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Journal of Microscopy, Vol. 205, Pt 2 February 2002, pp. 125 –135 Received 4 January 2001; accepted 7 September 2001
A method for quantifying cell size from differential interference contrast images: validation and application to osmotically stressed chondrocytes Blackwell Science Ltd
L. G. ALEXOPOULOS*‡, G. R. ERICKSON*† & F. GUILAK*†‡ *Orthopaedic Research Laboratories, Department of Surgery, Box 3093, Duke University Medical Center, Durham, NC 27710, U.S.A. †Department of Biomedical Engineering, Duke University, Box 90281, 136 Hudson Hall, Durham, NC 27708-0281, U.S.A. ‡Department of Mechanical Engineering & Materials Science, Duke University, Box 90300, 144 Hudson Hall, Durham, NC 27708-0300, U.S.A.
Key words. Cell measuring, chondrocytes, differential interference contrast (DIC), dynamic programming, edge detection, edge linking, image analysis, image processing, morphology, morphometry, osmotic stress, volume regulation. Summary An automatic image analysis method was developed to determine the shape and size of spheroidal cells from a time series of differential interference contrast (DIC) images. The program incorporates an edge detection algorithm and dynamic programming for edge linking. To assess the accuracy and working range of the method, results from DIC images of different focal planes and resolutions were compared to confocal images in which the cell membrane was fluorescently labelled. The results indicate that a 1-µm focal drift from the in-focus plane can lead to an overestimation of cell volume up to 14.1%, mostly due to shadowing effects of DIC microscopy. DIC images allow for accurate measurements when the focal plane lies in a zone slightly above the centre of a spherical cell. In this range the method performs with 1.9% overall volume error without taking into account the error introduced by the representation of the cell as a sphere. As a test case, the method was applied to quantify volume changes due to acute changes of osmotic stress. Introduction Under normal physiological conditions, cells are exposed to varying mechanical and physicochemical stresses that result in active and passive changes in cell volume and morphology. Correspondence: Farshid Guilak, PhD, Orthopaedic Research Laboratories, Duke University Medical Center, 375 MSR Bldg., Research Dr, Box 3093, Durham, NC 27710, U.S.A. Tel.: +1 919 684 2521; fax: +1 919 681 8490; e-mail:
[email protected] Received 4 January 2001; accepted 7 September 2001
© 2002 The Royal Microscopical Society
In articular cartilage, for example, chondrocyte phenotypic expression and metabolic activity are strongly influenced by changes in cell shape and volume secondary to mechanical and chemical (e.g. osmotic) stresses (Guilak et al., 1997). In this respect, the accurate measurement of cell shape and size is an important step in the interpretation of structure–function relationships in cells. A first step in determining cell shape and size from digital microscopy images is identification of the cell boundaries, and several different techniques have been adapted for quantitative analysis of cell morphology. However, by necessity, such methods are only applicable to a specific model system. For example, three-dimensional (3-D) volume images recorded by confocal or dual-photon microscopy may be well-suited for studying cell morphology in situ, but can be limited in certain cases due to the need for fluorescence imaging and the length of the time needed to acquire 3-D stacks of images(Guilak, 1994; Guilak et al., 1995; Errington et al., 1997; Errington & White, 1999; Kubinova et al., 1999). In studying isolated cells, 2-D images are often recorded via video or scanning microscopy using a variety of contrast techniques. Differential interference contrast (DIC) is a technique that is often used to increase image contrast in plated cells. However, quantitative determination of the cell border in DIC images is a non-trivial task owing to the differences in image contrast along the cell boundary. Reports in the literature show a variety of 2-D image processing algorithms for quantitative cell morphometry (Inoue & Spring, 1997; Sabri et al., 1997). Young & Gray (1997) developed an algorithm based on thresholding and gradientfollow methods. This method requires manual thresholding and identification of the boundary, which may introduce bias
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into the measurements. In order to reduce the bias of user intervention, automatic thresholding was suggested by Wu et al. (2000), which employs iterative thresholding based on repetitive segmentation. As an alternative to thresholding techniques mentioned above, Wu & Barba (1995) introduced a curve fitting based method for cell contour extraction. The method is fast and can be applied to many types of images; however, there is manual specification of boundary points and therefore the method is again subject to user bias. Another approach is based on the watershed analogy (Higgins & Ojard, 1993), in which images are viewed as topographical regions. ‘Flooding’ reveals regions of the image with local minima. A drawback of this method is its sensitivity to image noise. Another family of methods makes use of edge-based segmentations. These techniques are usually composed of an edge detection algorithm for identification of the cell boundary and an edge linking algorithm for connecting points of the cell boundary (Canny, 1986). A method to handle the edgelinking problem is to use dynamic programming, which is a method of searching for the optimal path between starting and ending points. Dynamic programming has been used in the past as a shape retrieval method in ultrasonic measurements of arterial size (Gustavsson et al., 1994; Liang et al., 2000). In the present paper, an automated method for quantifying the 2-D morphology of cells is presented. The method is applied to DIC images acquired by a scanning laser microscope (Cogswell & Sheppard, 1992). The program incorporates an edge detection algorithm followed by dynamic programming for edge linking. Using the edge detection algorithm, the cell boundary is identified by locating large differences in image intensity values around the membrane. The highlighted pixels that arise from this edge-detection step correspond to potential partners of the cell boundary and are linked by means of a dynamic programming algorithm. In this report, the method is validated and different sources of error are revealed. In addition, the proper parameters for image acquisition are established that allow for accurate extraction of the cell boundary from DIC images. As a test case for the method, morphological changes in osmotically stressed chondrocytes were quantified. Materials and methods Cell preparation Explants of articular cartilage were obtained from skeletally mature pigs immediately post mortem. The explants were enzymatically digested to isolate individual chondrocytes (Kuettner et al., 1982). The cells were seeded on sterile glass coverslips and maintained in Dulbecco’s Modified Eagle Medium (DMEM) with 10% fetal bovine serum (Gibco, Grand Island, NY) in a humidified atmosphere at 37 °C, 5% CO2 overnight. Cells were tested 12 h after isolation in order to avoid extracellular matrix formation and spreading of cells in the coverslip surface. The
cells retained a rounded state during the testing period and cell viability was found to be greater than 95% as defined by trypan blue exclusion assay. For fluorescent imaging the cells were treated for 5 min with 20 µM CellTrackerTM CM-DiI (Molecular Probes, Eugene, OR) at 37 °C, 5% CO2 and resuspended in DMEM prior to testing. This photostable fluorescent indicator provides a high-contrast image of the cell membrane and was used for calibration and comparison to the DIC images. DIC and fluorescence imaging Cells were imaged using both DIC microscopy and confocal fluorescence microscopy using a laser scanning microscope (LSM510, Zeiss, Thornwood, NY) with a C-Acroplan 63×, 1.2 NA water immersion objective lens (Zeiss). For the fluorescence images, the optical slice was adjusted to 1.4 µm. The images were captured in 8-bit TIF format, which provides 256 shades of grey. The resolution was varied between 512 × 512 and 2024 × 2024 pixels with scaling from 0.07 µm pixel–1 up to 0.4 µm pixel–1. Algorithm for determination of the cell boundary Determination of the cell boundary from DIC images involved the following general steps: (1) extraction of a region of interest from the source image; (2) edge enhancement and detection (using either the Sobel method or a custom-written radial edge detection algorithm); (3) mapping of the cell boundary from radial coordinates into a 2-D rectangular matrix; (4) application of an edge-linking algorithm, and finally; (5) quantitative assessment of the cell boundary and cell size. To begin, the user identifies two diametrical points near the cell boundary. The need for identification of these points is twofold. First, a subimage S is extracted that includes the cell and second, a wide annular region of interest is created that encloses the cell boundary (Fig. 1). Empirical studies showed that a width of the annular region W (in pixels) equal to 0.25 of the distance between the two selected points is sufficient to enclose the cell membrane, even if the cell is of irregular shape. In addition, the centre (cx, cy) of the annular region is calculated as the midpoint of the user identified points, and the internal and external radius (Rint, Rext) are determined. DIC images are characterized by a gradient of image intensity at the cell membrane, and therefore gradient operations can be used to enhance and identify the cell boundary. The Sobel edge detection algorithm, for example, is capable of detecting differences in image intensity in any direction, and thus the method is applicable to a wide range of images. In the present study a fast approximation of the Sobel edge detection algorithm is used. The output is a new image G, whereby the value of pixels G(i,j) is calculated as the sum of the absolute values of two convolutions X, Y in the source image S (Visual Numerics, 1994): © 2002 The Royal Microscopical Society, Journal of Microscopy, 205, 125 –135
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Fig. 1. The source DIC image S that has been extracted from the original image (not shown) after the selection of the two diametrical points from the user (shown with crosses). The wide annular region that is created encloses the cell boundary. The width of this region is set to 0.25 of the distance between the two selected points. The centre (cx, cy) of the annular region is calculated as the midpoint of the user identified points. The internal and external radii (Rext, Rint) are determined from the mean radius (half of the distance of the two selected points) plus or minus half of the width, respectively.
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X and Y are given by two 3 × 3 convolution kernels (see Fig. 2) of which X is more sensitive in the horizontal direction and Y is more sensitive to the vertical direction. Formally, X = (A2 + 2 · A3 + A4) − (A0 + 2 · A7 + A6)
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This edge operator was chosen because it is sensitive to the orientation of the edge, computationally inexpensive, and performs better in high-noise images with gradual transition © 2002 The Royal Microscopical Society, Journal of Microscopy, 205, 125–135
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Fig. 3. The output of the Sobel edge detection algorithm. The resulting image G highlights the cell membrane as well as other areas in the interior of the cell where neighbouring pixels have considerably different grey colour values.
zones (Castleman, 1979). The resulting image G highlights the cell membrane as well as other areas in the interior (Fig. 3). As an alternative to this edge detection step, a second method was developed and applied that incorporates a radial edge detection algorithm. In this case, the Sobel algorithm is omitted and the radial edge detection procedure is applied as part of the mapping step. In the mapping step, the annular region is mapped to a matrix P. A row of P represents pixels within the annular region and along a radius of a given angle (spoke). The first row corresponds to an angle of 0° and successive rows are 2π/N apart, where N is the number of spokes. Columns of P represent pixels within a given radial distance from the centre (Fig. 4). When the Sobel edge detection algorithm is used, the mapping procedure is applied to the matrix G. Formally, P(i,j) is calculated as: P (i,j) = G ( gx(i,j), gy(i,j) ) where
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gx(i,j) = cx + round[( Rint + j ) · cos(∆θ · i ) ] gy(i,j) = cy + round[( Rint + j ) · sin(∆θ · i )] i = 0 to N j = 0 to W ∆q = 2π/N
N is chosen to be less than or equal to πRint in order to avoid overlap of successive spokes (when ∆θ becomes too small). N also corresponds to the number of points in the cell membrane.
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Fig. 4. The mapping step. Left: the pixels of the annular region that are part of the mapped matrix P. The white arrow indicates the starting point of the mapping. Right: the mapped matrix P. A row of P represents pixels within the annular region and along a spoke. The first row corresponds to an angle of 0° and successive rows are 2π/N apart, where N is the number of spokes. Columns of P represent pixels within a given radial distance from the centre.
In the case of the radial edge detection algorithm, the mapping procedure is applied to the source image S. The procedure maps differences of colour values between two pixels in the annular region of the source image S that are located in the same spoke and are one pixel apart. The resulting matrix P(i,j) consists of the difference between the colour value of a pixel that is located at a distance R + 1 of a given angle from the centre minus the colour value of the pixel located at a distance R of the same angle. Negative values are set to zero. Formally, P(i,j) is calculated as: P (i, j) = S ( gx(i, j + 1), gy(i, j + 1)) − S ( gx(i, j), gy(i, j))
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When this difference is less than zero then P(i,j) = 0. This radial edge detection algorithm is capable of detecting transition from white to black in a radial manner and in a direction towards the centre of the annular region. The main advantage of this method is the minimum sensitivity to image noise but its application is limited to circular objects with transition zones from white to black. In both cases, the resulting Ν × W matrix P contains the boundary information of the cell. Note that P is actually a torus because the last row is adjacent to the first. The edge-linking step is then applied to link the high grey value pixels of P to form the boundary of the cell by using dynamic programming. This step is the same regardless of which method is chosen for edge detection and mapping. Each pixel of the torus P is a potential partner of the boundary depending on its grey level value. The purpose is to find a series of adjacent pixels (continuous path) in P that maximizes the sum of all pixel values along the path and contains only one pixel per row. To assess this problem a value function f is defined for each pixel (i,j) of P. The function f(i,j) encodes only the sum of pixel values along an as yet unknown optimal path that
Fig. 5. Calculation of the cost function f. The function f(i,j) encodes only the sum of pixel values along an unknown optimal path that begins at the first row and terminates at (i,j). It is calculated recursively as the sum of the pixels value P(i + 1,j) plus the maximum of the value functions of the three adjacent pixels in the preceding row i. A matrix T is filled with the directional information. T(i,j) can take values of –1 or 0 or 1 corresponding to which preceding value functions f (i,j – 1), f (i,j) or f (i,j + 1) is being chosen.
begins at the first row and terminates at (i,j). Assuming that f is available for row i, it can be computed recursively as f(i + 1, j) = P(i + 1, j) + max{f(i, j − 1) , f(i, j), f(i, j + 1)} (4) That is, for each pixel of row i + 1, the value function f(i + 1,j) is computed as the sum of the pixel value P(i + 1,j) plus the maximum of the value functions of the three adjacent pixels in the preceding row i (Fig. 5). In addition, a matrix T(i,j) is created to store the direction from which the maximum of f is chosen. T(i,j) can take values of –1,0,1 corresponding to the three preceding value functions f(i,j –1), f(i,j) and f(i,j + 1), respectively. To begin, the values of f in the first row are set to the grey level values of the corresponding pixels. In order to © 2002 The Royal Microscopical Society, Journal of Microscopy, 205, 125 –135
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Fig. 6. Results of dynamic programming and superimposition on the original image. When the calculation of the value function f finishes, the optimal path is constructed by selecting the pixel with the maximum value function (starting from the last row of matrix P) and proceeding backwards for a total of N steps using the directional information of T. Then the results are superimposed to the original image.
ensure continuity at θ = 0° the value function is updated in a torus-like manner several times throughout the matrix P. In the present study, it was found experimentally that 1.5 passes are sufficient. The optimal path is constructed by selecting the pixel with the maximum value function (starting from the last row of matrix P) and proceeding backwards for a total of N steps using the directional information of T. The resulting series of pixels corresponds to the cell boundary (Fig. 6). Finally, the results are superimposed to the original image and the user decides if the results are acceptable or if manual intervention is needed. Manual intervention allows the user to correct the boundaries that the program fails to find. Each pixel chosen gets a 50% higher value in the mapped matrix P and the dynamic programing is applied again. The output of the program is a data set of N points that resembles the cell membrane. The area of the cell is calculated as the area of the N-sided formatted polygon (Fig. 6). The volume of the cell is defined by assuming spherical geometry. In preparation of the next time step the new centre is calculated as the mid point of the N points and the diameter of the annular region is determined from the resulting area by representing the cell boundary as a circle. The algorithm was written in the PV-WAVE language, version 7.0, Visual Data Analysis software (Visual Numerics Inc., Boulder, CO) and implemented on a Pentium II, Windows NT computer. The processing time depends strongly on the width W and the rows N of the matrix P. In 512 × 512 resolution, scale 0.2 µm pixel–1, and 15 µm cell diameter the processing time was less than 0.5 s per cell and per frame. Accuracy of measurements and validation of algorithm In order to assess the accuracy and working range of the method, a series of calibration experiments was performed to evaluate errors that the focal shift and the image resolution introduce © 2002 The Royal Microscopical Society, Journal of Microscopy, 205, 125–135
in the measurements. In addition, the repeatability and the error from the polygon representation were calculated. Both algorithms (using the Sobel or radial edge detection procedure) were used. Fluorescent/DIC comparison Fluorescent images of cells stained with DiI were used as a standard because image noise is minimal and includes only a distinct cell boundary contour. For this reason a z-stack of fluorescent images was used to calibrate DIC results. As a reference point, the slice in the z-stacks with the largest cell area was used. The corresponding DIC image was assumed to be the in-focus plane with zero shift. Positive shifts were assumed to lie above that plane and negative below. Despite the importance of optical slice thickness on 3-D geometry, the z-shift as well as the maximum cross-sectional area were found to be independent on the optical slice thickness. For each cell, the maximum fluorescent area (in-focus plane) was converted to volume and was used to normalize all the volume results from the DIC images (inter-normalization). The ratio of DIC to fluorescent volumetric results for the in-focus plane was reported. The results were obtained from 13 different spherical cells. Out of focus response It is common to experience minor focal drifts during experiments due to small temperature fluctuations or change of cell shape. To assess the output of the method to out of focus images, z-stack scans of DiI-labelled spherical cells were recorded with a z-step equal to 0.2 µm. The inter-normalized volume was clustered every 0.1R and was reported as a percent distance of cell radius R from the in focus plane. Again, the cell radius R was obtained from the fluorescent images. In every cell that was measured, the DIC results form a plateau region between
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0.1R and 0.5R. Volumetric results were normalized either with the in-focus fluorescent volume (inter-normalization) or with the average DIC volume of the plateau (intra-normalization). The intra-normalized standard deviation (known as the coefficient of variation, CV) of the plateau is reported. In addition, the average inter-normalized DIC results in the plateau region as well as the standard deviation are reported. Resolution error Image resolution plays an important role in the accuracy of the results. In order to get a threshold of the minimum required resolution, DIC images were recorded in a scale of 0.07 µm pixel–1 and were scaled up to 0.4 µm pixel–1 with a total of 10 different resolutions. Five different spherical cells were analysed. Based on the out of focus response, the focal plane that was used to evaluate the resolution error corresponded a plane approximately 1.5 µm above the centre of the cell (in the plateau region). Polygon representation The output of the algorithm is a set of N (x,y) points. These N points are connected to form a polygon that approximates the cell membrane. An estimation of the error introduced from this representation can be calculated by comparing a perfectly circular cell membrane to a regular N-sided inscribed polygon. The percentage area error due to this underestimation is given as a function of N: Error = 1 −
N ⋅ sin(π/N ) ⋅ cos(π/N ) π
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Repeatability Despite the fact that the path produced by the algorithm is optimal, small displacements of the centre of the annular region or different image orientations lead to changes to the mapped matrix P. These changes cause small fluctuations in the results because the calculated optimal path is not the same. To assess this error, measurements of the same cell were repeated for different image orientations with a step of ∆θ = 10° from 0° to 90°. The measurements were performed for four different cells and for focal planes in the plateau region. Experimental procedure for osmotically stressed chondrocytes A typical application for such a method is the quantification of volume changes in chondrocytes in response to osmotic stress. In these experiments, the iso-osmotic solution was drawn off the cells and replaced immediately by a solution of different osmolarity (450 or 150 mOsm). The hyper-osmotic and hypoosmotic solutions were prepared by adding sucrose or water, respectively, to DMEM. DIC and fluorescence images were recorded
every 3 s for a total of 8 min and were stored as a series of TIFF images (160 images per set). All experiments were performed at room temperature. Results Validation and error analysis Fluorescent/DIC comparison Fluorescent images were used primarily to normalize the DIC result and to assess the in-focus plane. In the in-focus plane, the ratio of DIC to the fluorescent volume was 0.957 ± 0.046 with use of the radial edge detection algorithm and 0.983 ± 0.030 with use of the Sobel edge detection algorithm. Out of focus response Volumetric measurements were obtained from different focal planes (Figs 7 and 8). Figure 7(a) shows the results of the program and Fig. 7(b) presents the corresponding typical pattern of the inter-normalized volume for different focal planes. The shift of the focal plane in the z-axis has been expressed as a percentage of the cell radius in order to exclude the dependence of the result on cell size. By assuming an average radius of the cell as 7.5 µm, the shift from the focal plane can be converted into distance. Images with positive shift (A, B and C) can be characterized by the white cell boundaries (Fig. 7a) and those with negative shift (D, E and F) exhibit a black boundary. Near the focal plane (from –0.1R to 0.1R) there is an inherent volume increase of up to 14.1% (Fig. 8a). This apparent volume increase, introduced by a small focal shift (< 1.5 µm), is mostly due to shadowing and fading phenomena that take place below 0.1R. The inherent volume increase occurs at the transition from the white to black shadow in the cell boundary (Fig. 7a, images C and D). A consistent ‘plateau’ in the volume measurement was observed within a focus zone from 0.1R to 0.5R (Fig. 8a). For chondrocytes with average diameter of 15 µm this plateau corresponds to distance of approximately 3 µm. The plateau is defined as the focal region wherein individual clusters have inter-normalized standard deviation less than 2%. The plateau is shown with white bars in Fig. 8a. The internormalized volume average in the plateau region is 0.97 ± 0.023. The CV of the plateau region is 1.9%. Similar results were obtained with the Sobel edge detection algorithm (Fig. 8b). In this case the plateau region consisted of a smaller region (0.2R to 0.5R). The inter-normalized volume average in the plateau region is 0.99 ± 0.034 and the CV is 3.2%. Resolution error Errors in cell volume measurement increased as image resolution decreased (Fig. 9). The value on the x-axis (µm2 pixel–1) is the image scaling (µm pixel–1) multiplied by the characteristic © 2002 The Royal Microscopical Society, Journal of Microscopy, 205, 125 –135
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Fig. 7. Out of focus response. (a) The results of the method with the radial edge detection procedure for focal planes A to F. Images with positive shift (A, B and C) can be characterized by the white cell boundaries and those with negative shift (D, E and F) exhibit a black boundary. Note that images B and C, which are 1.83 µm apart produce the same results. Despite the fact that the white zone decreases as the focal plane approaches the in-focus plane, the results are consistent. The transition from C to D, which are only 0.24 µm apart (transition from white to black boundary) carries an inherent error of 18.97%. After that point, shadowing and fading phenomena may result in significant inconsistency. (b) The normalized volume results of the method with the radial edge detection algorithm for different focal planes and for a single cell. Points A to F correspond to the images on (a).
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length of the specimen (µm) (characteristic scaling), which is chosen to be the average diameter of chondrocytes (in this case 15 µm). Significant errors were apparent at values of 2.9 µm2 pixel–1, and for chondrocytes this value corresponds to an image scaling of 0.19 µm pixel–1. The same results were obtained using either radial or Sobel edge detection.
of a continuous curve is calculated from Eq. (5) as a function of N. For values of N greater than 70 the area error was underestimated by at most of 0.13%. Typically, N calculated from Eq. (2) corresponds to values much greater than 70; therefore this error can be neglected. This error is independent of the method used.
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An estimation of the percentage error introduced by the representation of the cell membrane as an N-sided polygon instead
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Fig. 9. Resolution response. The value on the x-axis (µm2 pixel–1) is the image scaling (µm pixel–1) multiplied by the characteristic length of cell (µm) (characteristic scaling). The graph indicates that accurate measurements can be obtained for values of at most 2.9 µm2 pixel–1 and for chondrocytes this value corresponds to an image scaling of 0.19 µm pixel–1 (characteristic length of chondrocytes = 15 µm).
the annular region introduce a fluctuation in the results. The CV of these measurements was 0.25% in the plateau region but can approach 1.5% near the zero focal plane. The results were independent of the edge detection procedure. Chondrocyte response to osmotic stress Chondrocyte volume rapidly changed in response to hyperosmotic and hypo-osmotic challenge and exhibited an active recovery towards the initial volume (Fig. 10). The radial edge detection algorithm was applied to these image series with no manual intervention. For the 450 mOsm solution the chondrocytes responded with a maximum volume decrease of 28.7 ± 14.6% at t = 27 s and with little tendency to recover (decrease of 21.8 ± 14.2% from the initial volume after t = 500 s). Under hypo-osmotic conditions (150 mOsm) the maximum increase of the cell volume was 34.2 ± 20.8% at t = 33 s and with a tendency for total recovery (increase of 3.7 ± 19.7% from the initial volume after t = 500 s).
This study presents an automated method for quantifying the morphology of the cell in a time series of DIC images. Overall, the method shows excellent precision and accuracy (in comparison to fluorescent images of the cell membrane) when applied to spherical cells attached to a glass substrate. The highest accuracy was obtained when the focal plane was initially in a zone slightly above the centre of a spherical cell. In this range, the overall volume error assuming a spherical cell was 1.9%. The calculation of cell volume from 2D DIC images can be inaccurate if the cell is not a sphere. In the present study we did not include this inherent error because it depends on the shape of the cell and is difficult to quantify. Moreover, we wanted to present the accuracy of the method in extracting cell size information from DIC images. However, we reported results as units of volume and not of area because volumetric measurements are more applicable. All the cells that were used for the validation of the algorithm and for the error analysis exhibited a nearly spherical shape (Fig. 11). A primary step in this algorithm involved enhancement of the cell boundary using one of two different edge detection procedures: a fast approximation of the Sobel algorithm and a custom-written radial edge detection algorithm. The Sobel algorithm is sensitive to any direction of gradient in colour values, and thus it can be applied to a wide range of images. The radial edge detection method can detect only transition from white to black in a radial manner, in the direction towards the centre of the annular region, and thus can be applied in the plateau region of the focal response. The fluorescent/DIC comparison in the in-focus plane indicates that the method with the Sobel algorithm agrees better with the fluorescent results and produces more consistent results in the in-focus plane. However, for the plateau region the radial edge detection algorithm is preferable because it creates a bigger plateau and has a much smaller CV (1.9% compared with 3.2% when the Sobel edge detection is used). If R is the radius of a spherical
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Fig. 10. Osmotically stressed chondrocytes. Cell volume decreased by 28.7% for 450 mOsm (bottom solid line ± standard deviation). Cells exhibited little tendency for recovery. For the hypotonic solution (150 mOsm), cell volume increased by 34.2% (top solid line ± standard deviation).
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Fig. 11. 3D image of a chondrocyte. The image was obtained from a series of confocal optical sections of the chondrocyte by using a geometric modelling method (Guilak, 1994).
cell then accurate measurements can be obtained by using the radial edge detection method in a z-zone between 0.1R and 0.5R above the in-focus plane and for values of characteristic scaling up to 2.9 µm2 pixel–1. For chondrocytes with a characteristic length of 15 µm the plateau lies between 0.75 µm and 3.75 µm, wherein the image scaling is optimally 0.19 µm pixel–1. The existence of a plateau region between 0.1R and 0.5R (when the radial edge procedure is used) plays an important role in the extraction of accurate results. When measurements take place in this region, and the characteristic scale is satisfied, the overall volume error in the plateau region is underestimated by a factor of 0.97 ± 0.023 compared with the fluorescent results in the in-focus plane. This error includes the fluctuation of DIC results superimposed upon the fluctuation of fluorescent results. Usually the experimental data are normalized with respect to themselves (e.g. initial volume). With that in mind, the intranormalized CV gives more insight to the actual volume error. In the plateau region the intra-sample CV is found to be 1.9% (by using the radial edge detection procedure). The method produces consistent results despite the drift of the focal plane inside the plateau range. It is recommended that measurements take place only in the plateau region despite the visually out of focus state of the image. These findings set a working space for the method that is valuable when the drift of the focal plane cannot be avoided. There are two types of focal drift: the actual focal drift that is caused by the change of the objective lens’ geometry (mostly due to thermal effects) and a virtual drift that is due to changes of cell morphology. An example of the second case is the swelling experiment of cells due to osmotic effects. Even if the objective is totally stable, the centre of a cell that is attached to the glass surface moves upwards due to cell swelling and thus, a down-
ward shift of focal plane is observed. For chondrocytes with an average diameter of 15 µm and a maximum increase of volume of 60% the virtual focal drift is approximately 1.2 µm. Despite the fact that this drift takes place in a period of a few seconds and cannot be avoided with manual finite adjustments of the focal plane, the 3 µm plateau gives space for the drift to take place inside the plateau zone without interfering with the results. Outside of the plateau region the images may include artefacts that can lead to a volume increase up to 14.1%. These artefacts arise from shadowing phenomena inherent in DIC microscopy and are associated with the geometry of the cell (Fig. 7a). In spherical cells, z-stack fluorescent images show a local maximum in the transverse cell area in the in-focus plane. That local maximum is responsible for the formation of the plateau zone. In cells that are spread across the glass surface and no local maximum exists, there are no plateau zones and no transition from white to black boundary as the focal plane moves downwards. In this case the preceding analysis cannot be applied. It is important to note that the method developed in this study was designed and validated for application to spherical cells, particularly with respect to calculations of cell volume. Future studies may wish to address the precision and accuracy of this method when applied to a more flattened cell shape. An advantage of this method is the minimal intervention from the user. The user has to specify only an annular region in which the cell membrane lies. In cases where the algorithm fails to locate the cell boundary, the user can intervene in a manual mode to suggest the location of the boundary, and the program tries to encompass these suggestions. In all test cases, no manual intervention was needed if the images were recorded in the ‘plateau zone’ of the focal plane. © 2002 The Royal Microscopical Society, Journal of Microscopy, 205, 125 –135
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The motivation for the development of this method was the need to quantify volume changes in spherical chondrocytes exposed to acute osmotic stress. In the experiments presented, chondrocytes were exposed to either hypo-osmotic or hyperosmotic stress. As can be seen in the results, cell stressed with a 150 mOsm solution swelled to 134.2% of their original volume. Following this maximum volume, the cells returned towards their original volume by initiating recovery mechanisms. The average final volume at the end of the experiments was 103.7% of the original volume. In chondrocytes, this mechanism, called regulatory volume decrease, is thought to primarily involve non-selective osmolyte channels (Hall et al., 1996). When the chondrocytes were exposed to hyper-osmotic stress, the cells shrank to 71.3% of their original volume and then recovered to 78.4% of the original volume. The mechanism primarily involved in this recovery, called regulatory volume increase, is the activation of the Na +/K +/Cl− cotransporter (Hall et al., 1996). Although the mechanisms of volume reaction and recovery were not analysed in this study, the method developed provides an excellent way to repeatedly measure volume changes in chondrocytes as they are exposed to varying osmotic stress. In conclusion, the method outlined in this paper gives accurate results of the cell volume when two conditions are preserved: the focal plane lies inside the plateau zone (0.1R to 0.5R) and the characteristic scaling is up to 2.9 µm2 pixel–1. With that in mind, this method can be a very helpful tool for investigation of the volume regulation in cells due to acute osmotic changes and can permit future studies to encompass cell morphology and motility. Acknowledgements The author would like to thank Larry Martin for excellent assistance with the data analysis, Michail Lagoudakis of the Department of Computer Science, Duke University, for his valuable input in the implementation of the algorithm and for his proof reading, Dan Northup for the cell isolation as well as Robert Nielsen for his technical assistance. This study was supported by the National Institutes of Health grants AR43876 and AG15768. References Canny, J. (1986) A computational approach to edge detection. IEEE Trans. Pattern Anal. Machine Intell. 8, 679 – 698.
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