Three-Dimensional Confocal Microscopy Indentation Method for

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Three-Dimensional Confocal Microscopy Indentation Method for Hydrogel Elasticity Measurement Donghee Lee,† Md. Mahmudur Rahman,† You Zhou,‡ and Sangjin Ryu*,† †

Department of Mechanical & Materials Engineering and ‡Center for Biotechnology, University of NebraskaLincoln, Lincoln, Nebraska 68588, United States S Supporting Information *

ABSTRACT: The stiffness of the extracellular matrix (ECM) plays an important role in controlling cell functions. As an alternative to the ECM, hydrogels of tunable elasticity are widely used for in vitro cell mechanobiology studies. Therefore, characterizing the Young’s modulus of the hydrogel substrate is crucial. In this paper, we propose a confocal microscopy indentation method for measuring the elasticity of polyacrylamide gel as a model hydrogel. Our new indentation method is based on three-dimensional imaging of the indented gel using confocal microscopy and automated image processing to measure indentation depth from the three-dimensional image stack. We tested and validated our method by indenting polyacrylamide gels of different rigidities with various sphere indentors and by comparing it with the rheometric method. Our measurements show consistent results regardless of the type of the indentors and agree with rheometric measurements. Therefore, the proposed confocal microscopy indentation method can accurately measure the stiffness of hydrogels.

I. INTRODUCTION The mechanical properties of the extracellular matrix (ECM) are known as crucial factors regulating cellular behaviors because these mechanical cues initiate changes in biological functions of the cells through mechanotransduction.1−4 Specifically, the Young’s modulus of the ECM affects cellular differentiation, adhesion, migration, death, and the development and metastasis of cancer cells.2,3,5−13 To study such mechanobiological interactions in vitro, hydrogels have been employed to mimic the ECM. For example, mesenchymal stem cells (MSCs) develop differently depending on the elasticity of the hydrogel substrate on which they are cultured: the MSCs differentiate into neurogenic, myogenic, and osteogenic cells on soft (0.1−1 kPa), medium (8−17 kPa), and rigid (25−40 kPa) hydrogel, respectively.2 When NIH 3T3 cells are cultured on hydrogel substrates with the gradient of elasticity, the gradient guides the cells’ migration: they move from the soft region (14 kPa) to the rigid region (30 kPa) along the elasticity gradient.5 Regarding breast cancer cell development, increases in the hydrogel rigidity lead to breast malignancy.11 For a hydrogel used in such cellular mechanobiology studies, polyacrylamide (PAAM) gel has been widely used because of its linear elasticity, transparency, and chemical inertness.14 Furthermore, its Young’s modulus (E) can be easily modulated by adjusting the ratio of the monomer (acrylamide) and the cross-linker (bis-acrylamide). The nominal E values of PAAM gel can be easily found in the literature as a function of the concentration of acrylamide and bis-acrylamide.15−18 However, © 2015 American Chemical Society

true values appear to rely on gel casting environment and fabrication methods.19 Because the elasticity of the ECM is critical for the cellular functions as introduced, it is indispensable in cellular mechanobiology research to measure quantitatively the Young’s modulus of the hydrogel substrate. Young’s modulus is a mechanical property of a material which represents how stiff the material is. The Young’s modulus of a hydrogel can be measured by finding the relationship between a force applied to the hydrogel and resultant deformation of the hydrogel. Common methods for Young’s modulus measurement include the rheometric method and the indentation method. In the rheometric method, a hydrogel sample undergoes shear deformation between the parallel plates of a rheometer, and its shear modulus (G) is measured and then converted to E.9 Since the sample needs to be cast between and removed from the parallel plates for every measurement, it can be timeand material-consuming to repetitively measure E using the rheometer. Also, the rheometric method can measure bulk mechanical properties of hydrogel only, so it cannot characterize rigidity variations on a single sample. The indentation method employs an indentor to gently press the surface of a hydrogel sample. The E of the sample is measured based on the relationship between the indentation force (F) from the indentor and the resultant indentation depth Received: April 7, 2015 Revised: July 30, 2015 Published: August 13, 2015 9684

DOI: 10.1021/acs.langmuir.5b01267 Langmuir 2015, 31, 9684−9693

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Langmuir Table 1. List of Spherical Indentors Indentors Indentor Indentor Indentor Indentor Indentor

1 2 3 4 5

Nominal diam (μm)

Measured diam (μm)

Material

Density (g/cm3)

Indentation force (μN)

Vendor

400 670 1000 794 1000

545 677 1173 797 1001

zirconium silicate stainless steel zirconium silicate tungsten carbide tungsten carbide

3.84 7.667 3.84 14.95 14.95

2.36 10.63 23.56 36.28 71.88

OPS Diagnostics LLC, Lebanon, NJ NEMB, Norkfolk, CT OPS Diagnostics LLC, Lebanon, NJ NEMB, Norkfolk, CT NEMB, Norkfolk, CT

ball. The deformed gel was imaged with confocal laser microscopy, and the indentation depth was automatically measured from the three-dimensional (3D) image stack of the gel. The E of the gel was estimated with an appropriate indentation model for the spherical indentor. We validated the proposed method in comparison with rheometric measurement. Overall, the proposed method is suitable for quick and easy measurement of hydrogel elasticity because it does not require removing the indentor from the gel for indentation depth measurement and because the indentation depth is measured automatically from 3D images of the indented gel.

(δ) of the sample. For soft samples such as cells and hydrogels, atomic force microscopy (AFM) is widely employed for nanoscale indentation tests,20,21 and their E is measured by fitting an indentation model (e.g., Hertz model,22 Sneddon’s model,23 DMT model,24 and JKR model25) against obtained F−δ curves. Although AFM is a versatile tool for probing the mechanical properties of soft materials, AFM indentation cannot be easily adopted because it requires a quite expensive AFM system. This AFM-based measurement is costly because AFM probes need to be replaced due to contamination and damage. Also, the method is low-throughput because careful calibrations of the system are needed for accurate measurement. Additionally, it is not always straightforward to determine the contact point between the AFM probe tip and the sample because of their adhesive interactions.26 Instead of the AFM nanoindentation method, the microscopic indentation method is employed for easier and quicker measurements of the E of hydrogel.5,19,27−30 Most conventional microscopic indentation methods for hydrogel consist of the following steps. First, fluorescent beads are embedded in the hydrogel to visualize its top surface, and a sphere or ball indentor is placed on the hydrogel in liquid. The indentation force from the indentor, which is the weight of the indentor in the liquid, deforms the gel surface locally. Then, the fluorescent beads at the bottom of the indented surface are identified with a fluorescence microscope. After the indentor is removed and the hydrogel is allowed to recover elastically, the fluorescent beads identified above are tracked by raising the focal plane. Finally, the indentation depth is measured from the displacement of the focal plane, and the E of the hydrogel is calculated from F and δ using a proper indentation model. Compared to the rheometer- and AFM-based measurement, the microscopic indentation method has advantages. The method is cost-effective because it does not require special equipment and sensor and because tested hydrogels can be used for other purposes. Thus, the microscopic indentation method can be easily adopted in normal laboratories with a fluorescent microscope, and it can be implemented in cell culture conditions on a microscope. However, the current microscopic method has limitations in characterizing the E of the hydrogel. First, the method requires additional time for indentor removal, gel recovery, and focus adjustment. Second, indentation depth measurement can be user-dependent because fluorescent beads need to be identified with human eyes. Last, the method cannot visualize how the indentor deforms and interacts with hydrogel. Such information can be useful for understanding gel−indentor interaction and thus choosing contact mechanics models. In this study, we propose an improved microscopic indentation method which uses confocal laser fluorescence microscopy and automated image processing to overcome the aforementioned limitations. Briefly, we fluorescently stained a whole PAAM gel and indented it with a submillimeter-sized

II. MATERIALS AND METHODS 1. PAAM Gel Fabrication. We adopted well-established protocols for PAAM gel fabrication15,16 as briefly follows. Prepolymer solution was made by mixing acrylamide and bis-acrylamide (Bio-Rad, Hercules, CA) in phosphate buffered saline (PBS; Amresco, Solon, OH). The prepolymer solution was filtered with a bottle top filter and then degassed for 15 min in a vacuum chamber. This stock solution could be stored for months.16 At gel casting, allylamine (Alfa Aesar, Ward Hill, MA) was added to the stock solution for fluorescent labeling at the ratio of 1% (mol/mol) of acrylamide,31 and then 1% ammonium persulfate and 0.1% tetramethylethylenediamine (SigmaAldrich, St. Louis, MO) were added to initiate polymerization. Amino-silanated cover glasses were prepared through the following four steps.15 First, we cleaned circular cover glasses (VistaVision, No. 2, diameter 25 mm, VWR, Radnor, PA) by shaking them at 55 rpm in 0.2 M HCl overnight at room temperature and then rinsed them with deionized water (diH2O). Second, the cover glasses were dispersed in 0.1 M NaOH for an hour at room temperature and then rinsed with diH2O. Then, they were placed in 1% (v/v) 3-aminopropyltrimethoxysilane (Sigma-Aldrich, St. Louis, MO) in diH2O for an hour and rinsed with diH2 O. Finally, the coverslips were coated with 0.5% glutaraldehyde (Sigma-Aldrich, St. Louis, MO) in PBS for an hour and rinsed with diH2O. For chlorosilanated glass plates, we squeezed and spread dichlorodimethylsilane (DCDMS; Sigma-Aldrich, St. Louis, MO) between two glass plates.16 The glass plates were separated in 5 min, and excess DCDMS was removed with KimWipes. The DCDMScoated glass plates were rinsed with diH2O for 1 min. For gel casting, we dropped a desired volume of the PAAM gel solution on the aminosilanated cover glasses. The solution was covered with the chlorosilanated glass plate and squeezed between the two surfaces with ∼750 μm thick spacers. After 1 h long polymerization in the chemical fume hood, we uncovered the chlorosilanated glass plate and obtained the PAAM gel fixed on the coverslip. Last, after having been rinsed in PBS twice for 5 min each, the PAAM gel was immersed in 20 μM Alex Fluor 488 dye solution (excitation peak = 490 nm, emission peak = 525 nm; Life Technologies, Carlsbad, CA) for 24 h and then rinsed in PBS five times for 15 min each. The thickness of the fabricated gel was measured to be 1−1.5 mm with the nominal z-step size of 5−10 μm based on the following 3D imaging method. 2. Confocal Microscopic Indentation. 2.1. 3D Imaging. For the microscopic indentation tests, we used five different spherical indentors (Table 1). One equatorial plane image was taken for each indentor with an inverted bright-field microscope (IX81, Olympus, Tokyo, Japan), and the diameter of the indentor was determined from 9685

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Langmuir the image and the circular fitting method developed by Kasa.32 We used these five ball indentors repeatedly for indentation. As the schematic shown in Figure 1, we gently placed a spherical indentor on a PAAM gel using a pair of tweezers and moved the

Figure 2. Height measurement of 400 μm high microfluidic channels for z-step size calibration. Red: intensity profile along the z-axis in the microfluidic channel. Blue: derivative of the intensity profile in the zaxis. The initial position of the focal plane is set to be z = 0. The measured channel height (hc) using the nominal z-step size (2 μm) is 291.6 ± 1.7 μm. Figure 1. Schematic of the confocal microscopy indentation test. R is the radius of the ball indentor, δ is the indentation depth, and h is the thickness of the PAAM gel.

selected xy-images to determine the coordinate (xc, yc) of the axis of symmetry. Second, we reconstructed the 3D image stack with the corrected zstep size and found the z-coordinate of the undeformed top surface of the PAAM gel (zu in Figure 4). For each side of the 3D stack, we chose three xz- or yz-images from the outermost side and averaged them to reduce noise. On the basis of the gradient of fluorescence intensity in the z-direction, we found pixels for the maximum gradient magnitude which indicate the gel−liquid interface, and fitted a horizontal line against these points for each side of the gel. Assuming that the gel’s top surface was horizontal, we averaged these four horizontal lines to determine the undeformed top surface of the gel (or the top surface of the gel without the indentor). Finally, zu was determined to be the distance between the averaged horizontal line and the bottom of the image set (i.e., z = 0). Third, we determined the indented surface of the gel using the xzand yz-cross sections of the 3D image stack at the axis of symmetry identified in the first step (Figure 5). For each cross section, we chose one image nearest the axis of symmetry and two adjacent images, and averaged them for noise reduction. We averaged the obtained two cross-sectional images with respect to the axis of symmetry, assuming that the indented surface was axisymmetric. After having applied the Wiener filter to the averaged cross-sectional image, we calculated the intensity gradient along the z-axis and found pixels of the maximum gradient magnitude. These pixels represent the top surface of the gel deformed by the indentor, as marked on the averaged cross-sectional image in Figure 5. Last, we fitted the circle equation of the ball indentor against the indented profile of the gel using the method of least-squares and then measured the indentation depth (Figure 6). The measured diameter (2R) of the ball indentor was used for the diameter of the fitting circle (Table 1), and the center of the circle was limited on the axis of symmetry. Therefore, the circle equation was

sample to locate the ball at the center of the field of view. Using a confocal laser fluorescence microscope (LSM 510, Carl Zeiss, Jena, Germany) with a 10× objective lens (EC Plan-Neofluar, NA = 0.30, Carl Zeiss, Jena, Germany), 3D image stacks were collected by moving the focal plane (pinhole size = 1 airy disk, confocal slice thickness = 12.6 μm) from below the ball to above the top surface of the gel with the nominal z-step size of 2 μm (Figure S1). Three PAAM gel samples were fabricated per gel composition, and 7−11 indentation tests were conducted with these samples per indentor. Although the nominal z-step size for 3D imaging was set for the zscanning of the objective lens, it differed from the actual z-step displacement of the focal plane because of different refractive indice of air and PAAM gel.19 Therefore, we calibrated the actual z-step size using microfluidic channels (μ-Slide I, ibidi, Germany) with the known heights (hr = 400 and 800 μm). The nominal channel heights were confirmed using a 3D laser scanning confocal microscope (VK-X200, Keyence, Osaka, Japan; see Table S1). We filled the channel with Alexa Fluor 488 dye solution and immersed it in PBS. After having taken three or five 3D image stacks per channel using the nominal zstep size (2 μm), we measured the channel height based on the derivative of fluorescence intensity profile31 (Figure 2 and Figure S2). The z-distance between the maximum and minimum gradient points was measured to be the channel height (hc) with the nominal z-step size. The average and standard deviation of hc were 291.6 ± 1.7 μm for three 400 μm high channels and 584.4 ± 3.6 μm for one 800 μm high channel (Table S2). Using the average value of hr and hc, we determined the calibration factor (c = hr/hc) to be 1.37 for the both channel heights and multiplied the calibration factor to the nominal zstep size (2 μm) to obtain the real z-step size (2.74 μm) for image analysis. 2.2. Image Processing. To automatically measure the indentation depth from the 3D image stack, we developed an image processing code consisting of four steps (Figure S3) using MATLAB (MathWorks, Natick, MA). First, we identified the axis of symmetry of the indented gel surface (Figure 3). We selected two-dimensional (2D) confocal sections or xy-images with the clear indented area appearing dark, and used the Wiener filter33 to remove noise from the images. Then the images were converted to binary images with Otsu’s method.34 If necessary, the threshold value for gray-to-binary image conversion was adjusted. In the binary images, the gel and the ball (or the indented part of the gel) looked white and black, respectively. After having switched black and white, we found the center of the indented area from each binary image using Kasa’s circular fitting method,32 and averaged the obtained center coordinates over the

x 2 + (z − zc)2 = R2

(1)

where zc is the z-coordinate of the indentor’s center. Here, xc was set to be 0 for simplicity. Because it was unknown how much of the indented surface made contact with the ball indentor, we used the following weight factor for fitting ⎛ max(zi) − zi ⎞n weight factor = ⎜ ⎟ ⎝ max(zi) − min(zi) ⎠

(2)

where zi is the z-coordinates of the indented gel surface (cyan dots in Figure 6) and n is an exponent. As n increases, the weight factor distribution becomes narrower toward the center (Figure S4). Therefore, our fitting found the center of the circle representing the 9686

DOI: 10.1021/acs.langmuir.5b01267 Langmuir 2015, 31, 9684−9693

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Figure 3. Determination of the axis of symmetry of the indented gel surface from 2D confocal sections. (a) Selected xy-image with the indented area at the center. (b) Filtered image using the Wiener filter. (c) Binary image. (d) Reversed binary image for boundary recognition. (e) The identified boundary (green) and center of the indented area (red). (f) The center coordinate from each xy-image was averaged to find the axis of symmetry of the ball indentor (xc, yc; red dashed lines). An image set of the softest PAAM gel (3% acrylamide and 0.06% bis-acrylamide) indented by Indentor 1 is used for Figures 3−6.

Figure 5. Determination of the cross-sectional profile of the indented surface. (a) Reconstructed 3D image of the PAAM gel with the axis of symmetry and (b) its xz- and yz-cross sections. For each cross section, three images near the axis of symmetry were averaged for noise reduction. (c) Averaged cross section with the identified deformed top surface (cyan) and the undeformed top surface (yellow). Image size: 499 × 53 pixels. Scale bar: 50 μm.

Figure 4. Determination of the undeformed top surface. (a) Reconstructed 3D image of the PAAM gel. (b) Four sides of the gel with the horizontal line representing the intact top surface (yellow). For each side, three images from the outermost side were averaged for noise reduction. (c) Averaged horizontal line representing the zcoordinate of the undeformed top surface of the gel (zu). Image size: 512 × 53 pixels. Scale bar: 50 μm.

where zp is the z-coordinates of the indentor profile (magenta circle in Figure 6) and N is the number of points in the interval [0, x] (Figure S5). Then, we found the local minimum of Δzrms farthest from the axis of symmetry and determined a to be distance from the axis of symmetry to the local minimum point. 2.3. Young’s Modulus Calculation. We evaluated the elasticity (E) of the gel based on the indentation force (F, sum of the weight and buoyant force of the indentor), the indentation depth (δ), the radius of the ball indentor (R), the thickness of the PAAM gel (h), and an appropriate contact mechanics model. For the parameter regime of 0 < δ < min(0.3R, 0.2h)28,35 and a/R < 0.1,36 the Hertz theory22 can be used to calculate E:

ball indentor, with higher weights on the center part of the indented gel surface. Finally, we calculated the indentation depth (δ) using δ = z u − (zc − R )

(3)

where zu is the z-coordinate of the undeformed top surface of the gel (yellow line in Figures 4 and 6). The radius of the contact area (or contact radius a) between the indentor and the gel was also measured based on the determined indentor profile. Assuming that the indented gel surface was symmetric, we calculated the root-mean-square difference (Δzrms) between the indentor and the indented gel profile

Δz rms(x) =

1 N

E=

j=1

(5)

where ν is the Poisson’s ratio of the PAAM gel. Although widely used, the Hertz model has two major limitations: the gel thickness should be much larger than other relevant length scales, and the resultant strain of the gel should be small enough.19 For gels of finite thickness, Dimitriadis et al.’s model can be used:37

N

∑ [z p(xj) − zi(xj)]2

3(1 − ν 2)F 4R0.5δ1.5

(0 ≤ xj ≤ x) (4) 9687

DOI: 10.1021/acs.langmuir.5b01267 Langmuir 2015, 31, 9684−9693

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for 90 min. To reduce evaporation of water from the gel, we used a custom-made humidity chamber. Similar to the thickness of the spacer used for gel fabrication, the gap distance of the parallel plates was maintained to be 0.75 mm. Through strain amplitude sweep (1 rad/s, 0.1−10% strain),9 the shear modulus (G) of the gel was measured at room temperature. Then, E was calculated with E = 2G(1 + ν). This rheometric E measurement was repeated three times per gel composition.

III. RESULTS For quicker and easier measurements of the Young’s modulus of hydrogel, we developed the confocal microscopy indentation method. As a model hydrogel, fluorescently stained PAAM gel was indented by a ball indentor and then imaged using confocal microscopy. For Young’s modulus measurement, the indentation depth of the gel was automatically measured based on image processing. To validate our method, we tested four different PAAM gels using the five different sphere indentors and compared our confocal microscopy indentation results with the rheometric measurement. 1. PAAM Gel Fabrication and Confocal Imaging. Using the well-established fabrication procedure,15,16 we could fabricate stable PAAM gel samples fixed on glass surface. For uniform gel fixation we used aminosilanated cover glasses within 48 h after the treatment,16 and for full cross-linking the gel was polymerized for more than an hour.38 Because indentation measurements of hydrogel are affected by the underlying glass substrate,28 we fabricated relatively thick PAAM gels using spacers. Although the spacers were ∼0.75 mm thick, the fabricated gels were measured to be 1−1.5 mm thick because of gel swelling in PBS. Based on known nominal E values of PAAM gel, four compositions of acrylamide and bisacrylamide were chosen to cover the E range of 0.3−10.6 kPa as summarized in Table 2. For fluorescence imaging, allylamine was included in PAAM gel, and the gel was stained sufficiently with fresh Alexa Fluor 488 solution. Because the trapped fluorescent dye solution was released from the gel, the gel was washed thoroughly before confocal imaging for best contrast between the gel and PBS. Although line averaging was not used for quicker imaging, clear 3D images of the gel could be obtained. As Table 2 shows, we chose the indentors depending on the expected elasticity of the gel. For example, the softest PAAM gel (3% acrylamide and 0.06% bis-acrylamide) was tested with two lighter indentors (Indentor 1 and 2) because too heavy indentors could deform the gel beyond the limit of the contact mechanics model that we used. In contrast, a too light indentor

Figure 6. Indented profile (cyan dots) of the softest PAAM gel with the determined position of Indentor 1 (magenta circle). From the zcoordinate of the undeformed top surface (zu = 101.8 μm; yellow dashed line) and the center coordinate (zc = 329.3 μm) and radius (R = 272.5 μm) of the indentor, we estimated the indentation depth (δ = 45.0 μm) and the contact radius (a = 124.7 μm, red dot). The bottom of the image set was set to be z = 0 μm. Inset: scaling relation δ ∼ (F/ E)2/3 among the average indentation depth measured by confocal imaging, the indentation force, and the average Young’s moduli measured by the rheometer. E=

2α0 4α 2 3(1 − ν 2)F ⎡ 8⎛ 4π 2 ⎞ 3 ⎢1 − χ + 20 χ 2 − 3 ⎜α0 3 + β ⎟χ 0.5 1.5 π 15 0⎠ π π ⎝ 4R δ ⎣ +

−1 16α0 ⎛ 3 3π 2 ⎞ 4 ⎤ ⎥ α + β χ ⎜ ⎟ 0 5 0⎠ ⎦ π4 ⎝

(6) where χ = (Rδ) /h, and α0 and β0 are given as 1/2

α0 = − β0 =

1.2876 − 1.4678ν + 1.3442ν 2 1−ν

0.6387 − 1.0277ν + 1.5164ν 2 1−ν

(7)

for a gel bonded on a coverslip. The above model is valid for the parameter regime of δ/h ≤ 0.1 and 0.1 ≤ h/R ≤ 12.8. In our study, Dimitriadis et al.’s model was used with an assumption that our PAAM gel was incompressible (ν = 0.5).19,37 3. Rheometric Measurement. To validate our confocal microscopy indentation method, we measured the Young’s modulus of PAAM gels using a rheometer (AR 1500ex, TA Instruments, New Castle, DE). The desired volume (368.2 μL) of the prepolymer solution was injected between the rheometer stage and a stainless steel parallel plate (25 mm in diameter), and it was allowed to polymerize

Table 2. Comparison of Young’s Moduli of Polyacrylamide Gel among the Confocal Microscopy Indentation Method, Rheometry Method, and Literature (Data Are Reported as Average ± Standard Deviation) Young’s modulus E (kPa) [Indentation depth δ (μm)] Confocal microscopy indentation (N = 7−11) Acrylamide (%)

Bis-acrylamide (%)

3

0.06

4

0.1

7.5

0.05

10

Indentor 1 0.24 ± 0.02 [45.4 ± 2.1]

Indentor 2 0.25 [105.3 2.06 [27.4

± ± ± ±

0.01 1.6] 0.27 2.3]

Indentor 3

1.86 [39.3 5.53 [20.2

± ± ± ±

0.10 1.3] 0.46 1.1]

0.1

9688

Indentor 4

1.81 [60.7 5.69 [30.1 13.15 [17.3

± ± ± ± ± ±

0.08 1.8] 0.36 1.3] 1.39 1.2]

Indentor 5

5.63 [43.4 13.17 [24.8

± ± ± ±

0.41 2.0] 1.48 1.8]

Rheometry (N = 3)

Lit. values

0.23 ± 0.01

0.48 ± 0.1616 0.6,17 0.318

1.86 ± 0.002

2.01 ± 0.7516

7.60 ± 0.02

415

13.37 ± 0.20

10.6116

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circular fitting to find the center of the spherical indentor and then calculated the indentation depth using eq 3. Because it was unknown how much the indented gel surface was in contact with the indentor, the weight factor given by eq 2 was used for circular fitting. To find a circle best representing the indented profile, we adjusted the exponent value (n) of eq 2 among between 1 and 4 with an interval of 0.5. Figure 6 shows as an example that the fitted circle well represents the indented profile of the softest PAAM gel indented by Indentor 1. For this case, we chose n = 2, and the distribution of the fitting weight factor became narrower toward the axis of symmetry as n increased from 1 to 2 (Figure S4). With the bottom of the 3D image set to be z = 0 μm, the zcoordinates of the undeformed top profile and the indentor center were estimated to be zu = 101.8 μm and zc = 329.3 μm, respectively. Because the radius of Indentor 1 was R = 272.5 μm, the indentation depth was measured to be δ = 45.0 μm. More examples of the indented gel with the fitting circle are shown in Figure S7. Table 2 summarizes the measured indentation depth values (shown in brackets), and it shows that the indentation depth increased with increasing indentation force or decreasing gel stiffness. It is also noticeable that the standard deviation of the measured δ is small compared to the average. The largest standard deviation is about 8% of the average for the case of the PAAM gel of 4% acrylamide and 0.1% bis-acrylamide and Indentor 2. According to the indentation models (eqs 5 and 6), a scaling relation δ ∼ (F/E)2/3R−1/3 can be assumed. Because R1/3 has similar values (8.2−10.5 μm1/3) for the used indentors, the above scaling relation becomes δ ∼ (F/E)2/3. Using the average E values measured with the rheometer, we confirmed that our average δ values conform to the scaling relation (inset of Figure 6). Because the used values of δ, F, and E were obtained separately, conforming to the scaling relation supports that our image-processing-based method can measure the indentation depth successfully. 4. Contact Radius Measurement. In addition to the indentation depth, the contact radius (a) between the indentor and the gel was measured. The root-mean-square difference between the indentor profile and the indented gel profile (Δzrms, eq 4) was calculated for the half of the PAAM gel as a function of the distance from the axis of symmetry (Figure S5a). Then, the first local minimum of Δzrms was searched inward, and the contact radius was determined to be the distance between the local minimum point and the axis of symmetry (Figure S5b). For the case of the softest PAAM gel and Indentor 1 as an example, the identified Δzrms minimum point (red dot in Figure 6) represents well the contact point between the gel and the indentor, and the contact radius was determined to be 124.7 μm. As summarized in Table S3, the standard deviation of a is less than 6% of the average for all cases. Similar to the indentation depth, the contact radius increased as a softer hydrogel sample was tested with a heavier indentor. The ratio of the contact radius to the indentor radius (a/R) can serve as a criterion for choosing a right indentation model. For instance, the Hertz model is reliable only when a/R < 0.1.36 As shown in Table S3, all a/R values are greater than 0.1 in our study, and thus we could not use the Hertz model for calculating E. 5. Young’s Modulus Measurement. In our measurement, Young’s modulus was calculated by using Dimitriadis et al.’s

could not be used for the stiffest PAAM gel (10% acrylamide and 0.1% bis-acrylamide) because it could not deform the gel sufficiently. 2. Image Processing. Our image processing method produced consistent results in identifying the axis of symmetry of the indentor. For the case of the softest PAAM gel and Indentor 1 as an example, the identified center coordinate of the indented area showed negligible deviation among the selected 2D confocal sections because the standard deviations of the identified center x- and y-coordinate (0.53 and 0.92 μm) are smaller than 1 pixel (= 1.73 μm) (Figure S6). Therefore, the indented areas of 2D confocal sections appear to share the common axis of symmetry, which passes through the center of the ball indentor, and our image processing method can successfully determine the axis of symmetry of the indented gel surface. In the proposed microscopic indentation method, we determined the intact top surface of the PAAM gel from a single 3D image stack without removing the ball indentor. To verify our method, we imaged a wider range (1697 μm × 1697 μm) of the softest PAAM gel with Indentor 2, which was the case of the maximum deformation. We took four sets of 3D image stack of which each approximately quartered the indented surface, and then stitched them into one single 3D image stack using an image stitching plugin39 of ImageJ.40 As shown in Figure 7, the gel thickness at dashed lines, which

Figure 7. Cross section of a wider 3D image (1697 μm × 1697 μm) of the softest PAAM gel with Indentor 2. Dashed lines indicate the image size (848.5 μm × 848.5 μm) for the confocal microscopy indentation method. Intensity adjusted. Scale bar: 200 μm.

represent the image size (848.5 μm) used for our indentation test, appears similar to the thickness at the boundary of the stitched image. Hence, our approach can reasonably determine the gel’s undeformed top surface even with the ball indentor on the gel. To determine the cross-sectional profile of the indented gel surface, we obtained the representative cross-sectional image of the gel by averaging the xz- and yz-cross sections containing the axis of symmetry. Figure 5 shows the case of the softest PAAM gel with Indentor 1 as an example. With clear gel boundary, the xz- and yz-cross sections resemble each other, which shows that the indented surface of the gel is approximately axisymmetric. With the averaged and filtered cross-sectional image of the gel, we determined the gel boundary based on the gradient of fluorescence intensity. As Figure 5c shows, the identified gel’s top surface (cyan) coincides well with the boundary of the averaged cross-sectional image and with the undeformed top surface (yellow) of the gel obtained from Figure 4. 3. Indentation Depth Measurement. At the end of the image processing procedure, we measured the indentation depth using the identified undeformed top profile and the indented profile of the gel. It was possible to use the zcoordinate of the indented profile nearest the axis of symmetry, but this might cause error in measuring the indentation depth. This is because some 3D confocal images showed rather flat gel boundary beneath the indentor, presumably due to fluorescent light reflected from the indentor surface. Instead, we used 9689

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optical coherence tomography was employed to image the cross section of the indented gel for the indentation test.41,42 Compared to these microscopy indentation methods, the proposed confocal microscopy indentation method has advantages. First, it does not require additional steps related to indentor removal because deformed hydrogel with the indentor is imaged. Second, our image processing method enables user-independent measurement of the indentation depth because the 3D image stack of the indented gel is automatically processed and analyzed. Third, using allylamine nanoparticles can reduce any possible changes in the mechanical property of hydrogel caused by including stiffer microscale tracking beads. Fourth, our method enables visualizing the indented gel profile using 3D confocal microscopy imaging. Thus, not only indentation depth but also contact radius can be measured by the method. Such information on contact radius and gel−indentor interface can provide basis for selecting an appropriate contact mechanics model. Fifth, the proposed method can facilitate highthroughput multipoint indentation if an array of spherical indentors is used to indent multiple spots on hydrogel. Because the method does not require the indentor to be removed for indentation depth measurement, 3D imaging can be repeated for the array to map gel stiffness. Last, our method can be easily adopted by normal laboratories as confocal laser fluorescent microscopy becomes more accessible in various research settings. As demonstrated in Table 2, our method can measure the Young’s moduli of hydrogel consistently regardless of the size and weight of the ball indentors. However, it is required to choose an appropriate indentor for reasonable indentation depth because most indentation models have certain parameter ranges to be valid. For example, two assumptions for the Hertz model (small strain and thick samples) can be easily violated if a heavy and large sphere indentor is used for a soft or thin sample. Moreover, the deformed region of the gel must be smaller than the field of view of a used microscope, which is necessary for reliable determination of zu. This requirement cannot be satisfied if too large indentors or too soft gels are used. For successful applications of the confocal microscopy indentation method, therefore it must be considered what kind of the indentation model and the ball indentor can be used, based on the expected thickness and elasticity of hydrogel. For 3D confocal imaging, z-step size calibration is crucial because the nominal step size for z-scan can be different from the actual z-displacement of the focal plane. This is caused by refractive index mismatch between air and hydrogel.19,43 To calibrate this difference in the z-step size, we measured the height of microfluidic channels filled with the fluorescent dye solution using the confocal microscope based on the similar refractive index of water (1.333) and PAAM gel (1.349).43 Since the microfluidic channel has 5% deviation in its height, the resultant uncertainty in our E measurements is estimated to be about 8% (see Supporting Information). Significant aberration might be induced in 3D confocal imaging because of the thickness of PAAM gels and the refractive index change between air and the gel. To evaluate aberration effects, we included a 94.5 μm diameter zirconium ball in our PAAM gel and imaged the gel volume including the ball using the same imaging condition. Because the ball settled to the cover glass substrate of the gel during gelation, the gel image shows the ball near the bottom and the long shadowed area above the bead (Figure S8a). Then the gel was flipped, and

model (eqs 6 and 7) since all measurements belonged to the parameter regime of the model. As Table 2 shows, the confocal microscopy indentation method measured similar E values of PAAM gels of a certain composition although the gels deformed differently depending on used indentors. For example, the PAAM gels of 4% acrylamide and 0.1% bisacrylamide were tested with Indentor 2, 3, and 4, and their average δ values were measured to be 27.4, 39.3, and 60.7 μm, respectively. Although the indentation depths are significantly different, the respective E values are 2.06, 1.86, and 1.81 kPa, which are very similar considering their standard deviations. Although all the gel samples show about 2-fold changes in the indentation depth, the measured Young’s modulus values show negligible differences. To validate the proposed confocal microscopy indentation method, we compare in Table 2 the confocal microscopy measurements with the rheometric measurements and literature values. The largest difference between the indentation and rheometric methods is observed with the case of 7.5% acrylamide and 0.05% bis-acrylamide. The average E of this sample group was measured to be 5.62 kPa with the indentation method, which shows about 26% difference compared to the rheometric measurements (7.60 kPa). The rest three groups show differences smaller than 7%. Although with larger differences, our microscopy measurements are in fair agreement with literature values. Therefore, it is demonstrated for the tested gel compositions that the confocal microscopy indentation measurements agree well with the rheometric measurements and literature values.

IV. DISCUSSION The microscopic indentation method for hydrogel elasticity measurement was first proposed by Lo et al.,5 and Damljanovic et al. established the conventional microscopic indentation method as an effective alternative of other methods such as AFM nanoindentation method, microneedle method, and uniaxial tension test.27 However, the current microscopy indentation method has limitations. First, indentation depth measurement requires multiple steps: placing a ball indentor on the hydrogel, focusing on fluorescent beads beneath the bottom of the indentor, removing the indentor from the gel, waiting for the gel to fully recover, and refocusing on the identified beads. Thus, the method can be time-consuming especially when measurements need to be repeated. Second, human-based identification of fluorescent bead markers in the hydrogel may produce inconsistent results in measuring the indentation depth. Last, the current microscopy indentation method has a limited ability to visualize the deformed profile of hydrogel although such information can be used for understanding gel− indentor interaction and selecting a right contact mechanics model. Later the microscopy indentation method was modified to exclude the indentor removal step. D’Sa et al. measured the z distance between the equator of a sphere indentor and the underformed top surface of hydrogel including fluorescent microbeads, and subtracted this distance from the radius of the indentor to measure the indentation depth.29 However, their microscopy indentation measurements show significant differences from the AFM nanoindentation measurements. Peng et al. used side-view images of hydrogel with an indentor on and used circular fitting to find the indentation depth.30 However, their hydrogel was exposed to air during imaging. Recently, 9690

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modulus and polymeric volume fraction of PAAM gel decrease significantly when C decreases from 1.13% to 0.66%.45,46 This seems due to loosely cross-linked polymers at low C, and thus we suspect that the gel of 7.5% acrylamide and 0.05% bisacrylamide behaved differently between the microscale indentation measurement and the macroscale rheometric measurement.

the same volume near the ball was imaged again. The image of the flipped gel now shows the ball below the cover glass and the shorter shadowed area (Figure S8b). Although the second imaging was done through the ∼1 mm thick gel, the crosssectional images of the bead resemble each other (Figure S8c,d). The lower hemisphere of the bead was applied with the imaging processing because of the shadowed area in the image, and the identified bead profiles coincide with the same fitted circular profiles (Figure S8e). In addition, we conducted the zstep size calibration for two different channel heights (400 and 800 μm) and found that the correction factor values were almost identical despite the 2-fold increase in the sample thickness. Therefore, these results indicate that aberration effects in our imaging were negligible. Moreover, it should be noted that fluorescent light reflected from the indentor can make the indented profile of the hydrogel indistinct. The gel−indentor boundary appeared blurred when more reflective indentors were used (Figure S9), and it appears to be caused by possible overlap between fluorescent light emitted from the gel and the light reflected from the indentor’s bottom surface. Especially when indentation is shallow, the indistinct or distorted gel−indentor interface may cause a difficulty in measuring the indentation depth. To prevent such a problem, one can use indentors with less reflective surface or adjust the exponent of the weight factor (n of eq 2) for best fitting between the indented profile and the circular equation. To evaluate the sensitivity of our measurements on n values, we calculated the indentation depth (δ) and Young’s modulus (E) as a function of n (representative results are shown in Figure S10). As n increases, δ decreases and accordingly E increases toward their asymptotic value. Usually when n = 2, δ reaches reasonably close to its asymptotic value, but the fitted indentor profile did not always match well with the deformed gel profile. Having examined overall agreement between the two profiles, therefore, we determined best n values and their frequency as shown by the green box and histogram in Figure S10 and recommend to try n = 2 and then to raise or lower n value depending on fitting results. The Young’s moduli measured by our confocal microscopy indentation method show good agreements with those measured by the rheometer and literature values. It is also noticeable in Table 2 that the literature values for the softest PAAM gel have deviation and are higher than our measurements. This is because E can be affected by every step in gel fabrication.19 Although the same concentration ratio of acrylamide and bis-acrylamide is used, resultant E can vary depending on humidity19 and temperature38 of casting environment. Thus, it is recommended to maintain constant PAAM gel fabrication procedure and environment and to measure the E of the PAAM gel in situ. It is also noticed that the PAAM gel of 7.5% acrylamide and 0.05% bis-acrylamide shows the largest discrepancy between the confocal indentation measurement and rheometric measurement. Because the gel structure and mechanical property of PAAM gel strongly depend on the total concentration of monomers (T) and the weight fraction of the cross-linker (C),44−46 we calculated the T and C of the four gel compositions (see Table S4). As the acrylamide concentration increases, T increases and accordingly E increases. In contrast, C is minimum (0.66%) for the case of 7.5% acrylamide and 0.05% bis-acrylamide whereas C ≥ 1% for the rest cases. It is known that for constant T the elastic

V. CONCLUSIONS Mechanical interactions between cells and the extracellular matrix (ECM) regulate biological functions of the cells. Especially, the elasticity of the ECM is critical for cellular behaviors such as differentiation, migration, and adhesion. Hydrogels have been used as a popular soft material platform to mimic the ECM for in vitro cell mechanobiology studies. Therefore, characterizing the Young’s modulus of the hydrogel platform is imperative. In this article, we propose the confocal microscopy indentation method using polyacrylamide (PAAM) gel as the model hydrogel. Using confocal laser fluorescent microscopy, we imaged fluorescently stained PAAM gels indented by various ball indentors. Our automated image processing method successfully measured the indentation depth and rigidity of the PAAM gel for the used indentor types and the tested gel compositions. The measured Young’s moduli agreed well with those from rheometric measurement and literature. Therefore, the proposed confocal microscopy indentation method can be utilized for accurate measurements of hydrogel stiffness if an appropriate indentor and indentation model are chosen based on expected elasticity and thickness of hydrogel samples. In comparison with the conventional microscopy indentation method, the proposed 3D-imaging-based method has advantages that it has eliminated steps for indentor removal, it enables user-independent measurement of indentation depth based on visualized deformed gel surface, and it can facilitate multiple indentations on a single gel using an array of indentors. As confocal fluorescence microscopy becomes more accessible, the proposed confocal microscopy indentation method can be more easily and widely implemented for measuring the stiffness of hydrogels.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b01267. Uncertainty analysis for the confocal microscopy indentation method; additional figures about confocal imaging, z-step size calibration, image analysis, measurement of indentation depth and contact radius and aberration test; tables for z-step size calibration, contact radius measurement and the T and C values of the tested PAAM gel compositions (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel +1-402-472-4313 (S.R.). Notes

The authors declare no competing financial interest. 9691

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ACKNOWLEDGMENTS This study was supported by Bioengineering for Human Health grant from the University of NebraskaLincoln (UNL) and the University of Nebraska Medical Center (UNMC). D.L. and S.R. appreciate Divya Bhagirath, Dr. Vimla Band, the UNL center for biotechnology, and the UNMC advanced microscopy core facility for confocal imaging.

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