Long-term live imaging with LSFM allows detailed visualisation of dynamic processes in organoid morphogenesis and reveals high heterogeneity in single-cell and individual-organoid behaviour
To gain deeper insights into the dynamic cellular processes occurring within organoid systems, we developed Z1-FEP cuvette holders for live imaging with the Zeiss Lightsheet Z.1 microscope system (Additional file 3: Fig. S2). As previously described [16], ultra-thin FEP-foil cuvettes are sample holders for LSFM which preserve physiological culture conditions for organoid cultures and allow the acquisition of high-resolution images at a single-cell level. Using the Z1-FEP cuvette, we recorded the formation and development of hCCAOs expressing H2B-eGFP (nuclei marker) and LifeAct-mCherry (F-actin cytoskeleton marker) and mPOs expressing Rosa26-nTnG (nuclei marker) for up to 7 days. The medium was exchanged every 48 h to ensure sufficient nutrient supply. Temperature and CO2 levels were controlled to ensure optimal growth conditions (Additional file 4: Fig. S3, Additional file 5: Fig. S4). The setup enabled us to monitor dynamic processes at high temporal and spatial resolution in up to 120 organoids simultaneously contained in one Z1-FEP cuvette (in this example in a total volume of 5.2 mm3 of technically possible 8 mm3) (Additional file 6: Fig. S5a, Additional file 7: Fig. S6; Additional file 15: Video 1). The images acquired by LSFM allow for detailed qualitative inspections and detailed feature tracking of several dynamic cellular processes at single-cell resolution (Additional file 16: Video 2).
Visual inspection of the acquired data revealed that the initially seeded organoid cell clusters contract before the cells within the clusters start to rearrange and form spherical structures (Fig. 1, Formation). The cells within these spherical structures begin to polarise and form a lumen (in this example around 13.5 h), indicated by a stronger F-actin signal at the apical (luminal) side of the cell membranes. Potentially dead cells accumulate within the lumen, indicated by loss of the LifeAct-mCherry signal and by smaller nuclei with stronger H2B-eGFP signals, hinting towards apoptotic nuclear condensation [29]. The polarisation of cells in the epithelial monolayer is maintained during luminal expansion and is still clearly visible at later stages of organoid development (in this example around 41.0 h) (Fig. 1, Polarisation). We also observed size oscillations (Additional file 1: Definitions) during luminal expansion, where the organoid inflates and then suddenly collapses to about its initial size before it starts to expand again (Fig. 1, Size oscillation). The recording interval of 30 min also allows us to visually track single-cell division events (here: over a time course of 2.5 h) (Fig. 1, Cell division). We were also able to observe polarisation and cell division events in isolated single cells (Additional file 6: Fig. S5b), which remained dormant for relatively long periods during observation but eventually started to form organoids. We identified an overall shrinking of the organoid, nuclear condensation, and a fading nuclei signal to be hallmarks of organoid degeneration (Additional file 1: Definitions) (Fig. 1, Degeneration; Additional file 15: Video 1). This process is initiated upon extended culturing without further medium exchange (here: after about 100 h).
Additional file 15: Video 1. Time-resolved observations of epithelial organoids growing in Z1-FEP-cuvettes. hCCAOs expressing H2B-eGFP as nuclei marker (red) and LifeAct-mCherry as F-actin cytoskeletal marker (green) and mPOs expressing Rosa26-nTnG (grey) as nuclei marker were recorded over 10 h and 143 h respectively. The formation of organoids from the initially seeded cell clusters, including cell cluster contraction, cell polarisation, lumen formation and expansion can be followed. After about 100 h of observation some mPOs begin to display signs of degeneration due to extended culturing without further medium exchange. These signs of degeneration include an overall shrinking of the organoid, followed by nuclear condensation and fading of the nuclei signal. The temporal loss of signal during the acquisition happens due to evaporation and a subsequent constant loss of mounting medium in the imaging chamber. A manual refill re-established optimal acquisition conditions. The loss of the mounting medium does not alter the organoids within the cuvette since the cuvette separates the mounting medium from the organoid growth medium. Microscope: Zeiss Lightsheet Z.1; detection objective: W Plan-Apochromat 20x/1.0, illumination objective: Zeiss LSFM 10x/0.2; laser lines: 488 nm, 561 nm; filters: laser block filter (LBF) 405/488/561; voxel size: 1.02 × 1.02 × 2.00 μm3; recording interval: 30 min; scale bar: 50 μm. (MP4 10,289 kb)
Additional file 16: Video 2. Time-resolved 3D volume rendering of the formation process of an entire organoid culture observed within one Z1-FEP-cuvette. hCCAOs expressing H2B-eGFP as nuclei marker (red) and LifeAct-mCherry as F-actin cytoskeletal marker (green) were imaged for 5 days. The movie shows an excerpt of the first 10 h of the recorded data set. All organoids within the cuvette were segmented and tracked over these first 10 h of recording. The initial processes of cell cluster contraction, lumen formation and subsequent expansion are shown. Depending on the initial cell-cluster size, organoids differ in the time they need to establish a lumen. The changing colours indicate a newly segmented object at each time point. The segmentation and tracking serves only to visualise the behaviour of the organoids on a single cell level and is neither evaluated nor manually curated. Therefore, a segmented cell can disappear because of a mis-segmentation or the cell loses its signal upon cell death. Microscope: Zeiss Lightsheet Z.1; detection objective: W Plan-Apochromat 20x/1.0, illumination objective: Zeiss LSFM 10x/0.2; laser lines: 488 nm, 561 nm; filters: laser block filter (LBF) 405/488/561; voxel size: 1.02 × 1.02 × 2.00 μm3; recording interval: 30 min; 3D rendering and tracking software: Arivis Vision4D. (MP4 88,754 kb)
Image-based segmentation and three-dimensional (3D) volume rendering of the acquired data allow for even more detailed inspections of features observed in the highly dynamic organoid system. While most processes can already be followed in maximum intensity z-projections of the acquired image data, 3D volume rendering facilitates a more detailed understanding of the underlying cellular dynamics from different perspectives. We identified organoid fusion to be a frequent phenomenon in the investigated cultures (Fig. 2, Fusion; Additional file 17: Video 3). After the epithelial monolayers of both organoids touch each other, they initiate an opening connecting both lumens. This opening then expands while cells migrate into one connected monolayer. Similar dynamics of cells migrating into one connected monolayer were observed in the formation, subsequent retraction and eventual rupture of duct-like structures within the lumen of a large organoid (diameter ≥ 500 μm), which presumably emerged from fusion of multiple organoids (Additional file 1: Definitions) (Fig. 2, Luminal dynamics – lower panel; Additional file 18: Video 4, Additional file 19: Video 5). In other examples, single organoids show similar behaviours which can be described as luminal constriction, spontaneous “budding” or duct-like structure formation (Additional file 8: Fig. S7 and Additional file 9: Fig. S8). Volume rendering of cell nuclei revealed that small organoids (diameter at end of observation (48 h): 100 μm) with large nuclei (longest axis: 52 μm) show less cell divisions and overall less cell movement than larger organoids (diameter at end of observation (48 h): 180 μm) with smaller nuclei (longest axis: 32 μm) (Additional file 20: Video 6). This further underlines the heterogeneity in the investigated organoid systems.
Additional file 17: Video 3. Time-resolved 3D volume rendering of the fusion process of two organoids. hCCAOs expressing H2B-eGFP as nuclei marker (red) and LifeAct-mCherry as F-actin cytoskeletal marker (green) were recorded in a Z1-FEP-cuvette for 5 days. The movie shows an excerpt of the recorded data of 12 h spanning the fusion process of two organoids. The fusion process is visualised by 3D volume rendering of the data acquired for the cytoskeletal marker (LifeAct-mCherry – green). After the epithelial monolayers of both organoids touch, they begin to form an opening connecting both lumens within one hour. This opening then expands while cells migrate into one connected monolayer. Microscope: Zeiss Lightsheet Z.1; detection objective: W Plan-Apochromat 20x/1.0, illumination objective: Zeiss LSFM 10x/0.2; laser lines: 488 nm, 561 nm; filters: laser block filter (LBF) 405/488/561; voxel size: 1.02 × 1.02 × 2.00 μm3; recording interval: 30 min; 3D rendering software: Arivis Vision4D. (MP4 37,946 kb)
Additional file 18: Video 4. Time-resolved 3D volume rendering of intra-organoid luminal dynamics. hCCAOs expressing H2B-eGFP as nuclei marker (red) and LifeAct-mCherry as F-actin cytoskeletal marker (green) were recorded in a Z1-FEP-cuvette for a total of 132 h. The movie shows data recorded between 84 and 108 h. Luminal dynamics are visualised by 3D volume rendering of the data acquired for the cytoskeletal marker (LifeAct-mCherry – green) of a large organoid (diameter: ≥ 500 μm), presumably formed after fusion of multiple organoids. We can follow the formation, subsequent retraction and eventual rupture of duct-like structures within the organoid’s lumen. Microscope: Zeiss Lightsheet Z.1; detection objective: W Plan-Apochromat 20x/1.0, illumination objective: Zeiss LSFM 10x/0.2; laser lines: 488 nm, 561 nm; filters: laser block filter (LBF) 405/488/561; voxel size: 1.02 × 1.02 × 2.00 μm3; recording interval: 30 min; 3D rendering software: Arivis Vision4D.
Additional file 19: Video 5. Time-resolved 3D volume rendering of a growing liver organoid with cell segmentation and tracking. hCCAOs expressing H2B-eGFP as nuclei marker (red) and LifeAct-mCherry as F-actin cytoskeletal marker (green) were recorded in a Z1-FEP-cuvette for a total of 132 h. The movie shows data recorded between 84 and 108 h. Red spheres illustrate tracked cell nuclei and rainbow-coloured lines indicate the travelled tracks (colour code: red to blue – timepoint 84 to 108). Single as well as multiple organoid tracking is shown. Rotation as well as uni-directional cell movements are visible. Microscope: Zeiss Lightsheet Z.1; detection objective: W Plan-Apochromat 20x/1.0, illumination objective: Zeiss LSFM 10x/0.2; laser lines: 488 nm, 561 nm; filters: laser block filter (LBF) 405/488/561; voxel size: 1.02 × 1.02 × 2.00 μm3; recording interval: 30 min; 3D rendering and tracking software: Arivis Vision4D. (MP4 36,759 kb)
Additional file 20: Video 6. Alterations in rotation velocity of neighbouring organoids. Video shows two mPOs as an excerpt from an entire culture grown within one Z1-FEP-cuvette. The organoids expressed Rosa26-nTnG (grey) as nuclei marker and were imaged over 20 h. Besides the differences in nuclei size, both organoids display different behaviour. Cell tracking revealed a rotational motion of the epithelial cell monolayer of the organoid with the small roundish nuclei and no rotational motion of the organoid with the big, elongated cell nuclei. The two organoids are in close contact but do not fuse or interact with each other. Microscope: Zeiss Lightsheet Z.1; detection objective: W Plan-Apochromat 20x/1.0, illumination objective: Zeiss LSFM 10x/0.2; laser lines: 488 nm, 561 nm; filters: laser block filter (LBF) 405/488/561; voxel size: 1.02 × 1.02 × 2.00 μm3; recording interval: 30 min; 3D rendering and segmentation software: Arivis Vision4D. (MP4 61,855 kb)
The observed heterogenic dynamic processes in organoids and organoid systems were further visualised using feature tracking tools. Single-cell tracking revealed that the previously observed cell movement in larger organoids with smaller cell nuclei can be described as a uniform rotation of the epithelial cell monolayer (Fig. 2, Rotation; Additional file 18: Video 5, Additional file 20: Video 6). Furthermore, we observed that prior to organoid formation, some of the initially seeded cell clusters migrate through the ECM before they start to form a spherical structure (Fig. 2, Migration; Additional file 21: Video 7). In this example (Additional file 21: Video 7), the cell cluster travels at an average speed of 10 μm per hour (maximum speed: 23 μm per hour), covering a distance of about 250 μm in total. Additional examples of all described processes occurring in hCCAO and mPO cultures are displayed in Additional files 6-9: Figs. S5-S8.
Additional file 21: Video 7. Organoid cell cluster migration prior to organoid formation Video shows one mPO as an excerpt of an entire culture grown within one Z1-FEP-cuvette. The organoids expressed Rosa26-nTnG (grey) as nuclei marker and were imaged over 20 h. Prior to organoid formation, the initially seeded organoid cell cluster migrates through the ECM for about 25 h before the cells rearrange to form a spherical structure. The migrated distance is about 250 μm with an average speed of 10 μm (from green/minimum to red/maximum: 2.5 μm/h – 23 μm/h). Microscope: Zeiss Lightsheet Z.1; detection objective: W Plan-Apochromat 20x/1.0, illumination objective: Zeiss LSFM 10x/0.2; laser lines: 488 nm, 561 nm; filters: laser block filter (LBF) 405/488/561; voxel size: 1.02 × 1.02 × 2.00 μm3; recording interval: 30 min; 3D rendering and tracking software: Arivis Vision4D. (MP4 8503 kb)
Additional file 22: Video 8. Exemplary segmentation and tracking of the formation process of organoids. Video shows an mPO as an excerpt of an entire culture grown within one Z1-FEP-cuvette. The organoids expressed Rosa26-nTnG (grey) as nuclei marker. The movie shows an excerpt of the first 10 h a recorded data set of 6 days. The formation starts with a conglomeration of the cells towards one compact structure and ends with the establishment of a lumen. Each coloured dot represents one cell nucleus, but not each nucleus was tracked (lines). To ensure a proper segmentation and tracking higher resolved images need to be acquired, e.g. detection objectives with a higher magnification can be used. Microscope: Zeiss Lightsheet Z.1; detection objective: W Plan-Apochromat 20x/1.0, illumination objective: Zeiss LSFM 10x/0.2; laser lines: 488 nm, 561 nm; filters: laser block filter (LBF) 405/488/561; voxel size: 1.02 × 1.02 × 2.00 μm3; recording interval: 30 min; 3D rendering and tracking software: Arivis Vision4D. (MP4 11,909 kb)
Long-term single-cell analysis of pancreas-derived organoids reveals cell-to-cell heterogeneity in cell proliferation
Next, we aimed for a deeper quantitative analysis of the dynamic cellular processes in luminal expansion, specifically regarding the observed size oscillations. The collected high-resolution LSFM images enabled the semi-automatic segmentation and quantitative feature extraction over the course of a 6-day acquisition. This provided robust, time-resolved data on cell nuclei numbers, organoid volume, surface area, the number of neighbouring cells for each cell, and the cell density.
Using our previously published segmentation pipeline [16, 22], we processed one time-lapse dataset of an mPO culture, which resulted in a total number of 288 segmented time points. To evaluate the segmentation performance, we generated ground truth data sets to estimate the F score (0.74 to 0.83, Additional file 10: Fig. S9, Additional file 23: Table S2). From the segmented data, we chose to analyse three representative organoids. One small organoid (diameter < 400 μm), one large organoid (diameter > 400 μm), and one which was size-comparable to the large organoid but showed a higher cell number. The three mPOs expressed Rosa26-nTnG as a nuclei marker (Fig. 3).
We observed that in individual organoids, the number of cells increases at different rates even if they have similar initial cell numbers. We show that an organoid with an initial cell number of eight increases at a low rate (average: 0.65 cells per hour) and reaches a maximum number of 107 cells after 6 days, whereas an organoid starting with nine cells increases at a high rate (average: 7.41 cells per hour) and ends up with 1077 cells after 6 days (Fig. 3a, blue and green frames). Since the splitting procedure results in different sizes of cell clusters, we also analysed one organoid that started with 37 cells and reaches a total number of 644 after 6 days (average: 4.12 cells per hour) (Fig. 3a, red frames).
To further understand the heterogeneity in proliferation potential and the collective cell behaviour in general, we also quantified the volume and surface area of the organoid as well as the neighbourhood relationships of the single cells (Fig. 3b). We observed that the organoid with the largest final number of cells did not show the largest volume and surface area (final cell number: 1077, final volume: 10 × 107 voxels, final surface area: 24 × 103 pixels, Fig. 3b, green lines). In this organoid, the mean number of neighbouring cells was higher within the proximity cell graph (PCG), meaning that cells are neighbours if they are closer than a certain distance (distance: 50 pixels, final PCG-value: 35), in comparison to the organoid with the largest volume and surface area (final PCG-value: 19, final cell number: 644, final volume: 15 × 107 voxels, final surface area: 30 × 103 pixels, Fig. 3b, red lines). These findings correlate with different cell densities, displayed by the number of neighbouring cells within the Delaunay cell graph (DCG) of 26 and 21 respectively.
All three organoids showed frequent size oscillations (Fig. 4). Thus, we analysed the size oscillations based on the organoid volume (Fig. 4c shows an example of size oscillation in the segmented data). However, over the time course of 6 days, the small organoid (Fig. 4a, b, blue lines) showed seven oscillations, whereas the two larger organoids showed three (Fig. 4a, b, red lines) and two (Fig. 4a, b, green lines) events, respectively. Interestingly, we did not observe any correlation between the size oscillation events and the changes in cell number or number and distance of neighbouring cells. Further, we did not observe any size oscillation events in the first 80 h (within the 5% threshold) nor did we observe any synchronised oscillation behaviour between the organoids within one culture.
Scaling law derived from simplifying assumptions indicates a dependence of size oscillation events on cell division dynamics
To solve the mechanical principles underlying size oscillation events, we developed a mathematical model based on the following assumptions. Since organoids are spherical single-layer multicellular clusters, they are described by their volume V(t) and the number of superficial cells N(t) at time point t. We propose a functional relationship for an organoid’s increase in volume \( \dot{V}(t) \), which is derived from two processes: (a) The internal pressure of an organoid increases with time, due to an influx following the segregation of an osmotic active substance by the cells. (b) Due to mitosis, the cell number N(t) grows and the surface area A(t) increases (Fig. 1, Cell division).
We hypothesise that the increase of the cell number \( \dot{N}(t) \) can balance the increase in inner pressure of an organoid and prevent size oscillation events. In the following, we show that this requires the cell count N(t) to grow faster than or equal to N(t)~t2. In return, we expect the occurrence of size oscillations in the case where the cell number increases slower than N(t)~t2. Our estimation is based on the following relations and simplifying assumptions:
-
i.
Organoids form spheres with a volume of
$$ V=\frac{1}{6}\pi \times {d}^3 $$
and a surface area of
The relation between volume and surface area can be written as
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ii.
Every cell produces substances, which are secreted into the lumen of the organoid. We assume that the production rate is constant in time and the same for all cells, and therefore proportional to the number of superficial cells.
$$ \dot{n}(t)\sim N(t) $$
-
iii.
We further assume that the relation between secreted substance and osmotic pressure (Π) follows the van-‘t-Hoff law
$$ \Pi =c\times {i}_{vH}\times R\times T=\frac{n}{V}\times {i}_{vH}\times R\times T\sim \frac{n}{V} $$
-
iv.
Because of cell division, the surface area grows as a function of time, A = A(t). We neglect cell growth and assume that the cell count N(t) is proportional to the surface of the organoid, A(t).
-
v.
The total amount of the substance inside the lumen, n, is the accumulated substance produced during organoid growth, therefore
This gives us the relation
$$ \Pi \sim \frac{\int A(t)}{A{(t)}^{3/2}} $$
In order to avoid a rupture, the growth of the surface A(t) has to balance the resulting osmotic pressure Π arising from constant production of n by A. We can compute the functional form of A(t) which leads to a constant osmotic pressure Π. We require
$$ \frac{\int A(t)}{A{(t)}^{3/2}}=\mathrm{const}. $$
This relationship is fulfilled when A(t)~t2. This scaling law provides the following direct implications: A constant cell division rate causes the cell count to increase exponentially. Exponential growth is faster than quadratic; due to the theoretical considerations here we expect no rupture and subsequent size oscillation events. Some of the organoids, however, show a quasi-linear increase in cell numbers, which corresponds to a mitosis rate that is decreasing with 1/t. A linear increase is slower than t2; hence, in these organoids, we expect rupture and size oscillations.
In addition, we point out that the surface to volume ratio of a sphere changes with the radius, since the volume grows much faster than the surface. Since the osmotically active substance in the lumen is produced by the surface, this implies that smaller organoids reach a critical internal pressure earlier than large organoids.
Agent-based mathematical model captures the experimental organoid dynamics and confirms theoretical considerations
In order to confirm our hypotheses, we developed a mechanical 3D agent-based model for organoid size oscillations, based on the experimental data obtained by long-term single cell analysis of mPOs (Fig. 5a; Additional file 11: Fig. S10).
We hypothesise that the organoids can be represented as elastic spheres with a growing surface due to cell division (Fig. 5b). The agents represent single cells applying mechanical forces onto neighbouring cells. Concerning the mechanical properties of the cells, we used a general framework describing epithelial cell-cell interaction, which was previously used to resolve the underlying dynamics of lung cancer cell migration and local cell fate clustering in inner cell mass organoids [25, 30]. We hypothesise that the observed polarisation of the cells (Fig. 1) is maintaining the spherical shape of the organoids. Thus, a bending potential is added to the model. Based on the findings of Ruiz-Herrero et al. [24], we assume that the cells continuously secrete a substance into the lumen, which leads to an osmotic influx. This influx leads to an increase in the internal pressure which, however, can be balanced by an increase in volume. When the average distance of neighbouring cells exceeds a certain limit, the organoid shell ruptures, leading to a substantial outflow of liquid and deflation of the organoid. Following the law of parsimony, we consider the mechanical properties, cell size, and each cell’s contribution to the osmotic influx to be homogeneous for all organoids. In agreement with the data, cell division dynamics in the simulations differ between the organoids, but are also assumed homogeneous within the same organoid. Based on these assumptions, we derived that the organoid can balance the inner pressure when the cell count increases at least quadratically (Additional file 24: Supplementary theoretical considerations). Furthermore, for small organoids, the ratio between surface and volume is smaller than for large organoids. Therefore, small organoids should reach a critical pressure for leakage faster than large organoids. Thus, we expect the size oscillations to critically depend on (a) the cell division dynamics and (b) the organoid size. The latter (b) is confirmed by the data obtained through bright-field analysis (Fig. 6e).
The model is used to support the theoretical considerations and to qualitatively reproduce the size oscillations of the three analysed mPOs (Fig. 4a, b). Hereby, the cell division rate is directly extracted from the experimental data (Fig. 3b). Simulations of two large organoids do not show a size oscillation during phases of exponential cell number increase but start to oscillate after transitioning to a linear growth (Fig. 5c, d, green and red lines). Simulations with a small organoid exhibit size oscillation even during the initial exponential growth, which confirms our hypothesis that small organoids are more prone to rupture and deflation (Fig. 5c, d, blue lines; Fig. 6e).
Hence, the simulation results show a large qualitatively agreement in the size oscillations with the experimental data and also coincide with the analytical results.
Time-resolved macro- and mesoscale analysis reveals organoid-to-organoid heterogeneity as well as core regulatory principles
The processes observed using LSFM suggest a vast variety of complex dynamic processes in organoid cultures. In order to analyse the growth characteristics on a macroscale level and to confirm the predictions suggested by the computational model, we established a pipeline based on time-resolved bright-field observations. The analysis allows to characterise a culture’s global behaviour. Via semi-automated watershed-based segmentation, the pipeline allows for quantification of the projected luminal areas [mm2] over time of several organoids in parallel (Additional file 2: Fig. S1). Subsequently, from the normalised projected areas, the relative size increase is evaluated. Further, expansion phases (timing, slope, duration), size oscillation events (timing, slope, duration), and minimum and maximum projected luminal areas are identified for individual organoids (Fig. 6b).
In Fig. 6c, the projected areas of 34 pancreas organoids growing within one well are plotted over 48 h. The projected areas illustrate the high heterogeneity, with an area distribution widening over time. After 48 h of observation, the projected areas have a median of 0.1 mm2, while their interquartile range (IQR) ranges from 0.03 to 0.17 mm2.
Further, we demonstrate that the bright-field pipeline provides consistent and robust growth analysis data in technical replicates (Additional file 1: Definitions) (three wells, n = 34, 31, 35) (Fig. 6d). The median values of the normalised projected areas show no significant differences between the technical replicates (Kruskal-Wallis ANOVA).
The extracted features can further be used in downstream analyses to categorise organoid behaviour. We found that the size of an organoid is crucial for the number of oscillation events it displays. The bright-field analysis shows that over the observation period the organoids increase their projected area approximately to the six-fold area. Initially smaller organoids (area < 0.01 mm2) feature more size oscillation events, while initially larger organoids display less oscillation events (area > 0.01 mm2) (Fig. 6e). This coincides with the mathematical considerations that the surface to volume ratio is important for the oscillating behaviour of the organoids. To test whether the mathematical model can also reproduce this observation, we use the initial and final size of the organoids which are known from the experiments. Since no cell division dynamics are extracted from the bright-field pipeline, we assume for simplicity a linear increase in the cell numbers for all simulated organoids. In this setting, the model strongly agrees with the experimental data, reproducing the tendency that initially smaller organoids display an increased number of size oscillation events (Additional file 12: Fig. S11). Thus, the model confirms an influence of organoid size and growth onto the oscillation events. Besides that, the average expansion factor (a measure for expansion speed consistency) with a median average value of 0.11 is similar between organoids with various initial areas—50% of all values range between 0.09 and 0.14, while only 12% of the evaluated organoids are outliers with values above 0.22 (Fig. 6f). Further, the linear correlation between the initial area and the final area becomes apparent (R2 = 0.7445), which shows that the growth is independent of the initial area (Additional file 13: Fig. S12a). This indicates strong similarities in expansion speed consistency between individual organoids within one culture despite their (high) size heterogeneity.
Besides the already mentioned features, other extracted features facilitate the definition of quantitative reference parameters of organoid systems. By comparing the final area to the maximum area, for example, continuous growth of mPOs during the analysed time window is proven. A comparison of the initial area to the minimum area identifies size oscillation events or overall descending size progression within organoid cultures. In mPOs, the minimum area falls only slightly below the initial area, which can be associated with oscillation events (Additional file 13: Fig. S12c). Besides the average expansion factor, analysis of the maximum expansion factor indicates expansion speed variations within organoid cultures. As a variable factor, the maximum expansion can be used to compare different culture conditions (Additional file 13: Fig. S12b). An additional feature, which is likely to change upon differentiation or other perturbations (e.g. drug treatment), is the organoid circularity. In healthy mPOs, the circularity is 0.9 on average and the deviation around the average narrows over time (Additional file 13: Fig. S12e). In addition to the analysis of monocystic epithelial organoids like mPOs, our bright-field pipeline can also be used to analyse deviating organoid morphologies like polycystic hCCAOs (Additional file 14: Fig. S13a-f). Polycystic hCCAOs show an average circularity of 0.8 over the course of 48 h of observation (Additional file 14: Fig. S13b). Therefore, as a general culture feature, the circularity can serve as an additional quality control parameter.