Determination of the rheological properties of Matrigel for optimum seeding conditions in microfluidic cell cultures

In a human soft tissue, all cells reside within a three-dimensional extracellular matrix, a viscous gel that mechanically strengthens the tissue and supports the cells within it. The extracellular matrix consists of a ground substance formed from large complex macromolecules, especially polysaccharides and proteoglycans, which attract water and ions, and fibrous proteins, especially collagen and elastin, which provide tensile strength and elasticity.^1,2 The cellular microenvironment consists of the extracellular matrix and the molecular species that can diffuse between cells and the microvasculature. The extracellular matrix permits free diffusion of molecules between cells and the microvasculature. Nevertheless, it has a strong influence on cellular phenotype.¹ Therefore, when attempting to mimic an in vivo microenvironment with an in vitro cell culture system, it is important to provide an appropriate surrogate extracellular matrix. An in vivo system refers to an experiment conducted within a whole living organism while an in vitro system is one that is conducted in the laboratory within, for example, a petri dish.

Several extracellular matrix surrogates from natural and synthetic origins have been developed in the form of hydrogels, for cell culture applications.³ Hydrogels are physically or chemically cross-linked polymer networks that absorb large amounts of water.⁴ Because of their biomechanical and biochemical properties, they are used as a surrogate extracellular matrix for 2D and 3D cell culture. Moreover, they are compatible with microscopy techniques. Hydrogels of natural origins are basement membrane-based gel preparations; some examples include fibrin gel, collagen gel, alginate gel and Matrigel.⁵ Matrigel is a commercial hydrogel of natural origins. It is a reconstituted basement membrane preparation extracted from Engelbreth-Holm-Swarm (EHS) mouse sarcoma that is biologically active and therefore, widely used in a variety of 2D and 3D cell cultures, including stem cells, cancer cells, induced pluripotent stem cells (iPSCs) and neuronal cells, among other applications.

Microfluidic cell culture concerns the development of devices and techniques for culturing, maintaining, analysing and experimenting with cells in micro-scale volumes.^6,7 Microfluidic cell culture in three-dimensions resembles the cellular microenvironment experienced by cells in vivo.⁸ Hydrogels have similar mechanical properties to soft tissues^3,9 making them suitable for use as substitutes for extracellular matrix in microfluidic devices.^5,9,10 Automated microfluidic cell culture has the potential to increase the quantity of experiments that can be completed in parallel and enables long-term cell culture maintenance with reduced manual labour. However, such systems rely on precise programming of robotics and liquid handlers, which first requires quantitative characterisation of the chemical and rheological properties of the fluids involved.

Matrigel is frequently used as a surrogate extracellular matrix in microfluidic cell culture, see e.g. Trietsch et al.¹¹ and Lucumi et al.⁵ As Matrigel is a liquid at low temperatures and a gel at room temperature it is suited for seeding of microfluidic cell culture devices, where the cell culture chamber is usually remote from the accessible input of the microfluidic cell culture device. The fluid properties of Matrigel for its application in 3D microfluidics have not been fully characterized yet.^12–14 In Trietsch et al.¹¹ and Lucumi et al.,⁵ a low temperature mixture of Matrigel and cells is used to seed each three dimensional microfluidic cell culture chamber, prior to restoration to body temperature and juxtaposed perfusion with liquid cell culture medium.

Rheology is the study of the flow of matter. It is utilised to determine physical properties of a material such as its viscosity or its shear moduli. Liquids (e. g. water and Matrigel) can be divided into two groups: Newtonian and non-Newtonian fluids. Non-Newtonian fluids are fluids for which the viscosity is dependent on the amount of applied shear stress, while the viscosity of Newtonian fluids is independent of the applied shear stress.

Cells have poroelastic mechanical properties: subjected to mechanical stress, they elastically deform and temporarily lose some fluid content. This behaviour is due to the porous nature of the cellular membrane.¹⁵ Therefore, it is important to quantify the shear stress and shear rates that cells are exposed to in a given microfluidic device under particular conditions. Herein, we employ rheology on isolated Matrigel to characterise its rheological properties at different temperatures. We also quantify the velocity field of Matrigel flow during seeding of an established three dimensional microfluidic cell culture device (OrganoPlate)¹¹ using particle image velocimetry. Combining the results of both techniques allows the prediction of the shear rates that cells are exposed to in a microfluidic device at different temperatures. To the best of our knowledge, this approach has never been reported for gels used in cell culture devices. In addition, through this study, we aim to provide the optimum conditions of flow of Matrigel to minimise the stresses experienced by cells as they are seeded into 3D microfluidic systems. This should allow to decrease the mortality of the cells and thus increase the applicability of hydrogels in microfluidic cell culture.

Matrigel was obtained from BD biosciences (Germany). Fluorescent polystyrene beads (PS-FluoGreen-Fi226) in an aqueous suspension (2.5 wt%) with an average diameter of 10 μm were purchased from Microparticles GmbH (Berlin, Germany).

Matrigel consists of about 60% laminin, 30% collagen IV, and 8% entactin. Entactin is a bridging molecule that interacts with laminin and collagen IV, and contributes to the structural organization of Matrigel. The latter is a non-Newtonian viscoelastic fluid that exhibits a Lower Critical Solution Temperature⁴ of about 6°C. In other terms, below that temperature it is liquid and can be filled into microfluidic devices using a pipette. The exact water content of Matrigel is unknown. Therefore, we performed a standard Differential Scanning Calorimetry (DSC) scan in the vicinity of the melting point of water (see Fig. 1). Since the difference between the measured heat of fusion (334.8 J/g) of Matrigel and the corresponding value for pure water (332.8 J/g)¹⁶ is below the experimental error, the water content of Matrigel can be assumed to be higher than 99 wt %.

For Particle Image Velocimetry (PIV) measurements, 2μL of the aqueous suspension containing the polystyrene beads was mixed with 8μL of Matrigel.

For all experimental studies, the same batch of Matrigel was used.

A 2-lane OrganoPlate (Mimetas BV, Leiden, The Netherlands) consists of an array of 96 chips embedded in a customised 384-well plate format, illustrated in Fig. 2. Each microfluidic chip is contained between two sheets of glass with the top sheet of glass having holes complementary to the underside of selected wells. Each chip is juxtaposed to 3 wells, one gel inlet well (Fig. 2 b1) for loading gel-embedded cells into the culture lane by capillary forces, one readout window (Fig. 2 b3) for monitoring the culture lane by inverted light microscopy. In addition, each bioreactor has a perfusion inlet well (Fig. 2 b2) connected to a perfusion outlet (Fig. 2 b4) well via a media perfusion lane. In each culture chamber, during cell loading a phaseguide prevents liquefied gel-embedded cells from leaving the culture lane and entering the medium lane.

A phaseguide is a patterned pinning barrier that controls the liquid-air interface by forcing it to align with the ridge and therefore allowing the filling of microfluidic structures. An inverted epifluorescence microscope (Leica DMI6000B) equipped with a cooled sCMOS camera (Neo 5.5, Andor Technology), within a temperature controlled incubation chamber (Incubator BLX, Pecon), was used to perform PIV during seeding. An ice bath was used to keep Matrigel from gelation while loading it into the OrganoPlate.

Rheological measurements were performed with an Anton Paar rheometer MCR 302. A schematic representation of the experimental setup is shown in Fig. 3. All measurements were done using parallel-plate configuration. The sample temperature was controlled with a liquid nitrogen cryostat. Measurement of the torque M and the angle φ allows to determine the shear stress σ(t) as well as the strain γ(t) or the shear rate $γ̇(t)$ respectively.¹⁷ 

Matrigel was kept at a temperature of -12°C until the start of the measurements. It was then put on the pre-cooled rheometer plates using a syringe. Due to the fact, that this process had to be done as fast as possible in order to avoid gelation of Matrigel and heating of the rheometer plates (the furnace has to be opened) the filling was not as homogeneous as possible. This certainly affects the absolute values of the viscosity and shear moduli. The power law behaviour of the viscosity as well as the gelation behaviour (gelation temperature) is not affected.

The flow properties, i.e. the dependency of the shear stress σ or the viscosity η on the shear rate $γ̇$ can be determined by recording so-called flow-curves.^17,18 A flow curve is a graph representing the shear stress or the viscosity of a sample as a function of the shear rate at constant temperatures. The following measurement protocol was applied while keeping the sample temperature constant at a defined value T: The viscosity of the samples has first been measured while increasing the shear rate from 0.1 s^-1 to 10 s^-1 (flow curves ↗). The recording time τ for each data point has always been chosen such that $τ>γ̇−1$ in order to assure the establishment of the desired shear field throughout the entire sample.¹⁹ Then the same measurement has been done with decreasing shear rates (flow curves ↘). Thereby, besides the shear rate dependency of the viscosity, the thixotropic character of the material or the dependency of the viscosity on the shear history can be determined.²⁰ 

SAOS measurements can be used to determine the storage and loss shear moduli of viscoelastic samples. A sinusoidal strain γ(t) = γ₀ sin(ωt) with amplitude γ₀ and angular frequency ω is applied to the samples.²¹ The resulting stress σ(t) is measured and linear response theory is used to calculate the real (storage) and imaginary (loss) parts $G′$ and $G″$ of the complex shear modulus respectively. The following measurement protocol has been used for the SAOS measurements presented in this work: For each temperature T, an amplitude sweep has been performed in order to determine the maximum value of the strain amplitude γ₀ for which linear response conditions (shear moduli independent of strain amplitude) hold. Then, isothermal frequency sweeps have been performed to determine the dynamic rheological properties.

To determine the velocity profiles of fluorescent beads mixed with Matrigel flowing in the culture lane of an OrganoPlate, Particle Image Velocimetry measurements were performed. Images were sampled at a rate of 50Hz and with a pixel size of 0.33um/pixel. To accurately estimate the velocity fields, out-of-focus beads were first removed. A bandpass was then applied to smoothen the images and subtract the background.²² A threshold for pixel intensities was set to suppress out-of-focus beads. The flow velocities were then determined using an open source framework for particle image velocimetry analysis, OpenPIV,²¹ which is implemented in MATLAB, C++ and Python (www.openpiv.net). Each image was subdivided into smaller areas termed interrogation windows. Interrogation windows having the size of 512x128 pixels with an overlap of 128x32 pixels were used. This determines the number of pixels by which adjacent windows overlap. For the same interrogation window of a pair of consecutive images, a Fast Fourier Transform based cross-correlation was calculated to infer the most probable displacement vector of the particles within the interrogation window. The magnitude of each displacement vector was divided by the time interval between two images (20ms) to estimate the velocity. The calculated velocity vectors were loaded into the Open PIV spatial analysis toolbox (https://github.com/OpenPIV/openpiv-spatial-analysis-toolbox/) which then allowed to determine the velocity profile of the fluorescent beads flowing in Matrigel within the culture lane of the OrganoPlate.

The peculiarity of Matrigel to be liquid at low temperatures and to form a stable gel above a certain temperature T_gel is the most important physical property that predestines it for its use as a surrogate extracellular matrix. Therefore, the first step in the characterization of Matrigel for its use in microfluidic cell cultures is the analysis of the gelation process. Rheology, especially small angle oscillatory shear (SAOS) measurements, is best suited for this study. In their seminal work,^23–25 Winter et al. showed that the onset of gelation can be identified in SAOS measurements as the temperature at which both parts of the elastic moduli, i.e. $G′$ and $G″$⁠, take the same values, independent of the probe frequency. It has to be stressed that this holds only true if linear response conditions are fulfilled (cf Section: Experimental). We tested this by measuring the elastic moduli as a function of the oscillation amplitude γ₀ (see Fig. 4).

For each temperature, an appropriate maximum strain amplitude in the linear response regime was selected. In the following analysis of the gelation behaviour of Matrigel, these limiting values of the strain amplitudes have been respected.

Fig. 5 shows isothermal measurements of the elastic shear moduli as a function of the oscillation frequency. Below 6°C, the storage modulus G′ is always smaller than the loss modulus G″, i.e. the system is in a liquid phase. Above 6°C, G′ which corresponds to the fully elastic response of the sample is higher than G″ and is independent of the frequency. This is a clear sign that the system exhibits solid-like behaviour. At 6°C finally, G′ equals G″ for all measured frequencies. This indicates that gelation starts around T_gel = 6°C. For the use of Matrigel in microfluidic devices, this experimental result indicates that it is important to cool the microfluidic device to a temperature below T_gel in order to avoid early gelation.

The flow behaviour and especially the viscosity of Matrigel is of special interest because it gives information about the shear stress that will act on embedded cells when filling the channels of a microfluidic device. Many materials such as dispersions, emulsions, polymer solutions or gels do not have a constant viscosity but show a dependency of viscosity on the shear rate:¹⁸ $η=η(γ̇)$⁠. The shear rate that a fluid is exposed to when it flows through a pipe or a microfluidic device is not constant along the cross-section of the device. Therefore, it is of great importance to determine the viscosity of Matrigel as a function of shear rate. Using state-of-the-art rheological equipment, flow behaviour can be analysed at different temperatures for a wide range of different shear and strain rates. Fig. 6 shows the viscosity of Matrigel as a function of applied shear rate at different temperatures. Please note that the absolute values of the viscosity greatly depend on the filling process (please see section Experimental).

First, a scan with increasing shear rates was conducted (filled symbols in Fig. 6). This scan was directly followed by a second scan with decreasing shear rates starting at the highest shear rate of about 10 s^-1 (open symbols in Fig. 6). As a result of this procedure, an influence of the shear history on the flow curves for temperatures equal or higher than 6°C can be stated. This was expected since the start of gelation at 6°C is also the start of structure formation (gel network) inside Matrigel (see Fig. 5). Shearing Matrigel at temperatures higher than 6°C leads to a competition between network formation due to gelation and network destruction due to shearing. Since network formation takes more time, the measured viscosities depend on the shear history. The temperature of 6°C above which this behaviour occurs, is a confirmation of the results of the determination of the gelation temperature from the isothermal frequency sweeps described in the previous paragraph (Fig. 5). The flow curves depict also that Matrigel behaves like a liquid at temperatures lower than 6°C. This is evidenced by the observation that the viscosity decreases with increasing temperature below 6°C, which is a behaviour expected for liquids.

The overall behaviour of the flow curves illustrated in Fig. 6 clearly shows non-Newtonian behaviour. This holds also true for the liquid phase below 6°C which is very unusual at first sight. It could be explained by precursors of the gel already present at lower temperatures. This experimental finding at lower temperatures certainly deserves further investigation.

The non-Newtonian behaviour of the flow curves can be modelled by a power law model:¹⁸ 

with σ and $γ̇$ being the shear stress and the shear rate respectively. k is a constant, n is the power law exponent and the term $kγ̇n−1$ corresponds to an apparent viscosity of Matrigel. Table I exhibits the power law parameters deduced from fits of the flow curves shown in Fig. 6.

In case of the first scans with increasing shear rates (↗), the exponents n are positive up to the gelation temperature. Above T_gel they become negative, i.e. the destruction of the gel structure induced by the shear forces becomes more dominant. The second scans with decreasing shear rates (↘) yield exponents which do not show a systematic behaviour due to the fact that the first applied shear stress which is the highest shear stress for this study already destroys the gel structure.

The flow behaviour of Matrigel retrieved from rheological measurements (Fig. 6 and Table I) can now be used to analyse the flow profile of Matrigel in a microfluidic device.

For the following analysis, the power law parameters of the decreasing shear rate curves have been used since they better reflect the state of Matrigel after it has been filled into the microfluidic device using a pipette. Fig. 7 shows the flow profile determined by PIV measurements at 8°C. Due to the asymmetric geometry of the microfluidic device (Fig. 2), only the left part of the data opposite to the phaseguide was used for fitting (filled symbols). The right side (empty symbols) have not been considered for fitting. The dashed line in Fig. 7 shows a fit according to a Hagen-Poiseuille law for Newtonian fluids flowing in a circular pipe^18,26

that did not fit the PIV data. The flow profile of a power law fluid takes the form:²⁶ 

Using this model, there is a much better fit to the PIV data (solid line in Fig. 7) and the resulting exponent n=0.15 is close to the value of 0.19 obtained from the rheological measurements.

A key parameter for the survival rate of cells during the filling process is the shear rate $γ̇=dγfluid/dt=dv/dr$ which can be directly deduced from the fit of the velocity profile (black solid line in Fig. 8).

Assuming that the cells can survive a maximum shear rate of 50 s^-1 (dashed horizontal red line in Fig. 8), all cells would survive filling of the microfluidic device at 8°C. To analyse the situation at another temperature for which no PIV data has been measured, we first use the shear stress at the wall (σ_wall = 1.03 Pa) obtained from the fit of the PIV data at 8°C (Fig. 7, eq. 3) in order to calculate the pressure difference Δp along the microfluidic device (L=2.5 mm) during the experiment:

For the same pressure difference and using the power law parameters from Table I, the shear rates at 2°C can now be calculated (dashed blue line in Fig. 8). Assuming again a maximum shear rate of 50 s^-1, all cells being closer to the borders than 40μm would not survive. A similar calculation (cf supplementary material) can be made for the more realistic situation that not the pressure difference but the flow rate Q across the microfluidic device is constant for all temperatures (e.g. by using automated pipettes). The corresponding results are also shown for 2°C in Fig. 8 (solid blue line). Again, many cells would not survive, when the filling of the microfluidic device would be performed at this temperature.

Thus, a single PIV measurement of Matrigel in a microfluidic device can be used in combination with standard rheological characterization to predict the shear rate that cells are imposed to during the filling of a microfluidic device. There are two competing parameters to optimise the loading in 3D microfluidic channels: the need to lower the temperature to avoid the early gelation of Matrigel and promote its flow through narrow lanes; and the need for higher temperatures to increase the viscosity and the non-Newtonian characteristic of Matrigel. Increasing the non-Newtonian characteristic leads to flatter velocity profiles, minimising the shear stress experienced by the cells during loading into microfluidic channels. This study suggests that the optimum loading temperature of Matrigel in microfluidic cell culture lies between 8°C and 10°C, with a lower temperature more suited to longer microfluidic channels, and a higher temperature for shorter channels where early gelation is less of a concern. This allows one to minimise the trial and error experimental efforts required to optimise survival rates of loaded cells.

We characterised the rheological properties of a hydrogel (Matrigel) during a process representative of seeding a three-dimensional microfluidic cell culture device (OrganoPlate, Mimetas B.V.) with live cells. We could show that Matrigel is a liquid at temperatures below 8°C. Above 8°C, the rheological measurements showed the typical signs of a solid (real part of shear modulus higher than imaginary part). Moreover it could be shown that the viscosity of Matrigel can be well described by a power law model. The PIV measurements lead to the conclusion that the minimum amount of shear stress is obtained when the hydrogel is loaded at a temperature between 8°C and 10°C. Higher temperatures lead to greater shear due to temperature induced gelation, while lower temperatures lead to greater shear stress due to temperature induced liquefaction leading to loss of non-Newtonian fluid flow behaviour. Our interdisciplinary approach of rheological characterisation combined with in situ particle image velocimetry is applicable for other types of microfluidic devices and other hydrogels. This is an important step towards rational optimisation of three dimensional microfluidic cell culture protocols.

See supplementary material for a movie of the PIV measurements and a description of the combination of PIV and rheological data.

KIWK and ELM received funding from the SysMedPD project from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 668738. ELM and SH were also supported by an Aides à la Formation-Recherche training allowance from Fonds National de la Recherche Luxembourg ref. 10099424.