FoCo: a simple and robust quantification algorithm of nuclear foci

To study the dynamics of the DNA damage response in MRC-5 primary human lung fibroblasts
we performed ?H2AX foci quantification on images obtained with a confocal laser scanning
microscope (see Implementation Section). The image set contained pictures of non-irradiated
cells at time points 1, 24, 72, 168 h after experiment start and images of cells after
a dose of 2.5 and 10 Gy IR at time points 1, 3, 6, 24, 72, 168 h after irradiation.
For each considered time point we analyzed from 3 to 9 images corresponding to about
100 cell nuclei. Refer to Additional file 5 for example images used in this study.

Automatic foci quantifications

We automatically quantified foci using the freely available software CellProfiler
16] and ImageJ 21], which were found to be the most promising in a recent study 20]. We described the optimization of parameter values for CellProfiler and ImageJ in
Additional file 1: sections S5, S6 and demonstrated foci detection on images in Additional file 1: Figure S8. An outlier analysis of obtained datasets revealed a presence of a few
outliers, which were removed from all calculations presented in this section (Additional
file 1: section S7).

Results of ?H2AX foci quantification in CellProfiler and ImageJ are represented in
Fig. 3a–c for cells after 10 Gy, 2.5 Gy IR and non-irradiated cells, respectively. According
to quantifications with ImageJ the mean foci number per nucleus is clearly higher
compared to quantifications with CellProfiler for all considered time points. In order
to explain observed differences we analyzed foci counting algorithms in ImageJ and
CellProfiler.

Fig. 3. Results of automatic ?H2AX foci quantification for images of MRC-5 cells from confocal
laser-scanning microscope. Quantifications were performed in ImageJ, CellProfiler
and FoCo. Image analysis of cells after 10 Gy irradiation (a) after 2.5 Gy irradiation (b) and control non-irradiated cells (c). Dots designate mean foci number per nucleus for considered time points after experiment
start. Error bars designate standard error of the mean (SEM) (n???100)

ImageJ defines foci as local maxima in the intensity matrix of the foci image corrected
for a constant threshold. This is a simple method, which utilizes only one parameter
for foci detection, i.e., the threshold value (‘Noise tolerance’). However, the algorithm
does not take into account the variation of the background signal neither within the
foci image nor between foci images. Therefore, this can lead to either overestimation
or underestimation of foci numbers depending on the threshold value and the background
intensity, which may change within or among images and nuclei (Additional file 1: Figure S8E).

In comparison, CellProfiler utilizes image processing modules for enhancing foci signal
over background and subsequent thresholding of the foci image. However, thresholding
alone without analysis of local or regional maxima may lead to clumping of potential
foci and underestimation of foci number (Additional file 1: Figure S8D). In addition, we found it cumbersome to use CellProfiler, because of
the many parameters the user has to adjust.

Thus, after comparing foci quantification results and analyzing foci counting algorithms
in ImageJ and CellProfiler we decided to create our own foci quantification approach
FoCo. FoCo aims to overcome limitations of CellProfiler and ImageJ such as i) poor
performance on images with low signal/noise ratio; ii) poor performance on images
with varying background; iii) difficulty to use.

We applied FoCo to count foci in images, which we used for foci quantification in
CellProfiler and ImageJ. The optimization of FoCo parameter values is presented in
the Additional file 1: section S3. In Additional file 1: Figures S7, S8C we demonstrated foci detection in FoCo on representative images.
As for ImageJ and CellProfiler, foci quantification results in FoCo were subjected
to outlier analysis (Additional file 1: section S7).

Figure 3 shows that quantification results in FoCo are located between quantification results
of CellProfiler and ImageJ at time points 1 and 3 h for irradiated cells. For later
time points quantification results from FoCo coincide or are located close to quantification
results from CellProfiler. Additionally, quantification results from FoCo are located
close to quantification results from CellProfiler for all time points for non-irradiated
cells.

According to quantification results in FoCo the mean foci number per nucleus is monotonically
decreasing in time 1 h after DNA damage for both 2.5 Gy and 10 Gy time series. This
corresponds well to previous studies of ?H2AX dynamics after irradiation 19], 23]. In contrast, quantifications in ImageJ show that the mean foci number per nucleus
has a transient peak 6 h after both 2.5 and 10 Gy. Quantifications in CellProfiler
demonstrate a transient plateau 6 h after 2.5 Gy. These non-consistent quantification
for ImageJ and CellProfiler are probably because of changes in foci composition and
increased background signal for the 6 h time point. Whereas CellProfiler underestimates
earlier time points because of densely distributed foci and only starts to deliver
reliable quantification after 3 h, ImageJ overestimates the 6 h quantification, because
of the increased background signal.

Benchmarking automatic foci quantifications

Manual quantifications

Performing automatic foci quantification by different methods we observed significant
difference in quantification results. Therefore, we questioned how automatic foci
quantifications would correlate with manual quantifications.

Manual foci count is time consuming and often criticized for being operator-biased.
Nevertheless, manual foci count is still considered to be the gold standard and is
regularly used as a benchmark to validate the performance of automatic methods 12]–14]. Here, to minimize the operator bias and to define an objective benchmark, we considered
manual foci counts from three independent operators to which the results of the automatic
methods were compared (see Additional file 1: Figure S12 and sections S8, S9).

For manual foci counting we created a subset of 16 representative images. This test
image set contained one image of control cells for each time point 1, 24, 72, 168 h
and one or two images of cells post 2.5 Gy and 10 Gy IR for each time point 1, 3,
6, 24, 72, 168 h, respectively. Then the test image set was quantified manually by
three independent operators and compared to the respective quantifications with FoCo,
CellProfiler and ImageJ. Note that for the automatic quantification of the test image
set we used the same parameters as for processing of the whole image set. The obtained
quantification results were subjected to statistical analysis. Detailed results of
automatic and manual foci quantifications for the test image set and details of statistical
analysis are located in Additional file 1: sections S8, S9. According to the orthogonal regression and rank correlation analysis,
foci quantifications with FoCo demonstrated better correlation with the three manual
quantifications than ImageJ and CellProfiler (Additional file 1: Tables S1, S2).

Quantification of simulated images

Statistical analysis of manual and automatic foci quantifications favored FoCo over
considered automatic methods. However, results of manual quantifications showed a
high variability in quantification results at time points 1–6 h after 2.5 and 10 Gy
IR. Shortly after irradiation foci are densely located and have a small size. This
complicates distinguishing between foci and background and between foci located close
to each other. This may result in observed variability in manual quantifications.
For that reason, manual counting seems to be a poor benchmark for automatic analysis
of our images at time points1-6 h after 2.5 and 10 Gy IR.

To this end, we decided to create an additional benchmark using artificial foci images
with the pre-defined number of foci. Since all considered automatic approaches detected
approximately the same number of cell nuclei (see Additional file 1: Table S3) and eventually average foci over the number of nuclei, we omitted simulation
of nuclei images and focused on simulated foci images. We assumed that every simulated
grayscale foci image corresponds to one nucleus.

For simulating artificial foci images we analyzed the foci and background structure
of images obtained 1 h after 10 Gy IR and foci images of non-irradiated cells (representative
foci images are depicted in Fig. 4a, b, respectively). As a result we created a range of focus templates representing a)
single foci having different size and shapes (Additional file 1: Figure S14A-D, G, H) and b) two foci located close to each other (Additional file
1: Figure S14E, F). For simulating a single cell foci image we sampled foci templates,
randomly put them on the empty image and added both homogeneous (background) and inhomogeneous
noise. The program for simulating images saves the coordinates of placed foci and
marks them by blue frames (Additional file 1: Figure S15A). This helps the user to distinguish between actual foci and background
and perform benchmarking of automatic foci quantifications (Additional file 1: Figure S15B-D). In this section, blue frames are not visualized to avoid image overloading.
For details of simulating foci images refer to the Additional file 1: section S10.

Fig. 4. Simulation of artificial foci images with pre-defined number of foci. a Foci image of a cell 1 h after 10 Gy irradiation. b Foci image of a non-irradiated cell. c Representative simulated foci image with 62 foci (Irradiated in panel (e)). d Representative simulated foci image with 6 foci (Control in panel (e)). e Comparison between pre-defined foci numbers and automatic quantification results.
The closer RelDiff₁
to 0, the more precise are the quantification result obtained by the automatic method.
f–h Demonstration of quantification results in FoCo, CellProfiler and ImageJ, respectively,
applied to the representative image in panel C. i–k Demonstration of quantification results in FoCo, CellProfiler and ImageJ applied
to the representative image in panel (d), respectively. Red frames, boundaries and circles designate detected foci in FoCo,
CellProfiler and ImageJ, respectively. White arrows designate representative foci,
which were either not split by the software or wrongly detected

We simulated two image sets:

“irradiated” – image set of 50 images mimicking foci images of irradiated cells and
containing between 57and 69 foci per image. The representative image with 62 foci
is depicted in Fig. 4c.

“control” – image set of 50 images mimicking foci images of control cells and containing
between 5 and 8 foci per image. The representative image with 6 foci is depicted in
Fig. 4d.

Further, we subjected simulated images to the automatic analysis in FoCo, ImageJ and
CellProfiler. Parameter values needed for automatic foci counting were optimized according
to parameter optimization algorithms presented in Additional file 1: sections S3-S6. We compared obtained quantification results with pre-defined foci
numbers using the relative difference RelDiff₁
:

Where N _Ref
is a pre-defined reference mean foci number per image and N _Auto
is a mean foci number per image obtained by an automatic method. A positive/negative
value of RelDiff₁
indicates an overestimation/ underestimation of the simulated foci number. The closer
RelDiff₁
to 0, the more precise are the quantification results obtained by the respective automatic
method.

For FoCo RelDiff₁
is about 10 % for the control image set and is about ?10 % for the irradiated image
set (Fig. 4e). Thus, FoCo slightly underestimates the foci number for the irradiated image set
and slightly overestimates the foci number for the control image set (Fig. 4f, i). For CellProfiler RelDiff₁
is close to 0 for the control image set and is about ?33 % for the irradiated image
set. Thus, CellProfiler demonstrates precise quantification results for the control
image set, whereas it strongly underestimates quantification results for the irradiated
image set (see Fig. 4g, j). ImageJ has RelDiff₁
about 53 % and about 23 % for control and irradiated image sets, respectively. Thus,
ImageJ strongly overestimates the number of simulated foci for both control and irradiated
image sets (Fig. 4h, k).

To summarize, in comparison to CellProfiler and ImageJ, quantification results in
FoCo vary from the reference value less than 10 % for both irradiated and control
image sets indicating the reliability of quantifications. We provide the source code
for simulating foci images (Additional file 6) for independent validation and as a basis for comparison of future algorithms. The
CellProfiler pipeline, which was used for analyzing simulated images, can be found
in Additional file 7. The representative simulated images depicted in Fig. 4c, d can be found in Additional file 8.

Robustness analysis of automatic foci quantifications

To test the robustness of the automatic foci count methods with respect to signal/niose
ratio, we artificially blurred high-quality images to different extend, re-quantified
foci and compared results.

To this end, we selected two images of neighboring focal planes from a z-stack image
of MRC-5 cells 1 h after 10 Gy irradiation obtained with a confocal laser-scanning
microscope. We considered one of images as a base image. The second image we called
the neighbor image. We used the neighbor image to create an artificial out-of-focus
background signal for the base image, which would be similar to the background signal
produced by wide-field fluorescent microscope. For that purpose, we split the neighbor
image on channels and blurred the green component, which corresponds to foci signal.
Blurring was performed in Matlab using circular averaging filter of radius f?=?1, 2, 3, 4, 5 and 6 pixels: the higher the value of radius f, the higher blur-effect. Then, we added the obtained blurred green component of the
neighbor image to the green component of the base image. In such way, we mimicked
the effect of foci signal leaking from the neighboring focal plane into the base focal
plane. The same procedure we applied to the z-stack image of MRC-5 cells 6 h after
10 Gy IR obtained on confocal laser-scanning microscope.

Figure 5a demonstrates representative nuclei from base and neighbor images of cells 1 and 6 h
after 10 Gy irradiation along with resulted images of nuclei with artificial out-of-focus
background signal obtained for filter radius f?=?1 and f?=?6 pixels, respectively. Note that the larger the blur-effect, the less the neighbor
signal influences the base signal, but the higher the background.

Fig. 5. Analysis of images with artificial out-of-focus background signal. a Representative nuclei from base und neighbour images of cells 1 and 6 h after 10 Gy
IR and corresponding base images with additional artificial out-of-focus background
signal for two different strengths of blur-effect (f?=?1, 6). b Relative differences RelDiff ₂
for images of cells 1 and 6 h after 10 Gy IR. Quantifications were performed in ImageJ,
CellProfiler and FoCo. The lower RelDiff ₂
, the more robust is the method in sense of suppressing out-of-focus background signal

Afterwards, base images and images with the artificial out-of-focus background signal
were subjected to the automatic foci count in FoCo, ImageJ and CellProfiler. Note
that for processing of these images we used the same parameter values that we used
for processing of the whole image set from the previous section.

Finally, as the measure of robustness, we quantified a relative difference RelDiff₂
:

where N _Base
and N _Art
are mean foci numbers per nucleus on the base image and on the base image with the
artificial out-of-focus background signal, respectively. Thus, the lower the relative
difference RelDiff₂
, the more robust is the quantification method in sense of suppressing out-of-focus
background signal.

As illustrated on Fig. 5b, RelDiff₂
in FoCo varies maximally 7.5 % for both test images and all filter radii. In comparison,
RelDiff₂
in ImageJ is approximately 1.5 times higher than in FoCo in all instances. For CellProfiler
RelDiff₂
varies up to 73 %.

This analysis shows that in comparison with CellProfiler and ImageJ foci quantifications
in FoCo are robust and insensitive to increased out-of-focus background signal. This
implies that FoCo is able to produce reliable foci quantification results not only
for images obtained on confocal laser-scanning fluorescent microscope, but also for
images obtained on conventional wide-field fluorescent microscopes or, generally,
on images with low signal/noise ratio.

Validation of robustness of foci quantifications in FoCo

To further explore the robustness of foci quantification with FoCo, we counted foci
per nucleus on images of cells at 1, 3, 6, 24, and 72 h after 10 Gy IR that were obtained
using both a wide-field and a confocal laser scanning microscope. Quantifications
and parameter optimization were conducted as above using around 100 nuclei per time
point (see Fig. 6).

Fig. 6. ?H2AX foci quantifications in FoCo for images from confocal laser-scanning and wide-field
fluorescent microscopes. Quantifications were performed for images of MRC-5 cells
non-irradiated and after 10 Gy irradiation. Dots designate mean foci number per nucleus
for considered time points after experiment start. Error bars designate standard error
of the mean (SEM) (n???100)

Despite different image qualities (see Additional file 1: Figure S7, S8 and Figure S10) quantification results of both image sets do not substantially
differ. One hour after 10 Gy irradiation the mean foci number per nucleus differs
by 2.4 foci. For all other time points quantification differ less than 1.3 foci. The
difference for control cells is less than 0.8 foci. Thus, FoCo delivers highly consistent
foci counts for varying image qualities and signal/noise ratios.