A hybrid blob-slice model for accurate and efficient detection of fluorescence labeled nuclei in 3D

Abstract

Background: To exploit the flood of data from advances in high throughput imaging of optically sectioned nuclei, image analysis methods need to correctly detect thousands of nuclei, ideally in real time. Variability in nuclear appearance and undersampled volumetric data make this a challenge.

Results: We present a novel 3D nuclear identification method, which subdivides the problem, first segmenting nuclear slices within each 2D image plane, then using a shape model to assemble these slices into 3D nuclei. This hybrid 2D/3D approach allows accurate accounting for nuclear shape but exploits the clear 2D nuclear boundaries that are present in sectional slices to avoid the computational burden of fitting a complex shape model to volume data. When tested over C. elegans, Drosophila, zebrafish and mouse data, our method yielded 0 to 3.7% error, up to six times more accurate as well as being 30 times faster than published performances. We demonstrate our method's potential by reconstructing the morphogenesis of the C. elegans pharynx. This is an important and much studied developmental process that could not previously be followed at this single cell level of detail.

Conclusions: Because our approach is specialized for the characteristics of optically sectioned nuclear images, it can achieve superior accuracy in significantly less time than other approaches. Both of these characteristics are necessary for practical analysis of overwhelmingly large data sets where processing must be scalable to hundreds of thousands of cells and where the time cost of manual error correction makes it impossible to use data with high error rates. Our approach is fast, accurate, available as open source software and its learned shape model is easy to retrain. As our pharynx development example shows, these characteristics make single cell analysis relatively easy and will enable novel experimental methods utilizing complex data sets.

Figure 1

Slice extraction and nuclear definition. a. An x,y plane through C. elegans volume data at the ~350 cell stage. b. the corresponding slice through the 3D DoG filtered volume. c. Slices are segmented by casting out rays in search of a zero crossing. The 2D intensity maxima where rays originate are marked as black dots. Final end points of search rays are marked as blue dots. These points define a polygonal slice; multiple slices can be assembled together to yield a 3D nuclear boundary. d. Nuclear shape definition. The position, intensity, and size of each slice that might be part of a nucleus are measured relative to the nuclear center, and also relative to the closest slice between the possible member and the nuclear center. These measurements make up the 7D vector that represents a slice and nucleus center pairing. Actual nuclear extraction starts from the center and in turn considers the likelihood of each slice as an endpoint for the nucleus.

Figure 2

Flowchart overview of the algorithm. Boxes represent major elements of the algorithm and arrows the flow of data between them.

Figure 3

Test Data. A representative plane of test sets and corresponding slice segmentation (see Figure 1 for C. elegans example plane). a. early Drosophila (stage 8, ~4 hpf) b. late Drosophila (stage 11, ~7 hpf) c. early zebrafish (~3 hpf) d. late zebrafish (~18 hpf) e. mouse ~E7.75

Figure 4

Nuclear separation as a predictor of performance. Nuclear separation is calculated as the average distance between the computed boundary of a nucleus and the boundary of its nearest neighbor, based on the bounding circle of the largest slice. This distance is expressed in units of slice spacing, the distance between successive z planes. Averages are displayed; error variability between data sets was typically 1-2 mistakes.

Figure 5

Reconstruction of C. elegans pharynx development. I. Assembly of the primordium. MSaa and MSpa lineages are in cyan. On the right side ABaraaap (and then its anterior daughter) is in red, ABarapaa in pink, ABarapap in yellow and ABaraapp in blue. On the left side, the symmetric sublineages are shown in the same colors but are marked by arrows, with ABalpaap (and then its anterior daughter) in red, ABalpaaa in pink, ABalpapp in yellow and ABaraapa in blue. White in frame a represents ABaraaaa, which gives rise to two L/R symmetric sublineages (in magenta in frame b and c) as well as a pair of cells one of which undergoes apoptosis and the other of which forms the third fold of symmetry for part of that sublineage (white in frame b and c). Grey represents a non-pharyngeal precursor, ABalpapa which interrupts the left side group at birth (frame a) but is excluded during subsequent development. For all frames in this figure, the non highlighted cells are shown as semi-transparent spheres. In frame a, at time 160, left-right symmetric precursor cells have been born but are not symmetric in their layout. Note the midline marked by the two rows of MS/cyan cells. MS cells have just started to enter the inside of the embryo. The blue cell that is part of the left side is born on the right side of the midline but will cross over to join the other left side cells. In frame b, time 207, the AB pharynx cells have moved to the midline to cover the MS cells. The blue cell of the left group has crossed the midline to assume a symmetrical position as its right counterpart. However, the pink cells of the left group are still disconnected from the yellow cells compared to the right side. The grey non-pharyngeal cells are now excluded from the primordium. In frame c, time 250, the left and right AB groups are fully assembled and symmetrical. II. The inflation of the primordium. To illustrate the topological mapping of the primordium to the mature pharynx, cells are colored as follows: white for buccal cavity, red for the corpus/anterior lobe, blue for the posterior lobe and purple for precursors whose descendents contribute to both lobes. The E/gut cells are shown in green for context. Frame a shows the primordium prior to inflation, where cells are arranged in two flat sheets that are left-right symmetric. In Frame b the sheets have begun to round slightly. In c they have rearranged to create a rounded shape, and the ventral MS portion of the pharynx moved anterior to the E cells. III. The emergence of threefold symmetry. Pharyngeal right side terminal cells (and their precursors) are in blue, those on the left are in red. Terminal cells and precursors are white if they, or their descendents, have no L/R counterpart. These cells make up the third component of the final threefold lumen symmetry. IV. Frame a shows the correspondence between pharynx cells whose lineages are annotated as left right symmetric with a line. A left view, angled slightly posterior-dorsal y, highlights the consistent alignment. Frame b, the position of cells at ~340 min pfc. Frames a and b use the same color scheme as in I with the addition of the E/gut cells in green. Frame c shows the final configuration of the pharynx colored as in II.