Figure 1. Block diagram of the simulation algorithm.
Stage 1. Defining population objects. The first stage in the process of simulating luminescent images of cellular systems is the determination of all the objects constituting the system. For each of the subpopulations the objects and relationships between them must be set. Each cell organelle must be linked with a specific cell or its nucleus, which in practice is achieved by directly specifying an anchor of the object. The definition of each cell or its objects shape using a parametric model with polygons also takes place at this stage.
Stage 2. Defining markers. The appearance of the generated shapes is determined by a set of markers for each object. This approach helps to create a texture and visual representation of the cell as a collection of various transformations applied to the basic marker of the cellular object.
Stage 3. Population location. Location of cells within the simulated image of the cellular population may be uniform random, but in real life cells are much more likely to be grouped in clusters. Assigned to the cluster cells will be located near the predetermined cluster centers, while other objects will be evenly distributed over the rest of the space.
Stage 4. Defining overlapping rules. Once all the parameters of the cellular system subpopulations are defined it is necessary to determine the interaction between these subpopulations. For this purpose a number of overlapping rules between the objects are defined. Overlaps can occur between the same objects at the object level of one and the same or different subpopulations.
Stage 5. Merging populations. The stage of merging populations is transparent to a user and does not require direct involvement. After determining all the objects of the cell population their placement in the final image takes place.
Stage 6. Measurement system errors. This is the final step for the entire modelling process. Imposition of distortions introduced by the measurement system and the environment is held at this stage. The output of this stage is a generated resulting image of the cell population with all possible errors taken into consideration.
Software that allows generating fluorescent images of microbiological objects was obtained as a result of realization of an appropriate simulation algorithm. Figure 2 shows some examples of the obtained images.
Visual similarity of experimental and generated synthetic images is not enough to ensure adequacy of the developed simulation model and its compliance with real experimental images. That is why numerical comparison of the available experimental images of cancer tumors and reproduced synthetic images was drawn.
Figure 2. Simulated synthetic images.
The analysis of the intensity histograms of the affected cells nuclei on simulated and experimental images in three colour channels was conducted. The results showed similarity of the images intensity. The χ2 goodness of fit was used to verify the quality of modelling and showed that the values did not exceed critical values of χ2 at a significance level of 0.95 indicating that the statistical conditions of χ2 were satisfied.
Moreover, the equivalent radii of nuclei on the experimental image were compared with those on the simulated synthetic image. The χ2 goodness of fit was used again for the objects distribution histogram according to the value of their equivalent radii to check their conformity with the laws of distribution. The calculation of χ2 values for 19 degrees of freedom gave 9.61 which was less than the critical value of χ2 equal to 10.1 at a significance level of 0.95.
During the process of cancer tumor cells modelling several simulation parameters varied. This provided an opportunity to examine how the simulated image changed depending on the errors of the measurement system. Measurement system illumination, optical aberrations that lead to blurring of registered objects, uneven labelling by fluorophores and photomultiplier noise were chosen as variable parameters. Thus, changing some simulation parameters allows reaching a wide variety of modelled images, which plays a very important role due to a great amount of possible experimental conditions.
As a result of simulation model practical realization the software package called CellPainter was implemented for simulating fluorescent images of microbiological objects. This package includes the simulation algorithm itself, as well as a graphical user interface that makes it possible to greatly simplify the software application (Figure 3).
CellPainter provides two different types of interface. The first type of interface is designed to work with a numerical description of the model parameters (mode User 1), while the second type of interface allows users to select values of the model parameters in accordance with the submitted sample (mode User 2). However, the range of options when working in user mode 2 is limited and covers only the most important stages of modelling.
