Users perform the analysis using the app step-by-step. An instruction manual, a detailed definition of all outcomes and an example analysis can be found in the GitHub repository [19]. The output of the app is saved in the same folder as the input images and consists of several images saved as PNGs in different steps of the analysis, as well as an Excel file with separate tabs for each step of the analysis. All output files are named after the input images, with a suffix specifying which function produced the output. The analysis is modular, meaning that each step can be revisited without having to redo all prior steps, and that some steps can be skipped or performed at a later stage.

Before analysis, an image set consisting of JPEG or PNG images must be selected. There are three channels available: blue is used for Hoechst (nuclei), red for MyHC protein (myotubes), and, optionally, green can be used to label nuclei which are positive for a certain marker (i.e., MYOD, a myoblast transcription factor, in this case).

The “Adjust levels” function makes use of an intensity windowing operation on the image histogram [20]. The histogram of each image can be adjusted to make the structures in the images visible, increase contrast, and decrease background staining (Fig. 1). This allows a reduction in exposure time and thereby avoids bleaching the cells during imaging. An input intensity range is specified by the user, and the pixels in this range are spread out over the whole possible intensity range of the image (e.g., 0–1). Adjusted images are saved as PNG files, which are used in all further steps of the analysis. Repeated use of the function will overwrite the previous adjusted image.

Adjusting image levels and mask editing. The upper panel shows the input, output and controls of the “Adjust levels” function. The lower panel shows the input, output and controls of the “Edit mask” function. The user first makes a rough mask (B) of the adjusted image (A) using regular thresholding. The rough mask is then edited using the editing functions to produce a mask ready for analysis (C)

The “Edit mask” function has been implemented to make a binary image that indicates which parts of the red channel are myotubes and which are not. Segmenting the image is done manually using a threshold, as the pixel intensity depends on the varying expression levels of the protein and on the equipment and settings used for imaging. The resulting binary image can be edited using the various editing tools [1] and is preferential for a correct analysis. Areas can be drawn on the image to add/remove parts of myotubes, lines can be drawn to separate/join myotubes, and junk (white objects < 1000 pixels) can be removed and holes (sets of black pixels that do not touch the image border) can be filled. The mask is saved as a PNG file, where every separate myotube is indicated in a different color. This manual mask editing is crucial for indicating separate myotubes and consequently assessing all parameters using the following functions.

The “Indicate nuclei” function provides initial indications for the nuclei centers, based on the centroids of objects segmented from the blue channel (nuclear staining by Hoechst, Fig. 2), and asks the user to input which pixel size is applied in all analyses, allowing the use of images made with different microscopes and magnifications. This segmentation uses a circular filter with a radius close to that of an average nucleus as a starting point for watershed segmentation [21], which provides the objects used for the initial centroid indication. Average nucleus diameter was determined based on the distance transform [22] and regular watershed segmentation on loose nuclei in the image sets. Averaging the small and large diameter of the mostly ellipse-shaped objects obtained in this way and scaling them for the applied pixel size resulted in an average nucleus diameter of around 10 μm. Adding or removing centroids in the program is possible through the available editing functions, both on the single blue (Hoechst) channel image and the image combining the blue and red (MyHC) channel. The mask created in the previous function allows for the marking of nuclei inside MyHC-positive myotubes, so that the fusion index can be calculated and manually adjusted as previously mentioned. The green channel image (if selected) is also segmented using a fixed intensity threshold, and the program indicates the nuclei inside the resulting mask as positive for the used marker (Fig. 3). The fusion index and other statistics (total number of nuclei, number of nuclei in myotubes, total number of marked nuclei, number of marked nuclei in myotubes) are saved to an Excel output file, along with the coordinates of all individual nuclei.

Nucleus indication. The upper panel shows both the original input image, as well as the “adjusted” image in the blue channel (nuclear staining using Hoechst). The lower panel shows editing controls, statistics panel and output of the “Nuclei indication” function. Nuclei are indicated with yellow asterisks and with red asterisks if they are positive for the marker in the green channel (due to the MyoD staining in this case). The right image does not show nuclei outside of the mask, meaning outside of the myotubes (based on MyHC, red channel). Centroids can be added or removed with the editing functions, using either the left or the right image as a guide

Nucleus clustering. Output of the “Cluster nuclei” function. Nuclei centroids receive a color based on their cluster assignment, with red (− 1) indicating nuclei centroids that do not belong to a particular cluster. Myosin heavy chain expression is shown in red

The “Cluster nuclei” function aims to quantify the clustering features of the nuclei. The function uses the coordinates of the nuclei obtained in the previous function to cluster the nuclei (Fig. 3) and subsequently perform a trendline analysis on the detected clusters. The trendline is calculated using orthogonal regression, and the RMSE resulting from this calculation is used as a measure for linearity. A nucleus cluster was arbitrarily defined as a group of at least four nuclei, and clustering is performed by an agglomerative hierarchical clustering algorithm [23]. The clustering algorithm starts out by considering each nucleus as a separate cluster and looking for the two closest clusters, i.e., those that have the shortest distance between two of their elements. The algorithm then merges these clusters and repeats until the shortest distance between two clusters goes above a fixed threshold. This threshold is set by adding the nucleus diameter and the largest allowed edge-to-edge distance between nuclei. In this study, the value was set at 14 μm, allowing a maximum distance of 4 μm between the edge of a nucleus in an existing cluster and the edge of a nucleus to be added to said cluster. Edge-to-edge distance between nuclei inside a cluster can be higher, as long as one other nucleus is within this maximum distance. The maximum allowed distance, as well as the nucleus diameter, can be changed before running the clustering algorithm. The descriptive parameters of the clusters and the regression outputs are saved to a separate tab in the Excel output file. The plot of the clusters shown in 3 is saved as a PNG file and includes a color legend to visualize all clusters separately, with red indicating nuclei that do not belong to a particular cluster (labelled “ − 1”).

The “Branching points” function provides an initial indication for the branching points in the myotubes, based on branching points in the myotube skeleton obtained using the built-in MATLAB function “bwskel” (Fig. 4). Branching points can be added or removed using the editing functions. The “Branching points” function also has the option to do diameter measurements. Points for measurement are indicated on a separate image containing the distance transform of the mask. The values of the transformed pixels contain the distance to the closest black pixel, meaning that a pixel in the middle of a myotube contains the myotube radius at that point. The user can select a set of pixels, and for each pixel, the value of the closest pixel that belongs to the myotube skeleton is doubled to obtain an estimate of the diameter. Using the pixels of the myotube skeleton gives the best possible estimate of the diameter, while also eliminating errors due to imprecise selection. Point selection is important, since the distance will no longer be measured perpendicular to the length of the myotube in the presence of myotube intersections and some myotube features, as illustrated in Fig. 5. Descriptive parameters (number of branching points, myotube coverage, number of myotubes, points per myotube), branching point coordinates, and diameter measurements are saved to separate tabs in the Excel output file. The image used for diameter measurements and a version of the mask with labels for separate myotubes are saved as separate PNG files (Fig. 6).

Branching points. Editing functions, statistics panel and output of the 'Branching points' function. Branching points are marked with a green circle, and can be removed or added using the editing functions. The myotube skeleton is shown in white on the left image and in black on the right image. Myosin heavy chain is shown in red, nuclear staining Hoechst in blue

Diameter measurements. Example of diameter measurement point sampling on a myosin heavy chain mask. The calculated myotube diameter (double of the radius) at different sampling points (blue) is shown for poor sampling points (red) and good sampling points (green). The radius of the myotube as calculated by the distance transform is shown using a brighter color

The protocol for muscle microbiopsy collection, as well as the procedures for cell culture, immunofluorescent staining, and imaging were previously described [6]. The satellite cells were extracted from microbiopsy samples of the Medial Gastrocnemius muscle from five patients with CP and three age-matched TD children, all aged between 4 and 9 years (mean age TD: 5.51 ± 1.46 years, CP: 7.88 ± 0.99 years). All included patients were diagnosed with spastic bilateral cerebral palsy and Gross Motor Function Classification System levels II or III. Therefore, by keeping the same conditions previously described, this study is based on human satellite cell differentiation, seeded at 60 000 cells/cm2 and fixed with 4% of paraformaldehyde (Eastman Kodak) at day 6. Immunofluorescent images were obtained using an Eclipse Ti microscope (Nikon), representative for the well. Nuclei were captured in blue, using Hoechst (1:3000, Thermofisher Scientific) and myotubes in red, using an anti-myosin heavy chain antibody (MyHC, mouse, 1:20, Hybridoma Bank). All analyses performed with the app were carried out following the guidelines described in Additional file 1.

A dataset comprised of 19 image sets, each consisting of immunofluorescent staining images for nuclei (using Hoechst) and myotubes (MyHC), was used to test the feasibility of the novel app and to define the inter-rater reliability and the known-group validity for a series of outcome parameters related to nucleus and myotube properties. The inter-rater reliability was defined using intra-class correlation coefficients (ICCs) and standard errors of measurement (SEMs). Six image sets were obtained from satellite cells of TD samples and 13 from CP samples. Subdividing the dataset in this way allowed a power of > 90% for ICCs higher than ~ 0.6 when considering the whole dataset and ICCs higher than 0.7 when considering only CP samples [24]. The CP dataset was more extended, since lower ICCs were expected due to patient heterogeneity. All image sets were analyzed by two cell biologists, specialized in cell culture analysis, using the newly developed Myotube Analyzer. To define inter-rater reliability, ICCs, SEMs, and the corresponding confidence intervals were calculated using a custom MATLAB script with the formulas provided in [25,26,27]. The minimal detectable differences (MDDs) were calculated as \(\mathrm*1.96*\sqrt\) [28]. The known-group validity was defined by comparing outcome parameters from children with CP to TD data. For each group, the median and inter-quartile range was defined. To test whether the hypothesized differences between TD and CP were quantified by the novel nucleus and myotube parameters, measurements from one analyzer were used to compare between-group differences using an unpaired two-tailed t-test. Statistical analyses were performed in JMP (SAS), with a significance level of 95%. In figures, the symbol “*” indicates a p value less than 0.05, “**” indicates p < 0.01, and “***” indicates p < 0.001. For each parameter, we also checked whether the observed significant differences exceeded the MDDs. An average difference that was larger than the MDD for a particular parameter indicated that the difference between TD and CP should be detectable in at least 95% of cases (when using an equal sample size). If not, the difference may not be large enough to distinguish from inter-rater variance, and will be detected in less than 95% of cases. An average difference that was smaller than the SEM indicates that it would be nearly indistinguishable from inter-rater variance. To comprehensively describe the features and potential added value of the semi-automatic approach of the Myotube Analyzer tool, we also explored its agreement with a fully manual approach for the parameters fusion index, number of clusters, myotubes, and nuclei. This inter-method analysis was performed on the same dataset of 19 images that was used to define the inter-rater reliability and was also based on the reliability indices ICC and SEM. For this inter-method analysis, the fully manual and the semi-automatic approach was always performed by the same rater.

Table 1 contains an overview of the definitions of each outcome parameter. All parameter calculations were implemented in the Myotube Analyzer. RMSE values and myotube coverage were also investigated for all individual clusters and myotubes, respectively.