The authors have declared that no competing interests exist.
Conceived and designed the experiments: KRM SGM. Performed the experiments: KRM RRN FX. Analyzed the data: KRM. Contributed reagents/materials/analysis tools: IAS. Wrote the paper: KRM SGM.
The quantification of cell shape, cell migration, and cell rearrangements is important for addressing classical questions in developmental biology such as patterning and tissue morphogenesis. Time-lapse microscopic imaging of transgenic embryos expressing fluorescent reporters is the method of choice for tracking morphogenetic changes and establishing cell lineages and fate maps
This is a
Pattern formation and tissue morphogenesis are two classical and unsolved problems in developmental biology. Patterning refers to the process by which the embryo generates the right kind of cells at the right place and time. Morphogenesis refers to how tissues are bent and molded to achieve the right shape and form. Modern systems-based approaches to understand these processes
In toto imaging generates large quantities of images depicting developmental dynamics in the embryo across space and time
Over the past decade, a number of automated methods were developed for
To address this need, we present a fully automated method with corresponding open-source, cross-platform software (ACME) to reconstruct weak membrane signals for achieving high-quality cell segmentations. We validated our algorithm using synthetically generated images for which ground-truth is known as well as with real images that were manually segmented by an expert. For generating synthetic data, we developed novel simulations of the image acquisition process replete with suitable noise models. Using simulated data, the performance of the algorithm was comprehensively evaluated against different noise conditions. To further demonstrate the utility of our method, we quantified cell shape and size, and the development of epithelial and mesenchymal characteristics in images of the zebrafish presomitic mesoderm. Our algorithm enabled us to quantify differences in the dynamics of cell sub-populations that correlate with the mesenchymal to epithelial differentiation process. Our methods are computationally-efficient, powerful, and widely-applicable to the quantitative analysis of cell dynamics during morphogenesis.
Two big challenges with membrane data are the presence of intensity inhomogeneities and punctuated gaps along the three-dimensional boundary. In
A single cell membrane is shown across (A)
In order to correct these two problems, we developed signal reconstruction techniques. Our algorithms are inspired by work on vessel-detection from MR and CT imagery in which Hessian-based filters were designed to detect vessels
Our method has three stages (
Using our preliminary work in
In a local coordinate reference frame placed at a membrane voxel, we are interested in identifying the neighborhood intensity distribution. There are three types of distribution shapes that can be detected: rod, plane and ball (
A symbolic illustration of a generic tensor represented in terms of basis tensors of type plane, rod and ball.
Structure |
|
A | B | S |
Foreground | - | - | - | high |
Plane |
|
0 | high | |
rod |
|
0 | 0 | high |
Ball |
|
high | ||
Background | - | - | - | low |
An overview of the local intensity structures determined by their eigen-system. Parameters
In order to detect membrane structures, we want to selectively identify pixels that belong to a plane distribution rather than a ball or a rod. Hence, we define the
Here,
A heat map of the sampled function
Earlier, we described how membranes have crisp or diffuse profiles depending on their orientation with respect to the optical planes (
The dot product of
In
Significant improvement in membrane signal quality is shown in XY, XZ and YZ planes. (A–D) Raw data showing dorsal view (anterior on top) of zebrafish neuroepithelium (ne) and notochord at 12 hpf, (E–H) Planarity function intermediate output and (I–L) Tensor voting final output. The last image in each panel shows a color-mapped zoomed view for easy comparison.
The principle of tensor voting is that image voxels vote in their surrounding neighborhood to propagate information about the presence of a surface passing through them
The application of tensor voting to membrane images has previously been considered. Loss and colleagues developed an iterative extension of the tensor voting framework to demonstrate its application on low fidelity
There are three stages of the tensor voting process: (i) initialize a tensor image, (ii) cast and accumulate votes at each voxel, and (iii) extract membrane saliency image.
First, a tensor image
In a local coordinate system at each voxel, there are three possible geometric structures that can pass through a voxel namely, a
In the above equation, a plane is encoded as the inner-product of its normal (
To construct a tensor image
Once the initial token image
The construction of a plane voting field describing the rotation is given in Supplementary
We earlier mentioned that the identified voxels in the planarity output belong to either spurious structures generated by noise or lie on
We use the watershed algorithm for obtaining high quality segmentations once the reconstruction procedure is completed
(A–C) Raw image data showing presomitic mesoderm on 2D image planes (XY,YZ, and XZ) at 3ss. (D–F) Segmentation meshes overlaid on reconstructed membrane images demonstrate excellent localization. Each mesh was randomly colored for visually separating adjacent cells easily. (G,H) 3D rendering of membrane segmentations at 3ss and 5ss. Somites 3, 4 and 5 at 5ss are formed from the presomitic tissue at 3ss by cell sorting and rearrangement.
In order to validate our segmentation results, we quantified segmentation accuracy on synthetic images where ground truth is known and on real images manually segmented by experts using four metrics: average volume overlap (Dice), average L2 Hausdorff distance, over-segmentation and under-segmentation rates. The Dice coefficient for measuring volume overlap between the automated results and the ground truth for a single cell is defined as:
(A–C) Synthesized cell structures in
In
Data | ( |
#Cells | U | O | M | Dice | Encroach | Prec. | Recall |
1 | (0.01, 1.0) | 1000 | 0 | 0 | 1000 | 0.99 | 0.25 | 1.0 | 1.0 |
2 | (0.02, 0.9) | 1000 | 0 | 0 | 1000 | 0.97 | 0.27 | 1.0 | 1.0 |
3 | (0.03, 0.8) | 1000 | 0 | 0 | 1000 | 0.94 | 0.35 | 1.0 | 1.0 |
4 | (0.04, 0.7) | 1005 | 0 | 5 | 1000 | 0.92 | 0.47 | 0.99 | 1.0 |
5 | (0.05, 0.6) | 1010 | 2 | 12 | 998 | 0.91 | 0.52 | 0.98 | 0.99 |
6 | (0.06, 0.5) | 1021 | 4 | 25 | 996 | 0.89 | 0.70 | 0.97 | 0.99 |
7 | (0.07, 0.4) | 1027 | 6 | 33 | 994 | 0.87 | 0.85 | 0.96 | 0.99 |
8 | (0.08, 0.3) | 1032 | 8 | 40 | 992 | 0.87 | 1.11 | 0.96 | 0.99 |
9 | (0.09, 0.2) | 1033 | 11 | 44 | 989 | 0.86 | 1.31 | 0.95 | 0.98 |
10 | (0.1, 0.1) | 1038 | 16 | 54 | 984 | 0.84 | 1.42 | 0.94 | 0.98 |
Algorithm performance was measured against ten synthetic datasets with progressively higher noise parameters (
Dataset | #Cells | Algorithm | O | U | M | Dice | Encroach | Precision | Recall |
1 | 6 | 9 | 37 | 0.88 | 0.45 | 0.63 | 0.71 | ||
1 | 52 | 2 | 3 | 4 | 45 | 0.91 | 0.39 | 0.81 | 0.86 |
3 | 2 | 2 | 48 | 0.93 | 0.21 | 0.88 | 0.92 | ||
1 | 8 | 7 | 43 | 0.90 | 0.37 | 0.65 | 0.74 | ||
2 | 58 | 2 | 4 | 3 | 51 | 0.92 | 0.41 | 0.82 | 0.87 |
3 | 4 | 2 | 53 | 0.94 | 0.28 | 0.89 | 0.91 | ||
1 | 7 | 8 | 47 | 0.87 | 0.52 | 0.68 | 0.75 | ||
3 | 62 | 2 | 4 | 3 | 55 | 0.90 | 0.47 | 0.83 | 0.88 |
3 | 2 | 2 | 58 | 0.91 | 0.31 | 0.90 | 0.93 | ||
1 | 10 | 12 | 42 | 0.91 | 0.42 | 0.56 | 0.65 | ||
4 | 64 | 2 | 7 | 5 | 52 | 0.91 | 0.41 | 0.73 | 0.81 |
3 | 3 | 2 | 59 | 0.95 | 0.29 | 0.88 | 0.92 | ||
13.06% | 13.48% | 0.89 | 0.44 | 0.63 | 0.71 | ||||
Average | 7.51% | 5.92% | 0.91 | 0.42 | 0.79 | 0.85 | |||
4.66% | 3.3% | 0.93 | 0.27 | 0.89 | 0.92 |
Automated algorithm performance was measured against manually-segmented membrane images of the zebrafish presomitic mesoderm from four different time-points. The proposed algorithm 3 recorded an average precision of 89%, average recall of 92%, average encroachment of 0.27
Since there is no gold standard available for evaluating algorithm performance, we synthesized
We next applied the method to images of zebrafish mesoderm obtained at 12 hpf (
watershed on intensity data directly,
watershed on planarity filtered data, and
watershed on planarity filtering and tensor voting.
In
The two scale parameters
Precision and recall measures are plotted against different settings of (A)
We also applied the method to three
Algorithm performance was assessed by matching automated segmentations obtained from the nuclear and membrane channels. In the ideal case, each individual nucleus would match with a unique membrane and vice-versa. (A) A single 2D image plane is shown with contours of membrane and nuclear segmentations overlaid on raw data. Some cells have their corresponding nuclei located out-of-plane. The lack of a one-to-one correspondence indicates an error. For example, an over-segmentation of the membrane channel (white arrow) causes one of the membrane components to not contain a nucleus. (B) 3D renderings of cells from membrane and nuclear segmentations.
Data | #Cells | #Nuclei | #Matched | #Unmatched Cells | #Unmatched Nuclei |
1 | 312 | 291 | 279 | 33 | 12 |
2 | 217 | 194 | 186 | 31 | 8 |
3 | 241 | 228 | 219 | 22 | 9 |
Detection and error rates of the automated algorithm was compared with standard nuclear segmentation algorithms. The assumption was that perfect segmentations of both algorithms should theoretically establish a one-to-one correspondence between nuclei and membranes detected.
During zebrafish somitogenesis, a series of epithelial tissue blocks forms rhythmically by separating from the presomitic mesoderm tissue (PSM)
Therefore, our goal was to obtain time-lapse membrane images during somite formation, apply our reconstruction techniques, and quantify cell dynamics. We chose to
Retrospective cell tracing of epithelial (yellow) and mesenchymal (red) cells from formed somites at (B) 5ss back to the presomitic mesoderm at (A) 3ss. (C) Corresponding decrease in somite tissue surface area during the formation of somites 3, 4, and 5. (D) Epithelial and mesenchymal cell numbers in respective somites at 5ss. (E,F) Three-dimensional cell shape quantified by the length of their principal axes at 3ss and 5ss. (G,H) Scatter plots of elongation (
In order to understand the corresponding changes in cell parameters, we then identified the number of epithelial and mesenchymal cells in the formed somites. Mesenchymal cells which do not touch the surface of the somite were a small fraction (
Our work successfully demonstrates the utility of our algorithms in enabling the quantification of cell shape and size, tissue interface areas and volumes, and reconstruction of cell lineages and fate maps by tracking segmented cells. By recovering individual cell dynamics and their collective behavior in tissue from time-lapse images, a deeper understanding of the mechanisms involved in morphogenesis can be obtained. Thus, our algorithms are computationally robust and can be deployed to facilitate the analysis of a wide-variety of morphogenesis systems.
Our method has several advantages over previous approaches. The first major advantage of the method is the ability to robustly segment tightly-packed cells without relying on their absolute fluorescence levels. Since we detect membranes based on local shape information computed from second derivatives of the image intensity function, the absolute values are not important. This is very relevant for time-lapse imaging data because membrane-tagged fluorophores can photobleach. With our method, it will be possible to segment cells and track them for a longer developmental time-window using only the membrane channel. The second major advantage is that our technique deals with intensity inhomogeneities that occur in membrane surfaces due to their orientation with respect to the imaging planes. Our method can easily be extended to using nuclear information when available as seed-points for the watershed that will further reduce the amount of over and under-segmentations. Conversely, the reconstructed and localized membranes can also be used to refine nuclear segmentations. Currently the method is implemented in C/C++ language and uses The Insight Toolkit (ITK) libraries (
In conclusion, our software enables the efficient and accurate quantification of cell shape, size, and position from large time-lapse images in an automated manner. We believe that this work is immensely useful to research aimed at understanding individual and collective cell behavior using high-resolution microscopy, especially in the context of tissue morphogenesis and organ formation.
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We thank members of Megason lab for comments and support, Mr. Dante D'India for fish care, and Dr. Arnaud Gelas, Mr. Nicolas Rannou, and Ms. Lydie Souhait for technical advice and help with GoFigure2 software. We thank Ms. Suzanne Mosaliganti for proof-reading and editing the manuscript.