Cancer cell viscoelasticity measurement by quantitative phase and flow stress induction

Abstract

Cell viscoelastic properties are affected by the cell cycle, differentiation, and pathological processes such as malignant transformation. Therefore, evaluation of the mechanical properties of the cells proved to be an approach to obtaining information on the functional state of the cells. Most of the currently used methods for cell mechanophenotyping are limited by low robustness or the need for highly expert operation. In this paper, the system and method for viscoelasticity measurement using shear stress induction by fluid flow is described and tested. Quantitative phase imaging (QPI) is used for image acquisition because this technique enables one to quantify optical path length delays introduced by the sample, thus providing a label-free objective measure of morphology and dynamics. Viscosity and elasticity determination were refined using a new approach based on the linear system model and parametric deconvolution. The proposed method allows high-throughput measurements during live-cell experiments and even through a time lapse, whereby we demonstrated the possibility of simultaneous extraction of shear modulus, viscosity, cell morphology, and QPI-derived cell parameters such as circularity or cell mass. Additionally, the proposed method provides a simple approach to measure cell refractive index with the same setup, which is required for reliable cell height measurement with QPI, an essential parameter for viscoelasticity calculation. Reliability of the proposed viscoelasticity measurement system was tested in several experiments including cell types of different Young/shear modulus and treatment with cytochalasin D or docetaxel, and an agreement with atomic force microscopy was observed. The applicability of the proposed approach was also confirmed by a time-lapse experiment with cytochalasin D washout, whereby an increase of stiffness corresponded to actin repolymerization in time.

Significance

We present an approach for viscoelasticity measurement using QPI and shear stress induction by fluid flow. Our system builds and extends a recently published approach by parametric deconvolution, which allows us to eliminate the influence of the fluidic system and reliably measure both the shear modulus and viscosity of the cells in high throughput. Additionally, the proposed method enables simultaneous determination of the cell refractive index map, cell dry mass map, and morphology, thereby enabling a multimodal cellular characterization in a single measurement.

Introduction

The mechanical response of cells is affected by the cell cycle, differentiation, and pathological processes such as malignant transformation, cardiovascular diseases, or aging (1, 2, 3). Evaluation of the mechanical properties of the cells thereby proved to be an approach to obtaining information on the functional state of the cells potentially relevant for the clinical setting (4).

There are plenty of methods of measuring cell mechanical characteristics based on various principles, including atomic force microscopy (AFM), microfluidics, micropipette aspiration, magnetic or optical tweezers, particle tracking rheology, and acoustic methods (5,6). However, the measured values are not comparable between these methods, with variations in the mechanical properties of cells by orders of magnitude (7,8).

A widely established method for cell mechanophenotyping is AFM (9,10). This method is based on direct contact of a cantilever tip; from the degree of its deflection Young’s modulus is calculated. As the cantilever mechanically scans the cells with a single probe, it non-physiologically stresses the cells, which can unnaturally affect the results. Furthermore, the method is also low throughput and limited by the necessity of highly expert operators and the need for selection of appropriate probes (11). Microfluidic-based approaches can on the other hand be implemented in a high-throughput setup. These methods employ various strategies including microconstriction of cells in small channels, flow in cross-slot microchannels, or application of shear forces. With an appropriate model, these approaches can obtain more information on the mechanical properties (viscosity and elasticity). The connection of flow shear stress induction with quantitative phase imaging (QPI), introduced by Eldrige et al. (12,13), brings a new possibility to reliably evaluate the viscoelastic properties of the cells. Compared with common light microscopy techniques, QPI enables rapid determination of the cell geometry, including the estimation of cell height, a parameter needed for shear modulus estimation.

The systems for shear stress experiments typically consist of flow chambers, which allow the generation of stable shear stress gradients using a suitable pump and tubing. The characteristics of each component determine the final properties of the entire system, which might have a significant effect on the subsequent analysis of the cell’s properties. This can be especially important in cases where the responses to the fast temporal changes of the shear stress are examined. To minimize the influence of the fluidic system, a deconvolution-based approach for the estimation of the cell mechanical properties is employed.

To estimate the shear modulus, the cell height needs to be estimated. Although this can be calculated from the phase and cell refractive index (RI), the latter is typically considered a constant for the whole cell population. Further refinement was made possible by estimation of RI using a method published by Rappaz et al. (14). In this approach, two perfusion media with different RIs are used to estimate both cell RI and cell height.

In this paper, we describe a complex QPI-based approach for shear modulus estimation consisting of hardware and software parts including simultaneous RI determination and parametric deconvolution. The proposed method allows fast and reliable measurements during live-cell experiments, where QPI images can be used for simultaneous analysis of cell morphology.

Materials and methods

Hardware setup

The block scheme of our experimental setup with photos of the individual components is shown in Fig. 1. A programmable dual syringe pump (Fusion 4000; Chemyx, Stafford, TX) is utilized as a flow source. The chamber used in our setup is a commercially available, shear stress optimized chamber (μ-Slide VI 0.1; Ibidi, Gräfelfing, Germany). The flow meter (SLF3S-1300F; Sensirion, Stäfa, Switzerland) is connected to our setup at the output of the flow chamber. All components are connected to appropriate adapters and tubing. To ensure the rigidity of the system, we selected polytetrafluoroethylene material for the tubing. Our preliminary experiments showed that the main influence on the flow temporal profile is the syringe inserted in the syringe pump; the tubing material as shown in supporting material, section 8.

Figure 1.

Shear flow system. (a) Block diagram of components; pink arrows indicate medium flow and the yellow arrow indicates light passing through the sample. (b) Photo of connected components. (c) Detail of 3D model of custom luer slip to μ-Slide VI 0.1 adapter. The black part is a rubber plastic preventing fluid leakage. (d) Photo of whole fluidic setup. (e) Detail of cell chamber inside the microscope. To see this figure in color, go online.

For the acquisition of quantitative phase images, a coherence-controlled holographic microscope (Q-Phase; Telight, Brno, Czech Republic) was used. A Nikon Objective Plan 10×/0.3 lens (Nikon, Tokyo, Japan) was used for hologram acquisition with a CCD camera (MR4021MC; Ximea, Münster, Germany). Holographic images were numerically reconstructed with the Fourier transform method (described in (15)), and phase unwrapping was used on the phase image. Moreover, background compensation with polynomial fitting was applied, which set the background phase delay to zero. Near-maximum available frame rate (3 frames/s) was used to acquire frames with the highest temporal resolution.

Shear stress ${\tau }_0$ (inducing skin friction drag of the cells) for the flow rate Q provided by the syringe pump was calculated on the basis of the Ibidi μ-Slide IV 0.1 Application Note (16), which provides the same values as the calculation ${\tau }_0=\frac{6\mu Q}{W{h}^2}$ from (13), where μ is the dynamic viscosity of the medium, W is the width of the flow channel, and h is the height of the flow channel. In this case (cell aerodynamic shape, chamber dimensions), the form drag of the cells is negligible compared with their skin friction drag (see supporting material for more details). The value of actual flow in the system was measured by a liquid flow sensor connected to the output of the flow chamber (see Fig. 1).

Data processing pipeline

The whole data processing pipeline is shown in Fig. 2 a, where the image sequence and measured flow are processed to estimate the viscoelastic properties of cells, specifically, shear modulus G and viscosity η. First, the shear stress signal $\tau \left(t\right)$ is calculated from the measured flow. Second, individual cells or cell clusters are segmented and tracked in the acquired image stack and their center of mass deflection over time ($CoM\left(t\right)$) is extracted. Moreover, thanks to the quantitative property of the QPI image, the cell height $L_{cell}$ is estimated from the QPI image. Shear strain signal $\gamma \left(t\right)$ can then be estimated from $CoM\left(t\right)$ and $L_{cell}$, as shown in Fig. 2 b. Finally, the viscoelastic properties (G and η) are estimated from the shear stress and shear strain signal using parametric deconvolution. A more detailed explanation of the individual data processing steps follows.

Figure 2.

Explanation of data processing and viscoelasticity measurement. (a) Block diagram of the data processing pipeline. (b) A model used in our calculation. The cell is approximated by a block with specific dimensions (solid lines); the block is skewed during the flow (dashed lines). (c) Strain signal generation model for parametric deconvolution based on a model of the connected linear systems. (d) Schematic representation of Kelvin-Voight (KV) model, which can be represented by the parallel combination of a purely viscous damper and purely elastic spring. (e) Example of shear strain response to ideal step function for low and high viscosity/shear modulus. To see this figure in color, go online.

Image processing

To measure the viscoelastic properties of the cells, images are processed to obtain the height of individual cells and temporal changes of centroid position ($CoM\left(t\right)$). Cell height and $CoM\left(t\right)$ are used for the calculation of the shear strain signal, which is consequently used for the calculation of viscoelastic parameters as described in “viscoelastic model estimation.” The individual steps needed to obtain shear strain for a particular cell or cell cluster are described below, which include segmentation, tracking, extraction of $CoM\left(t\right)$, and extraction of cell height. Precise segmentation and tracking of individual cells is very problematic for touching cells. In QPI, boundaries between cells are very indistinct, which cause segmentation errors in individual frames. Consequently, this leads to large mass exchange between those incorrectly divided cells, resulting in very noisy $CoM\left(t\right)$ signals. For this reason, touching cells are not divided, but rather analyzed together as a cell cluster. Despite the analysis of cell clusters providing a single number for the whole cluster (average of viscoelastic parameters of cells in a cluster), it is more accurate because segmentation errors of touching cells are eliminated. From here on, the analysis is described for cells; however, the same applies to the cell clusters.

Segmentation

A stack of reconstructed phase video frames was filtered by a three-dimensional (3D) median filter (of size $3\times 3\times 7$ for x, y, and t, respectively) to suppress noise in each frame and to filter the areas where the phase values are distorted due to fluid flow. The segmented cells were obtained by thresholding of the filtered image using a small positive threshold value of 0.35 rad, generally corresponding to the lowest phase values on the cell periphery. Obtained binary frames were post-processed by area filtering, which removed objects smaller than the selected threshold of 100 px (39.27 μm²). Cells touching the border of the actual field of view were removed in each frame to achieve the correct $CoM\left(t\right)$ estimation.

Tracking

Due to the 3D median filtering used in the segmentation step and the relatively high acquisition frame rate, the segmented cells create a compact 3D object in the video stack, i.e., the cell area in each frame is overlapped with the same cell area in the following frame. When each separate cell in the first video frame acquired a unique label and the 3D connected component analysis was done through all frames starting from the first one, the same cell obtained the same label throughout the whole video sequence. In the post-processing step, the cell was removed from further analysis if: 1) the cell was not presented in the first frame (probably false detection such as a bubble or part of a dead or detached cell); and/or 2) the cell was not detected in at least 60% of all frames (e.g., not a well-adhered cell). Finally, the position of the center of mass of each cell was computed in each video frame as a weighted average of the values of the mass density image belonging to the segmented cell.

Center of mass deflection

The center of mass $CoM\left(t\right)$ signal for a particular cell is extracted from the reconstructed phase image $\phi \left(x,y\right)$. Center of mass deflection of each cell was computed as the difference between the actual $CoM\left(t\right)$ and initial $CoM\left(t_0\right)$, where the deflection was considered in the direction of the applied flow only (in the y axis only from the image point of view), which produces signal $dY\left(t\right)$ used in the shear strain calculation as shown in Fig. 2 b. The deflection in the direction orthogonal to the applied flow (x axis) could be caused only by unwanted cell migration in our experiments.

Cell height measurement

The QPI microscope provides the phase image $\phi \left(x,y\right)$ that represents the phase delay produced by the cell, which depends on the difference of RIs between the cells and the surrounding medium. Assuming a homogeneous cell with constant RI, the cell height map can be estimated as (17)

$$\tilde{d}\left(x,y\right)=\frac{\phi \left(x,y\right)\lambda }{2\pi \left(n_c-n_m\right)}=\frac{\phi \left(x,y\right)\lambda }{2\pi \text{Δ}n},$$ (1)

where $\lambda =650\text{nm}$ is light wavelength and $n_c$ and $n_m$ is RI of cells and surrounding medium, respectively. The RI estimation is described in “cell height calculation and refractive index measurement.” Height of the individual cells was calculated as the median of cell pixels over the whole time stack ($L_{cell}$). The $L_{cell}$ value represents the cell height required for shear strain calculation.

Shear strain

Finally, the shear strain temporal change can be calculated from CoM deflection signal $dY\left(t\right)$ and cell height $L_{cell}$ as

$$\gamma \left(t\right)=\frac{dY\left(t\right)}{L_{cell}},$$ (2)

which is schematically depicted in Fig. 2 b. In this model, the cell is approximated with a rectangular block of homogeneous material of constant viscosity and shear modulus, which are estimated using this method. With this approximation, whole cell movement can be represented by CoM deflection. The suitability of this approximation was verified by numerical simulation, which demonstrated negligible difference in a CoM deflection between differently shaped models (block, cylinder, and conical dome) as shown in supporting material, section 4.

Viscoelastic model estimation

A Kelvin-Voight (KV) model is a linear model often used for the representation of viscoelastic properties of a single cell (18). The parallel connection of a spring (with elastic modulus G, N/m) and a damper (with viscosity η, Ns/m) enables quantification of the cell elasticity and viscosity (see Fig. 2 d). When this model is applied in a setup involving shear stress, the quantity G is referred to as a shear modulus and it expresses the stiffness of the particular cell. Furthermore, for isotropic elasticity, a linear relation between the shear modulus and Young’s modulus exists (13).

The response of the KV system to the positive step change of the external shear stress can be described by an exponential function as

$${\gamma }_{step}\left(t\right)=\frac{{\tau }_0}{G}\left(1-e^{-\frac{G}{\eta }t}\right).$$ (3)

The quantity ${\tau }_0$ represents the magnitude of the shear stress step function, which is set during the experiments. Examples of shear strain response to step function shear stress with various G and η are shown in Fig. 2 e. These parameters can be obtained by an exponential fitting of the cell response signal represented by Eq. 2. As mentioned in the hardware setup, the non-rigid properties of the entire setup influence the whole experiment, particularly the shear stress signal $\tau \left(t\right)$ and shear strain $\gamma \left(t\right)$ signals. This influence can be modeled as a serial connection of linear systems as shown in Fig. 2 c. The input of this connection is a signal driving the movement of the syringe. This is typically a step function or a square signal. The generated flow (i.e., the shear stress) is distorted by the flow system, which can be described by an unknown impulse response.

Consequently, the distorted shear stress waveform $\tau \left(t-t_0\right)$ deforms the adhered cells and changes their $CoM\left(t\right)$. Under the assumption of linear systems, the final model of the shear strain ${\gamma }_{model}\left(t\right)$ is a convolution:

$${\gamma }_{model}\left(t\right)=h_{\eta ,G}\left(t\right)\ast \tau \left(t-t_0\right),$$ (4)

where $h_{\eta ,G}\left(t\right)$ is a parametric impulse response with unknown parameters η (cell viscosity) and G (cell shear modulus), and $\tau \left(t-t_0\right)$ is a shear stress applied on the cell (generally shifted by unknown time $t_0$). The parametric impulse response $h_{\eta ,G}\left(t\right)$ can be easily computed as a differentiation of the step response (Eq. 3):

$$h_{\eta ,G}\left(t\right)=\frac{d}{dt}{\gamma }_{step}\left(t\right)=\frac{{\tau }_0}{G}{e}^{-\frac{G}{\eta }t}.$$ (5)

This convolution model enables us to formulate a simple cost function: $\left|\right|\gamma \left(t\right)-{\gamma }_{model}\left(t\right)|{|}_1$, or more specifically $\left|\right|\gamma \left(t\right)-\tau \left(t-t_0\right)\ast h_{\eta ,G}\left(t\right)|{|}_1$, and estimate the parameters of the KV model using a suitable optimization method. Parametric deconvolution is described in more detail in (19).

Cell height calculation and refractive index measurement

The cell height calculation according to Eq. 1 is not straightforward, as the exact RI values ($n_c$ and $n_m$) are not known. The RI of the medium $n_m$ can be easily measured by a refractometer. However, the cell RI $n_c$ is unknown.

Fortunately, the presented setup of shear stress induction enables us to relatively easily estimate $n_c$. Specifically, two syringes with media of different (but known) RIs can be connected to the cell chamber and can be used for fast exchange of the surrounding medium (see Fig. 3 a). Thus, we can measure image ${\phi }_1\left(x,y\right)$ with the first medium with RI $n_{m1}$ (Fig. 3 b, upper left) and image ${\phi }_2\left(x,y\right)$ with the second medium with RI $n_{m2}$ (Fig. 3 b, upper right). Therefore, if we assume that the cell height $d\left(x,y\right)$ and RI of cell $n_{cell}$ are equal for both measurements, then

$$\frac{{\phi }_1\left(x,y\right)\lambda }{2\pi \left(n_c\left(x,y\right)-n_{m1}\right)}=\frac{{\phi }_2\left(x,y\right)\lambda }{2\pi \left(n_c\left(x,y\right)-n_{m2}\right)}.$$ (6)

Figure 3.

Refractive index (RI) measurements. (a) RI measurement setup diagram of medium exchange. (b) Images acquired with different media solutions (iodixanol solution and mixture of iodixanol and RPMI medium); cell RI image was calculated with Eq. 7, and cell height image was calculated with Eq. 8. (c) Measured RIs for PC-3 and 22Rv1 cells. Values are medians of manually selected cell interior of RI image, t test used for statistics. (d) An example of confocal microscopy image used for cell height verification. (e) Comparison of cell height calculated by Eq. 8 and Eq. 1, and measured by confocal microscopy, Benjamini-Hochberg-corrected t test used for statistics. Scale bar, 10 μm. In the boxplots the boxes show 25th/75th percentile, the central line shows the median and whiskers show the lowest/highest value within 1.5-time inter-quartile range. To see this figure in color, go online.

By rearrangement of the terms in this equation, the RI of cells can be calculated as

$$n_c\left(x,y\right)=\frac{{\phi }_2\left(x,y\right)n_{m1}-{\phi }_1\left(x,y\right)n_{m2}}{{\phi }_2\left(x,y\right)-{\phi }_1\left(x,y\right)}.$$ (7)

This equation can be used to compute the RI for each pixel and to estimate the RI of a specific cell line as an average of RI values inside these cells (Fig. 3 b, lower left). Moreover, this approach enables us to compute the spatial distribution of cell height (i.e., for each pixel position) using a combination of Eqs 1 and 7:

$$d\left(x,y\right)=\frac{\lambda \left({\phi }_2\left(x,y\right)-{\phi }_1\left(x,y\right)\right)}{2\pi (n_{m1}-n_{m2})}.$$ (8)

Application of this double-syringe approach provides a possibility to measure the cell height $d\left(x,y\right)$ for every pixel in the field of view (FOV) in the shear induction experiments (Fig. 3 b, lower right). However, this requires a medium exchange measurement for each measured FOV, which is time consuming and might not be necessary for morphologically homogeneous cell populations. Thus, to simplify the measurements, RI (i.e., $n_c$) for each cell line was determined only once using Eq. 7, and this value was used in Eq. 1 to determine the cell height. Cell height of individual cells for shear modulus calculation in this paper was calculated as the median of cell height image $\tilde{d}\left(x,y\right)$ of the cell over the whole image sequence based on Eq. 1.

Flow sequence

First, a 60 s initialization pulse was applied with flow 129.8 μL/min. This flow caused shear stress of 1 Pa, which minimally influenced the cells, as tested in the optimization. The purpose of initialization is to fill the outlet tubing with medium, flush out nonadherent cells and debris, and remove microbubbles. After this initialization, a sequence of 3 × 30 s pulses of 5 Pa shear stress with 30 s pauses between them was used, as shown in Fig. 4 a. Responses to the whole sequence serve as input to parametric deconvolution viscoelasticity estimation, whereby the purpose of repeated pulses is to make the estimation more precise and robust.

Figure 4.

Cell response to standardized shear stress sequence. (a) Schematic of standardized experiment shear stress sequence. (b) Kymograph of representative 22Rv1 cell cluster. (c) Plot showing measured flow and cell center of mass (CoM) difference over flow sequence. Scale bar, 10 μm. To see this figure in color, go online.

Results

Refractive index

As described in “cell height calculation and refractive index measurement,” the measurement of cell RIs is required to reliably estimate the cell height. Calculation of an RI image is possible by the acquisition of images of cells with two different media of two different RIs. The first medium $m1$ was the RPMI medium (RI 1.3353) used in shear stress induction experiments, and the second medium $m2$ consists of 33.4% iodixanol (RI 1.3864), which was demonstrated to be suitable for live-cell experiments (20). Example of images with $m1$ and $m2$, and the calculated RI and cell height image using Eqs 7 and 8, are shown in Fig. 3 b.

Measured RI for PC-3 and 22Rv1 cells is shown in Fig. 3 c. Values are medians of manually labeled cell interiors, in order to omit large noisy values on cell edges. The estimated height of the cells was confirmed by measurement using a confocal microscope (example in Fig. 3 d). A boxplot of this comparison is shown in Fig. 3 e where similar medians of cell heights were measured using confocal microscopy, using the calculated cell height image $d\left(x,y\right)$ (Eq. 8) and cell height calculated from the phase image using the measured RI (Eq. 1), which is used for our viscoelasticity analysis.

Cell types

Cell lines previously used in our lab (10) characterized by different Young’s moduli were used to test the system. PC-3 and 22Rv1 cells were used as a model of lowly and highly deformable cells, respectively. Cell-culture conditions are described in supporting material, section 1. The selected standardized shear stress sequence was applied as shown in Fig. 5 a and Videos S1 and S2, while the shear strain value optimization is available in supporting material, section 4.

Figure 5.

Results of viscoelasticity measurement of different cell types (22Rv1 and PC-3). (a) Schematic of applied shear stress sequence. (b) Example of quantitative phase images before applied shear stress (first column), a merge of the image before and with applied shear stress (second column), detail corresponding to white square (third column), phase shift profile corresponding to red dashed line (fourth column), and detail of cell center with highlighted center of mass (CoM) deflection after flow pulse. (c) Plot of average strain signal of PC-3 and 22Rv1 cells. (d) Results of shear modulus. (e) Results of viscosity. (f) Scatterplot of shear modulus and viscosity. Scale bar, 50 μm. In the boxplots the boxes show 25th/75th percentile, the central line shows the median and whiskers show the lowest/highest value within 1.5-time inter-quartile range, t test used for statistics. To see this figure in color, go online.

Representative images of cells with applied shear stress are shown in Fig. 5 b. The average strain response curve for PC-3 and 22Rv1 cells is shown in Fig. 5 c, and boxplots of viscoelastic parameters are shown in Fig. 5, d and e. Those values were extracted using parametric deconvolution described in “viscoelastic model estimation.” Resulting shear modulus G showed an agreement of stiffness trend with previously published results, i.e., that PC-3 cells have higher stiffness than 22Rv1 cells (see Fig. 5 d). Contrary to G, the 22Rv1 cells have higher viscosity: 468.7 Pa·s for 22Rv1 versus 296.5 Pa·s for PC-3 (see Fig. 5 e). Fig. 5 f shows the dependence of viscosity and shear modulus for PC-3 and 22Rv1 cells, where values of viscosity and shear modulus have a linear relation; however, the relation of viscosity on shear modulus has different slopes for PC-3 and 22Rv1 cell types. This difference can be also seen from the average shear strain signal in Fig. 5 c: the response of PC-3 cells is faster due to smaller viscosity, but it reaches a similar maximal strain for each pulse as 22Rv1 cells due to their larger elasticity.

Treatments

Similarly, the responses of PC-3 cells to two types of treatments were tested to prove the validity of the proposed viscoelasticity measurements, which were measured again with our standardized experimental shear stress sequence (Fig. 5 a) and analyzed using parametric deconvolution. Cells were affected by the cytoskeleton-targeting drugs cytochalasin D (CytD) and docetaxel. The average shear strain signal response is shown in Fig. 6 b and Videos S3 and S4. Specifically, CytD is known to interfere with actin polymerization (21) and was applied to decrease the cell stiffness and cytoplasmic viscosity (22), while docetaxel was applied to increase cell stiffness based on (23). For details about the treatment dose and application see supporting material, section 1.

Figure 6.

Results of viscoelasticity measurement of PC-3 cells treated with cytochalasin D (CytD) and docetaxel (dctx) compared with AFM measurement. (a) An example of images before applied shear stress (left), the merge of the image before and with applied shear stress (middle), and AFM measured Young’s modulus example (right). (b) Plot of average strain signal for individual treatments. (c) Results of shear modulus and viscosity. The boxes show 25th/75th percentile, the central line shows the median and whiskers show the lowest/highest value within 1.5-time inter-quartile range, ANOVA used for statistics. (d) AFM measurement of Young’s modulus (left, total 92 cells) and a scatterplot of Young’s modulus determined by AFM and QPI. Shown as mean and standard deviation, Holm-Sidak t test used for statistics. (e) Scatterplot of shear modulus and cell circularity. Outlines correspond to kernel density estimate. Scale bar, 50 μm. To see this figure in color, go online.

Results of the measured shear modulus and viscosity are shown in Fig. 6 c. The measured stiffness was, as expected, higher for docetaxel treatment and lower for CytD treatment with 51.4 Pa, 22.0 Pa, and 67.5 Pa for untreated, docetaxel-treated, and CytD-treated cells, respectively. Viscosity followed a similar trend with 296.2 Pa·s, 132.9 Pa·s, and 427.7 Pa·s for untreated, docetaxel-treated, and CytD-treated cells, respectively. The acquired data were furthermore verified by AFM (Fig. 6 d), where the shear modulus values were roughly 9-fold lower compared with Young’s modulus and cell elastic parameters determined by both methods demonstrated to be linearly dependent. For AFM methodology see supporting material, section 2.

As a consequence of CytD-mediated inhibition of actin polymerization, the cells also changed their morphology, where membrane blebbing was evident (Fig. 6 a). Docetaxel-mediated tubulin stabilization, on the other hand, results in a tubulin rearrangement, which can also be reflected in cell morphology (10). Cell morphological parameters can be extracted from the acquired images, so dependence between morphology and viscoelastic properties of the cells can be studied using the proposed approach. Circularity, as shown in Fig. 6 e, was demonstrated to be different between these treatments. For the evaluation of circularity, only individual cells (not cell clusters) were manually selected, whereby the circularity was calculated as in (24). Data indicate that a combination of viscoelastic and morphological parameters can be beneficial to differentiate cell populations when compared with differentiation based solely on viscosity or elasticity. Similarly, parameters calculated from phase-cell dry mass, dry mass density (25), or RI can further supplement such analyses for more complex cell characterization.

Actin cytoskeleton recovery

To demonstrate the possibility of measurement in a time-lapse setting, we measured viscoelasticity during 20 min of actin repolymerization after washout of CytD. We observed that the morphology of CytD-treated cells recovered quickly after application of flow during shear stress induction experiments (see example image in Fig. 7 b). As measured in (26), full recovery of actin fibers of most cell compartments is expected within 15–30 min after CytD washout. To measure cell viscoelasticity during actin recovery, we designed a longer shear stress induction sequence consisting of four standardized subsequences of three pulses as shown in Fig. 7 a, while average shear strain response signal for individual subsequences at different times is shown in Fig. 7 c, where reduction of shear strain deviation is observable as cells recover from CytD treatment. Each subsequence is used in parametric deconvolution to measure viscoelasticity. As shown in Fig. 7, d–f, elasticity, viscosity, and circularity recovered to almost nontreated values within 16 min after CytD washout. For the evaluation of circularity, only individual cells (not cell clusters) were manually selected, whereby the circularity was calculated as in (24).

Figure 7.

Results of viscoelasticity measurement of PC-3 cells after cytochalasin D (CytD) washout. (a) Schematic of applied shear stress sequence. (b) An example of images acquired at 4th and 22nd minute during CytD washout (left) and example of its reaction to the shear stress—merge of the image before and with applied shear stress (right). (c) Plot of average strain signals during CytD washout recovery. (d–f) Results of shear modulus (d), viscosity (e), and cell circularity (f) during CytD washout recovery. Red dashed line indicates median modulus, elasticity, and circularity values for untreated cells. Scale bars, 50 μm, in the boxplots the boxes show 25th/75th percentile, the central line shows the median and whiskers show the lowest/highest value within 1.5-time inter-quartile range. To see this figure in color, go online.

Discussion

Evaluation of the mechanical properties of the cells proved to be a successful approach to obtaining information on the functional state of the cells. Most of the currently used methods for cell mechanophenotyping are limited by low robustness or the need for highly expert operation. In this paper, we described and tested the system and methodology for viscoelasticity measurement using QPI and shear stress induction by fluid flow. We tested the whole system in different types of experiments to show its benefits and properties. The proposed system and method are based on the original approach of Eldrige et al. (13); however, our approach employs a parametric deconvolution, which makes the viscosity measurement independent of fluidics.

The system also includes a reliable method to measure the RI directly during the measurement. RI of measured cells or cell clusters is then used to determine the cell height from the phase image. This is crucial, as this value strongly influences the precision of model parameter estimation. Furthermore, the observed RI appears to be a parameter relevant to cellular physiology (27). Two modifications of cell height measurement approach are possible. Accurate method in QPI-based cell height detection employs the exchange of perfusion media with different RIs around the cells during each experiment. Two phase images of cells are created, from which the cell height and RI maps are calculated. The final maps provide a spatial distribution of the cell height and RI over the whole FOV. The RI map can furthermore be correlatively used with other phase-derived imaging data such as cell dry mass. It has been demonstrated that RI is relevant for cellular processes such as the cell cycle and is an important parameter for pathologies, including cancer and hematologic diseases (28). The second, simpler and faster approach of determining cell height using QPI is based on the determination of average RI using changes in perfusion media only once for a specific set of experiments. This approach, however, assumes that RI is identical for all cells in a sample and that the subcellular RI distribution is homogeneous. On the other hand, homogeneity of cells might not be an issue, as median cell height is used for calculation of viscoelastic parameters. Results comparing these two approaches indicate no significant difference in cell height between these approaches (Fig. 3).

In addition, the impact of shear stress on RI is evaluated in section 8 of supporting material, where we measured the same values of RI before and after application of measurement sequence of shear stress pulses. Regardless of the strategy used, the determination of cell height is the reason for using QPI. This is not possible using conventional bright-field microscopy techniques. Cell height can be determined using a confocal microscope (as shown in Fig. 3), but the scanning speed of confocal sections is not sufficient to capture the dynamics of the change in the positions of the center of gravity of the cells. A frame rate below 0.5 frames/s is required for reliable viscosity determination.

In various studies the moduli of cells vary substantially from cell to cell. The origin of this spread in stiffness values is largely unknown and might limit the significance of measurements (29). Cell seeding density may be one of the factors influencing variability, as shown by Chiou and colleagues. These authors point out the increase in modulus depending on cell confluence in some cell types (30). To define the optimal conditions for our analysis, we verified the effect of confluence by model and experiment (supporting material, sections 5 and 6). In agreement with the modeling results, our experimental data provide evidence that the viscosity and elasticity values of the cells do not change at low confluences. At the same time, cells seeded at low confluence negligibly affect the chamber height and, thus, the shear stress within it (supporting material, section 5).

The proposed estimation also provides the cell viscosity. Its value, however, is largely influenced by the system components, especially the tubing and syringe used in the pump. We, therefore, demonstrated that the issue is diminished by the parametric deconvolution, and the viscosity values are then independent of the flow system characteristics (see characteristics of various setups in supporting material, section 8). Elimination of the effect of the system also provides practical benefits for the measurement setup. The plastic syringes are significantly easier to manipulate and, unlike glass syringes, their pistons seal properly. Moreover, the applied pulses are not so steep, which makes it more gentle on the cells; thus, fewer cells are detached by flow during the experiment. Parametric deconvolution also provides the possibility to apply different flow waveforms (not only rectangular pulses) to estimate cell viscoelastic properties. Furthermore, the elimination of the flow system properties via deconvolution provides a way to compare model parameters between laboratories.

In agreement with our previous study (10), we confirmed that PC-3 cells measured by the proposed method have larger stiffness than 22Rv1 cells. The reliability of the proposed viscoelasticity measurement was also confirmed by force mapping using AFM. Shear modulus showed a similar trend to Young’s modulus in cells exposed to docetaxel and CytD, respectively. Following CytD treatment, a similar trend in elasticity was observed in the study by Wakatsuki et al. (21) and specifically, an agreement regarding shear modulus was described by Eldridge et al. (13). In accordance with Spedden et al. (31), an overall increase in global cell stiffness was observed following treatment with paclitaxel, another taxane-based drug, using an AFM-based technique. However, although different techniques measuring the modulus of different cells show agreement, quantitative comparison between techniques is problematic, and modulus values measured on the same sample often differ by an order of magnitude. The most relevant source of this variation is differential mechanical responses of cells to the different force profiles produced by these different methods (7). Specifically, the AFM system provides a local measurement of stiffness, while QPI offers a global measurement of whole cells, making AFM and QPI not clearly comparable. To extract the average stiffness of the cells using AFM, an adequate spherical tip with a diameter of 5.7 μm was chosen in this experiment. Sharp tips, on the other hand, not only provide local measurement of stiffness but especially lead to higher Young’s moduli (32).

Compared with AFM, this approach is easy to implement on a QPI microscope. In addition, the proposed approach is able to measure a large number of cells quickly as it measures the whole FOV of cells simultaneously (10–50 cells using our QPI microscope FOV size). Moreover, this hands-on approach is applicable during live-cell experiments, while QPI images can be used for simultaneous analysis of cell morphology, which can provide interesting information such as cell viability or the distinction between apoptosis and necrosis (25). It also allows for multiple measurements of viscoelasticity during the experiment, which, for example, allows monitoring of influence of specific treatment. We have shown this in the CytD washout experiment, where we performed multiple viscoelasticity measurements in time while simultaneously observing cell morphology.

Using the KV model together with deconvolution, the average viscosity level of the cells can also be determined. Studies show that viscosity varies significantly between different cell types and also depending on the state of a particular cell (22): an increase was described during mitosis (33), due to docetaxel treatment (34), or during the development of drug resistance (35). Interestingly, a study dating to 1941 reports tumor cells to be characterized by a higher viscosity as determined by high-speed centrifugation (36). Regarding the effect of cytoskeleton-targeting drugs on viscosity, our results are in agreement with Wang et al. (22) who demonstrated a viscosity decrease following CytD treatment in H1299 cells by micropipette-based measurement. Conversely to our results, Yun et al. (34) determined that the factor of cell viscosity decreased after docetaxel treatment in HeLa cells. Thus, in contrast to the number of studies focusing on the biological significance of cell elasticity, viscosity remains an area with many uncertainties. These findings, therefore, call for more studies to address basic questions on cell viscosity in physiology and pathology. Analysis of viscosity using our proposed methodology is one way to clarify these uncertainties.

Conclusion

In this paper, the system and method for viscoelasticity measurement using QPI and shear stress is described and tested. Reliability of the proposed viscoelasticity measurement system was tested in several experiments including different cell types and treatments, where the results correspond to the literature and measurements using AFM. The proposed method allows high-throughput measurements during live-cell experiments. Processing using parametric deconvolution enables minimization of the effect of the hardware setup on the shear modulus and viscosity estimation. Moreover, we have shown that the proposed approach is suitable for the simultaneous measurement of cell morphology together with cell viscoelastic parameters. The proposed method also provides a simple approach to measure cell RI, which is required for reliable cell height measurement with QPI, where cell height is essential for viscoelasticity calculation.

Author contributions

T.V., J.G., J.C., and R.K. wrote the manuscript text. T.V., J.G., J.N., and L.C. conducted experiments. T.V. and J.C. wrote the code and conducted analyses on the data. J.N. prepared samples. R.K., V.C., I.P., and J.J. performed computational fluid dynamics and structural simulations, and consequent analysis of the results. M.M. conceived the experimental design and managed the project.

Editor: Philip R. LeDuc.