© 2002 The Royal Microscopical Society

Journal of Microscopy, Vol. 205, Pt 2 February 2002, pp. 125–135

Received 4 January 2001; accepted 7 September 2001

Blackwell Science Ltd

A method for quantifying cell size from differential interference contrast images: validation and application to osmotically stressed chondrocytes

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 deter-mine the shape and size of spheroidal cells from a time series ofdifferential interference contrast (DIC) images. The programincorporates an edge detection algorithm and dynamic pro-gramming for edge linking. To assess the accuracy and work-ing range of the method, results from DIC images of differentfocal planes and resolutions were compared to confocal imagesin which the cell membrane was fluorescently labelled. Theresults indicate that a 1-

µ

m focal drift from the in-focus planecan lead to an overestimation of cell volume up to 14.1%, mostlydue to shadowing effects of DIC microscopy. DIC images allowfor accurate measurements when the focal plane lies in a zoneslightly above the centre of a spherical cell. In this range themethod performs with 1.9% overall volume error withouttaking into account the error introduced by the representationof the cell as a sphere. As a test case, the method was appliedto quantify volume changes due to acute changes of osmoticstress.

Introduction

Under normal physiological conditions, cells are exposed tovarying mechanical and physicochemical stresses that resultin active and passive changes in cell volume and morphology.

In articular cartilage, for example, chondrocyte phenotypicexpression and metabolic activity are strongly influenced bychanges in cell shape and volume secondary to mechanicaland chemical (e.g. osmotic) stresses (Guilak

et al.

, 1997). In thisrespect, the accurate measurement of cell shape and size isan important step in the interpretation of structure–functionrelationships in cells.

A first step in determining cell shape and size from digitalmicroscopy images is identification of the cell boundaries, andseveral different techniques have been adapted for quantitat-ive analysis of cell morphology. However, by necessity, suchmethods are only applicable to a specific model system. Forexample, three-dimensional (3-D) volume images recorded byconfocal or dual-photon microscopy may be well-suited forstudying cell morphology

in situ

, but can be limited in certaincases due to the need for fluorescence imaging and the lengthof 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 micro-scopy using a variety of contrast techniques. Differential inter-ference contrast (DIC) is a technique that is often used toincrease image contrast in plated cells. However, quantitativedetermination of the cell border in DIC images is a non-trivialtask owing to the differences in image contrast along the cellboundary. Reports in the literature show a variety of 2-D imageprocessing algorithms for quantitative cell morphometry (Inoue& Spring, 1997; Sabri

et al.

, 1997). Young & Gray (1997)developed an algorithm based on thresholding and gradient-follow methods. This method requires manual thresholdingand identification of the boundary, which may introduce bias

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: guilak@duke.edu

Received 4 January 2001; accepted 7 September 2001

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, 125–135

into the measurements. In order to reduce the bias of userintervention, automatic thresholding was suggested by Wu

et al

. (2000), which employs iterative thresholding basedon repetitive segmentation. As an alternative to thresholdingtechniques mentioned above, Wu & Barba (1995) introduceda curve fitting based method for cell contour extraction. Themethod is fast and can be applied to many types of images;however, there is manual specification of boundary points andtherefore the method is again subject to user bias. Anotherapproach 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. Adrawback of this method is its sensitivity to image noise.

Another family of methods makes use of edge-based seg-mentations. These techniques are usually composed of an edgedetection algorithm for identification of the cell boundaryand an edge linking algorithm for connecting points of thecell boundary (Canny, 1986). A method to handle the edge-linking problem is to use dynamic programming, which is amethod of searching for the optimal path between startingand ending points. Dynamic programming has been used inthe past as a shape retrieval method in ultrasonic measure-ments of arterial size (Gustavsson

et al.

, 1994; Liang

et al.

,2000).

In the present paper, an automated method for quantifyingthe 2-D morphology of cells is presented. The method is appliedto DIC images acquired by a scanning laser microscope (Cogswell& Sheppard, 1992). The program incorporates an edge detec-tion algorithm followed by dynamic programming for edgelinking. Using the edge detection algorithm, the cell boundaryis identified by locating large differences in image intensityvalues around the membrane. The highlighted pixels thatarise from this edge-detection step correspond to potentialpartners of the cell boundary and are linked by means of adynamic programming algorithm. In this report, the method isvalidated and different sources of error are revealed. In addition,the proper parameters for image acquisition are establishedthat allow for accurate extraction of the cell boundary from DICimages. As a test case for the method, morphological changesin osmotically stressed chondrocytes were quantified.

Materials and methods

Cell preparation

Explants of articular cartilage were obtained from skeletallymature pigs immediately post mortem. The explants were enzym-atically digested to isolate individual chondrocytes (Kuettner

et al.

, 1982). The cells were seeded on sterile glass coverslipsand maintained in Dulbecco’s Modified Eagle Medium (DMEM)with 10% fetal bovine serum (Gibco, Grand Island, NY) in ahumidified atmosphere at 37

°

C, 5% CO

2

overnight. Cells weretested 12 h after isolation in order to avoid extracellular matrixformation and spreading of cells in the coverslip surface. The

cells retained a rounded state during the testing period andcell viability was found to be greater than 95% as defined bytrypan blue exclusion assay.

For fluorescent imaging the cells were treated for 5 min with20

µ

M CellTracker

TM

CM-DiI (Molecular Probes, Eugene, OR)at 37

°

C, 5% CO

2

and resuspended in DMEM prior to testing.This photostable fluorescent indicator provides a high-contrastimage of the cell membrane and was used for calibration andcomparison to the DIC images.

DIC and fluorescence imaging

Cells were imaged using both DIC microscopy and confocalfluorescence microscopy using a laser scanning microscope(LSM510, Zeiss, Thornwood, NY) with a C-Acroplan 63

×

, 1.2NA water immersion objective lens (Zeiss). For the fluorescenceimages, the optical slice was adjusted to 1.4

µ

m. The imageswere captured in 8-bit TIF format, which provides 256 shadesof grey. The resolution was varied between 512

×

512 and2024

×

2024 pixels with scaling from 0.07

µ

m pixel

–1

up to0.4

µ

m

pixel

–1

.

Algorithm for determination of the cell boundary

Determination of the cell boundary from DIC images involvedthe following general steps: (1) extraction of a region of interestfrom the source image; (2) edge enhancement and detection(using either the Sobel method or a custom-written radial edgedetection algorithm); (3) mapping of the cell boundary fromradial coordinates into a 2-D rectangular matrix; (4) applica-tion of an edge-linking algorithm, and finally; (5) quantitativeassessment of the cell boundary and cell size.

To begin, the user identifies two diametrical points near thecell boundary. The need for identification of these points istwofold. First, a subimage

S

is extracted that includes the celland second, a wide annular region of interest is created thatencloses the cell boundary (Fig. 1). Empirical studies showedthat a width of the annular region

W

(in pixels) equal to 0.25of the distance between the two selected points is sufficientto enclose the cell membrane, even if the cell is of irregularshape. In addition, the centre (

c

x

, c

y

) of the annular region iscalculated as the midpoint of the user identified points, and theinternal and external radius (

R

int

, R

ext

) are determined.DIC images are characterized by a gradient of image inten-

sity at the cell membrane, and therefore gradient operationscan be used to enhance and identify the cell boundary. TheSobel edge detection algorithm, for example, is capable of detect-ing differences in image intensity in any direction, and thusthe method is applicable to a wide range of images. In thepresent study a fast approximation of the Sobel edge detectionalgorithm is used. The output is a new image

G

, whereby thevalue of pixels

G(i,j)

is calculated as the sum of the absolutevalues of two convolutions

X

,

Y

in the source image

S

(VisualNumerics, 1994):

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G

(

i

,

j

) = |

X

| + |

Y

| (1a)

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

ismore sensitive to the vertical direction.

Formally,

X

= (

A

2 + 2 ·

A

3 +

A

4)

−

(

A

0 + 2 ·

A

7 +

A

6) (1b)

Y

= (

A

0 + 2 ·

A

1 +

A

2)

−

(

A

6 + 2 ·

A

5 +

A

4) (1c)

This edge operator was chosen because it is sensitive to theorientation of the edge, computationally inexpensive, andperforms better in high-noise images with gradual transition

zones (Castleman, 1979). The resulting image

G

highlights thecell membrane as well as other areas in the interior (Fig. 3).

As an alternative to this edge detection step, a second methodwas developed and applied that incorporates a radial edge detec-tion algorithm. In this case, the Sobel algorithm is omitted andthe radial edge detection procedure is applied as part of themapping step.

In the mapping step, the annular region is mapped to amatrix

P

. A row of

P

represents pixels within the annularregion and along a radius of a given angle (spoke). The first rowcorresponds to an angle of 0

°

and successive rows are 2

π

/N

apart, where

N

is the number of spokes. Columns of

P

rep-resent pixels within a given radial distance from the centre(Fig. 4). When the Sobel edge detection algorithm is used, themapping procedure is applied to the matrix

G

. Formally,

P(i,j)

is calculated as:

P

(

i

,

j

) =

G

(

g

x

(

i

,

j

),

g

y

(

i

,

j

) ) (2)

where

g

x

(

i

,

j

) =

c

x

+ round[(

R

int

+

j

) · cos(

∆θ

·

i

) ]

g

y

(

i

,

j

) =

c

y

+ round[(

R

int

+

j

) · sin(

∆θ

·

i

) ]

i

= 0 to

Nj

= 0 to

W

∆

q

= 2

π

/

N

N

is chosen to be less than or equal to

π

R

int

in order to avoidoverlap of successive spokes (when

∆θ

becomes too small).

N

alsocorresponds to the number of points in the cell membrane.

Fig. 1. The source DIC image S that has been extracted from the originalimage (not shown) after the selection of the two diametrical points fromthe user (shown with crosses). The wide annular region that is createdencloses the cell boundary. The width of this region is set to 0.25 of thedistance between the two selected points. The centre (cx, cy) of the annularregion is calculated as the midpoint of the user identified points. Theinternal and external radii (Rext, Rint) are determined from the meanradius (half of the distance of the two selected points) plus or minus half ofthe width, respectively.

A0 A1 A2

A7 G(j,k) A3

A6 A5 A4

Fig. 2. Numbering convention for the Sobel edge operator.

Fig. 3. The output of the Sobel edge detection algorithm. The resultingimage G highlights the cell membrane as well as other areas in the interiorof the cell where neighbouring pixels have considerably different greycolour values.

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Journal of Microscopy

,

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, 125–135

In the case of the radial edge detection algorithm, the map-ping procedure is applied to the source image

S

. The proceduremaps differences of colour values between two pixels in theannular region of the source image

S

that are located in thesame spoke and are one pixel apart. The resulting matrix

P

(

i

,

j

)consists of the difference between the colour value of a pixelthat is located at a distance

R

+ 1 of a given angle from thecentre 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

(

g

x

(

i

,

j

+ 1),

g

y

(

i

,

j

+ 1))

−

S

(

g

x

(

i

,

j

),

g

y

(

i

,

j) ) (3)

When this difference is less than zero then P(i,j) = 0. Thisradial edge detection algorithm is capable of detecting transi-tion from white to black in a radial manner and in a directiontowards the centre of the annular region. The main advant-age of this method is the minimum sensitivity to image noisebut its application is limited to circular objects with transitionzones from white to black. In both cases, the resulting Ν × Wmatrix P contains the boundary information of the cell. Notethat P is actually a torus because the last row is adjacent tothe first.

The edge-linking step is then applied to link the high greyvalue pixels of P to form the boundary of the cell by usingdynamic programming. This step is the same regardless ofwhich method is chosen for edge detection and mapping. Eachpixel of the torus P is a potential partner of the boundarydepending on its grey level value. The purpose is to find a seriesof adjacent pixels (continuous path) in P that maximizes thesum of all pixel values along the path and contains only onepixel per row. To assess this problem a value function f is definedfor each pixel (i,j) of P. The function f (i,j) encodes only the sumof pixel values along an as yet unknown optimal path that

begins at the first row and terminates at (i,j). Assuming that fis 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 themaximum of the value functions of the three adjacent pixelsin the preceding row i (Fig. 5). In addition, a matrix T (i,j) iscreated to store the direction from which the maximum of f ischosen. T (i,j) can take values of –1,0,1 corresponding to thethree 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 tothe grey level values of the corresponding pixels. In order to

Fig. 4. The mapping step. Left: the pixels of the annularregion that are part of the mapped matrix P. The whitearrow indicates the starting point of the mapping.Right: the mapped matrix P. A row of P represents pixelswithin the annular region and along a spoke. The firstrow corresponds to an angle of 0° and successive rowsare 2π/N apart, where N is the number of spokes.Columns of P represent pixels within a given radialdistance from the centre.

f (i+1,j)

i,j-1 (-1)

i,j (0)

i,j+1 (1)

Fig. 5. Calculation of the cost function f. The function f (i,j) encodes onlythe sum of pixel values along an unknown optimal path that begins at thefirst row and terminates at (i,j). It is calculated recursively as the sum of thepixels value P(i + 1,j) plus the maximum of the value functions of the threeadjacent pixels in the preceding row i. A matrix T is filled with the direc-tional information. T(i,j) can take values of –1 or 0 or 1 corresponding towhich preceding value functions f (i,j – 1), f (i,j) or f (i,j + 1) is being chosen.

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ensure continuity at θ = 0° the value function is updated in atorus-like manner several times throughout the matrix P. Inthe present study, it was found experimentally that 1.5 passesare sufficient. The optimal path is constructed by selecting thepixel with the maximum value function (starting from the lastrow of matrix P) and proceeding backwards for a total of Nsteps using the directional information of T. The resulting seriesof pixels corresponds to the cell boundary (Fig. 6).

Finally, the results are superimposed to the original imageand the user decides if the results are acceptable or if manualintervention is needed. Manual intervention allows the userto correct the boundaries that the program fails to find. Eachpixel chosen gets a 50% higher value in the mapped matrix Pand the dynamic programing is applied again.

The output of the program is a data set of N points thatresembles the cell membrane. The area of the cell is calculatedas the area of the N-sided formatted polygon (Fig. 6). The volumeof the cell is defined by assuming spherical geometry. In prepara-tion of the next time step the new centre is calculated as themid point of the N points and the diameter of the annularregion is determined from the resulting area by representingthe cell boundary as a circle.

The algorithm was written in the PV-WAVE language,version 7.0, Visual Data Analysis software (Visual NumericsInc., Boulder, CO) and implemented on a Pentium II, WindowsNT computer. The processing time depends strongly on the widthW and the rows N of the matrix P. In 512 × 512 resolution,scale 0.2 µm pixel–1, and 15 µm cell diameter the processingtime 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 evaluateerrors that the focal shift and the image resolution introduce

in the measurements. In addition, the repeatability and theerror from the polygon representation were calculated. Bothalgorithms (using the Sobel or radial edge detection proced-ure) were used.

Fluorescent/DIC comparison

Fluorescent images of cells stained with DiI were used as astandard because image noise is minimal and includes only adistinct cell boundary contour. For this reason a z-stack offluorescent images was used to calibrate DIC results. As areference point, the slice in the z-stacks with the largest cellarea was used. The corresponding DIC image was assumed tobe the in-focus plane with zero shift. Positive shifts were assumedto lie above that plane and negative below. Despite the import-ance of optical slice thickness on 3-D geometry, the z-shift aswell as the maximum cross-sectional area were found to beindependent on the optical slice thickness. For each cell, themaximum fluorescent area (in-focus plane) was converted tovolume and was used to normalize all the volume results fromthe DIC images (inter-normalization). The ratio of DIC to fluo-rescent 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 experi-ments due to small temperature fluctuations or change ofcell shape. To assess the output of the method to out of focusimages, z-stack scans of DiI-labelled spherical cells were recordedwith a z-step equal to 0.2 µm. The inter-normalized volume wasclustered every 0.1R and was reported as a percent distance ofcell radius R from the in focus plane. Again, the cell radius Rwas obtained from the fluorescent images. In every cell thatwas measured, the DIC results form a plateau region between

Fig. 6. Results of dynamic programming and super-imposition on the original image. When the calculationof the value function f finishes, the optimal path isconstructed by selecting the pixel with the maximumvalue function (starting from the last row of matrix P)and proceeding backwards for a total of N steps usingthe directional information of T. Then the results aresuperimposed to the original image.

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0.1R and 0.5R. Volumetric results were normalized either withthe in-focus fluorescent volume (inter-normalization) or withthe average DIC volume of the plateau (intra-normalization). Theintra-normalized standard deviation (known as the coefficientof variation, CV) of the plateau is reported. In addition, theaverage inter-normalized DIC results in the plateau region aswell as the standard deviation are reported.

Resolution error

Image resolution plays an important role in the accuracy ofthe results. In order to get a threshold of the minimum requiredresolution, DIC images were recorded in a scale of 0.07 µmpixel–1 and were scaled up to 0.4 µm pixel–1 with a total of 10different resolutions. Five different spherical cells were analysed.Based on the out of focus response, the focal plane that wasused to evaluate the resolution error corresponded a planeapproximately 1.5 µm above the centre of the cell (in the plateauregion).

Polygon representation

The output of the algorithm is a set of N (x,y) points. These Npoints are connected to form a polygon that approximates thecell membrane. An estimation of the error introduced fromthis representation can be calculated by comparing a perfectlycircular cell membrane to a regular N-sided inscribed polygon.The percentage area error due to this underestimation is givenas a function of N:

(5)

Repeatability

Despite the fact that the path produced by the algorithm isoptimal, small displacements of the centre of the annular regionor different image orientations lead to changes to the mappedmatrix P. These changes cause small fluctuations in the resultsbecause the calculated optimal path is not the same. To assessthis error, measurements of the same cell were repeated fordifferent image orientations with a step of ∆θ = 10° from 0° to90°. The measurements were performed for four different cellsand for focal planes in the plateau region.

Experimental procedure for osmotically stressed chondrocytes

A typical application for such a method is the quantification ofvolume changes in chondrocytes in response to osmotic stress.In these experiments, the iso-osmotic solution was drawn offthe cells and replaced immediately by a solution of differentosmolarity (450 or 150 mOsm). The hyper-osmotic and hypo-osmotic 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 TIFFimages (160 images per set). All experiments were performedat room temperature.

Results

Validation and error analysis

Fluorescent/DIC comparisonFluorescent images were used primarily to normalize the DICresult and to assess the in-focus plane. In the in-focus plane,the ratio of DIC to the fluorescent volume was 0.957 ± 0.046with 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 focalplanes (Figs 7 and 8). Figure 7(a) shows the results of the pro-gram and Fig. 7(b) presents the corresponding typical patternof the inter-normalized volume for different focal planes. Theshift of the focal plane in the z-axis has been expressed as apercentage of the cell radius in order to exclude the dependenceof the result on cell size. By assuming an average radius of thecell as 7.5 µm, the shift from the focal plane can be convertedinto distance. Images with positive shift (A, B and C) can becharacterized by the white cell boundaries (Fig. 7a) and thosewith negative shift (D, E and F) exhibit a black boundary.Near the focal plane (from –0.1R to 0.1R) there is an inherentvolume increase of up to 14.1% (Fig. 8a). This apparent volumeincrease, introduced by a small focal shift (< 1.5 µm), is mostlydue to shadowing and fading phenomena that take place below0.1R. The inherent volume increase occurs at the transitionfrom the white to black shadow in the cell boundary (Fig. 7a,images C and D). A consistent ‘plateau’ in the volume meas-urement was observed within a focus zone from 0.1R to 0.5R(Fig. 8a). For chondrocytes with average diameter of 15 µmthis plateau corresponds to distance of approximately 3 µm.The plateau is defined as the focal region wherein individualclusters have inter-normalized standard deviation less than2%. The plateau is shown with white bars in Fig. 8a. The inter-normalized 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 detectionalgorithm (Fig. 8b). In this case the plateau region consistedof a smaller region (0.2R to 0.5R). The inter-normalized volumeaverage in the plateau region is 0.99 ± 0.034 and the CV is3.2%.

Resolution error

Errors in cell volume measurement increased as image resolu-tion decreased (Fig. 9). The value on the x-axis (µm2 pixel–1) isthe image scaling (µm pixel–1) multiplied by the characteristic

ErrorN N N

sin( / ) cos( / )

= −⋅ ⋅

1π π

π

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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, Band 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, theresults 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 of18.97%. After that point, shadowing and fading phenomena may result in significant inconsistency. (b) The normalized volume results of the methodwith 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 ischosen to be the average diameter of chondrocytes (in this case15 µm). Significant errors were apparent at values of 2.9 µm2

pixel–1, and for chondrocytes this value corresponds to animage scaling of 0.19 µm pixel–1. The same results were obtainedusing either radial or Sobel edge detection.

Polygon representation

An estimation of the percentage error introduced by the rep-resentation of the cell membrane as an N-sided polygon instead

of a continuous curve is calculated from Eq. (5) as a function ofN. For values of N greater than 70 the area error was under-estimated by at most of 0.13%. Typically, N calculated fromEq. (2) corresponds to values much greater than 70; thereforethis error can be neglected. This error is independent of themethod used.

Repeatability

Small changes to the mapped matrix P produced from differentimage orientation or from small displacements of the centre of

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

–50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100

Focal Shift as Percentage of Cell Radius [%]

Nor

mal

ized

Cel

l Vol

ume

Zero

foca

l pla

ne

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

–50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90 100

Focal Shift as Percentage of Cell Radius [%]

Nor

mal

ized

Cel

l Vol

ume

Zero

foca

l pla

ne

(b)

(a)

Fig. 8. Normalized volume results in different focalplanes. The shift of the focal plane is reported as apercentage of the cell radius in order to exclude thedependence of the results on the cell radius. Theconsistency of the results in a positive shift range ispromising for accurate measurements. (a) Resultsusing the radial edge detection method. (b) Resultsusing the Sobel edge detection algorithm.

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the annular region introduce a fluctuation in the results. TheCV of these measurements was 0.25% in the plateau regionbut can approach 1.5% near the zero focal plane. The resultswere independent of the edge detection procedure.

Chondrocyte response to osmotic stress

Chondrocyte volume rapidly changed in response to hyper-osmotic and hypo-osmotic challenge and exhibited an activerecovery towards the initial volume (Fig. 10). The radial edgedetection algorithm was applied to these image series withno manual intervention. For the 450 mOsm solution the chon-drocytes responded with a maximum volume decrease of 28.7 ±14.6% at t = 27 s and with little tendency to recover (decreaseof 21.8 ± 14.2% from the initial volume after t = 500 s). Underhypo-osmotic conditions (150 mOsm) the maximum increaseof the cell volume was 34.2 ± 20.8% at t = 33 s and with atendency for total recovery (increase of 3.7 ± 19.7% from theinitial volume after t = 500 s).

Discussion

This study presents an automated method for quantifyingthe morphology of the cell in a time series of DIC images. Over-all, the method shows excellent precision and accuracy (incomparison to fluorescent images of the cell membrane) whenapplied to spherical cells attached to a glass substrate. Thehighest accuracy was obtained when the focal plane was ini-tially in a zone slightly above the centre of a spherical cell. Inthis range, the overall volume error assuming a spherical cellwas 1.9%.

The calculation of cell volume from 2D DIC images can beinaccurate if the cell is not a sphere. In the present study we didnot include this inherent error because it depends on the shapeof the cell and is difficult to quantify. Moreover, we wantedto present the accuracy of the method in extracting cell sizeinformation from DIC images. However, we reported results asunits of volume and not of area because volumetric measure-ments are more applicable. All the cells that were used for thevalidation of the algorithm and for the error analysis exhibiteda nearly spherical shape (Fig. 11).

A primary step in this algorithm involved enhancement ofthe cell boundary using one of two different edge detectionprocedures: a fast approximation of the Sobel algorithm anda custom-written radial edge detection algorithm. The Sobelalgorithm is sensitive to any direction of gradient in colourvalues, and thus it can be applied to a wide range of images. Theradial edge detection method can detect only transition fromwhite to black in a radial manner, in the direction towardsthe centre of the annular region, and thus can be applied inthe plateau region of the focal response. The fluorescent/DICcomparison in the in-focus plane indicates that the methodwith the Sobel algorithm agrees better with the fluorescentresults and produces more consistent results in the in-focusplane. However, for the plateau region the radial edge detectionalgorithm is preferable because it creates a bigger plateau andhas a much smaller CV (1.9% compared with 3.2% when theSobel edge detection is used). If R is the radius of a spherical

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Fig. 9. Resolution response. The value on the x-axis (µm2 pixel–1) is theimage scaling (µm pixel–1) multiplied by the characteristic length of cell(µm) (characteristic scaling). The graph indicates that accurate measurementscan be obtained for values of at most 2.9 µm2 pixel–1 and for chondrocytesthis value corresponds to an image scaling of 0.19 µm pixel–1 (characteristiclength of chondrocytes = 15 µm).

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Fig. 10. Osmotically stressed chondrocytes. Cell volumedecreased by 28.7% for 450 mOsm (bottom solid line ±standard deviation). Cells exhibited little tendency forrecovery. For the hypotonic solution (150 mOsm), cell volumeincreased by 34.2% (top solid line ± standard deviation).

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cell then accurate measurements can be obtained by using theradial edge detection method in a z-zone between 0.1R and0.5R above the in-focus plane and for values of characteristicscaling up to 2.9 µm2 pixel–1. For chondrocytes with a charac-teristic length of 15 µm the plateau lies between 0.75 µm and3.75 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 importantrole in the extraction of accurate results. When measurementstake place in this region, and the characteristic scale is satisfied,the overall volume error in the plateau region is underestimatedby a factor of 0.97 ± 0.023 compared with the fluorescent resultsin the in-focus plane. This error includes the fluctuation of DICresults superimposed upon the fluctuation of fluorescent results.Usually the experimental data are normalized with respect tothemselves (e.g. initial volume). With that in mind, the intra-normalized 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 methodproduces consistent results despite the drift of the focal planeinside the plateau range. It is recommended that measure-ments take place only in the plateau region despite the visuallyout of focus state of the image. These findings set a workingspace for the method that is valuable when the drift of the focalplane cannot be avoided.

There are two types of focal drift: the actual focal drift that iscaused by the change of the objective lens’ geometry (mostly dueto thermal effects) and a virtual drift that is due to changes ofcell morphology. An example of the second case is the swellingexperiment of cells due to osmotic effects. Even if the objectiveis totally stable, the centre of a cell that is attached to the glasssurface moves upwards due to cell swelling and thus, a down-

ward shift of focal plane is observed. For chondrocytes with anaverage diameter of 15 µm and a maximum increase of volumeof 60% the virtual focal drift is approximately 1.2 µm. Despitethe fact that this drift takes place in a period of a few seconds andcannot be avoided with manual finite adjustments of the focalplane, the 3 µm plateau gives space for the drift to take placeinside the plateau zone without interfering with the results.

Outside of the plateau region the images may include arte-facts that can lead to a volume increase up to 14.1%. Theseartefacts arise from shadowing phenomena inherent in DICmicroscopy and are associated with the geometry of the cell(Fig. 7a). In spherical cells, z-stack fluorescent images show alocal maximum in the transverse cell area in the in-focus plane.That local maximum is responsible for the formation of theplateau zone. In cells that are spread across the glass surfaceand no local maximum exists, there are no plateau zones andno transition from white to black boundary as the focal planemoves downwards. In this case the preceding analysis cannotbe applied. It is important to note that the method developedin this study was designed and validated for application tospherical cells, particularly with respect to calculations of cellvolume. Future studies may wish to address the precision andaccuracy of this method when applied to a more flattened cellshape.

An advantage of this method is the minimal interventionfrom the user. The user has to specify only an annular regionin which the cell membrane lies. In cases where the algorithmfails to locate the cell boundary, the user can intervene in amanual mode to suggest the location of the boundary, and theprogram tries to encompass these suggestions. In all test cases,no manual intervention was needed if the images were recordedin the ‘plateau zone’ of the focal plane.

Fig. 11. 3D image of a chondrocyte. The image wasobtained from a series of confocal optical sections of thechondrocyte by using a geometric modelling method(Guilak, 1994).

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The motivation for the development of this method was theneed to quantify volume changes in spherical chondrocytesexposed to acute osmotic stress. In the experiments presented,chondrocytes were exposed to either hypo-osmotic or hyper-osmotic stress. As can be seen in the results, cell stressed witha 150 mOsm solution swelled to 134.2% of their original volume.Following this maximum volume, the cells returned towardstheir original volume by initiating recovery mechanisms.The average final volume at the end of the experiments was103.7% of the original volume. In chondrocytes, this mechan-ism, called regulatory volume decrease, is thought to primarilyinvolve 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 thenrecovered to 78.4% of the original volume. The mechanismprimarily involved in this recovery, called regulatory volumeincrease, is the activation of the Na +/K +/Cl− cotransporter(Hall et al., 1996). Although the mechanisms of volume reac-tion and recovery were not analysed in this study, the methoddeveloped provides an excellent way to repeatedly measurevolume changes in chondrocytes as they are exposed to vary-ing osmotic stress.

In conclusion, the method outlined in this paper gives accu-rate results of the cell volume when two conditions are pre-served: the focal plane lies inside the plateau zone (0.1R to0.5R) and the characteristic scaling is up to 2.9 µm2 pixel–1.With that in mind, this method can be a very helpful tool forinvestigation of the volume regulation in cells due to acuteosmotic changes and can permit future studies to encompasscell morphology and motility.

Acknowledgements

The author would like to thank Larry Martin for excellentassistance with the data analysis, Michail Lagoudakis of theDepartment of Computer Science, Duke University, for hisvaluable input in the implementation of the algorithm andfor his proof reading, Dan Northup for the cell isolation aswell as Robert Nielsen for his technical assistance. This studywas supported by the National Institutes of Health grantsAR43876 and AG15768.

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