Cell culture

Plasmodium falciparum laboratory strains are cultivated according to standard protocols [23] under shaking conditions during cultivation. By enrichment in a Ficoll-gradient solution or through enrichment with monoclonal antibodies (mAbs) [23] the rosetting phenotype is maintained.

Image acquisition and analysis

Software

With the goal of creating a free, stand-alone application MATLAB ^® is chosen as the underlying software framework. The collection of scripts that make up ARAM is then compiled and accessible as executable file. This allows ARAM to run without a MATLAB ^® installation. The basic concept in detecting objects on the images is to separate them from the background. Therefore, an algorithm transforms the image into a binary map of the original, where pixels that are part of the cell object are white, and background pixels are black. There are different methods to identify objects. In default mode ARAM works with a derivation-based algorithm to detect parasitaemia, rosetting rate and rosette size distribution from micrographs with fluorescent pRBC. A second operation mode is included which can use an additional threshold based algorithm to detect size distribution and location of arbitrary objects, such as nano-particles or vesicles. During development of the software a third background based algorithm for object identification was created but is not implemented in ARAM: as this algorithm utilizes the most apparent procedure it is described in the following paragraph to explain why it does not meet the requirements of an automated detection method.

Background-based algorithm

To separate cell objects from the background this algorithm creates a background-only version of the analysed image by line wise fitting of intensity values, that is subtracted from the original image. To account for non-conformity of illumination in typical micrographs the algorithm applies two threshold operations near the mean intensity of the image to isolate the background. Areas that do not meet the threshold range are filled with the mean intensity value. The resulting matrix is line wise fitted with a polynomial to create a smooth background-only image that includes non-uniform illumination. The algorithm subtracts this new background-version from the original image leaving a black background and lighter cells (as shown in Additional file 1: Figure S1). For highly non-uniform backgrounds the algorithm is slowed down due to the great number of necessary polynomial fits.

Threshold-based algorithm

For very uniformly lit backgrounds and high contrast between objects and background a threshold-based algorithm delivers the best object detection results. Therefore, every pixel of the grey value image is compared to a threshold value: pixels with higher intensity are displayed white, pixels with lower intensity are displayed black. The analysis part of the algorithm then searches the resulting binary image for the detected objects. An example for this algorithm is shown in the Additional file 2: Figure S2. ARAM optionally uses this algorithm in the object counting mode but not in the default mode as the background is lighter than the cells but darker than the pRBC, which would need two threshold operations simultaneously.

Gradient based algorithm

This algorithm detects object contours in an image through the local derivation of neighboring pixel values. Therefore, RGB-colored micrographs are transformed to 8-bit grey value images. As the standard edge detection procedure the algorithm uses the Prewitt filter with the Prewitt operator as the kernel of this filter. This operator determines the gradient in x-direction and y-direction of the image. With the original image A the vertical and horizontal operators are

$${\mathbf{G}}_{x} = \left[ {\begin{array}{*{20}c} { - 1} & 0 & {{ + }1} \\ { - 1} & 0 & {{ + }1} \\ { - 1} & 0 & {{ + }1} \\ \end{array} } \right]*{\mathbf{A}} ,$$

(3)

$${\mathbf{G}}_{y} = \left[ {\begin{array}{*{20}c} { + 1} & { + 1} & { + 1} \\ 0 & 0 & 0 \\ { - 1} & 1 & { - 1} \\ \end{array} } \right]*{\mathbf{A}}$$

The operation * represents the 2D convolution of kernel k (the matrix in Eq. 3) and image A. Because the matrices are not continuous functions the discrete formulation of a 2D convolution is utilized:

$$\begin{aligned}{\mathbf{G}}_{i} \,\left( {x,y} \right) &= {\mathbf{k}}_{i} \,\left( {m,n} \right) \otimes {\mathbf{A}}\,\left( {x,y} \right)\\&=\sum_{m = - 1}^{1} \sum_{n = - 1}^{1} {\mathbf{k}}_{i} \;\left( {m,n} \right){\mathbf{A }}\;(x - m,y - n) \nonumber\end{aligned}$$

(4)

For every pixel the algorithm calculates the gradient magnitude from both contributions in Eq. (3) as

$${\mathbf{G}} = \sqrt {{\mathbf{G}}_{x}^{2} + {\mathbf{G}}_{y}^{2} }$$

(5)

The result is a matrix of derivative approximations for every pixel, where a threshold filter creates binary entries from the calculated magnitude values. The background is now black (0) and the found edges white (1). In Fig. 1(b) a typical result is shown. Detected edges are marked as points and stripes with a width of one pixel. A dilation of these white structures in horizontal and vertical direction, as depicted in Fig. 1c, connect the whole cell boundary (adjustable in the configuration file expansion factor for cell detection; default value: 5). In Fig. 2, the process is schematically displayed for a single point and for multiple lines. To fill enclosed areas within the cell wall outline the algorithm uses the MATLAB ^® function imfill. The so detected and marked cell areas are bigger than indicated by the edge detection filter. A correction is applied by an erosion filter with a diamond-shaped structuring element of tunable size (adjustable in the configuration file factor for adjusting dilation in cell detection; default value: 2). This filter skims white pixels on the 2D-surface of the areas. The resulting detected objects render the cells in the original image, as shown clearly in Fig. 1f.

The advantages of this algorithm are the ability to handle a wide range of object shapes, sizes and structure without the need for an image dependent pre-processing. For images with pronounced noise a blur- or smooth-preprocessing step helps to avoid erroneous edge-detections. Since ARAM is intended to be fast, applicable to all kinds of images without significant preprocessing and without the operator input the gradient-based algorithm is used for detecting cell objects on micrographs as default detection algorithm in both above named operation modes.

Detecting parasitized RBC and rosettes

To assure the quality of the results ARAM performs an error analysis. Uncertainties in the analysis are small compared to the influence of statistical deviations in e.g. cell size. Since a few microscope images with a small amount of cell objects do not represent the entire population of cells and cell size distribution in the sample a statistical approach is necessary. This way it is possible to quantify the impact of non-uniform cell and rosette distribution throughout the specimen. Additionally, the software does not have algorithm induced errors and detects 100 % of objects and observables in ideal images. A measurement or algorithm error would depend on the analysed image series and is hard to quantify. Therefore, ARAM calculates error margins ε for a given confidence probability.

Validation of ARAM

To characterize ARAM’s capability to analyse parasitaemia, rosetting rate and rosette sizes in comparison to manual analysis, 100 images are taken from a specimen and analysed by independent operators (in Figs. 4, 5 shown as operator 1–3) as well as the software. Values for RBC and pRBC detected by ARAM are similar to the manually acquired results, shown in Fig. 4. Results for parasitaemia show significant agreement with the manual analysis, as is also confirmed by the Bland–Altman test (see Additional file 3: Figure S3). The error bars mark the statistical error which display the 90 % confidence intervals of the measures and overlap with the manually obtained results. ARAM detects a parasitaemia of 4.81 % whereas the operators count 4.75, 4.98 and 4.75 %. The statistical error is about 0.63 % each time. For the rosetting rate in Fig. 4 ARAM and the operator’s results are akin (ARAM 58.70 ± 6.70 %; operators 63.09, 59.03, 63.51 %). The rosette sizes are in good accordance within ARAM’s error range, although slightly larger deviations can be seen. The operators determine the mean rosette size as 3.87, 3.47 and 4.09 while ARAM gets 3.65 with an interquartile range of 1.39. The comparison of determined rosette size is not as obvious as the above mentioned measures due to technical reasons: ARAM only detects a two dimensional projection of the 3D object, like described above which leads to a less accurate calculation of rosette size than the calculation for the rosetting rate. Overall, the uncertainties are dominated by the statistical error in all cases here. For instance, to decrease the confidence interval to half of its width a sample size of about 12,500 RBC would be necessary, independent of the determination mode (manual or automated).

Application of ARAM: rosette inhibition study

As an example for the application of ARAM, a study of the inhibitory effect of heparin on rosetting rate and size is performed. Three different heparin concentrations are chosen. Each sample is analysed by manual counting in the microscope, manual counting from the images (50 images each) and ARAM analysis (same 50 images each) to compare the results. Heparin interacts with the surface expressed P. falciparum erythrocyte membrane protein 1 (PfEMP1) competing out the receptor on the RBC involved in the formation of rosettes. This leads to the disruption of already formed rosettes or inhibiting rosette formation [25, 26]. The detected parasitaemia is independent on heparin concentration within the confidence intervals, as can be seen in Fig. 5. The values are 6.21 ± 0.68, 7.84 ± 1.04 and 6.74 ± 0.88 %. The rosette rate is decreasing with increasing inhibitor concentration as analysed with any of the three methods, see Fig. 5 top right part. The differences between automatic and manual analysis of the images are much smaller than between manual image analysis and manual analysis directly performed with the microscope, probably due to the inhomogeneous distribution of RBC, pRBC and rosettes throughout the slide. By performing the analysis on a greater amount of samples this deviation is reduced, but without automation this is a time consuming task. The mean rosette size is greater for the specimen without inhibitor and so is the interquartile range of the rosette size distribution. The heparin treated specimens show smaller rosettes with a more narrow size distribution. The rosette size distribution (projection area) is depicted in the lower right part of Fig. 5. The trend of each measurement can be described by a rapidly decreasing function towards greater rosette size (positive x-axis). Additionally, a higher inhibitor concentration reduces the size of rosettes.

To the authors’ knowledge, currently there are no reports on rosette size distribution within in vivo or in vitro studies. Hence, the basic form of such a distribution is estimated with a simple model (see Additional file 4: Supplementary information). As argued, it is plausible to assume a Gaussian distribution of rosette size in terms of volume as indicated in Fig. 3 bottom bar chart. It is important to note that with the definition in Eq. 6 this Gaussian distribution is cut at the left side when there are non-zero values for rosette sizes smaller than the threshold. Since there are no studies about rosette size distribution, ARAM for the first time offers an easy way to analyse those and determine the amount of rosette objects necessary to get reliable and quantitative results of this highly important measure.

Error analysis

Above the necessity of utilizing a statistical error is described. In Fig. 6 the impact of sample size on the results is exemplarily demonstrated. On the x-axis the count of analysed RBC is shown. The groups of measurement values correspond to the amount of RBC found on 5, 10, 20, 50 and 100 images. Obviously the width of the confidence interval and hence the statistical uncertainty of the experiment is reduced with increasing sample size for parasitaemia as well as rosetting rate. Especially for rare effects this dependency will be much more pronounced. With ARAM it is possible to gather such very rare effects, as it can realize a statistically significant amount of measurements with the necessary uniformity. Otherwise these effects can be simply rare or hidden in the measurement uncertainties. In order to get reliable conclusions, the amount of analysed RBC or images has to be large enough that rare effects are analysed in sufficient extend. ARAM offers the option to calculate the amount of images for desired confidence probabilities and width of confidence intervals from measured rosetting rate, number of analysed rosette objects and images. Assuming e.g. a value of interest v = 0.01 one would need 270 measurements to get ε = 0.01. And to get a reliable result with ε = 0.0023 a minimum of 5000 images has to be analysed.

Image requirements

One major convenience of ARAM is the simplicity of performing an analysis: in a standard analysis the algorithm does not need additional input. Nevertheless, to ensure this simple operation the images have to meet some specifications. There obviously is a limitation for high cell density and low contrast. For the edge detection via Prewitt-filtering there needs to be a sufficient difference between the grey value of background and cell wall pixels and edges should not be blurred. For the detection of the pRBC, the fluorescence needs to be bright enough and clearly visible compared to the image background. To identify a cell cluster from the first analysis step (object detection with Prewitt-filter) as a rosette there has to be a detected pRBC and at least two RBC within the cluster. The size cut-off value m (see Eq. 6) can be adjusted in the configuration file. This might be necessary when rosettes appear too small and are therefore not detected.

The possibility to save the analysed images with rosettes and detected RBC marked, allows easy verification of the results by the operator and readjustment of the analysis with help of the configuration-file. The text export transferring and saving of the calculated values makes data collection easy and time-saving. Additional scripts could read those text files and create automated plots if desired.

The most important preparation parameter is the cell density on the micrographs. Hence, one has to account for a suitable haematocrit: if cells are too close to a cluster but not part of it they may be mistakenly detected as part of the rosette. To reduce this error the cell dilution of the specimen has to be chosen accordingly as illustrated in Fig. 7. Here the cell density is so high that non-bound RBC are in contact, leading to problems in single cell identification. This implies the intrinsic limitation of the presented algorithm.

Above-mentioned published software [17, 19, 21, 22] calculate parasitaemia from images, while [19] claim to additionally determine the parasites stage. ARAM not only calculates parasitaemia but also gives the statistical error to estimate the quality of the results. Beyond that ARAM is the only available software solution to analyse rosetting rate and rosette size distributions. The easy usage of ARAM is supported by its independence from other software, its graphical user interface and its results-text-export functionality, features the other solutions do not include. With these abilities ARAM is the only software suitable for laboratory work-flows to automatically analyse and characterize parasitaemia and rosetting in malaria infected specimens.