Elastic volume reconstruction from series of ultra-thin microscopy sections

Abstract

Anatomy of large biological specimens is often reconstructed from serially sectioned volumes imaged by high-resolution microscopy. We developed a method to reassemble a continuous volume from such large section series that explicitly minimizes artificial deformation by applying a global elastic constraint. We demonstrate our method on a series of transmission electron microscopy sections covering the entire 558-cell Caenorhabditis elegans embryo and a segment of the Drosophila melanogaster larval ventral nerve cord.

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Figure 1: The elastic alignment method.
Figure 2: Reconstruction of two exemplary TEM section series.
Figure 3: Comparison of the reconstructed shapes of neuronal arbors using rigid series alignment and our elastic method.

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Acknowledgements

We thank C. Bargmann at Rockefeller University for making the C. elegans data available and F. Collman, N. Weiler, K. Micheva and S. Smith at Stanford University for sharing the exemplary array tomography data set; T. Pietzsch for insightful discussion of algorithmic details; S. Grill for helpful comments on the manuscript; and D. Berger and I. Arganda for inspiration on regularized affine series alignment. S.S. and P.T. were funded by the Max Planck Institute of Molecular Cell Biology and Genetics, Dresden. R.F. is supported by the Howard Hughes Medical Institute. A.C. was funded by the Institute of Neuroinformatics, the University of Zurich and ETH Zurich. A.C. thanks J. Simpson and the Visitor Program at the Howard Hughes Medical Institute, Janelia Farm.

Author information

S.S. and A.C. conceived the research and analyzed the data. S.S. designed the algorithms and wrote the software. R.F. and A.C. collected image data. A.C. reconstructed neuronal arbors. S.S. and P.T. wrote the paper with input from the coauthors.

Correspondence to Albert Cardona or Pavel Tomancak.

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Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–16, Supplementary Table 1 and Supplementary Note (PDF 8720 kb)

Supplementary Video 1

Visualization of the behavior of spring meshes during elastic alignment. The movie shows the iterative relaxation of the spring-particle system for five exemplary serial sections from the C. elegans series. Sections were prealigned rigidly such that all section spring meshes start from the same initial position. Zero-length cross-section springs connect all vertices to their corresponding location in other sections (except for those where no match could be found by block matching). Springs are displayed as lines with their color reflecting the relative stress applied. The color ranges from green (fully relaxed) to red (maximally stressed) and is scaled relative to the maximum stress present in the system. Initially, all intra-section mesh springs are green and all cross-section springs are maximally stressed. After relaxation, stresses are distributed throughout the system. Cross-section springs have contracted and the series is warped into alignment. (MOV 4258 kb)

Supplementary Video 2

Evaluation series A. The series consists of 400 sections of 2,000 × 2,000 pixels each; all sections show the same artificially generated image. The original series has been deformed nonlinearly and then aligned using a rigid or affine model per section (rigid, affine) and using our elastic method (elastic). (MOV 43899 kb)

Supplementary Video 3

Evaluation series B. The series consists of 400 sections from an artificially generated volume of 2,000 × 2,000 × 800 pixels. The section thickness is 2 pixels. The original series has been deformed nonlinearly and then aligned using a rigid or affine model per section (rigid, affine) and using our elastic method (elastic). (MOV 46551 kb)

Supplementary Video 4

Walkthrough of the rigidly aligned C. elegans series. The movie shows in each frame a single section from the rigidly aligned TEM section series of a C. elegans three-fold stage embryo at four different zoom levels (A–D, where B shows the close-up of the blue rectangle–bounded area in A, etc.). The scale bars in each panel are 4 μm (A), 2 μm (B), 1 μm (C) and 0.5 μm (D). The lateral resolution of the raw data is 4 nm per pixel. The number in the upper right corner indicates the section index. Note the significant nonlinear distortion remaining in the rigidly aligned series. A high-resolution version of the movie can be downloaded from http://fly.mpi-cbg.de/elastic/. (MOV 77963 kb)

Supplementary Video 5

Walkthrough of the rigidly aligned C. elegans series orthogonally re-sliced. The movie shows in each frame a single computationally generated section, orthogonal to the physical sectioning plane, through the rigidly aligned TEM section series of a C. elegans three-fold stage embryo. Sections were down-sampled such that their lateral resolution matches the section thickness of 50 nm per pixel. Accordingly, orthogonal sections are generated at a step size of 50 nm. The number in the upper right corner indicates the virtual section index. Two different zoom levels are shown (A,B), where B corresponds to the blue rectangle in A. The scale bars in the panels are 5 μm (A) and 2 μm (B). Note the strong nonlinear distortion remaining in the rigidly aligned series that effectively prevents identification of biologically relevant features in the axial direction. A high-resolution version of the movie can be downloaded from http://fly.mpi-cbg.de/elastic/. (MOV 19798 kb)

Supplementary Video 6

Walkthrough of the elastically aligned C. elegans series. The movie shows in each frame a single section from the elastically aligned TEM section series of a C. elegans three-fold stage embryo at four different zoom levels (A–D, where B shows the close-up of the blue rectangle–bounded area in A, etc.). The scale bars in each panel are 4 μm (A), 2 μm (B), 1 μm (C) and 0.5 μm (D). The lateral resolution of the raw data is 4 nm per pixel. The number in the upper right corner indicates the section index. Note the noticeable improvement in the amount of nonlinear distortion remaining in the elastically aligned series compared to the rigidly aligned series (Supplementary Video 4). A high-resolution version of the movie can be downloaded from http://fly.mpi-cbg.de/elastic/. The data can be interactively browsed in CATMAID at http://fly.mpi-cbg.de/c-elegans. (MOV 77909 kb)

Supplementary Video 7

Walkthrough of the elastically aligned C. elegans series orthogonally re-sliced. The movie shows in each frame a single computationally generated section, orthogonal to the physical sectioning plane, through the elastically aligned TEM section series of a C. elegans three-fold stage embryo. Sections were down-sampled such that their lateral resolution matches the section thickness of 50 nm per pixel. Accordingly, orthogonal sections are generated at a step size of 50 nm. The number in the upper right corner indicates the virtual section index. Two different zoom levels are shown (A,B), where B corresponds to the blue rectangle in A. The scale bars in the panels are 5 μm (A) and 2 μm (B). Note that the data have a familiar TEM appearance in the axial direction owing to the near-complete removal of nonlinear distortion by the elastic alignment method. A high-resolution version of the movie can be downloaded from http://fly.mpi-cbg.de/elastic/. (MOV 18111 kb)

Supplementary Video 8

Walkthrough of the rigidly aligned Drosophila series. The movie shows in each frame a single section from the rigidly aligned TEM section series, imaged as mosaic of overlapping tiles, of the D. melanogaster first-instar larval ventral nerve cord at four different zoom levels (A–D, where B shows the close-up of the blue rectangle-bounded area in A, etc.). The scale bars in each panel are 10 μm (A), 3 μm (B), 1 μm (C) and 0.5 μm (D). The lateral resolution of the raw data is 4 nm per pixel. The number in the upper right corner indicates the section index. Note the significant nonlinear distortion remaining in the rigidly aligned data. A high-resolution version of the movie can be downloaded from http://fly.mpi-cbg.de/elastic/. (MOV 44871 kb)

Supplementary Video 9

Walkthrough of the rigidly aligned Drosophila series orthogonally re-sliced. The movie shows in each frame a single computationally generated section, orthogonal to the physical sectioning plane, through the rigidly aligned TEM section series of the D. melanogaster first-instar larval ventral nerve cord imaged as mosaic of overlapping tiles. Sections were down-sampled such that their lateral resolution matches the section thickness of 45 nm per pixel. Accordingly, orthogonal sections are generated at a step size of 45 nm. The number in the upper right corner indicates the virtual section index. Two different zoom levels are shown (A,B), where B corresponds to the blue rectangle in A. The scale bars in the panels are 5 μm (A) and 3 μm (B). The lateral resolution of the raw data is equal to the section thickness that is 45 nm per pixel. Note the strong nonlinear distortion remaining in the rigidly aligned data that effectively prevents identification of biologically relevant features in the axial direction. A high-resolution version of the movie can be downloaded from http://fly.mpi-cbg.de/elastic/. (MOV 158925 kb)

Supplementary Video 10

Walkthrough of the elastically aligned Drosophila series. The movie shows in each frame a single section from the elastically aligned TEM section series, imaged as mosaic of overlapping tiles, of the D. melanogaster first-instar larval ventral nerve cord at four different zoom levels (A–D, where B shows the close-up of the blue rectangle-bounded area in A, etc.). The scale bars in each panel are 10 μm (A), 3 μm (B), 1 μm (C) and 0.5 μm (D). The lateral resolution of the raw data is 4 nm per pixel. The number in the upper right corner indicates the section index. Note the noticeable improvement in amount of nonlinear distortion remaining in the elastically aligned series compared to the rigidly aligned series (Supplementary Video 8). A high-resolution version of the movie can be downloaded from http://fly.mpi-cbg.de/elastic/. (MOV 71634 kb)

Supplementary Video 11

Walkthrough of the elastically aligned Drosophila series orthogonally re-sliced. The movie shows in each frame a single, computationally generated section, orthogonal to the physical sectioning plane, through the elastically aligned TEM section series of the D. melanogaster first-instar larval ventral nerve cord imaged as mosaic of overlapping tiles. Sections were down-sampled such that their lateral resolution matches the section thickness of 45 nm per pixel. Accordingly, orthogonal sections are generated at a step size of 45 nm. The number in the upper right corner indicates the virtual section index. Two different zoom levels are shown (A,B), where B corresponds to blue rectangle in A. The scale bars in the panels are 5 μm (A) and 3 μm (B). Note that the data have a familiar TEM appearance in the axial direction owing to the near complete removal of nonlinear distortion by the elastic alignment method. A high-resolution version of the movie can be downloaded from http://fly.mpi-cbg.de/elastic/. (MOV 97056 kb)

Supplementary Video 12

Rigid alignment of an array tomography series. The movie shows a sample series of 43 serial sections of 70 nm thickness each from barrel cortex of an adult Line H YFP mouse18 expressing YFP in a subset of layer 5b pyramidal cells, pial surface at the top. Each section shows three fluorescent channels imaged by light microscopy as an arbitrary RGB overlay, DAPI (blue), YFP (green) and Synapsin (red). As with ssTEM data, there is significant remaining nonlinear distortion present in the rigidly aligned dataset. Data courtesy of Forrest Collman, Nick Weiler, Kristina Micheva and Stephen Smith. (MOV 8703 kb)

Supplementary Video 13

Elastic alignment of an array tomography series. The movie shows a sample series of 43 serial sections of 70 nm thickness each from barrel cortex of an adult Line H YFP mouse18 expressing YFP in a subset of layer 5b pyramidal cells, pial surface at the top. Each section shows three fluorescent channels imaged by light microscopy as an arbitrary RGB overlay, DAPI (blue), YFP (green) and Synapsin (red). Analogously to ssTEM data, the elastic alignment removes most of the nonlinear distortion from the light microscopy section series. Data courtesy of Forrest Collman, Nick Weiler, Kristina Micheva and Stephen Smith. (MOV 8806 kb)

Supplementary Video 14

3D rendering of elastically aligned array tomography series. Part of the elastically aligned dataset shown in Supplementary Video 13 was used to generate a three-dimesional volume rendering that demonstrates how well neuronal morphology can be reconstructed from the elastically aligned series. Data courtesy of Forrest Collman, Nick Weiler, Kristina Micheva and Stephen Smith. (MOV 5265 kb)

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Saalfeld, S., Fetter, R., Cardona, A. et al. Elastic volume reconstruction from series of ultra-thin microscopy sections. Nat Methods 9, 717–720 (2012) doi:10.1038/nmeth.2072

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