Automated measurement of cell motility and proliferation
© Bahnson et al; licensee BioMed Central Ltd. 2005
Received: 30 June 2004
Accepted: 14 April 2005
Published: 14 April 2005
Time-lapse microscopic imaging provides a powerful approach for following changes in cell phenotype over time. Visible responses of whole cells can yield insight into functional changes that underlie physiological processes in health and disease. For example, features of cell motility accompany molecular changes that are central to the immune response, to carcinogenesis and metastasis, to wound healing and tissue regeneration, and to the myriad developmental processes that generate an organism. Previously reported image processing methods for motility analysis required custom viewing devices and manual interactions that may introduce bias, that slow throughput, and that constrain the scope of experiments in terms of the number of treatment variables, time period of observation, replication and statistical options. Here we describe a fully automated system in which images are acquired 24/7 from 384 well plates and are automatically processed to yield high-content motility and morphological data.
We have applied this technology to study the effects of different extracellular matrix compounds on human osteoblast-like cell lines to explore functional changes that may underlie processes involved in bone formation and maintenance. We show dose-response and kinetic data for induction of increased motility by laminin and collagen type I without significant effects on growth rate. Differential motility response was evident within 4 hours of plating cells; long-term responses differed depending upon cell type and surface coating. Average velocities were increased approximately 0.1 um/min by ten-fold increases in laminin coating concentration in some cases. Comparison with manual tracking demonstrated the accuracy of the automated method and highlighted the comparative imprecision of human tracking for analysis of cell motility data. Quality statistics are reported that associate with stage noise, interference by non-cell objects, and uncertainty in the outlining and positioning of cells by automated image analysis. Exponential growth, as monitored by total cell area, did not linearly correlate with absolute cell number, but proved valuable for selection of reliable tracking data and for disclosing between-experiment variations in cell growth.
These results demonstrate the applicability of a system that uses fully automated image acquisition and analysis to study cell motility and growth. Cellular motility response is determined in an unbiased and comparatively high throughput manner. Abundant ancillary data provide opportunities for uniform filtering according to criteria that select for biological relevance and for providing insight into features of system performance. Data quality measures have been developed that can serve as a basis for the design and quality control of experiments that are facilitated by automation and the 384 well plate format. This system is applicable to large-scale studies such as drug screening and research into effects of complex combinations of factors and matrices on cell phenotype.
Cell-matrix interactions are key components of many physiological processes in health and disease. Frequently these interactions result in changes in cellular motility, morphology, and/or growth, and so quantitation of these changes is useful for comparing matrix and soluble factor effects and for assessing sensitivity of cells to varying concentrations of these factors [1, 2]. A variety of methods are used to measure cell migration, including most commonly the transwell assay  often modified by fluorescence quantitation , and less commonly the under-agarose migration assay , the soft-agarose drop method , the phagokinetic track motility assay for phagocytic cell types , wound healing , and time-lapse video microscopy.
Although the transwell assay has been applied to random migration , video time-lapse microscopy provides advantages by yielding actual speeds of individual cells and additional features of motion, e.g. persistence . The video time-lapse approach has been applied since the late 1930's using film-projected images and manual methods for tracking cell paths for determination of velocities . The introduction of video imaging and computer-assisted methods of tracking have aided this approach [12, 13]. However, even with computer-assisted methods, analysis of video time-lapse images can be labour intensive, particularly if the data have been gathered over extended time periods, and the opportunities for human fatigue and inadvertent selection using such methods may introduce bias. Moreover, the normal cell culture environment must be maintained during imaging. Although sophisticated studies are being conducted within special chambers  or under mineral oil , an ideal system would incorporate acquisition of images simultaneously from multiple wells under normal culture conditions maintained throughout the entire experiment.
A fully automated system for acquiring and analysing time-lapse images over extended time periods from multiple wells within 384 well plates has been developed [16–21]. The system includes an electronically controlled incubated cell culture environment for continuous monitoring over extended periods. Automated image analysis is used to determine cell morphological properties and cell location, and proprietary algorithms are used to construct cell paths or tracks through time, yielding magnitude and direction of motion. Cell proliferation is also monitored based upon processing of the same set of images. The data set provides a rich source of unbiased quantitative information about cell behaviour that can be accessed at the individual cell level and filtered in a manner similar to gating in flow cytometry. Here we apply this technology to examine responses of osteoblast-type cells to surface coatings of extracellular matrix compounds that may be involved in osteoblast differentiation and growth. This study is part of an ongoing effort seeking to uncover underlying factors that influence osteoblasts in the process of osteogenesis and in the dysregulation of this process leading to osteoporosis.
Differential cell velocity on different ECM coatings
KM101 cells and MG-63 cells were chosen as models for this study because of their potential for differentiation into cells with osteoblast-like phenotypes. KM101 cells, from primary human bone marrow stroma , have been shown to secrete bone-type alkaline phosphatase upon differentiation [Julie Goff, personal observations]. The MG-63 cell line, originating from a human osteosarcoma , exhibits characteristics of bone forming cells including high levels of 1,25-(OH)2D3-responsive alkaline phosphatase activity and osteoblast-like regulated synthesis of osteocalcin and collagen type I . Responses in cell motility may reflect functional changes that accompany osteoblast migration into areas of newly forming bone.
Additional File 1: Time-lapse motility and proliferation of KM101 and MG-63 cells. Images from four wells were combined to show the differential effects of laminin (upper left), collagen type I (upper right), collagen type IV (lower left) and mock-coated plastic (lower right). Red outlines indicate the perimeters of the cell "objects" from which object areas and centroid positions are derived. Green lines indicate tracks that are established between successive centroid positions that define the individual cell paths. In this image sequence, track segments are erased following 10 hours elapsed time. The total elapsed time of 114 hours for each cell type shows cells from shortly after seeding to near confluence. Images were acquired at 30-minute intervals and are displayed in the video at a rate of 6 images per second. (MP4 4 MB)
Data selection for single live-cell velocity
Kinetics of velocity response
Additional File 2: Acceleration of MG-63 cells. Time-lapse videos show MG-63 cells on laminin-coated (10 ug/ml, first image sequence "I04") and mock-coated plastic (second image sequence "J03"). Images were acquired at 30-minute intervals and are displayed in the video at a rate of 6 images per second. Green lines indicate automatically generated tracks connecting successive centroid positions of objects. Track segments are erased after 15 images, so the maximum track length represents 7.5 hours' migration. A total of 118 hours elapsed time is shown for each image sequence. (MP4 5 MB)
Velocity measurement heterogeneity
The individual cell velocity distribution modes were noticeably shifted toward higher velocities with laminin and to a lesser extent with collagen type I surface coatings, in comparison with mock-coated plastic and collagen type IV. These histograms provide a more descriptive picture of the nature of the response of the cell populations to the surface treatments than that provided by measures of central tendency alone, without invoking complex statistical models.
Technical precision and quality control
Comparison of automated tracking versus manual tracking
To better understand the magnitude of these errors in practice, we examined the actual differences in locating cell positions by the automated and manual tracking methods. Our data set consisted of 716 cell positions that were co-located by automated tracking and by the first and second manual exercises according to the matching algorithm (see Methods). No single position can be considered the "true" position; however, the differences between replicates can be used to estimate precision, S, according to the relationship, S = 1/v2 times the standard deviation of the differences, where the differences retain the sign; for example, if the second comparison measurement is larger than the first, the sign is negative. By this approach, for the first and second manual exercises, the precision was 1.91 and 2.03 pixels in the x and y coordinates, respectively. For the comparison between automated tracking and manual tracking the precision ranged between 2.04 to 2.28, but when automated tracking was compared with the mean from the two manual tracking exercises, the precision improved to 1.87 and 1.91 pixels in the x and y coordinates, respectively. Thus, the automatically determined cell positions were closer to the mean positions from the two manual determinations than any individually determined position was to any other. Under the settings used, a distance of 2 pixels corresponded to an error of less than 1/32 inch, easily within the realm of human error for mouse-clicking on a monitor.
Regardless of the non-linearity of area-based cell numbers, the monitoring of cell growth based upon total cell area provided extremely valuable information. Within experiments, the log-based slopes were similar for the different treatments, with the pronounced exception of laminin and KM101 cells in the second experiment, even when starting with different initial seeding densities and when absolute cell numbers differ considerably over time as was evident in the three experiments performed for this study. A faster doubling rate for all treatments in the first experiment contrasted with slower doubling in the second and third experiments for both cell types. Treatment-related patterns occurred within experiments that were not evident between experiments, and even without quantitative analysis it is clear that no reliable pattern of surface-treatment effect on cell growth can be found. Hazards are evident, however, if conclusions were to be drawn from a more limited number of experiments, even with convincing within-experiment data.
One can speculate on possible causes for the between and within-experiment patterns shown here. For the second experiment, seeding densities were unusually low, and an atypical initial period of cell death was evident in the time-lapse videos during the first day after plating (data not shown) and is shown also by the unusual "lag phase" in the log-based charts for both KM101 and MG-63 cells in the second experiment. Typically, healthy cells under normal conditions begin exponential growth immediately upon re-plating, as evident in the linear log-based graphs for the first and third experiments from the point of initiation up to the point of confluence. The departure evident for the second experiment in the growth charts holds implications for variability between experiments in the velocity data presented above (Figure 5). Standardization of procedures and testing for robustness are called for. The value of our system for assisting in such efforts is prominently evident in these charts, apart from the question of treatment-related effects on growth in this study. In future studies, consistency in growth parameters could be made a prerequisite for acceptability of results for other parameters; here the results serve to demonstrate system potential.
This study demonstrates the applicability of a fully automated image acquisition and analysis system for quantitative measurement of cell motility and for monitoring cell proliferation in a relatively high-throughput manner. Simultaneous comparison of multiple treatment variables in a 364 well plate format over extended periods of time is possible. Here we show how various surface coatings of extracellular matrix compounds can induce increased velocity in two types of osteogenic cell lines, how these responses vary over time periods of more than three days, and how they vary by surface coating concentration, i.e. dose-response. We show that laminin and to a lesser extent collagen type I surface treatments brought about increased migratory activity, while collagen type IV did not, in comparison to mock-coated plastic for KM101 cells and MG-63 cells. We show further how the extensive multiparametric output can be used to selectively isolate data of interest for improvement of bio-informational content and for characterization of system performance.
We believe our system is the first to accomplish full automation of time-lapse motion analysis of cells in culture, broadening the scope of application well beyond the practical limits imposed by manually interactive methods. Image sets consisting of hundreds to thousands of scans from up to 384 locations over extensive time periods (days to weeks) can be acquired and batch processed, first to segment cell-like objects and clusters of such objects, and subsequently to construct tracks for the segmented objects over time. Quantitative data is seamlessly exported to a Sequel Server Data Base from which results are presented in various forms as shown here. The relational data base is absolutely necessary for handling the large volume of multi-parametric data – over three million records for this study, including one for each object at each time point containing more than 40 fields of positional, textural, morphological, and motility-related data. Additional fluorescence measurements are also commonly used [19–21].
Our analysis contrasts in some respects with the exquisite optical characteristics and advanced analytical details of migratory activity achieved in systems where parallel plane surfaces are provided by specially constructed chambers [e.g. [25, 26]]. Such non-conventional culture environments overcome the meniscus problem, but are not readily adaptable to simultaneous analysis of multiple treatment conditions in a high throughput manner. Most importantly for screening and discovery purposes, our system preserves the essential features of trajectory analysis that were emphasized by Friedl and co-workers for evaluating subtle changes that reveal treatment effects on cell locomotion [27, 28].
To support the introduction of fully automated cell tracking, we have included a thorough analysis of measurement variability, system errors, and accuracy. Biological differences between individual cells dominated the velocity measurement heterogeneity for the cells chosen for this study, while stage noise, cell segmentation, and cell positioning were shown to be relatively minor sources of error. For more slowly moving cells, i.e. those with velocities less than 0.4 um/min, the latter relatively minor errors will result in large coefficients of variation under current conditions. Rational data-filtering methods, such as exclusion of data from non-cell stationary objects based upon "fence size" and exclusion of data from objects with areas outside of single-cell ranges (see Methods), yielded further improvements to the detectability of biological response from single cells. The accuracy and validity of these approaches were supported by comparison of the automated data with data from manually tracked cells. A significant feature of this analysis was the finding that, in general, automatically determined cell positions were closer to the mean positions from manual tracking than the replicate manual positions were to each other. Thus a major limitation of this comparison was the imprecision of manual tracking.
On the other hand, the perfect precision of automated tracking represents a two-sided coin. It will precisely repeat any errors, posing an obstacle to data control based upon monitoring internal consistency. At the same time, small variations in processing variables can be readily applied, tested, and evaluated. For example, in current experiments, we are exploring the possibility of obtaining better "average" cell positions by acquiring replicate non-identical images closely spaced in time, e.g. one minute apart, for characterizing motion over longer intervals, typically 30-minutes. Such an approach should improve precision and segmentation reliability at the individual cell level, while simultaneously providing a foundation for routine control based on inherent data consistency. The ability to perform automated batch processing will in due course be utilized more broadly for quality control and for optimization of image processing variables. Advantage can be leveraged from perfect precision by applying and evaluating systematic changes to variables of a contrast enhancement algorithm, for example, followed by repeated cell segmentation and cell track processing of representative image sets, such that cell track lengths, in terms of linked segments, would be maximized for non-collision-related scenarios. Automated routines for such optimization are not yet implemented, but are entirely feasible.
In seeking higher levels of automation, however, it is important to continue to manually monitor for and evaluate consistency between the raw data input and the processed data output. For each cell type, and for varying treatment conditions, processing variables are checked and evaluated. With each experiment, we manually verify that cell segmentation and cell track formation proceed reliably throughout representative regions of the image sets. The processing software presents the operator with cell outlines and tracks as shown in Figure 1 [see also Additional file 3], and Spotfire™ visualization software is used extensively to verify consistency in the quantitative data. Tracking patterns dominated by short fragments indicate, for example, problems requiring adjustment in image processing variables. Representative image sets are first examined for such problems before initiating batch processing of the full experiment; but it is not impractical to automatically reprocess image sets from an entire experiment when evidence demonstrates a need for it. It should be pointed out that most of the refinements in data filtering, thresholding, and so on for this study were conducted at the level of data base querying, not at the level of image processing or track construction. Whereas image processing requires hours to complete for a full experiment image set, data base queries can be run and re-run in a matter of minutes, and so the effect of changing thresholds or "gates" may be readily examined and interpreted using statistics or visualization software such as Spotfire™. Part of the beauty of automated analysis lies in our ability to make incremental improvements in both image processing and data querying approaches over time, leading to increasingly more accurate and reliable data. In contrast, manual analysis will remain decidedly imprecise and variable over time.
Quantitative results from other published studies further support the general accuracy of our system. For example, Huttenlocher et al. reported speeds ranging from 0.2 to 1.5 um/min for individual CHO cells plated on fibrinogen coated surfaces and later reported average speeds of approximately 0.3 um/min for myoblasts on fibronectin using manually-assisted computer based methods . Similarly, Ware et al. reported maximal average velocities of a 3T3-derived cell line of approximately 1.5 um/min and presented histograms for individual cell velocities ranging from near-zero to approximately 2.5 um/min on a mixed extracellular matrix derivative in the presence and absence of epidermal growth factor . It has been shown that experimental conditions such as pH and temperature, among others, can have a profound influence on motility , nevertheless, reported velocities for adherent cells in other published studies are consistent with our findings.
Determining cell proliferation using area-based measurement was shown to be vulnerable to non-linearity between area and cell numbers. But area-based growth curves exhibit exponential characteristics of high quality, and so automated quantitative monitoring of total cell area can be highly informative and useful. Image processing algorithms for segmentation of individual cells within colonies or clusters using transmitted light will yield more reliable data as improvement continues with auto-focusing and contrast optimisation. The use of nuclear fluorescence staining is a reliable alternative for automated cell counting, but known stains are toxic and therefore were not used in this study. Application of a mathematical adjustment factor based upon 'calibration' with manual or fluorescent counts might be considered; the risk here is that treatment effects could be masked, so this approach has not been used.
Velocity enhancement of osteogenic cells with extracellular matrix compounds provided a useful illustration for this pilot investigation of the automated system. It should be pointed out that collagen extra-cellular matrices consist of a 3D network of polymerised fibers, and that the 2D non-polymerised surface coatings used here may not reveal representative cellular response to the normal polymerised form of the extracellular matrix. An unexpected finding from this study was the continued acceleration of MG-63 cells on mock-coated plastic as well as on the extracellular matrix compound coated surfaces in contrast to KM101 cells that did not accelerate on mock-coated plastic or collagen type IV coated surfaces. Trypsinization cleaves cell adhesion receptors at the time of replating, and it is possible that the re-synthesis and transport of such receptors played a role in the kinetics of the responses shown in this study. The effects of such recovery would not seem to explain the continued acceleration of MG-63 cells through several cell cycles, however. Migration inducing-factors secreted by osteoblasts have been reported [6, 30], and it is possible that an effect from such a factor is involved here. Alternatively, MG-63 cells may secrete extra-cellular matrix proteins that gradually accumulate on the surface to enhance migration rates.
This study demonstrates performance of a system for fully automated, time-resolved, and high throughput analysis of cell migration and proliferation, applied to continuously growing cultures in standard 384-well plates. This format permits the study and comparison of cellular responses to a large number of different treatment conditions, as shown here for three different extracellular matrix coatings on cultureware plastic for two different osteoblast-type cell lines. The simultaneous determination of multiple parameters at the individual cell level affords opportunities for data-base filtering and mining in order to select biologically relevant information. The automated velocity analysis has been demonstrated to be accurate within a level of uncertainly that is imposed by manual analysis of cell velocity from time-lapse image sets. Data quality and system performance measures have been developed that can serve as a basis for the design and quality control of large scale experiments for which this system is broadly applicable.
Cells and cell culture
MG-63 cells were obtained from ATCC and were grown according to recommended protocol (ATCC). Specifically, MG-63 cells were cultured in Minimum Essential Medium (Gibco/Invitrogen) with 2 mM L-glutamine and Earle's BSS adjusted to contain 1.5 g/L sodium bicarbonate, 0.1 mM non-essential amino acids, and 1.0 mM sodium pyruvate with 10% heat-inactivated fetal bovine serum (FBS). KM101 cells, a human bone marrow stromal cell line  were grown in 10% FBS in Iscove's Modified Dulbecco's Medium (Gibco/Invitrogen). Cells were cultured at 37°C in humidified atmosphere with 5% CO2. Prior to plating, cells were trypsinized with 0.25% trypsin (Gibco) and resuspended at a density of 2000 cell/ml. Aliquots of 60 ul were seeded into 384 well plates (Costar, black wall) yielding approximately 5 to 15 individual cells in the camera viewfield at the outset of imaging.
The plate layout included triplicate wells for each compound at each coating concentration for both cell lines. All operations were performed using multi-tip pipettors so that inter-well variations within-treatments were minimized to the greatest possible extent. Although the ideal plating pattern would be fully random, for practical purposes, advantage was taken of the interspacing of wells that occurs using 96 well multi-tip pipettors for applying solutions from 96 well "seed" plates into every-other well of the 384 well plate, producing "checker-board" patterns that intermixed treatments, doses, and uniform mock-coated control wells across the plate. Cell suspensions were pipetted from solution basins uniformly across each row.
Extracellular matrix surface coating
Mouse laminin I (Cultrex), mouse collagen type IV (Cultrex) and collagen type I (Sigma) were stored and reconstituted according to the manufacturer's instructions. Dilutions for coating were performed either in sterile water for collagen types I and IV or in Iscove's Modified Dulbecco's Medium (IMDM; Gibco/Invitrogen) without added serum for laminin I. Control wells were mock-coated using IMDM without added serum. Aliquots of 10 ul of solution were added to each well of a 384-well plate (Costar), and the plate was incubated for 1 hour at 37C. The collagen solutions were aspirated, and collagen-coated wells were allowed to air dry for about 20 minutes in a laminar flow hood. The laminin and mock-coated wells were then aspirated and all wells were rinsed with IMDM and aspirated prior to addition of cell suspensions.
Cell culture imaging cystem
The cell culture imaging system consists of a custom made environmentally controlled biochamber on an electronically controlled x-y motorized stage driven by stepper motor drive systems (Ludl Electronics, Ltd.) mounted upon an inverted microscope (Nikon TE 300) with electronically controlled motorized focus. The stage moves precisely to each well in the multi-well plate or to any number of locations within each well with a positioning repeatability of ± 1.5 um over the longest distance traveled by the stage. The biochamber temperature is controlled via heating cartridges with temperature feedback loops, and the humidity and CO2 content are controlled via commercial sensors to control feedback loops to a water reservoir heater and low pressure CO2 solenoid valve, respectively. The glass windows for illumination and microscope imaging are specifically heated through an electrically conductive indium tin oxide (ITO) coating using feedback temperature regulation so that condensation does not occur on these surfaces. A custom instrument control program, written in Visual Basic and C++, integrates control of the microscope stage, focus, optical filters, shutters, camera, fluidics, image storing functions, thermal zones, and subsystems through a specialized serial interface board with eight RS-232 connections.
Video time-lapse imaging and analysis
Images were acquired at 30 minute intervals with a 10× objective on a Nikon TE300 inverted microscope with a Photometrics SenSys high resolution (7 × 9 mm, 1036 × 1318 pixel chip) CCD camera (Roper Scientific). Image sequences were processed using a custom software program that identifies and records the location and morphological characteristics of cell-like objects (see Cell Segmentation and Outline Determination). The centroids of cell-like objects are then linked through sequential images to construct "tracks" that trace the route of individual cells according to proprietary algorithms [see Cell tracking algorithm]. The information accumulated during the processing is represented in probabilistic form so that the decision-making process does not have to be "black-and-white" (e.g. is the given object a cell or not, or is the given track the right track or not?), but is postponed until the end of the decision-making chain allowing for corrections for "lost" cells.
In each experiment for this study, 96 or more wells were imaged for at least 3 days, yielding more than a million records, each containing multiple measurements acquired for each object at each imaging time-point, i.e. every 30 minutes. These measurements fall into the categories of motility (scalar and vector forms of velocity, linearity, measures of deviation and frequency of oscillation of cell paths, track size and boundary), morphology and texture (area, perimeter, elongation, eccentricity, roughness, intensity and variation of intensity), summary statistics (object counts, cell counts, apoptotic frequency when fluorescence vital staining is applied) and complex parameters such as cell motility persistence , proximity analysis (cell-cell interaction, frequency and duration), division detection, growth rate, and viability (not all are applicable).
Cell segmentation and outline determination
The optical characteristics for inverted light microscopy of 384-well plates present challenges for robust segmentation of live cells. The meniscus obviates phase contrast; brightfield images are low in contrast and require significant processing. So a succession of filters is used to increase the difference (signal to noise ratio) between the background and foreground (cell-like objects), followed by an efficient region-growing operation that segments cell-like objects from the background. Heterogeneity of illumination across the image is reduced using local histogram equalization. Variations in illumination between images (across time) are handled using histogram matching. Background variations are smoothed using anisotropic filtering and adaptive median filtering, preserving cell detail and texture. Finally with brightfield microscopy, the cell boundary produced by the cytoplasmic membrane easily blends into the surrounding background, so a unique set of gradient variation and texture filters is applied to enhance the cell outline. Following filter-based enhancement, a region-growing operation identifies contiguous areas of cell-like or background-like pixels to segment cell-like objects from the background. A still more involved cell boundary determination can be achieved via active contour techniques (snakes) at the operator's discretion.
Cell tracking algorithm
The time-lapse interval in multi-well experiments is dependent upon practical considerations including the cell-type specific rate of motion, the total number of wells, the rates of stage movement, camera operation, and so on. For very fast cells such as T cells, imaging is performed on subsets of wells on a rotational basis in order to achieve intervals short enough for reliable track construction. At longer intervals, and particularly for view-fields containing many similar cells, cell track linking across the interval becomes increasingly unreliable because cells change shape and direction frequently, and as their paths converge, incorrect links may be assigned probabilities equal to or greater than correct ones.
Tracking is achieved by linking the matched cell-like objects between consecutive images in a probabilistic manner using a succession of increasingly stringent criteria. First, for each cell-like object, a set of candidate matches is chosen from within maximum speed and acceleration limits. Within this set, cell-like objects (blobs) are assigned to tracks based on match probabilities. Blobs are compared using multiple features such as location displacement, size difference, eccentricity changes, grayscale intensity IQR changes and normalized cross-correlation of the respective image portions. Converting distances into probabilities is done using a Gaussian probability density function. Because we assume that the features are independent, we can also assume that the resulting probabilities are independent. Therefore we can combine the different probabilities,
into the matching probability P(match ij | i, j), where match ij is a candidate match between track i and blob j and d n is the distance for feature n.
Cell objects in one image may compete simultaneously for multiple matches to different cells in the next image. A rule-based algorithm develops tracks based upon the values of the matching probability and tracking scenario. "Tracking scenario" includes the recent history and circumstances such as cell merging and splitting. For example, when two tracked cells that are similar collide, the merged object cannot be assigned to either track so both tracks are terminated. When two merged cells subsequently split apart, two new tracks are initiated because the matching of cells before and after the collision is ambiguous [see Additional file 3]. The cell tracking algorithm is very efficient in comparison to the cell segmentation; both are completed at the rate of 32 images/min, for 658 × 517 images on an Intel P4 2.8 GHz PC with 512MB RAM.
Both magnitude and directional velocity information are output from the linked positions of objects in sequential images. In this study, and for general investigation, we use a scalar average across several time points to smooth variation due to many factors. This average velocity represents the actual distance travelled, as determined by the movement of the centroid of the cell, divided by the elapsed time. Track lengths with fewer than 3 segments were not considered, and a maximum of 10 segments were included such that, for tracks longer than 10 segments, the velocity represents a running average. An exception to this method was used for "instantaneous velocity", as shown in Figure 8, where calculation was based upon displacement divided by time for the single track segment between the previous and current image. In order to exclude objects containing multiple cells in clusters or colonies, only velocity measurements for objects with areas less than three standard deviations above the mean area for each cell type were considered. The mean cell area and standard deviation was 1800 +/- 400 and 3100 +/- 900 square microns for KM101 and MG-63 cells, respectively. The lower limit for object area was 1200 square microns in both cases, based upon optimal visual exclusion of non-cell objects during set up of image processing variables. Velocity measurements were not included when the total area occupied by cells was greater than 30% of the viewfield area, i.e. when the cells were greater than 30% confluent. Finally, in order to filter out plate surface imperfections and adherent particles that gave rise to cell-like objects, data were excluded from tracks with fence sizes of less than 20 microns (See Results).
The technical accuracy of the imaging processing and data conversion steps were verified manually by constructing idealized image sequences with objects "seeded" at known pixel distances in order to generate known velocities based upon typical magnification and binning settings. Microscope optical magnification levels have been verified and calibrated with image pixel dimensions using a standard reticle.
Technical precision and quality control
Technical precision is here defined as the square root of the average variance for sets of triplicate velocity measurements (each measurement representing the mean velocity for all cells in the image) at single time points. Since absolute precision tended to increase in value for wells with cells of higher average velocity, and since there were sufficient data for analysis across the full range of velocities, we calculated summary precision values for triplicate sets ranked according to their measurement means (Figure 9). These data may be interpreted to indicate that the uncertainty in the mean velocity for a single well at a single time point ranged from approximately ± 0.08 um/min at the 0.2 um/min mean velocity level (CV = 40%) to approximately ± 0.12 at the 0.8 um/min level (CV = 15%) for KM101 cells, and it was slightly better for MG-63 cells. Sources of this measurement variability include the irreducible variation expected from random sampling from populations shown in Figure 6, taking into account the number, n, of cells in each sample, i.e. the number of cells imaged in each view-field as indicated in Figure 7.
Incidentally, the bin-based population variance, in which these precision estimates are rooted, should be employed when using the t-Test, rather than the variance of individual sets of replicates, to evaluate the significance of differences observed within experiments between triplicate means, i.e. for testing whether cell velocity was affected by an experimental treatment compared to a control treatment. The reason for this is that the sample mean and sample variance are independent when sampling from a normally distributed population. In other words, counter-intuitively, the mean of a set of three replicates that are widely spaced is likely to be as close to the "true value" as the mean of a set of replicates that are very closely spaced. The abundance of measurements made available by automation supports the validity of this claim, and would allow for slight adjustment of this principle when the data depart from normality, as it does here.
At the most fundamental level, because the stage mechanism re-centers each well into view after each time interval, images and data derived from them are subject to random errors associated with slight misalignment of the culture plate at each scan. The limits of this misalignment were determined by expanding images and manually tracking the motion of highlighted features of small imperfections on the culture surface throughout example image sequences. Such features were confined within a boundary of 3 square pixels over greater than 100 sequential images in all three experiments. Assuming Gaussian statistics, a limit of less than 1 pixel was estimated for the standard deviation of alignment of a single-pixel object, i.e. "stage noise". Under the magnification (10×) and binning conditions (2 × 2) used in these experiments, one pixel corresponds to 2 microns; this displacement for an object within a 30 minute time interval yields an upper limit for velocity of approximately 0.07 um/min. This calculation represents an upper limit to the contribution of stage noise, because in practice, stage-positioning error is expected to be a relatively small component of the total error that includes image-processing variability in determining cell outlines and object centroids.
Comparison of manual and automated tracking
Manual tracking was performed with a custom viewing program that enabled the user to store x and y coordinates by clicking on cells in sequential images with a computer-mouse. The 517 × 658 pixel images were displayed at approximately 7 × 8.5 inches on the monitor (approximately 75 pixels/inch) with a zooming option. A total of 27 cells were manually tracked from each of the four selected treatments. (For this exercise, a 27-cell limit was imposed by the nature of data output into a Microsoft Excel worksheet). The "rules" for manually placing the "centroid" and for terminating or initiating tracks were somewhat discretionary, e.g. the author continued to manually track cells through periods of contact with other cells, even though such scenarios were expected to involve track termination and re-initiation by the automated tracking algorithm [see Additional file 3].
For comparison of tracks on an object-by-object, point-by-point basis, we developed an algorithm to match objects from automated image analysis with manually tracked cells from each image. This algorithm identified and tabulated data from objects with automatically located centroids that fell within 10 pixels (20 um) of the x and y coordinates of the manually located cell positions that were determined by clicking with the mouse pointer. Following the initial comparison, both the manual tracking and the automated analysis were repeated on the four identical image sets, and the algorithm was applied to identify matched objects between the replicate manual and automated operations as well. Regression analysis and t-Test calculations were performed using R Project for Statistics [V. 2.0, see http://www.r-project.org].
Cell numbers and growth rates
Individual cells within colonies and cell clusters are not reliably recognized by current automated software using brightfield imaging. Instead, colonies and clusters are segmented as individual objects, and the areas of these objects provide a basis for estimating cell numbers. Doubling rates are calculated using linear regression of log transformed area-based cell numbers over time. Briefly, the slope of Log2(Cell Number) versus Time equals the doubling rate. As shown in this study, however, cell numbers do not correlate linearly will total cell area, and so doubling rates based upon an exponential growth model for area were called "area-doubling" rates.
Experimental design, normalization, and statistical analysis
A randomized complete block design  was used so that all informative factors (cell-line, compound, and dose) could be individually evaluated and separated from nuisance factors contributed by between-experiment variation and technical variability as evaluated between replicate wells within each experiment.
The behaviour of the cell velocities over time was analysed using 4-hour intervals and linear regression. First, velocity measurements were averaged for wells with the same cell line and treatment. Each data-point represents the average for 8 images (acquired every 30 minutes over 4-hour time intervals) from triplicate wells in each of 3 experiments. Second, a linear trend line was fitted to each profile. Finally the intercept (initial average velocity) and the slope (behaviour of average velocity over time) were compared across cell-line and treatment. The model fitting was done using SAS Proc Mixed. The significance of coefficients in these models is tested with student's t test. Overall tests for the equivalence of starting velocities are performed using the Chi-square test. Tests for equivalence of slopes are also performed. Pair-wise comparison with Bonferroni adjustment is also employed to see differences within each pair of treatments.
The dose-response of the cell-velocities was analysed within a 24-hour period. There was considerable variation between experiments as measured by the intra-class correlation (ICC), or ratio of variance from individual factors to the total variance . Therefore, prior to combining across experiments, all data for velocity and growth rates were normalized using an additive model based upon the difference between mock-coated plastic wells for each experiment. That is, the normalized measurements, Mn, were calculated from the original measurements, Mi, as follows: Mn = (Mi - Pi) + Pe, where Pe equalled the overall mean measurement for mock-coated wells for all experiments, and Pi equalled the individual means for mock-coated wells within experiments. Means were estimated using Tukey's biweight single-step M-estimator . The ICC for informative factors increased from 0.41 to 0.89, while that for the major nuisance factor, between-experiment variability, decreased from 0.58 to 0.09. The proportional contribution from technical variability (replication error) increased slightly from 0.005 to 0.011 due the decrease in overall variance after normalization.
We thank Julie Glowacki and Joel Greenberger for inspiration in the development of the automated system and in the performance of this study. We thank William Golding for assistance with statistical issues, Darrin Sabol for assistance with image processing, Yifang Song for manual cell counting, and Lori McKenzie and Kris Sachsenmeier for technical advice. The author thanks Sallie Boggs for seed ideas and John Wolf, Peter Friedl, and the anonymous reviewers for helpful comments on the manuscript. This investigation was supported by the National Institutes of Health grant number 1 RO1 EB 001051-01A2 from the National Institute of Biomedical Imaging and Bioengineering to R.K.H.
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