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Comparison of cellular strain with applied substrate strain in vitro
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Journal of Biomechanics 40 (2007) 173–181 www.elsevier.com/locate/jbiomech www.JBiomech.com
Comparison of cellular strain with applied substrate strain in vitro Michelle E. Walla,b, Paul S. Weinholda,b, Tung Siuc, Thomas D. Brownd, Albert J. Banesa,c,e, a
Joint Department of Biomedical Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 27559, USA b Department of Orthopaedics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27559, USA c Curriculum in Applied and Material Sciences, University of North Carolina at Chapel Hill, Chapel Hill, NC 27559, USA d Department of Orthopaedics and Rehabilitation, University of Iowa, Iowa City, IA 52242, USA e Flexcell International Corporation, Hillsborough, NC 27278, USA Accepted 27 October 2005
Abstract Strain magnitudes within tenocytes undergoing substrate tensile strain are not well defined. It was hypothesized that strain magnitudes at the cellular level would reflect those of the applied substrate (equibiaxial or uniaxial) strain. A vacuum-operated device was used to apply equibiaxial or uniaxial tension to a flexible substrate upon which tenocytes were cultured in monolayer. Images of tenocytes labeled with Fura-2, to detect free intracellular calcium ions, and MitoFluorTM Green, to detect mitochondria, were taken prior to strain and for 20 min during application of static strain. A custom-written, texture correlation program computed strain magnitudes in the cell based on the change in pixel pattern displacements between images of non-strained and strained cells. On average, cellular strain was approximately 3778% and 63711% of the applied equibiaxial and uniaxial substrate strain, respectively. The largest cell strains were detected in cells oriented parallel to the direction of applied uniaxial tensile strain. However, strain magnitudes within a cell were heterogeneous. The variance in strain magnitude within and among tenocytes is dependent on cell orientation, cell stiffness, cytoskeleton organization, subcellular organelles, or placement and type of cell-substrate contacts. Results of the present study indicate that cultured tenocytes experience a moderate fraction of the applied substrate strain. r 2005 Elsevier Ltd. All rights reserved. Keywords: Texture correlation; Tenocytes; Equibiaxial strain; Uniaxial strain
1. Introduction Tenocytes subjected to select strain regimens have been monitored with a variety of bio-readouts to better understand how substrate tension affects measured cellular strain and resulting processes (Arnoczky et al., 2002b; Banes et al., 1999a, b; Loitz et al., 1989; Ralphs et al., 2002). For instance, tenocytes activate signaling pathways, increase mRNA and protein levels, re-orient Corresponding author. Joint Department of Biomedical Engineering, North Carolina State University, Campus Box 7115, 1217L Textiles Bldg., Raleigh, NC 27695-7115, USA. Tel.: +1 919 732 1591; fax: +1 919 732 5196. E-mail addresses: [email protected], [email protected] (A.J. Banes).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.10.032
themselves, and proliferate in response to substrate strain (Arnoczky et al., 2002b; Banes et al., 1999a, b; Gilbert et al., 1994). However, the actual strain(s) at the cell level both in vitro and in vivo is (are) not well defined. In recent years, the availability of techniques to apply mechanical loads to cells (Banes et al., 2003) has stimulated interest in quantifying actual strain magnitudes at cellular and subcellular levels (Arnoczky et al., 2002a; Barbee et al., 1994; Charras and Horton, 2002; Screen et al., 2003; Simon and Schmid-Schonbein, 1990; Winston et al., 1989). Methods utilized to determine these strain values have included measuring displacement of fluorescent beads and finite element modeling (Barbee et al., 1994; Caille et al., 1998; Charras and Horton, 2002; Winston et al., 1989).
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The purpose of the present study was to utilize texture correlation to determine strain magnitudes in tenocytes subjected to a defined equibiaxial or uniaxial substrate strain. A device was used that applied strain across the central portion of a flexible membrane upon which tenocytes were cultured (Banes et al., 1985, 1990; Gilbert et al., 1994). Images of tenocytes labeled with two dyes, to create two different pixel patterns, were recorded prior to strain and during 20 min of applied strain. A texture correlation program computed cellular strain based on the change in pixel pattern displacements between images of non-strained and strained cells. It was hypothesized that the strain magnitudes at the cellular level would be comparable with those of the applied substrate equibiaxial or uniaxial strain.
2. Methods 2.1. Cell isolation and culture Avian feet were processed according to the approved protocol for abattoir specimens by the University of North Carolina Institutional Animal Care and Use Committee. Internal fibroblasts from flexor digitorum profundus tendons of seven, 61-day-old Ross chickens (Townsend, Pittsboro and Siler City, NC) were isolated by sequential enzymatic and mechanical scraping techniques modified from the method of Banes et al. (1988). Internal fibroblasts were grown in Dulbecco’s Modified Eagle’s medium supplemented with 5% fetal bovine serum, 100 mg/ml streptomycin, 100 units/ml penicillin, 0.25 mg/ml amphotericin B, 0.1 mM ascorbate-2-phosphate, and 20 mM Hepes, pH 7.2. Tenocytes
were seeded in micromass cultures at 3000 cells/10 mL on collagen I-coated StageFlexerTM membranes (4 micromass cultures/membrane; Flexcell International, Hillsborough, NC). Cells were grown to confluence and quiescence by halving the serum content on days 3 and 5 post-plating since tenocytes in vivo are normally in the G0 state. Cell culture chemicals and supplies were purchased from Sigma (St. Louis, MO), GIBCO BRL (Grand Island, NY), or HyClone (Logan, UT). 2.2. Cell labeling On the sixth day after culture, tenocytes were rinsed with Earles’ Balanced Salt Solution with 20 mM Hepes, pH 7.2, 1.80 mM calcium chloride and 0.8 mM magnesium sulfate (EBSS), incubated at room temperature in 200 nM MitoFluorTM Green and 5 mM Fura-2 acetoxy methylester (Fura-2AM) for 45 min each (Molecular Probes, Eugene, OR). MitoFluorTM Green labels the mitochondria within the cell, and Fura-2 reacts with free intracellular calcium ions. An Olympus BX-51 upright fluorescence microscope (Melville, NY) equipped with a 40x water immersion ultraviolet objective lens, a Sutter Lambda DG4 wavelength switcher and light guide (Novato, CA), and a CoolSnap digital camera (Roper Scientific, Trenton, NJ) was used along with image analysis software (ISee Imaging Systems, Raleigh, NC) to view the cells and to produce 8-bit, grayscale images (696 520 pixels, 0.032 mm/pixel). 2.3. Mechanically induced substrate strain After labeling the tenocytes, the membranes were transferred to a StageFlexerTM (Fig. 1; Flexcell International),
Fig. 1. (A) Cylindrical and ArctangularTM loading posts. (B) A StageFlexerTM with a planar-faced, cylindrical loading post. (C) A schematic of how strain is applied to cells with the StageFlexerTM apparatus. Cells are plated on the central portion of a rubber membrane. The membrane is clamped into the device. When a vacuum is applied (controlled by the FlexercellTM Strain Unit (FSU)), the membrane is deformed downward across the loading post imparting strain to the cells.
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a device used to apply equibiaxial or uniaxial strain to the substrate. Clamping the 43 mm diameter membrane into the StageFlexerTM (35 mm inner well diameter) did not alter baseline substrate strain values (data not shown). Equibiaxial strain was applied to the tenocytes via vacuum deformation of the membrane downward at the periphery of a 25 mm diameter, planarfaced, cylindrical loading post, causing equibiaxial translation of the membrane across the loading post face (Fig. 1C). Uniaxial strain was similarly applied to the tenocytes, but a 35 mm diameter ArcTangleTM loading post was utilized (Fig. 1A). The curved short ends of this loading post (north and south poles) were flush with the StageFlexerTM inner wall allowing downward deformation of the membrane only at the east and west poles. Cells were viewed over the center of the arctangular loading post since there is a diminution in strain magnitude from the loading post center axis to the clamped edge along the north–south axis (Vande Geest et al., 2004) (Fig. 2B Suppl). The device was mounted on the microscope stage to permit assessment of cell morphology. Separate membranes were used for each of the six strain conditions: 3%, 4%, and 7% equibiaxial or uniaxial static substrate strain (as determined by texture correlation). Strain was applied for 20 min to determine if cellular strain would equal substrate strain throughout this duration or if cells would retract to some homeostatic set-point position. Three randomly selected regions in the center of the membrane containing 1–6 non- or minimally contacting cells were sequentially observed for 1 min (each region observed every 3 min) throughout the strain period. Cells were incubated in EBSS throughout the strain period.
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2.4. Cell strain calculated with the texture correlation program Cell strain magnitudes were determined with a custom, texture correlation (Bay, 1995), strain analysis program written in Matlab language (Siu, 2004). The program filtered the images with a two-dimensional Wiener filter, and then bi-cubically interpolated the images at 1/3 pixel to increase pixels (from 696 520 to 2086 1558). A grid of user-defined nodes was placed over a region of interest on an interpolated image of non-strained cells (Fig. 2). The program performed a two-dimensional normalized cross-correlation to determine which area of the image of strained cells best matched the pixel pattern of the non-strained image template, a square area of pixels around each node (Fig. 2C). A zero-order approach, which assumes that the template remains square, was utilized to determine the displacement of the pixels in the template (Bay, 1995). The center of the pixel pattern that returned the greatest correlation coefficient was determined to be the displaced node on the strained image. The coordinates of the displaced nodes were used to calculate strain with a strain-displacement matrix computed for a four-node quadrilateral element. Grids of 9–36 nodes with 50 50, 75 75, or 100 100 pixels per element and with templates ranging from 81 81 to 241 241 pixels were used for computing cell strain. Grid and element sizes were chosen such that nodes were distributed solely over the cell of interest without contribution from pixels of the adjacent membrane or cells. Template sizes were chosen to maximally cover an area around a node without returning an error. Displacements between nodes were assumed to vary
Fig. 2. A nodal grid superimposed on an interpolated image of a tenocyte labeled with (A) Fura-2, a calcium-sensitive dye, and (B) MitoFluorTM Green, a mitochondrial dye. (C) Schematic of a template (gray boxes) which is a group of pixels (single box) surrounding the node (white cross on black box) of interest. (D) Schematic of a quadrilateral element (light gray square), which encompasses the pixels among four nodes. The elements in the Fura-2 and MitoFluorTM Green images are 75 75 pixels.
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linearly within each element. Strain magnitudes were calculated with the Lagrangian finite strain tensor for a continuum body (Fung, 1994). Strain values of common nodes of adjacent elements were averaged to give a single value for a given node. The strain magnitude in the cells calculated from the image pattern of structures containing calcium ions labeled with Fura-2 was compared with the image pattern of mitochondria labeled with MitoFluorTM Green (Figs. 2A, B) to determine the degree of concordance between the computed strain values. Cellular orientation was measured in terms of the angle created between the long axis of the cell and the x-axis of the image. The long axis of the cell was subjectively determined by visualization. The orientation angle between 01 and 901 was measured with the measuring tool in Photoshops. 2.5. Validation of texture correlation calculations for cell strain To verify the cell strain values computed with the texture correlation program, the following two manual line measurements were made in each cell using the measuring tool in Photoshops: (1) parallel to the x-axis of the image and (2) parallel to the y-axis of the image. Three line measurements were made in both directions at the same location within the same cell and averaged. Measurements were taken at the same ‘‘landmark’’ point in the non-strained image and the first image after the onset of substrate strain for all cells analyzed by texture correlation (n ¼ 29241 cells). Engineering strain (dl/l) was used to calculate strain with all manual measurements. 2.6. Substrate strain calculated with the texture correlation program The applied substrate strain was calculated by determining the change in pixel pattern displacements of the Fura2-labeled cells across the entire field of view in noninterpolated images. Nodal grids of 16–24 nodes with 75 75 or 100 100 pixels per element were used for computing substrate displacements. One field per membrane (n ¼ 4 membranes) was analyzed for substrate strain. Additionally, the pixel intensities of these images were adjusted in Photoshops to remove small structures in the cell such as calcium-free vesicles that might offset the analysis (Fig. 1A Suppl). Additional validation of the texture correlation calculations for substrate strain is available on-line as Supplementary Data. 2.7. Statistical analysis Data were analyzed using SigmaStats (SPSS Inc., Chicago, IL). A Mann–Whitney Rank Sum test or t-test
was used to determine significance (po0.05) for the following groups: between cell and substrate strain values calculated by texture correlation, between strains computed from Fura-2 and MitoFluorTM Green images, between measurement methods, and between the orientation of the cell relative to the axis of measurement (i.e. 01 and 451 along the x-axis of the image). A one-way analysis of variance was used to determine significance (po0.05) between cell strain values calculated for cells with different shapes and between strains in different regions of the cell. Data are presented as the mean 7 standard deviation. Substrate strain values reported in the results section were determined by texture correlation unless noted otherwise.
3. Results The cell strains calculated with the texture correlation program on images of tenocytes labeled with Fura-2 and MitoFluorTM Green are shown in Table 1. For cells subjected to equibiaxial strain, strains calculated using the MitoFluorTM Green images were 7–60% greater than the strains calculated using Fura-2 images (Table 1). The cell strains in the x-direction were 22–84% greater than strains in the y-direction at the higher strain magnitudes indicating that at these levels, cells are strained more biaxially then equibiaxially (Tables 1 and 2). Cells with a long axis oriented and measured along this long axis (exx in cells oriented 01 from x-axis or eyy in cells oriented 901 from x-axis) had the greatest strain magnitudes (Fig. 3). On average, cell strain was 3778% of the applied equibiaxial substrate strain (Table 2).
Table 1 Cellular strains computed with the texture correlation program from images of the tenocytes labeled with Fura-2 and MitoFluorTM Green MitoFluorTM Green
Fura-2 exx Equibiaxial strain 1.171.0* 1.870.5] 3.272.0]^ Uniaxial strain 1.170.7 3.170.8 4.671.8
eyy
1.470.7 1.870.9 1.372.2]^ 0.970.6 1.470.7 2.070.9
exx
1.971.0* 2.270.6] 4.472.3]^ 1.170.8 3.371.0 5.272.4
eyy
1.570.8 2.371.3 2.471.9]^ 1.071.1 1.270.5 1.871.1
Values are mean7standard deviation. exx, strain in the x-axis of the image; eyy, strain in the y-axis of the images; *po0.001, Fura-2 vs. MitoFluorTM Green in respective direction (Mann–Whitney Rank Sum Test); ]po0.05, Fura-2 vs. MitoFluorTM Green in respective direction (t-test); ^po0.001, eyy vs. exx (t-test); n ¼ 2 isolations.
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Table 2 Cell and substrate strain values (%) calculated with the texture correlation program Cell straina
exx
eyy
Equibiaxial strain 1.270.8* 1.270.7* 1.771.1*^ 1.071.1*^ 2.571.6*^ 2.071.8*^ Uniaxial strain 1.470.8* 0.770.5 2.670.9# 1.070.7 4.771.4* 2.470.9
Substrate strain
Ratio (cell/ substrate)
exx
exx
eyy
0.46 0.44 0.33
0.41 0.27 0.29
0.52 0.74 0.62
0.88 0.77 0.96
2.670.4* 3.970.5* 7.571.6* 2.770.4* 3.570.9# 7.671.8*
eyy
2.970.6* 3.770.9* 6.871.3* 0.870.4 1.370.7 2.570.7
Values are mean7standard deviation. exx, strain in the x-axis of the image; eyy, strain in the y-axis of the images; *po0.001, cell vs. substrate strain in respective direction (Mann–Whitney Rank Sum Test); ^po0.001, eyy vs. exx (t-test); #po0.001, cell vs. substrate strain in respective direction (t-test). a Values for cell strain were calculated using images of the Fura-2labeled cells (n ¼ 2 isolations of cells labeled with Fura-2AM only and 2 isolations of cells labeled with both Fura-2AM and MitoFluorTM Green).
For uniaxial strain, tenocytes elongated along the principal strain direction (x-axis) (Table 1). Additionally, the membrane had a Poisson effect with negative strain normal to the direction of the applied strain. Tenocytes also experienced similar negative strains in the y-direction (Table 1). Cells oriented parallel to the applied tensile strain direction (01 for uniaxial strain) had the greatest strain magnitudes. Cells oriented around 451 from the x-axis had smaller magnitudes (Fig. 3). Cell orientation, however, did not affect the negative deformation in the cells under uniaxial tension (Fig. 3). On average, cell strain was 63711% of the applied uniaxial substrate strain (Table 2). Cells also deformed 87710% of the negative strain in the y-direction (Table 2). Even though most cells appeared to elongate in response to the applied tension, some cells did not. Moreover, some cells under equibiaxial strain only elongated in one direction. This observation may account for the smaller cell-to-substrate strain ratios during application of equibiaxial strain (Table 2). The strain distributions across the measured area of the cell were typically non-uniform (Fig. 4). To determine if there were significant differences in the strains within a cell, strain values were averaged among nodes that were over the cytoplasm, the nucleus, or in the peri-nuclear area of the cell. There were no significant differences in the percent of substrate strain experienced by the cell among these subcellular areas (data not shown). At some sites, strains within the cell were greater than the applied substrate strain. Cell shape as determined by a
Fig. 3. The percentage of the substrate strain, which was detected in the Fura-2-labeled cells by the texture correlation program, in the xand y-directions, exx and eyy, respectively, was dependent on cell orientation from the x-axis. (A) For applied equibiaxial strain, only eyy was linearly related to the orientation. Cells oriented parallel to the xaxis of the image (01) had significantly greater strain magnitudes in the x-direction than cells oriented normal to the x-axis (901). (B) For applied uniaxial strain, exx was not linearly related to cell orientation. The negative strain (eyy) in the cells induced by the Poisson effect of the silicone membrane was not dependent on cell orientation. Cells oriented parallel to the x-axis of the image (01) had significantly greater strain magnitudes in the x-direction than cells oriented between 251 and 651 from the x-axis.
qualitative classification (round/square, elongated, or triangular, trapezoidal, or oval morphology) did not affect the average cellular strain (data not shown). In addition, although cell strains manually measured were statistically greater than those strains calculated by the texture correlation program (Fig. 5), they were still less than the applied substrate strains.
4. Discussion Tenocytes have been subjected to various mechanical stimuli in vitro to understand how they respond to loading conditions to which they are subjected during daily activities (Archambault et al., 2002; Arnoczky
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Fig. 4. Contour maps of strain fields in the x- (exx) and y- (eyy) directions superimposed on tenocytes (labeled with Fura-2) subjected to equibiaxial (A and C) and uniaxial (B and D) substrate strains of about 7% elongation. Arrows represent the directions of the applied strain.
et al., 2002a, b; Banes et al., 1999a, b; Gilbert et al., 1994; Ralphs et al., 2002; Tsuzaki et al., 2003). The magnitude of strain imparted to the tenocyte from the underlying substrate is not well established for cells strained on flexible two-dimensional surfaces. The hypothesis posed in this study was that cells would be strained to an equivalent degree as the substrate upon which the cells were cultured. Tenocytes elongated 3778% of the applied equibiaxial substrate strain and 63711% of the applied uniaxial strain. The finding that tenocytes subjected to a given substrate strain reflected a value of 37% of the applied equibiaxial strain was not consistent with results of other in vitro studies that reported cells elongated 60–100% of the applied biaxial strain (Barbee et al., 1994; Winston et al., 1989). The method employed in those studies to calculate cell strain quantitated displacement of fluorescent beads attached to the cell membrane. Strain was determined by measuring the change in bead marker displacement using cells with a minimum of two to three beads. The advantage of the present method over those utilizing fluorescent beads
was that multiple markers (minimum of nine superimposed markers) were used to determine an average cellular strain. Marker displacement was determined by the change in pixel patterns of images of non-strained and strained tenocytes. The computed strain values were based on the relative displacement among the intracellular organelles or non-tethered vesicles. Moreover, the results were confirmed by using dyes that labeled different structures within a viable cell as well as by manual measurement of cell displacements. Results of the present study also indicated that strain distributions in the cell were not uniform. Barbee et al. (1994) reported similar results where strains in lamellipods were greater than strains in the cell body. Caille et al. (1998) reported that nuclear strains were less than cytoplasmic strains. Even though the results of the present study indicated that there were no statistically significant differences between average nuclear and cytoplasmic strain values, strains within both of these subcellular regions were heterogeneous (Fig. 4). The calculated cellular strains may vary depending on the method used to determine cellular strain as well as which
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Fig. 5. Manual measurements of cell strain were statistically greater than the cell strain computed by the texture correlation program on images of tenocytes labeled with the Fura-2 dye and subjected to (A) equibiaxial or (B) uniaxial strain. exx is the strain in the x-direction and eyy is the strain in the y-direction. Substrate elongation was determined by texture correlation program.
area of the cell was used for measurements. Additionally, some tenocytes did not appear to elongate in response to applied substrate strain. Lack of detectable cell strain could be due to differences in the degree of cell-substrate attachment, cytoskeletal organization, cell orientation, cell shape, and cell stiffness (Barbee et al., 1994; Charras and Horton, 2002; Winston et al., 1989). Substrate strain is imparted to the cell via focal adhesion connections between the exterior matrix (substrate) and the cytoskeleton via integrins. Cells with robust and numerous focal adhesions may be subjected to a greater proportion of substrate strain than are cells with fewer focal contacts. Results of a finite element model study of osteoblasts constrained along the entire underside of the cell and subjected to uniaxial strain indicated that the cell strains were similar to substrate strains (Charras and Horton, 2002). That model predicted strains in a cell with maximal focal contacts: the entire underside of the cell was tethered to the substrate. However, cells in vitro have varying number of focal contacts, which can
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increase in number in response to strain (Smith et al., 1997). The fraction of substrate strain imparted to the cell could be related to the area of the cell anchored by focal contacts. Cell strain could also vary depending on the orientation of subcellular elements such as actin in the cytoskeleton. Cell stiffness is related to the amount of cross-links and organization of the cytoskeletal components (Trickey et al., 2004). Varying the moduli of the cytoskeletal components varies the cell stiffness as determined by finite element models (McGarry and Prendergast, 2004). A cell that has a more robustly organized cytoskeleton may physically elongate less than a cell with a less organized cytoskeleton. Additionally, cellular orientation with respect to the direction of the applied tension could also affect the magnitude of cellular strain due to the anisotropic nature of the cytoskeleton as well as cells themselves. The results of this study indicated that tenocytes oriented between 251 and 651 from the direction of applied tension had strain magnitudes smaller than cells oriented parallel to the direction of applied uniaxial strain (exx). Thus, cell orientation, in part, determines the magnitude of applied substrate strain conveyed to the cell (Wang et al., 1995). In some cases, strain magnitudes measured in portions of the cell were greater than the applied substrate strain (Fig. 4). In these instances, the cell surface area may have increased as the cell actively added plasma membrane to withstand the applied strain similar to the volume increase known to occur in osmotic loading (Dai et al., 1998). However, the methods utilized in this study cannot detect additions to the plasma membrane. Active random motion of calcium-free vesicles and mitochondria could also have influenced the computed strain magnitudes. Besides these cellular variables, there are limitations to the measurement method used in the present study. The dyes utilized for the texture correlation program were chosen because they created different patterns within the cell, and they readily permeated the plasma membrane without disruption and remained bound inside the cell. However, one cannot account for active movement of mitochondria as well as calcium-free vesicles in the cell. Such subcellular motions could influence the displacements of the nodes and in turn the calculated strains. Furthermore, the pixel-to-millimeter ratio of the microscope/camera system, the resolution of the image analysis software, and the finite element method used placed limitations on the strain resolution that could be computed by the program. For the present system, the smallest strain increment that could be computed was 1% in a 50 50 pixel element. In addition, the program only allowed for rectangular grids with a minimum of nine nodes. Elements smaller than 50 50 pixels were not used, keeping strain resolution at 1% . Therefore, cellular strains in localized
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areas such as pseudopods could not be calculated. Only the central portion of the cell, usually around the nucleus, could be used for strain. Additionally, template sizes were chosen to be large enough to ensure there were sufficient pixels to identify the same region in the loaded image. However, overlapping of pixels from neighboring templates could contribute to an underestimation of the strain field calculated by the texture correlation program. Finally, the texture correlation program accounted for motion in a two-dimensional plane and assumed that the image pixel pattern in the strained image had the same aspect ratio as in the nonstrained image. The program also utilized a zero-order approach to determine the displacement of the pixels in the template. A first-order approach would reduce error in detecting strain (Gilchrist et al., 2004; Wang et al., 2002); however, the program does not yet allow for the first-order approach. In conclusion, this study is the first to identify and compare cellular strains in cells subjected to either equibiaxial or uniaxial substrate strain in vitro. Two independent dye-based methods and manual measurements within the cell were used to compute cell strain. The results from each method indicated that tenocytes experience a moderate fraction of the applied substrate strain. Tenocytes returned rapidly to a baseline configuration upon removal of substrate strain, and their strain remained essentially constant for a given state of substrate strain. These results indicate that passive viscoelastic effects and active adaptive effects were negligible over the time period studied. However, there were variances in strain magnitudes within and among tenocytes, which could depend on cell orientation, cell stiffness, cytoskeleton organization, subcellular organelles, and placement and type of cell-substrate contacts.
Acknowledgments This study was supported by NIH AR38121, the Hunt Foundation, and Flexcell International Corporation. AJB is president of Flexcell International Corp. and is compensated as such.
Appendix A. Supplementary Materials Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jbiomech. 2005.10.032.
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ARTICLE IN PRESS M.E. Wall et al. / Journal of Biomechanics 40 (2007) 173–181 and first-order texture correlation. IEEE Transactions on Medical Imaging 23, 546– 553. Loitz, B.J., Zernicke, R.F., Vailas, A.C., Kody, M.H., Meals, R.A., 1989. Effects of short-term immobilization versus continuous passive motion on the biomechanical and biochemical properties of the rabbit tendon. Clinical Orthopaedics and Related Research 244, 265– 271. McGarry, J.G., Prendergast, P.J., 2004. A three-dimensional finite element model of an adherent eukaryotic cell. European Cells and Materials Journal 7, 27– 34. Ralphs, J.R., Waggett, A.D., Benjamin, M., 2002. Actin stress fibers and cell– cell adhesion molecules in tendons: organisation in vivo and response to mechanical loading of tendon cells in vitro. Matrix Biology 21, 67– 74. Screen, H.R., Lee, D.A., Bader, D.L., Shelton, J.C., 2003. Development of a technique to determine strains in tendons using the cell nuclei. Biorheology 40, 361– 368. Simon, S.I., Schmid-Schonbein, G.W., 1990. Cytoplasmic strains and strain rates in motile polymorphonuclear leukocytes. Biophysical Journal 58, 319– 332. Siu, T., 2004. Development of a texture correlation strain analysis program and its application for monitoring strain in achilles tendons treated with shockwave therapy. Senior Honors Thesis, University of North Carolina, Chapel Hill.
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Smith, P.G., Garcia, R., Kogerman, L., 1997. Strain reorganizes focal adhesions and cytoskeleton in cultured airway smooth muscle cells. Experimental Cell Research 232, 127– 136. Trickey, W.R., Vail, T.P., Guilak, F., 2004. The role of the cytoskeleton in the viscoelastic properties of human articular chondrocytes. Journal of Orthopaedic Research 22, 131– 139. Tsuzaki, M., Bynum, D., Almekinders, L., Yang, X., Faber, J., Banes, A.J., 2003. ATP modulates load-inducible IL-1b, COX 2, and MMP-3 gene expression in human tendon cells. Journal of Cellular Biochemistry 89, 556– 562. Vande Geest, J.P., Di Martino, E.S., Vorp, D.A., 2004. An analysis of the complete strain field within FlexercellTM membranes. Journal of Biomechanics 37, 1923– 1928. Wang, C.C., Deng, J.M., Ateshian, G.A., Hung, C.T., 2002. An automated approach for direct measurement of two-dimensional strain distributions within articular cartilage under unconfined compression. Journal of Biomechanical Engineering 124, 557– 567. Wang, H., Ip, W., Boissy, R., Grood, E.S., 1995. Cell orientation response to cyclically deformed substrates: experimental validation of a cell model. Journal of Biomechanics 28, 1543– 1552. Winston, F.K., Macarak, E.J., Gorfien, S.F., Thibault, L.E., 1989. A system to reproduce and quantify the biomechanical environment of the cell. Journal of Applied Physiology 67, 397– 405.
Journal of Biomechanics 40 (2007) 173–181 www.elsevier.com/locate/jbiomech www.JBiomech.com
Comparison of cellular strain with applied substrate strain in vitro Michelle E. Walla,b, Paul S. Weinholda,b, Tung Siuc, Thomas D. Brownd, Albert J. Banesa,c,e, a
Joint Department of Biomedical Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 27559, USA b Department of Orthopaedics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27559, USA c Curriculum in Applied and Material Sciences, University of North Carolina at Chapel Hill, Chapel Hill, NC 27559, USA d Department of Orthopaedics and Rehabilitation, University of Iowa, Iowa City, IA 52242, USA e Flexcell International Corporation, Hillsborough, NC 27278, USA Accepted 27 October 2005
Abstract Strain magnitudes within tenocytes undergoing substrate tensile strain are not well defined. It was hypothesized that strain magnitudes at the cellular level would reflect those of the applied substrate (equibiaxial or uniaxial) strain. A vacuum-operated device was used to apply equibiaxial or uniaxial tension to a flexible substrate upon which tenocytes were cultured in monolayer. Images of tenocytes labeled with Fura-2, to detect free intracellular calcium ions, and MitoFluorTM Green, to detect mitochondria, were taken prior to strain and for 20 min during application of static strain. A custom-written, texture correlation program computed strain magnitudes in the cell based on the change in pixel pattern displacements between images of non-strained and strained cells. On average, cellular strain was approximately 3778% and 63711% of the applied equibiaxial and uniaxial substrate strain, respectively. The largest cell strains were detected in cells oriented parallel to the direction of applied uniaxial tensile strain. However, strain magnitudes within a cell were heterogeneous. The variance in strain magnitude within and among tenocytes is dependent on cell orientation, cell stiffness, cytoskeleton organization, subcellular organelles, or placement and type of cell-substrate contacts. Results of the present study indicate that cultured tenocytes experience a moderate fraction of the applied substrate strain. r 2005 Elsevier Ltd. All rights reserved. Keywords: Texture correlation; Tenocytes; Equibiaxial strain; Uniaxial strain
1. Introduction Tenocytes subjected to select strain regimens have been monitored with a variety of bio-readouts to better understand how substrate tension affects measured cellular strain and resulting processes (Arnoczky et al., 2002b; Banes et al., 1999a, b; Loitz et al., 1989; Ralphs et al., 2002). For instance, tenocytes activate signaling pathways, increase mRNA and protein levels, re-orient Corresponding author. Joint Department of Biomedical Engineering, North Carolina State University, Campus Box 7115, 1217L Textiles Bldg., Raleigh, NC 27695-7115, USA. Tel.: +1 919 732 1591; fax: +1 919 732 5196. E-mail addresses: [email protected], [email protected] (A.J. Banes).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.10.032
themselves, and proliferate in response to substrate strain (Arnoczky et al., 2002b; Banes et al., 1999a, b; Gilbert et al., 1994). However, the actual strain(s) at the cell level both in vitro and in vivo is (are) not well defined. In recent years, the availability of techniques to apply mechanical loads to cells (Banes et al., 2003) has stimulated interest in quantifying actual strain magnitudes at cellular and subcellular levels (Arnoczky et al., 2002a; Barbee et al., 1994; Charras and Horton, 2002; Screen et al., 2003; Simon and Schmid-Schonbein, 1990; Winston et al., 1989). Methods utilized to determine these strain values have included measuring displacement of fluorescent beads and finite element modeling (Barbee et al., 1994; Caille et al., 1998; Charras and Horton, 2002; Winston et al., 1989).
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The purpose of the present study was to utilize texture correlation to determine strain magnitudes in tenocytes subjected to a defined equibiaxial or uniaxial substrate strain. A device was used that applied strain across the central portion of a flexible membrane upon which tenocytes were cultured (Banes et al., 1985, 1990; Gilbert et al., 1994). Images of tenocytes labeled with two dyes, to create two different pixel patterns, were recorded prior to strain and during 20 min of applied strain. A texture correlation program computed cellular strain based on the change in pixel pattern displacements between images of non-strained and strained cells. It was hypothesized that the strain magnitudes at the cellular level would be comparable with those of the applied substrate equibiaxial or uniaxial strain.
2. Methods 2.1. Cell isolation and culture Avian feet were processed according to the approved protocol for abattoir specimens by the University of North Carolina Institutional Animal Care and Use Committee. Internal fibroblasts from flexor digitorum profundus tendons of seven, 61-day-old Ross chickens (Townsend, Pittsboro and Siler City, NC) were isolated by sequential enzymatic and mechanical scraping techniques modified from the method of Banes et al. (1988). Internal fibroblasts were grown in Dulbecco’s Modified Eagle’s medium supplemented with 5% fetal bovine serum, 100 mg/ml streptomycin, 100 units/ml penicillin, 0.25 mg/ml amphotericin B, 0.1 mM ascorbate-2-phosphate, and 20 mM Hepes, pH 7.2. Tenocytes
were seeded in micromass cultures at 3000 cells/10 mL on collagen I-coated StageFlexerTM membranes (4 micromass cultures/membrane; Flexcell International, Hillsborough, NC). Cells were grown to confluence and quiescence by halving the serum content on days 3 and 5 post-plating since tenocytes in vivo are normally in the G0 state. Cell culture chemicals and supplies were purchased from Sigma (St. Louis, MO), GIBCO BRL (Grand Island, NY), or HyClone (Logan, UT). 2.2. Cell labeling On the sixth day after culture, tenocytes were rinsed with Earles’ Balanced Salt Solution with 20 mM Hepes, pH 7.2, 1.80 mM calcium chloride and 0.8 mM magnesium sulfate (EBSS), incubated at room temperature in 200 nM MitoFluorTM Green and 5 mM Fura-2 acetoxy methylester (Fura-2AM) for 45 min each (Molecular Probes, Eugene, OR). MitoFluorTM Green labels the mitochondria within the cell, and Fura-2 reacts with free intracellular calcium ions. An Olympus BX-51 upright fluorescence microscope (Melville, NY) equipped with a 40x water immersion ultraviolet objective lens, a Sutter Lambda DG4 wavelength switcher and light guide (Novato, CA), and a CoolSnap digital camera (Roper Scientific, Trenton, NJ) was used along with image analysis software (ISee Imaging Systems, Raleigh, NC) to view the cells and to produce 8-bit, grayscale images (696 520 pixels, 0.032 mm/pixel). 2.3. Mechanically induced substrate strain After labeling the tenocytes, the membranes were transferred to a StageFlexerTM (Fig. 1; Flexcell International),
Fig. 1. (A) Cylindrical and ArctangularTM loading posts. (B) A StageFlexerTM with a planar-faced, cylindrical loading post. (C) A schematic of how strain is applied to cells with the StageFlexerTM apparatus. Cells are plated on the central portion of a rubber membrane. The membrane is clamped into the device. When a vacuum is applied (controlled by the FlexercellTM Strain Unit (FSU)), the membrane is deformed downward across the loading post imparting strain to the cells.
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a device used to apply equibiaxial or uniaxial strain to the substrate. Clamping the 43 mm diameter membrane into the StageFlexerTM (35 mm inner well diameter) did not alter baseline substrate strain values (data not shown). Equibiaxial strain was applied to the tenocytes via vacuum deformation of the membrane downward at the periphery of a 25 mm diameter, planarfaced, cylindrical loading post, causing equibiaxial translation of the membrane across the loading post face (Fig. 1C). Uniaxial strain was similarly applied to the tenocytes, but a 35 mm diameter ArcTangleTM loading post was utilized (Fig. 1A). The curved short ends of this loading post (north and south poles) were flush with the StageFlexerTM inner wall allowing downward deformation of the membrane only at the east and west poles. Cells were viewed over the center of the arctangular loading post since there is a diminution in strain magnitude from the loading post center axis to the clamped edge along the north–south axis (Vande Geest et al., 2004) (Fig. 2B Suppl). The device was mounted on the microscope stage to permit assessment of cell morphology. Separate membranes were used for each of the six strain conditions: 3%, 4%, and 7% equibiaxial or uniaxial static substrate strain (as determined by texture correlation). Strain was applied for 20 min to determine if cellular strain would equal substrate strain throughout this duration or if cells would retract to some homeostatic set-point position. Three randomly selected regions in the center of the membrane containing 1–6 non- or minimally contacting cells were sequentially observed for 1 min (each region observed every 3 min) throughout the strain period. Cells were incubated in EBSS throughout the strain period.
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2.4. Cell strain calculated with the texture correlation program Cell strain magnitudes were determined with a custom, texture correlation (Bay, 1995), strain analysis program written in Matlab language (Siu, 2004). The program filtered the images with a two-dimensional Wiener filter, and then bi-cubically interpolated the images at 1/3 pixel to increase pixels (from 696 520 to 2086 1558). A grid of user-defined nodes was placed over a region of interest on an interpolated image of non-strained cells (Fig. 2). The program performed a two-dimensional normalized cross-correlation to determine which area of the image of strained cells best matched the pixel pattern of the non-strained image template, a square area of pixels around each node (Fig. 2C). A zero-order approach, which assumes that the template remains square, was utilized to determine the displacement of the pixels in the template (Bay, 1995). The center of the pixel pattern that returned the greatest correlation coefficient was determined to be the displaced node on the strained image. The coordinates of the displaced nodes were used to calculate strain with a strain-displacement matrix computed for a four-node quadrilateral element. Grids of 9–36 nodes with 50 50, 75 75, or 100 100 pixels per element and with templates ranging from 81 81 to 241 241 pixels were used for computing cell strain. Grid and element sizes were chosen such that nodes were distributed solely over the cell of interest without contribution from pixels of the adjacent membrane or cells. Template sizes were chosen to maximally cover an area around a node without returning an error. Displacements between nodes were assumed to vary
Fig. 2. A nodal grid superimposed on an interpolated image of a tenocyte labeled with (A) Fura-2, a calcium-sensitive dye, and (B) MitoFluorTM Green, a mitochondrial dye. (C) Schematic of a template (gray boxes) which is a group of pixels (single box) surrounding the node (white cross on black box) of interest. (D) Schematic of a quadrilateral element (light gray square), which encompasses the pixels among four nodes. The elements in the Fura-2 and MitoFluorTM Green images are 75 75 pixels.
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linearly within each element. Strain magnitudes were calculated with the Lagrangian finite strain tensor for a continuum body (Fung, 1994). Strain values of common nodes of adjacent elements were averaged to give a single value for a given node. The strain magnitude in the cells calculated from the image pattern of structures containing calcium ions labeled with Fura-2 was compared with the image pattern of mitochondria labeled with MitoFluorTM Green (Figs. 2A, B) to determine the degree of concordance between the computed strain values. Cellular orientation was measured in terms of the angle created between the long axis of the cell and the x-axis of the image. The long axis of the cell was subjectively determined by visualization. The orientation angle between 01 and 901 was measured with the measuring tool in Photoshops. 2.5. Validation of texture correlation calculations for cell strain To verify the cell strain values computed with the texture correlation program, the following two manual line measurements were made in each cell using the measuring tool in Photoshops: (1) parallel to the x-axis of the image and (2) parallel to the y-axis of the image. Three line measurements were made in both directions at the same location within the same cell and averaged. Measurements were taken at the same ‘‘landmark’’ point in the non-strained image and the first image after the onset of substrate strain for all cells analyzed by texture correlation (n ¼ 29241 cells). Engineering strain (dl/l) was used to calculate strain with all manual measurements. 2.6. Substrate strain calculated with the texture correlation program The applied substrate strain was calculated by determining the change in pixel pattern displacements of the Fura2-labeled cells across the entire field of view in noninterpolated images. Nodal grids of 16–24 nodes with 75 75 or 100 100 pixels per element were used for computing substrate displacements. One field per membrane (n ¼ 4 membranes) was analyzed for substrate strain. Additionally, the pixel intensities of these images were adjusted in Photoshops to remove small structures in the cell such as calcium-free vesicles that might offset the analysis (Fig. 1A Suppl). Additional validation of the texture correlation calculations for substrate strain is available on-line as Supplementary Data. 2.7. Statistical analysis Data were analyzed using SigmaStats (SPSS Inc., Chicago, IL). A Mann–Whitney Rank Sum test or t-test
was used to determine significance (po0.05) for the following groups: between cell and substrate strain values calculated by texture correlation, between strains computed from Fura-2 and MitoFluorTM Green images, between measurement methods, and between the orientation of the cell relative to the axis of measurement (i.e. 01 and 451 along the x-axis of the image). A one-way analysis of variance was used to determine significance (po0.05) between cell strain values calculated for cells with different shapes and between strains in different regions of the cell. Data are presented as the mean 7 standard deviation. Substrate strain values reported in the results section were determined by texture correlation unless noted otherwise.
3. Results The cell strains calculated with the texture correlation program on images of tenocytes labeled with Fura-2 and MitoFluorTM Green are shown in Table 1. For cells subjected to equibiaxial strain, strains calculated using the MitoFluorTM Green images were 7–60% greater than the strains calculated using Fura-2 images (Table 1). The cell strains in the x-direction were 22–84% greater than strains in the y-direction at the higher strain magnitudes indicating that at these levels, cells are strained more biaxially then equibiaxially (Tables 1 and 2). Cells with a long axis oriented and measured along this long axis (exx in cells oriented 01 from x-axis or eyy in cells oriented 901 from x-axis) had the greatest strain magnitudes (Fig. 3). On average, cell strain was 3778% of the applied equibiaxial substrate strain (Table 2).
Table 1 Cellular strains computed with the texture correlation program from images of the tenocytes labeled with Fura-2 and MitoFluorTM Green MitoFluorTM Green
Fura-2 exx Equibiaxial strain 1.171.0* 1.870.5] 3.272.0]^ Uniaxial strain 1.170.7 3.170.8 4.671.8
eyy
1.470.7 1.870.9 1.372.2]^ 0.970.6 1.470.7 2.070.9
exx
1.971.0* 2.270.6] 4.472.3]^ 1.170.8 3.371.0 5.272.4
eyy
1.570.8 2.371.3 2.471.9]^ 1.071.1 1.270.5 1.871.1
Values are mean7standard deviation. exx, strain in the x-axis of the image; eyy, strain in the y-axis of the images; *po0.001, Fura-2 vs. MitoFluorTM Green in respective direction (Mann–Whitney Rank Sum Test); ]po0.05, Fura-2 vs. MitoFluorTM Green in respective direction (t-test); ^po0.001, eyy vs. exx (t-test); n ¼ 2 isolations.
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Table 2 Cell and substrate strain values (%) calculated with the texture correlation program Cell straina
exx
eyy
Equibiaxial strain 1.270.8* 1.270.7* 1.771.1*^ 1.071.1*^ 2.571.6*^ 2.071.8*^ Uniaxial strain 1.470.8* 0.770.5 2.670.9# 1.070.7 4.771.4* 2.470.9
Substrate strain
Ratio (cell/ substrate)
exx
exx
eyy
0.46 0.44 0.33
0.41 0.27 0.29
0.52 0.74 0.62
0.88 0.77 0.96
2.670.4* 3.970.5* 7.571.6* 2.770.4* 3.570.9# 7.671.8*
eyy
2.970.6* 3.770.9* 6.871.3* 0.870.4 1.370.7 2.570.7
Values are mean7standard deviation. exx, strain in the x-axis of the image; eyy, strain in the y-axis of the images; *po0.001, cell vs. substrate strain in respective direction (Mann–Whitney Rank Sum Test); ^po0.001, eyy vs. exx (t-test); #po0.001, cell vs. substrate strain in respective direction (t-test). a Values for cell strain were calculated using images of the Fura-2labeled cells (n ¼ 2 isolations of cells labeled with Fura-2AM only and 2 isolations of cells labeled with both Fura-2AM and MitoFluorTM Green).
For uniaxial strain, tenocytes elongated along the principal strain direction (x-axis) (Table 1). Additionally, the membrane had a Poisson effect with negative strain normal to the direction of the applied strain. Tenocytes also experienced similar negative strains in the y-direction (Table 1). Cells oriented parallel to the applied tensile strain direction (01 for uniaxial strain) had the greatest strain magnitudes. Cells oriented around 451 from the x-axis had smaller magnitudes (Fig. 3). Cell orientation, however, did not affect the negative deformation in the cells under uniaxial tension (Fig. 3). On average, cell strain was 63711% of the applied uniaxial substrate strain (Table 2). Cells also deformed 87710% of the negative strain in the y-direction (Table 2). Even though most cells appeared to elongate in response to the applied tension, some cells did not. Moreover, some cells under equibiaxial strain only elongated in one direction. This observation may account for the smaller cell-to-substrate strain ratios during application of equibiaxial strain (Table 2). The strain distributions across the measured area of the cell were typically non-uniform (Fig. 4). To determine if there were significant differences in the strains within a cell, strain values were averaged among nodes that were over the cytoplasm, the nucleus, or in the peri-nuclear area of the cell. There were no significant differences in the percent of substrate strain experienced by the cell among these subcellular areas (data not shown). At some sites, strains within the cell were greater than the applied substrate strain. Cell shape as determined by a
Fig. 3. The percentage of the substrate strain, which was detected in the Fura-2-labeled cells by the texture correlation program, in the xand y-directions, exx and eyy, respectively, was dependent on cell orientation from the x-axis. (A) For applied equibiaxial strain, only eyy was linearly related to the orientation. Cells oriented parallel to the xaxis of the image (01) had significantly greater strain magnitudes in the x-direction than cells oriented normal to the x-axis (901). (B) For applied uniaxial strain, exx was not linearly related to cell orientation. The negative strain (eyy) in the cells induced by the Poisson effect of the silicone membrane was not dependent on cell orientation. Cells oriented parallel to the x-axis of the image (01) had significantly greater strain magnitudes in the x-direction than cells oriented between 251 and 651 from the x-axis.
qualitative classification (round/square, elongated, or triangular, trapezoidal, or oval morphology) did not affect the average cellular strain (data not shown). In addition, although cell strains manually measured were statistically greater than those strains calculated by the texture correlation program (Fig. 5), they were still less than the applied substrate strains.
4. Discussion Tenocytes have been subjected to various mechanical stimuli in vitro to understand how they respond to loading conditions to which they are subjected during daily activities (Archambault et al., 2002; Arnoczky
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Fig. 4. Contour maps of strain fields in the x- (exx) and y- (eyy) directions superimposed on tenocytes (labeled with Fura-2) subjected to equibiaxial (A and C) and uniaxial (B and D) substrate strains of about 7% elongation. Arrows represent the directions of the applied strain.
et al., 2002a, b; Banes et al., 1999a, b; Gilbert et al., 1994; Ralphs et al., 2002; Tsuzaki et al., 2003). The magnitude of strain imparted to the tenocyte from the underlying substrate is not well established for cells strained on flexible two-dimensional surfaces. The hypothesis posed in this study was that cells would be strained to an equivalent degree as the substrate upon which the cells were cultured. Tenocytes elongated 3778% of the applied equibiaxial substrate strain and 63711% of the applied uniaxial strain. The finding that tenocytes subjected to a given substrate strain reflected a value of 37% of the applied equibiaxial strain was not consistent with results of other in vitro studies that reported cells elongated 60–100% of the applied biaxial strain (Barbee et al., 1994; Winston et al., 1989). The method employed in those studies to calculate cell strain quantitated displacement of fluorescent beads attached to the cell membrane. Strain was determined by measuring the change in bead marker displacement using cells with a minimum of two to three beads. The advantage of the present method over those utilizing fluorescent beads
was that multiple markers (minimum of nine superimposed markers) were used to determine an average cellular strain. Marker displacement was determined by the change in pixel patterns of images of non-strained and strained tenocytes. The computed strain values were based on the relative displacement among the intracellular organelles or non-tethered vesicles. Moreover, the results were confirmed by using dyes that labeled different structures within a viable cell as well as by manual measurement of cell displacements. Results of the present study also indicated that strain distributions in the cell were not uniform. Barbee et al. (1994) reported similar results where strains in lamellipods were greater than strains in the cell body. Caille et al. (1998) reported that nuclear strains were less than cytoplasmic strains. Even though the results of the present study indicated that there were no statistically significant differences between average nuclear and cytoplasmic strain values, strains within both of these subcellular regions were heterogeneous (Fig. 4). The calculated cellular strains may vary depending on the method used to determine cellular strain as well as which
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Fig. 5. Manual measurements of cell strain were statistically greater than the cell strain computed by the texture correlation program on images of tenocytes labeled with the Fura-2 dye and subjected to (A) equibiaxial or (B) uniaxial strain. exx is the strain in the x-direction and eyy is the strain in the y-direction. Substrate elongation was determined by texture correlation program.
area of the cell was used for measurements. Additionally, some tenocytes did not appear to elongate in response to applied substrate strain. Lack of detectable cell strain could be due to differences in the degree of cell-substrate attachment, cytoskeletal organization, cell orientation, cell shape, and cell stiffness (Barbee et al., 1994; Charras and Horton, 2002; Winston et al., 1989). Substrate strain is imparted to the cell via focal adhesion connections between the exterior matrix (substrate) and the cytoskeleton via integrins. Cells with robust and numerous focal adhesions may be subjected to a greater proportion of substrate strain than are cells with fewer focal contacts. Results of a finite element model study of osteoblasts constrained along the entire underside of the cell and subjected to uniaxial strain indicated that the cell strains were similar to substrate strains (Charras and Horton, 2002). That model predicted strains in a cell with maximal focal contacts: the entire underside of the cell was tethered to the substrate. However, cells in vitro have varying number of focal contacts, which can
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increase in number in response to strain (Smith et al., 1997). The fraction of substrate strain imparted to the cell could be related to the area of the cell anchored by focal contacts. Cell strain could also vary depending on the orientation of subcellular elements such as actin in the cytoskeleton. Cell stiffness is related to the amount of cross-links and organization of the cytoskeletal components (Trickey et al., 2004). Varying the moduli of the cytoskeletal components varies the cell stiffness as determined by finite element models (McGarry and Prendergast, 2004). A cell that has a more robustly organized cytoskeleton may physically elongate less than a cell with a less organized cytoskeleton. Additionally, cellular orientation with respect to the direction of the applied tension could also affect the magnitude of cellular strain due to the anisotropic nature of the cytoskeleton as well as cells themselves. The results of this study indicated that tenocytes oriented between 251 and 651 from the direction of applied tension had strain magnitudes smaller than cells oriented parallel to the direction of applied uniaxial strain (exx). Thus, cell orientation, in part, determines the magnitude of applied substrate strain conveyed to the cell (Wang et al., 1995). In some cases, strain magnitudes measured in portions of the cell were greater than the applied substrate strain (Fig. 4). In these instances, the cell surface area may have increased as the cell actively added plasma membrane to withstand the applied strain similar to the volume increase known to occur in osmotic loading (Dai et al., 1998). However, the methods utilized in this study cannot detect additions to the plasma membrane. Active random motion of calcium-free vesicles and mitochondria could also have influenced the computed strain magnitudes. Besides these cellular variables, there are limitations to the measurement method used in the present study. The dyes utilized for the texture correlation program were chosen because they created different patterns within the cell, and they readily permeated the plasma membrane without disruption and remained bound inside the cell. However, one cannot account for active movement of mitochondria as well as calcium-free vesicles in the cell. Such subcellular motions could influence the displacements of the nodes and in turn the calculated strains. Furthermore, the pixel-to-millimeter ratio of the microscope/camera system, the resolution of the image analysis software, and the finite element method used placed limitations on the strain resolution that could be computed by the program. For the present system, the smallest strain increment that could be computed was 1% in a 50 50 pixel element. In addition, the program only allowed for rectangular grids with a minimum of nine nodes. Elements smaller than 50 50 pixels were not used, keeping strain resolution at 1% . Therefore, cellular strains in localized
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areas such as pseudopods could not be calculated. Only the central portion of the cell, usually around the nucleus, could be used for strain. Additionally, template sizes were chosen to be large enough to ensure there were sufficient pixels to identify the same region in the loaded image. However, overlapping of pixels from neighboring templates could contribute to an underestimation of the strain field calculated by the texture correlation program. Finally, the texture correlation program accounted for motion in a two-dimensional plane and assumed that the image pixel pattern in the strained image had the same aspect ratio as in the nonstrained image. The program also utilized a zero-order approach to determine the displacement of the pixels in the template. A first-order approach would reduce error in detecting strain (Gilchrist et al., 2004; Wang et al., 2002); however, the program does not yet allow for the first-order approach. In conclusion, this study is the first to identify and compare cellular strains in cells subjected to either equibiaxial or uniaxial substrate strain in vitro. Two independent dye-based methods and manual measurements within the cell were used to compute cell strain. The results from each method indicated that tenocytes experience a moderate fraction of the applied substrate strain. Tenocytes returned rapidly to a baseline configuration upon removal of substrate strain, and their strain remained essentially constant for a given state of substrate strain. These results indicate that passive viscoelastic effects and active adaptive effects were negligible over the time period studied. However, there were variances in strain magnitudes within and among tenocytes, which could depend on cell orientation, cell stiffness, cytoskeleton organization, subcellular organelles, and placement and type of cell-substrate contacts.
Acknowledgments This study was supported by NIH AR38121, the Hunt Foundation, and Flexcell International Corporation. AJB is president of Flexcell International Corp. and is compensated as such.
Appendix A. Supplementary Materials Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jbiomech. 2005.10.032.
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