluorescent particles (yellow arrow) near the spheroid-matrix interface that are persistently remained even after 3 days of culture. Scale bar: 50 μm. mean values ± standard deviations. (*, p < 0.05; **, p < 0.01)

Assessing the disintegration of GelMA network during cancer growth

In the event of the GelMA network breaking down, we expect the embedded fluorescent particles to be liberated. Using confocal image stacks of stiff and soft spheroid-laden hydrogels acquired at day 0, we chose different fields of view (25 by 25 μm) at the periphery of the spheroid from the mid-transverse plane of the hydrogel and tracked these fields as a function of culture time.

Fluorescent live cell staining of cancer spheroids

CellMask Orange plasma membrane dye (Thermofisher Scientific) was diluted in growth medium to achieve a concentration of 5 μg/mL. Cancer spheroids were exposed to this dye solution for 5 hours at 37°C and 5% CO₂. Afterwards, the spheroids were thoroughly rinsed with PBS and incubated in GM during the imaging process.

Mechanical relaxation of encapsulated spheroid after GelMA Removal

We examined the cancer spheroid recovery using a stress-free reference state achieved via removal of the mechanical confinement imposed by the GelMA hydrogel. The fluidic device containing fluorescently labeled cancer spheroids was mounted onto a confocal stage. The device was attached to a GM reservoir syringe positioned such that the top of the fluid column is at the same height as the mounted sample. Next, the Z stack images of the cancer spheroids were recorded by acquiring a 2×2 stitched XY field of view from the bottom of the hydrogel surface to 60 μm above with Z intervals of 0.5 μm.

In order to breakdown the GelMA hydrogel surrounding the cancer spheroid, the GM reservoir syringe was detached, and a 1 mL syringe containing approximately 200 μL of 75 μg/mL collagenase II solution (Thermofisher Scientific) (made in GM) took its place. The device’s outlet valve was then closed. To create a time-lapse revealing the recovery of the cancer spheroids, image volumes were recorded at the following times, post incubation in collagenase solution: 5, 10, and 15 minutes. Control experiments with free-floating spheroids were used to determine whether if exposure to the collagenase solution could facilitate spheroid expansion. To this end, fluorescent spheroids were suspended in 1 mL of collagenase solution and transferred onto a confocal dish. At intervals of 5 minutes, confocal image volumes were taken of several suspended spheroids. Using a custom Matlab algorithm, cross-sectional areas of a spheroid, taken at various Z positions, were used to calculate its volume.

Calculation of Dev and $\mathit{\Delta }\mathit{D}\mathit{e}\mathit{v}$ values for acellular and spheroid-laden GelMA hydrogels

We define a parameter describing the volumetric strain deviation as $Dev$ described by the equation:

$$100\mathrm{*}\left({ϵ}_V^{Emp}-{ϵ}_V^{Theo}\right)/abs\left({ϵ}_V^{Theo}\right)$$

where ${ϵ}_V^{Emp}$ and ${ϵ}_V^{Theo}$ respectively represent the experimentally observed and theoretically simulated volumetric strain fields. To obtain ${ϵ}_V^{Emp}$, we first quantified 3D Cartesian displacements within a hydrogel exposed to hydrostatic pressure using PIV. From the generated displacement vectors ($u,v$, and $w$), we calculated the empirical volumetric strain field given by the following equation: ${ϵ}_V^{Emp}=\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}$. Comparatively, ${ϵ}_V^{Theo}$ is theoretically generated by subjecting a hydrogel with bulk and shear modulus of 33 and 3.45 kPa, respectively, to a vertical extension of 3 μm at the top and bottom surfaces of the hydrogel along with a peripheral compression of 2.8 kPa. By comparing the experimental volumetric strain field to the theoretical one, based on their position in the hydrogel, we calculated the $Dev$ value within the mid-transverse plane. Positive and negative $Dev$ values indicate that the hydrogel has either a higher or lower bulk modulus than the theoretically assigned value of 33 kPa, respectively.

To illustrate how the bulk modulus of a hydrogel is changing with spheroid growth, we normalized the Dev values quantified at different time points to a reference state (day 0 culture). Here, we define $\Delta Dev$ as $\left({Dev}_{D>0}-{Dev}_0\right)/{abs(Dev}_0)$, where ${Dev}_0$ is the $Dev$ values observed at day 0 while ${Dev}_{D>0}$ are the values observed at days 2, 4, or 6. Positive and negative $\Delta Dev$ values highlight regions with bulk modulus increasing or decreasing with respect to day 0.

Confocal Microscopy Imaging

Perkin Elmer UltraVIEW Vox Spinning Disk, with a 40x magnification oil immersion UMPlanFl lens, was used to image the samples. Image volumes were acquired with Z step size of 0.2 μm and different fields of view were stitched together with 20% overlap using Perkin Elmer software.

Statistical Analysis

Statistical significance for all experiments for carried out using GraphPad Prism 7.0 (GraphPad Software, CA). The specific statistical test for each graph is listed within the figure captions along with the sample size for each group analyzed. The P values for statistically significant findings are also listed within the figure captions.

Results and Discussion

Microfluidic platform for in situ mechanical characterization of degradable hydrogels embedded with cancer spheroids

We have used a microfluidic platform that can support spatial positioning and confinement of single tumor spheroids within a 3D hydrogel system [13, 17]. The platform involves photopatterning of cell-laden GelMA hydrogels within a flow chamber, where the cell-laden hydrogel is sandwiched between two thin polyacrylamide (PAm) hydrogel layers tethered to glass coverslips at the top and bottom surfaces of the flow chamber [15–17]. To allow for mechanical actuation, we used thin No.1 coverslips which allows for the flow chamber to readily expand with increasing fluid pressure (Fig. 1A, S1A–D). GelMA solution containing MCF7 spheroids, 0.2 μm fluorescent particles, and photoinitiator was injected into the flow chamber. Spheroids were encapsulated within cylindrically shaped hydrogels (diameter and height of 320 and 100 μm, respectively), where they were individually confined within the center of the hydrogel (Fig. 1A, B). These spheroid-laden hydrogels were maintained in perfusion culture media supported by a syringe pump and were intermittently exposed to hydrostatic pressure to determine the mechanical properties of both the spheroid and the surrounding hydrogel (Fig. 1C, D). Towards this, the inlet tubing of the device was connected to an open syringe containing culture media and raised to a height of 11.25 inches from the base of the chip, while the outlet was blocked to halt gravity driven fluid flow (Fig. 1D). This resulted in a 2.8 kPa of hydrostatic pressure at which the GelMA hydrogel behaves more like a linearly elastic material, and this pressure value is also within the reported range of interstitial pressure in solid tumors [16, 18]. Moreover, computational analysis showed that the application of 2.8 kPa hydrostatic pressure generates compressive stresses on the circumferential surface of the GelMA hydrogel and drives the extension of both the top and bottom surfaces of the hydrogel during flow chamber expansion (Fig. 1D, Fig. S1C–D). The finite element analyses show that the applied hydrostatic pressure along with the vertical extensions on the spheroid laden hydrogel (due to the tethered nature of the construct at the top and bottom) induces the highest magnitude of radial strain when compared to constructs that encounter only hydrostatic pressure or vertical extension (Fig. S1E–F). The deformation of both acellular and spheroid laden GelMA hydrogels was further experimentally confirmed via inward radial and outward vertical deformations of the spheroid and hydrogel following the application of hydrostatic pressure for 30 minutes at 37 °C (Fig. 1E–F, Supplementary Movie 1). As expected, free floating MCF7 spheroids within the device did not exhibit any deformations under the hydrostatic loading. (Fig. 1G–H). This is consistent with prior studies demonstrating that cell spheroids are nearly incompressible under loading [19, 20].

Figure 1: Hydrostatic loading of cell-laden GelMA hydrogels within a microfluidic device.

(A-C) Schematic illustrating photoencapsulation of cancer spheroids within GelMA hydrogels and culture within a microfluidic device. (D) Application of hydrostatic pressure to mechanically probe spheroid-laden hydrogels (E) 3-D displacement field quantifying the deformation of the acellular hydrogel in the mid-transverse XY plane of the hydrogel cylinder and XZ cross-sections. Arrows and color denote the direction and magnitude, respectively, of the displacement vectors. (F-G) XZ and XY confocal sections of encapsulated (F) or free-floating (G) spheroid before and after exposing to the hydrostatic pressure. XY planes are shown at 50 μm above the bottom of the fluidic device. The red and blue dashed lines trace the contour of the spheroids before and after the application of the hydrostatic pressure, respectively. The yellow arrows in the XZ section indicate the vertical position of the XY image. The insets (scale bar: 40 μm) in F show the cancer spheroid (green) surrounded by GelMA hydrogel containing fluorescent particles (magenta). Scale bar for XY and XZ sections: 20 μm. (H) Quantification of cross-sectional area change after application of hydrostatic pressure for encapsulated and free-floating spheroids in the fluidic device. (n = 5–7 spheroids/group; Student’s T-test comparison between encapsulated (Encap) and free spheroids (Free). All plots show mean values ± standard deviations. ****, p < 0.0001.)

Changes in Young’s moduli of MCF7 spheroids and GelMA hydrogel as a function of spheroid growth

To understand the mechanical interdependency between the cancer spheroid and its surrounding matrix during growth, we investigated the changes in the Young’s moduli of MCF7 spheroid relative to its “local matrix”, defined as the region within a 20 μm distance away from the periphery of the spheroid (Fig. 2A). To this end, we created a finite element model (FEM) consisting of a sphere within a cylinder segmented and assigned the spheroid and local matrix regions. The material properties of each region were assumed to be spatially homogeneous, but varied relative to each other (spheroid and local matrix) as shown in the Figure 2B (Fig. 2A, B). This cylindrical hydrogel containing a spheroid was exposed to a compressive stress of 2.8 kPa on the lateral surface with an extension of 3 μm on each of the vertical surfaces, based on the experimentally determined values (Fig. 2A). Under the conditions that the spheroid and local matrix have similar Young’s moduli, the computational analyses showed a decaying magnitude in radial strains from the center of the cylinder to the edge (Fig. 2B). However, this radial strain distribution substantially changed when the relative Young’s modulus between the spheroid and the surrounding matrix differed, which is characterized by using Young’s modulus ratio (see Fig. 2C). Young’s modulus ratio is defined as the ratio of the Young’s modulus of the local matrix to that of the spheroid. The simulation results collectively demonstrated that the ratio of the average radial strain of the local matrix to that of the spheroid, denoted as $\mathit{\lambda }$, decreases as the ratio between the Young’s modulus of the local matrix to that of the spheroid increases (Fig 2C). Specifically, when $\mathit{\lambda }$ ≥ 2, the Young’s modulus of the local matrix is less than that of the spheroid and when $\mathit{\lambda }$ < 1, the local matrix is significantly stiffer than that of the spheroid (Fig. 2C, S2). Additional analysis of $\mathit{\lambda }$ suggested that it is also dependent on the size of the spheroid and the Young’s modulus of the distal matrix, a region from the edge of the local matrix to the hydrogel periphery (Fig. S2). To experimentally validate the parameter $\mathit{\lambda }$, we used acellular bi-layer hydrogels with differing Young’s moduli and calculated the radial strains within each of the hydrogel layers in response to hydrostatic pressure (Fig. S3A). Our results showed mean $\mathit{\lambda }$ values of 0.75 for the bilayer with stiffer exterior and softer interior and 1.8 for the bi-layer hydrogels with stiffer interior and softer exterior layers (Fig. S3B). These findings agree with the computational analyses.

Using $\mathit{\lambda }$, we examined the relative changes in the Young’s moduli of MCF7 spheroids grown in soft (~7 kPa) and stiff (~19 kPa) GelMA hydrogels for 6 days. Fluorescent images of MCF7 and its quantification showed that spheroids with radii of ~ 50 μm in both stiff and soft hydrogels increased in size and cell number relative to Day 0 irrespective of the Young’s moduli of the GelMA hydrogels (Fig. 2D–E, Fig. S4). Using a coarse grain approach, we averaged $\mathit{\lambda }$ values along the circumference and quantified them over time to determine whether the Young’s modulus of the matrix is decreasing with respect to the spheroid. Indeed, averaged $\mathit{\lambda }$ values were found to increase compared to day 0 but plateaued off at ~0.8 and ~0.4 for soft and stiff hydrogels, respectively (Fig. 2F). Despite softening of the matrix (relative to day 0), these $\mathit{\lambda }$ values were significantly less than 2 in all cases. This result suggests that the Young’s modulus of the local matrix remains greater than that of the spheroid. Since the averaging of $\mathit{\lambda }$ around the spheroid can potentially mask regions with high values, we further examined $\mathit{\lambda }$ values at different circumferential positions for spheroids within both the soft and stiff hydrogels (Fig. 2G, H). The polar plots showed highly variable $\mathit{\lambda }$ with peak values of ~2 for spheroids in soft hydrogels, while $\mathit{\lambda }$ remained significantly low for spheroids in stiff hydrogels (Fig. 2G, H). This suggests that in soft hydrogels, the Young’s moduli of the local matrix decreased to an extent that is comparable or lower than that of the spheroid at distinct locations along its periphery. This finding is further supported by relatively high variance in $\mathit{\lambda }$ along the circumference of the spheroids in soft hydrogels (Fig. 2I). On the other hand, low variance of $\mathit{\lambda }$ values in stiff hydrogels suggests that Young’s moduli in local matrix remains uniformly higher than that of the spheroid.

To determine whether the decrease in Young’s moduli of soft hydrogel is associated with matrix breakdown, we examined the structural changes of the network by assessing the loss of fluorescent particles within the hydrogel, especially near the edge of the spheroid. Confocal images of the cancer spheroid grown within soft GelMA hydrogels showed an accumulation of fluorescent particles within the interior of the spheroid after 3 days (Fig. 2J). A closer examination of the spheroid-matrix interface at the growth front of the spheroids, Sites 1 and 2, detected internalized particles (Fig. 2J). These findings collectively indicate that the GelMA networks at the interface encounter breakdown at distinct locations along the periphery of the spheroid, resulting in the release of embedded fluorescent particles. In contrast, particles at the edge of spheroids embedded in stiff hydrogels were found to persist throughout the culture time and no particles were observed within the cancer spheroids (Fig. 2K). This suggests that the stiff hydrogels are not undergoing any significant network breakdown; hence, the fluorescent particles remain confined within the GelMA hydrogel.

Examining the role of bulk modulus in the growth of spheroid in stiff GelMA hydrogels

The aforementioned findings suggest that material properties other than the Young’s modulus must be considered to explain the growth of MCF7 spheroids within the stiff hydrogels where low $\mathit{\lambda }$ values and no significant matrix breakdown were observed. To this end, we evaluated whether the bulk modulus that describes a materials’ resistance to volume change could explain spheroid growth in stiff hydrogels. For free floating spheroids, a decrease in volume was not observed after applying 2.8 kPa of hydrostatic pressure within the device (Fig. 1H). In contrast, acellular stiff hydrogels showed negative volumetric strains (${ϵ}_V$) under the same loading conditions suggesting that spheroids possess higher bulk modulus than that of the stiff GelMA hydrogels (Fig. S5). This result was expected due to the incompressible nature of cancer spheroids [19, 20]. Furthermore, the compaction of spheroids within a stiff hydrogel would only further increase the bulk modulus of the cell cluster [4, 21]. These results collectively suggest that MCF7 spheroids have a higher bulk modulus compared to the surrounding hydrogel matrix and may offer an explanation as to how they grow despite having lower Young’s modulus.

We further examined how the bulk modulus of the spheroid enables its growth within a 3D matrix despite having a lower Young’s modulus than the matrix. We generated an FE model of a sphere with various growth fronts representing potential shapes that can be taken by the spheroid during growth within a 3D matrix, and determined whether bulk modulus dependent proliferation favors a particular geometry. The shapes A to C have the same volume but differing shapes of growth fronts, as characterized by circularity values of 1.02, 0.96, and 0.88 (Fig. 3A). Furthermore, the spheroid surface away from the growth fronts (purple) were fixed in place while the surface of the growth front (green) was exposed to a normal traction stress to mimic the resistance that the spheroid growth would experience as it presses against the matrix. Using this simulation, we specifically examined the strain value, ${\epsilon }_{Avg}$, which represents the retraction of the growth front as it attempts to grow against the surrounding matrix and found that Shape A, with the highest circularity value, experiences the least ${\epsilon }_{Avg}$. Moreover, the ${\epsilon }_{Avg}$ of shape A was further decreased compared to shapes B and C with increasing spheroid bulk modulus or compressive stress experienced by the growth fronts (Fig. 3B). These results suggest that the spheroid favors a more uniform growth geometry when its bulk modulus is high and that the smooth shape could be coarsely approximated by high circularity values. At Day 0, some level of irregularities in the spheroid shapes were observed (Fig. S6A), and the circularity measurements indicate similar level of irregularities in both the stiff and soft hydrogels (Fig. S6B). However, after 3 days of culture, spheroids in soft hydrogels retained an irregular shape while spheroids in stiff hydrogels were found to have a more uniform or smooth shape as in seen in shape A (see Fig. 3A) (Fig. 3C). This is further supported by higher circularity values measured for the spheroids in stiff hydrogels compared to soft hydrogels (Fig. 3D).

Figure 3: Role of bulk modulus on spheroid growth within the stiff hydrogel.

(A) FE model examining the effect of mechanical resistance of the surrounding matrix on spheroid growth. Three distinct growth geometries, Shape A through C, with unique circularity factors are shown in the top row. The green bulges experience normal traction stress (T_n) boundary condition and represent the active growth front while the purple surfaces are the non-growing portions of the spheroid and are fixed in place. The bottom row contains the heat maps of the X-displacement values at the mid-transverse plane of each shape A, B, C. ε_avg denotes the location at which the shortening of the growth front is observed as it experiences forces from the surrounding. (B) ε_avg normalized to that of Shape A as a function of different bulk modulus of the spheroid (33.3 – 200 kPa) and magnitude of normal traction stress (T_n = 125 or 250 Pa) applied to the green bulges. (C) XY confocal sections at mid-transverse plane of fluorescently labeled cancer spheroids encapsulated within soft and stiff hydrogels for 6 days. (D) Bar plots comparing the circularity factor of cancer spheroids grown in soft and stiff hydrogels for 6 days. (n = 6–8 spheroids/group. Student’s T-test comparison between soft and stiff hydrogels). (E-F) The XZ and XY confocal sections of cancer spheroids (green) and the hydrogel containing fluorescent particles before and after collagenase treatment for soft (E) and stiff (F) hydrogels. The cell-laden hydrogels were cultured for 3 days prior to enzymatic degradation. The yellow arrows in the XZ section indicate the vertical position of the XY image. The red and blue lines show the contours of the spheroid before and after collagenase treatment, respectively. All vertical and horizontal scale bars are 50 μm. (G) The cross-sectional area of the spheroid at different Z positions after treatment of spheroid-laden GelMA hydrogel with collagenase. The Z position of 0 indicate the bottom surface of fluidic device. The blue and red lines show spheroids within soft and stiff hydrogels, respectively. (H) The normalized spheroid volume change, which is the ratio of the volume after to before collagenase treatment, for free floating spheroids (control) and encapsulated spheroids in soft and stiff hydrogels. The bar plot shows mean value with standard deviation. (n = 6–7 spheroid/ group. One way ANOVA followed by Bonferroni post-hoc test). All plots show mean values ± standard deviations. ns = not significant; *, p < 0.05.

The images and the circularity values only provide a static image of the encapsulated spheroids and do not fully convey the dynamic geometry adapted during its growth. In order to quantify this dynamic geometry, the GelMA hydrogel was slowly removed using collagenase, and Z-stack images of fluorescently labeled spheroids within the soft and stiff hydrogels was acquired and used for determining the contour of the spheroid. The XY confocal sections of the spheroid in the soft hydrogels displayed an expansion of the spheroid boundary but only at distinct locations along the periphery as GelMA network breakdown (Fig. 3E). The XZ sections also showed minor expansion of the spheroid in soft gels following GelMA removal (Fig. 3E). In contrast, spheroids in stiff hydrogels were found to uniformly expand along the entire periphery as indicated by the XY and XZ planes after collagenase treatment (Fig. 3F). We also quantified the volumetric expansion from the confocal images, which were used to identify the boundary of the spheroids at different Z positions and estimate the changes in the overall volume before and after treatment with collagenase (Fig. 3G, 3H). The results showed that the spheroids in stiff hydrogels exhibited higher volumetric expansion after GelMA removal when compared to the soft hydrogels (Fig. 3H). These experimental observations are in agreement with the computational results. Taken together, these findings suggest that the spheroids grow in stiff GelMA hydrogel via uniform expansion and rely on bulk modulus while spheroids in soft gels proliferate via localized, discrete protrusions.

Quantifying changes in bulk modulus during spheroid growth within GelMA hydrogels

Since our results suggest that spheroids within the stiff hydrogels rely on their bulk modulus to grow, we examined the changes in bulk modulus of the surrounding matrix. We first approximated the localized bulk modulus of the GelMA hydrogel by comparing experimentally observed volumetric strain field (${ϵ}_V^{Emp}$) to the theoretical volumetric strain field (${ϵ}_V^{Theo}$) generated under an arbitrary assigned bulk and shear modulus. We next defined a parameter, $Dev$, which represents the difference between the experimental and theoretical volumetric strain values and the values for this parameter should depend on differences in shear moduli between the theoretical and experimental values. Indeed, a closer characterization of $Dev$ values indicates that it is primarily correlated with the changes in bulk modulus within a cylindrical hydrogel starting at a radial position of 100 μm although at lower radial positions, $Dev$ values can also be affected by shear moduli (Fig. S7).

The framework of analyzing$Dev$ values to assess changes in bulk modulus was also applied towards understanding spheroid growth in 3D hydrogel matrices. To this end, we examined the temporal changes in $Dev$ by defining $\Delta Dev$ as the normalized difference of $Dev$ values calculated at days 2, 4, or 6 relative to day 0. The $\Delta Dev$ is described by the following equation: $\left({Dev}_{D>0}-{Dev}_0\right)/{abs(Dev}_0)$. Positive and negative values of $\Delta Dev$, respectively, indicate that bulk modulus is increasing or decreasing with culture time. For spheroids within the soft hydrogels, the representative heat map of $\Delta Dev$ showed small regions of matrix softening and stiffening along the periphery of the spheroids. This further substantiates the findings from $\mathit{\lambda }$ calculations and is expected since Young’s modulus is a function of bulk and shear modulus (Fig. 4A). For spheroids in stiff hydrogels, the heat map showed increasing bulk modulus around the circumference of the spheroid at day 4 (Fig. 4B). This finding is consistent with the observation that spheroids expand in stiff hydrogels upon GelMA removal (Fig. 3G–H). Moreover, this finding suggests that the spheroid growth exerts high compressive stresses on the surrounding matrix, which could potentially contribute to bulk modulus stiffening of the matrix. Matrix stiffening was observed throughout the culture time (up to day 6), which peaked at day 4 and then decreased by day 6 while the spheroid size continued to increase (Fig. 4B). These observations are quantified through histograms that exhibit similar distribution of $\Delta Dev$ for soft hydrogels irrespective of culture time (Fig. 4C, D). However, the $\Delta Dev$ value distribution for stiff hydrogels were found to shift towards highly positive values prior to returning to lower values by day 6 (Fig. 4C, D).

Figure 4: Changes in the bulk modulus of the surrounding matrix during cancer growth.

(A-B) Heat map of $\Delta Dev$ values within mid-transverse plane of soft (A) and stiff (B) GelMA hydrogels containing cancer spheroids. Positive and negative $\Delta Dev$ value indicate increasing and decreasing bulk modulus of the matrix relative to day 0. (C-D) Histograms of $\Delta Dev$ values at days 2, 4, and 6 within the soft (C) and stiff (D) hydrogels. The histograms show the average frequency within each $\Delta Dev$ bin along with the standard deviation. (n = 4–5 spheroids/group. One way ANOVA along with post-hoc Tukey test for multiple comparisons within each bin for different days). All plots show mean values ± standard deviations. * P < 0.05.

To summarize, the study described here devises a microfluidic system to study tumor spheroid growth within a 3D matrix with differing mechanical properties. The microfluidic platform along with the imaging analyses used in this study enables simultaneous mechanical characterization of the tumor spheroid and the surrounding matrix. This approach offers high spatial resolution, on the order of microns, allowing scanning of single cells to cell spheroids. Most studies that have examined the mechanical forces associated with tumor cell growth largely rely on measurements of excised tumors. Unlike these methods that utilize isolated spheroids or spheroids stripped out of the matrix, the method employed in this study allows mechanical probing of the growing spheroids as well as their surrounding matrix in their native environment in a non-destructive way. Our experimental results along with computational analyses suggest that the spheroids in soft matrices primarily rely on local matrix breakdown to grow while spheroids in stiff matrix rely on volumetric expansion which is mostly governed by their bulk modulus. These findings are supported by the report by Islam et al. which characterized tumor growth in vivo using elastography (7). Similarly, the matrix stiffening or increase in bulk modulus during spheroid growth in stiff hydrogels suggest high compressive stresses are imparted by the cancer cells to the environment, which is in line with reports that solid tumor can generate high compressive stresses [4, 22]; and in vivo studies suggesting that these tumor-generated stresses are sufficient to collapse the surrounding vascular and lymphatic networks [23]. Studies have also shown an increase in packing density [23] and accumulation of hyaluronic acid in and around the cancer spheroid when cultured within stiff matrices [24]. All of these factors, cellular packing and new ECM accumulation, could contribute to increased bulk modulus. One of the limitations of the current study is that the analyses of material properties are relative to each other (spheroid and matrix) and not absolute. Nonetheless, by referencing to day 0 we are able to discern changes in material properties associated with spheroid growth. Though an assumption widely adopted in the field, another concern is that the system is assumed to be elastic [4]. However, future work could extend the platform described in this study to include viscoelastic properties. Nevertheless, the findings described in this study contribute to a better understanding of how cancer cells grow in confined stiff matrix in 3D environment.