Computational reconstruction of cell and tissue surfaces for modeling and data analysis.
ABSTRACT We present a method for the computational reconstruction of the 3D morphology of biological objects, such as cells, cell conjugates or 3D arrangements of tissue structures, using data from highresolution microscopy modalities. The method is based on the iterative optimization of Voronoi representations of the spatial structures. The reconstructions of biological surfaces automatically adapt to morphological features of varying complexity with flexible degrees of resolution. We show how 3D confocal images of single cells can be used to generate numerical representations of cellular membranes that may serve as the basis for realistic, spatially resolved computational models of membrane processes or intracellular signaling. Another example shows how the protocol can be used to reconstruct tissue boundaries from segmented twophoton image data that facilitate the quantitative analysis of lymphocyte migration behavior in relation to microanatomical structures. Processing time is of the order of minutes depending on data features and reconstruction parameters.

Article: The Future of Immunoimaging  Deeper, Bigger, More Precise, and Definitively More Colorful.
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ABSTRACT: Immune cells are thoroughbreds, moving farther and faster and surveying more diverse tissue space than their nonhematopoietic brethren. Intravital 2photon microscopy has provided insights into the movements and interactions of many immune cell types in diverse tissues, but much more information is needed to link such analyses of dynamic cell behavior to function. Here we describe additional methods whose application promises to extend our vision, allowing more complete, multiscale dissection of how immune cell positioning and movement are linked to system state, host defense, and disease.European Journal of Immunology 04/2013; 43(6). · 4.52 Impact Factor  SourceAvailable from: Antonio LlombartBoschClaudia Bühnemann, Simon Li, Haiyue Yu, Branford White H, Schäfer KL, Antonio LlombartBosch, Isidro Machado, Piero Picci, Hogendoorn PC, Athanasou NA, J. Alison Noble, A. Bassim Hassan[Show abstract] [Hide abstract]
ABSTRACT: Driven by genomic somatic variation, tumour tissues are typically heterogeneous, yet unbiased quantitative methods are rarely used to analyse heterogeneity at the protein level. Motivated by this problem, we developed automated image segmentation of images of multiple biomarkers in Ewing sarcoma to generate distributions of biomarkers between and within tumour cells. We further integrate high dimensional data with patient clinical outcomes utilising random survival forest (RSF) machine learning. Using material from cohorts of genetically diagnosed Ewing sarcoma with EWSR1 chromosomal translocations, confocal images of tissue microarrays were segmented with level sets and watershed algorithms. Each cell nucleus and cytoplasm were identified in relation to DAPI and CD99, respectively, and protein biomarkers (e.g. Ki67, pS6, Foxo3a, EGR1, MAPK) localised relative to nuclear and cytoplasmic regions of each cell in order to generate image feature distributions. The image distribution features were analysed with RSF in relation to known overall patient survival from three separate cohorts (185 informative cases). Variation in preanalytical processing resulted in elimination of a high number of noninformative images that had poor DAPI localisation or biomarker preservation (67 cases, 36%). The distribution of image features for biomarkers in the remaining high quality material (118 cases, 104 features per case) were analysed by RSF with feature selection, and performance assessed using internal crossvalidation, rather than a separate validation cohort. A prognostic classifier for Ewing sarcoma with low crossvalidation error rates (0.36) was comprised of multiple features, including the Ki67 proliferative marker and a subpopulation of cells with low cytoplasmic/nuclear ratio of CD99. Through elimination of bias, the evaluation of highdimensionality biomarker distribution within cell populations of a tumour using random forest analysis in quality controlled tumour material could be achieved. Such an automated and integrated methodology has potential application in the identification of prognostic classifiers based on tumour cell heterogeneity.PLoS ONE 09/2014; PLoS One. 2014 Sep 22;9(9):e107105(9). · 3.53 Impact Factor  SourceAvailable from: Attila TárnokPablo B. Tozetti, Ewelyne M. Lima, Andrews M. Nascimento, Denise C. Endringer, Fernanda E. Pinto, Tadeu U. Andrade, Anja Mittag, Attila Tarnok, Dominik Lenz[Show abstract] [Hide abstract]
ABSTRACT: Introduction Recent studies in image cytometry evaluated the replacement of specific markers by morphological parameters. The aim of this study was to develop and evaluate a method to identify subtypes of leukocytes using morphometric data of the nuclei. Method The analyzed images were generated with a laser scanning cytometer. Two free programs were used for image analysis and statistical evaluation: Cellprofiler and Tanagra respectively. A sample of leukocytes with 200 sets of images (DAPI, CD45 and CD14) was analyzed. Using feature selection, the 20 best parameters were chosen to conduct crossvalidation. Results The morphometric data identified the subpopulations of the analyzed leukocytes with a sensitivity and specificity of 0.95 per sample. Conclusion The present study is the first that identifies subpopulations of leukocytes by nuclear morphology.Hematology/ Oncology and Stem Cell Therapy 06/2014;
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Computational reconstruction of cell and tissue surfaces for
modeling and data analysis
Frederick Klauschen1,*, Hai Qi2, Jackson G. Egen2, Ronald N. Germain1,2, and Martin Meier
Schellersheim1,*
1Program in Systems Immunology and Infectious Disease Modeling, National Institute of Allergy
and Infectious Diseases, National Institutes of Health, 9000 Rockville Pike, Bethesda MD 20892,
USA
2Lymphocyte Biology Section, Laboratory of Immunology, National Institute of Allergy and
Infectious Diseases, National Institutes of Health, 9000 Rockville Pike, Bethesda MD 20892, USA
Abstract
We present a method for computational reconstruction of the 3D morphology of biological
objects, such as cells, cell conjugates or 3D arrangements of tissue structures, using data from
highresolution microscopy modalities. The method is based on the iterative optimization of
Voronoi representations of the spatial structures. The reconstructions of biological surfaces
automatically adapt to morphological features of varying complexity with flexible degrees of
resolution. We show how 3D confocal images of single cells can be used to generate numerical
representations of cellular membranes that may serve as the basis for realistic, spatially resolved
computational models of membrane processes or intracellular signaling. Another example shows
how the protocol can be used to reconstruct tissue boundaries from segmented twophoton image
data that facilitate the quantitative analysis of lymphocyte migration behavior in relation to
microanatomical structures. Processing time is of the order of minutes depending on data features
and reconstruction parameters.
INTRODUCTION
The increased availability and use of advanced 3D imaging techniques such as fluorescence
confocal and multiphoton or electron tomographic microscopy has enabled researchers to
investigate biological structures and processes with a high degree of spatial resolution. The
applications range from highresolution mapping of (sub)cellular morphology and dynamic
tracking of fluorescently labeled proteins in subcellular compartments to in situ imaging of
cell population behavior1–3. Because many biological processes are closely related to and
influenced by the spatial context in which they occur – information made accessible by 3D
microscopy – it is essential to include these spatial properties in the analysis of such data.
Moreover, because data sets acquired in these experiments are usually large and the relevant
biological objects are numerous and/or the spatial properties complex, manual analyses are
laborious and frequently involve subjective choices that render them problematic for
quantitative data analysis. Here, we describe the application of an approach, implemented in
a userfriendly software tool, that allows for the automated threedimensional reconstruction
of the surfaces of biological objects ranging from (sub) cellular membranes to tissue/organ
*Correspondence to Frederick Klauschen (fklauschen@niaid.nih.gov) or Martin MeierSchellersheim (mms@niaid.nih.gov).
COMPETING FINANCIAL INTERESTS STATEMENT
The authors declare that they have no competing financial interests.
NIH Public Access
Author Manuscript
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Published in final edited form as:
Nat Protoc. 2009 ; 4(7): 1006–1012. doi:10.1038/nprot.2009.94.
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boundaries and the subsequent integration of these reconstructions with automated tissue
contextual cell migration data analysis and modeling.
Introduction to Voronoi diagrams
Many different strategies for computational surface reconstruction have been developed,
frequently based either on higherorder polygonal 4, 5 or triangular 6, 7 surface meshes (for a
review, see e.g. 8). Most approaches were designed mainly for visualization purposes in
software used to process microscopy data, as for instance in Imaris® (Bitplane). The
difference between those approaches and the technique introduced here are that our
approach uses adaptive resolution of surface features, can reduce artefacts resulting from
lower outofplane resolution, and is capable of highquality mesh generation required for
computational modeling. The price that has to be paid for the combination of these
advantages is that the iterative optimization procedure may cause longer processing times
compared to conventional approaches if high mesh resolutions are desired. Our method,
used to obtain the results published in ref. 9 is based on the geometric concept of ‘Voronoi
diagrams10’ that combines the concepts of polygonal and triangular meshes and offers
specific advantages for numerical simulations 11. In two dimensions, a Voronoi diagram
(also called Dirichlet tesselation12) of a set of points, here called ‘vertices’, is constructed by
subdividing the area containing the vertices into geometric mesh elements in such a way that
the Voronoi element of each vertex comprises the region surrounding the vertex that is
closer to this than to any other vertex13 (Fig. 1). Because Voronoi diagrams can be
computed for arbitrary vertex distributions, their shapes can also be highly variable (Fig.
1A). There exist, however, vertex distributions for which the Voronoi diagrams have
properties that are particularly desirable for computational analyses: the variation of the
distances between neighboring vertices is minimized (equally spaced mesh) and the ratio of
the element circumference and element area are minimal. In 2D, these optimized Voronoi
diagrams, or meshes, are hexagonal lattices (Fig. 1D). They occur naturally, for instance, in
bee honeycombs, minimizing the material needed for building robust planar structures.
Voronoilike shapes generated during isotropic growth or diffusion processes starting from
initial seed points, as in turtle carapaces or giraffe fur, show similar but sometimes less
optimized hexagonal structures. Perfectly hexagonal structures can be viewed as limiting
cases toward which ‘real’ meshes, i. e. 2D meshes constrained by boundaries or embedded
in 3D, may evolve if appropriate algorithms are used. Such meshes are called ‘optimal’ (or
also ‘highquality’ meshes).
An important characteristic of optimal Voronoi meshes is that the center points (also called
forming points) have the same coordinates as the centroids of the elements. While vertex
distributions resulting in optimal Voronoi meshes can be easily generated in a two
dimensional plane without boundaries or with rectangular borders, this task is nontrivial if
curved boundaries are present or for curved surfaces embedded in 3D, which is the case for
computational reconstructions of cell/tissue surfaces. The computational method we
describe here uses an iterative optimization algorithm that produces optimal meshes for
arbitrary shapes and boundaries from arbitrary initial vertex distributions. Initial “seed”
vertices are distributed randomly within the confines of the surface layer defined by a 3
dimensional binary mask created from microscopy image series (Figure 2). Then the
Voronoi surface elements are computed for the initial distribution and the vertices are
subsequently moved to the centroids of these elements. In the next step the Voronoi
elements are recomputed for the centroids, which starts an iterative process (computation of
Voronoi diagram → computation of Voronoi centroid → replacement of Voronoi center
vertex with centroid ↲) that converges to an optimal Voronoi mesh with hexagonal element
geometry (Figures 1E,F and 3).
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Our approach permits to automatically and adaptively produce optimized meshes and
resolve morphological details of varying complexity with an optimal number of elements for
a given desired accuracy. More precisely, our method offers two reconstruction alternatives
that may also be combined. The first option requires the definition of the total number of
elements/vertices used in the reconstruction. The method then iteratively optimizes the
distribution of the vertices so that a uniform (highquality) mesh is generated (Figure 4 and
Box 1 ‘Description of the reconstruction algorithm’), which approximates the surface with
an accuracy not lower than the average distance between neighboring vertices. The second
(and default) option allows for the automatic adaptation of the reconstruction to local
differences in spatial detail in the image data and ensures that a certain accuracy of the
surface reconstruction is reached with a minimal number of elements (Figure 5). This
approach is based on the computation of local quality measures (for instance, angles
between surface elements or Euclidean vs. geodesic vertex distances) and uses local mesh
refinement if quality criteria are not met (see Box 2 ‘Local adaptivity’ for details). These
numerical Voronoi reconstructions are useful whenever quantitatively precise
representations of spatial features have to be extracted from 3D microscopy images. Here
we focus on two example applications at distinct scales of biological resolution.
BOX 1
Description of the reconstruction algorithm
The following steps are performed automatically without any user intervention and are
listed here only to present details of the algorithm.
1)
Extraction/labeling of the surface voxels.
2.1)
Initial random distribution of a number (depending on the intended
resolution) of seed vertices within the surface layer defined in step 1 and
2.2)
Definition of a minimum reconstruction accuracy (optional, see below for
details).
3)
Computation of the Voronoi diagram for the current vertex locations
embedded in the voxel surface data. Algorithm: Assign each surface voxel
the label of the closest seed vertex.
4)
Computation of the centroid for each Voronoi element. Algorithm: Compute
the arithmetic means of the coordinates of all surface voxels of each Voronoi
element and assign the centroid to the surface voxel closest to the mean
coordinates.
5)
Replacement of the current Voronoi vertices with the centroids of the
Voronoi element.
6)
Iteration of steps 3–6 for a predefined number of loops or until the average
distance between the centroid and the Voronoi center vertex drops below a
(default or userdefinable) threshold.
BOX 2
Local adaptivity
The reconstruction algorithm without local adaptivity results in a homogeneous mesh,
i.e., the mesh vertices are equally distributed over the surface resulting in an optimal
mesh approximating the surface with a accuracy given by the mesh constant (average
distance between neighboring vertices) (Supplementary Figure 1). With locally adaptive
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reconstruction, the surface reconstruction adaptively resolves morphological details until
a certain, definable accuracy is reached. This is achieved by computing the angles
between every pair of adjacent triangles. If this angle is smaller than a certain threshold,
the mesh is locally refined by inserting an additional vertex at the center of the common
side of the two adjacent triangles. To maintain a locally optimized grid structure, one
‘regular’ iteration step is performed following the insertion of additional vertices. This
adaptivity generates surface parameterization of higher accuracy with a locally higher
density of vertices in regions of higher spatial complexity, while limiting the total
number of elements (Figure 5). The relevant options and parameters can be set in the
MorphologyModeler Params menu.
Example applications
The first example describes surface reconstruction based on microscopy images of cellular
morphology. Computational studies in cell biology increasingly take into account that many
aspects of cellular function cannot be understood or modeled without proper treatment of
cellular morphology14–17. Analyzing or simulating intracellular biochemical dynamics,
such as nonisotropic reactiondiffusion processes in the cytoplasm or on the cell membrane
or intracellular transport mechanisms, requires computational representations (spatial
discretizations) of cellular morphology. The elements of high quality Voronoi meshes are
particularly suitable for such discretizations because they ensure locally homogeneous mesh
spacings even for complex cell morphologies and the lines connecting the Voronoi centroids
are perpendicular to the element boundaries, properties that greatly facilitate mathematical
analyses and simulation of diffusion and fluxes18. Because our reconstruction method can
adapt its spatial resolution to the morphological properties of the cells being analyzed, we
obtain high quality representations of cellular structure with a minimal number of volume
elements, thereby minimizing computational costs of numerical analyses and simulations
(Fig. 5).
On a slightly higher spatial scale, analyzing the dynamic organization of physically
interacting cell populations in specialized tissues requires computational representations of
microanatomical structures and cellular motion tracks. Recent advances in insitu two
photon microscopy have facilitated the investigation of cell behavior dynamics within
complex tissue environments. These technological developments have been particularly
beneficial for immunological research, as the analysis of migration and interaction of
leucocytes, lymphocytes, and antigen presenting cells in secondary lymphoid organs and at
sites of chronic inflammation is critical for a deeper understanding of the immune
response19. Because the microanatomy of secondary lymphoid organs reflects the
compartmentalization of T and B cells and antigen presenting cells and provides guidance
for entry, internal movement, and exit of cells, cell migration analysis must take into account
the microanatomical context. In the tissue surface reconstruction example presented here
we specifically look at germinal centers (GCs), which are organized lymphoid tissue
structures where high affinity antibody responses are generated. Lymphocytes that occupy
GCs mainly include antigenspecific B and T cells, while naïve B cells are largely excluded
from the GC proper. Intravital 2photon microscopy has been increasingly utilized to
understand how the GC tissue structure is dynamically organized and maintained and how
the trafficking of its cellular components is controlled20–22. To analyze imaging data from
such studies, it is often necessary to define GCrelated tissue domains. Typically, this is
accomplished by manual annotation of tissue boundaries on optical sections according to
relevant fluorescentlylabeled tissue landmarks. Ideally, these boundaries defined on series
of axially adjacent 2D imaging planes are further digitally combined to allow visualization
and mathematic description of the reconstructed tissue structure in full 3D space (Figures
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7). The tissue reconstructions generated using this protocol have been used in a recent
research publication9 to quantitatively analyze the cellular migration behavior of
lymphocytes in the context of germinal center tissue structure. In that study computing and
comparing the speed and location/distance of a SLAMassociatedprotein and wildtype
lymphocytes relative to the virtual germinal center surface over each track length permitted
the automatic quantification and classification of the cell behaviour. The analysis revealed
that in contrast to wildtype, SAP KO T lymphocytes are incapable of crossing the border of
and moving into germinal centers (see 9 for details).
In addition to these types of applications, our method may improve the computational
efficiency of standard surface reconstruction applications, such as morphological
measurements or surface visualization, because it minimizes the number of surface elements
for a given reconstruction accuracy. Conventional approaches, on the other hand, use
triangular meshes with high homogeneous resolution and cannot locally adapt the mesh to
surface features.
MATERIALS
Reagents
•
Image data, see Reagent Setup for details of preparation/segmentation. The
Morphology Modeler requires (binary) segmented image data as input, which may
be either generated manually using a standard image manipulation software such as
Photoshop® (http://www.adobe.com/products/photoshop/) or GIMP (http://
gimp.org) or automatically from fluorescence microscopy data using image
segmentation software (e. g., 2PISA (Klauschen et al., in preparation)).
Equipment
•
Reconstruction software: The software package MoMo (Morphology Modeler) we
developed and use here is available for Windows XP/Vista, MacOS X and Linux
32/64bit and may be obtained free of charge for noncommercial use. It can be
downloaded at http://www3.niaid.nih.gov/labs/aboutlabs/psiim/
computationalBiology. The surface reconstruction and cell track analysis method
we present here may also be implemented using any modern programming
language and the explanations of the method we present would be sufficient for that
purpose.)
•
Computer hardware: The computations can be performed on most computers with
current standard specifications (OpenGL capabilities are required for surface
visualization), limited only by the memory required to handle 3D microscopy data.
The reconstructions shown here were performed on an Apple MacPro®
Workstation with 16GB main memory (http://www.apple.com) running 64bit SuSE
Linux (http://www.opensuse.org).
Reagent set up
Image data preparation—The surface reconstruction protocol described in the procedure
may be used with any kind of segmented image data whose format represents an object
whose surface is to be reconstructed with intensity values equal to or larger than 1 while the
background pixels are zero. The images have to be provided in individual z stack files and
may have the following formats: JPEG, TIFF, or PNG. Files have to be named using a prefix
followed by numbers indicating the z slice (the index format is detected automatically) and
the corresponding image format suffix.
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To generate the binary segmentations of the 3D confocal microscopy images of the T cell
used in our first example application, we manually defined an intensity threshold to
differentiate between cell and background pixels using standard image processing software
(e. g. Photoshop or GIMP) and applied that threshold to the whole zstack (Figure 2). In case
of image data of lower quality, for instance due to zstack intensity inhomogeneities, we
recommend using automatic segmentation software (see Reagents). To define binary masks
of the germinal center area on individual imaging planes, which serve as the input for the
tessellation program, we took advantage of the fact that naive B cells as a population are
substantially excluded from GCs (Figure 7A). Therefore, fluorescent signals associated with
naïve B cells were timeaveraged for each imaging time series, and the follicular area and
approximation of the GC–mantle border on individual optical sections were manually
marked using the Photoshop mask function. Such marked images were then transformed into
binary images in Photoshop, with pixel size and dimension maintained. The resulting zstack
of segmented germinal center masks essentially represents the average configuration of the
visualized GC during the imaging period (Figure 7B,C).
PROCEDURE
Surface Reconstruction (using the Morphology Modeler MoMo)
1
Start the Morphology Modeler software MoMo.
2
In the SurfParam menu select item Load Microscopy Data.
3
Select the first slice of the data set to load the complete image series and click
‘open’.
4
Choose between homogeneous vertex distribution or locally adaptive surface
reconstruction. For homogeneous reconstruction, set the number of vertices/
mesh elements. For locally adaptive reconstruction, set the refinement threshold
angle parameter (between −1.0 for minimum and +1.0 for maximum
refinement).
?Troubleshooting.
5
Enter the z stack factor, which is the ratio of the outofplane and inplane
resolution.
6
Select if top or bottom elements should be labeled in case the z stack does not
fully contain the microanatomical object.
7
The software will automatically check if input data contains more than one class
label. If data contains only background and a single object/class label the
program automatically continues to step 8 and no user action is required. If data
contains more than one class label choose a class label for reconstruction or
enter ‘0’ to merge all labels.
8
In the SurfParam menu select item Save Surface Tesselation to save the result.
9
Rotate the mouse wheel to visualize the surface and hold the left mouse button
clicked and move the mouse to rotate the surface rendering.
Load and visualize surface
10
In the SurfParam menu select item Load Surface Tesselation to load surface.
11
Scroll mouse wheel to visualize surface.
12
In the GridVis menu select toggle Transparency, toggle Lighting, or ClipPlane
to modify rendering options.
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Transform coordinates to true spatial distances
13
In the SurfParam menu select item Transform to real space.
14
Enter the true/real spatial length of a voxel unit in meters.
15
In the SurfParam menu select item Save Surface Tesselation to save the result.
Cell track analysis
16
If you wish to use the protocol for surface reconstruction with subsequent cell
track analysis, follow the extended protocol (Supplementary Manual 1).
TROUBLESHOOTING
Since the Voronoi mesh computation utilizes discrete voxel coordinates given by the image
data, the precision of the Voronoi centroid computation decreases when a Voronoi element
contains only relatively few voxels, i.e., the Voronoi resolution comes close to the image
resolution. However, this is not a limitation of the reconstruction method, but related to the
image quality and if necessary has to be overcome by an increase in image resolution. Low
image resolutions mainly pose a problem in form of discrepancies between a higher inplane
and a lower outofplane (zdirection) resolution and visible ‘steps’ or ‘kinks’ may occur
along the z direction. One intrinsic feature of the method presented here is that such z
direction ‘steps’ can be automatically interpolated. However, this only works as long as the
zsteps are smaller than the reconstruction mesh element size (see Supp. Fig. 2, 3). If the
Voronoi mesh elements have a higher resolution than the zresolution of the image data, the
zsteps are ‘precisely’ reconstructed (see Supp. Fig. 3 and 4), an unwanted phenomenon that
is present in surface visualizations of microscopy data performed with most conventional
software packages (e.g. Imaris®) that are widely used in biological microscopy that do not
offer adaptive reconstructions. Thus, there is an optimum number of surface vertices that
may correct limitations of microscopy data and more accurately represent the actual, real
biological surface than higherresolution surface meshes. In the method described here, this
problem is automatically avoided when the number of vertices is adaptively adjusted (option
B), but it has to be taken into account if the number of surface vertices used for the
reconstruction is defined by the user (more is not necessarily better!). If adaptive
reconstruction (option B) is used it has to be kept in mind that setting the quality parameter
to high values (approaching the maximum 1.0) may in certain cases lead to very long
processing times due to a large number of iterations. We therefore recommend starting with
medium quality values.
TIMING
The computational time required to perform the task outlined above depends on the size of
the microscopy data set, the intended reconstruction accuracy and the performance of the
computer hardware. Typical times using recent computers for surface reconstruction are on
the order of minutes.
ANTICIPATED RESULTS
Application of this protocol to segmented image data produces surface tesselations that
consist of mesh points (‘vertices’) and a mesh topology (vertex connections, ‘edges’). The
general features of the results that can be anticipated from the surface reconstruction
protocol in general depend on the features of the true object, the image resolution with
which the object is represented and the choice of the reconstruction parameters and their
combination: First, it can be expected that with increasing number of Voronoi mesh
elements the image data is more accurately reconstructed. We call this type of accuracy
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imagerelated accuracy and define it as the distance of the centroids of the triangular mesh
that is formed by connected the Voronoi center points (the ‘dual’ mesh) from the voxel
image surface. The second type of reconstruction quality is the accuracy with which the true
object is represented by the surface tesselation, called ‘objectrelated accuracy’. While an
increasing mesh resolution always leads to an increasing imagerelated accuracy, an increase
in the number of mesh elements does not always produce better objectrelated accuracy and
in such cases, a lower number of mesh elements might lead to a higherobject accuracy due
to smoothing effects (see also ‘Troubleshooting’ and Supp. Fig. 3 and 4).
The iterative optimization process (both the homogenous and locally adaptive options)
converges to optimal (highquality) meshes (see Fig. 1), if the resolution of the voxel data is
sufficiently fine in relation to the mesh element size (see also ‘Troubleshooting’). The effect
of locally adaptive surface reconstruction on the results depends on the spatial properties of
the image data. A spherical object will produce a result similar to that of homogeneous
reconstruction, because the iterative refinement process depends on local membrane
curvature, which is constant on a sphere. However, when objects have special spatial
features (which are resolved in the image data), the local adaptivity produces
inhomogeneously resolved surface meshes. An example for the latter case is the T cell
surface reconstruction in which the membrane protrusion (shown in the lower right part of
the cell in Fig. 5C and middle part of Fig. 5D) is automatically resolved by local adaptive
mesh refinement.
The results of the surface reconstruction of the T cell alone, the TBcell conjugate and the
germinal center border reconstruction are presented in Figures 4–6. Figure 4 (+ Supp. Video
1) and Fig. 5 (+ Supp. Video 2) offer a comparison between adaptive and homogeneous
reconstruction and illustrate the optimization process. See also Supplementary Figures for
additional examples. Supplementary Figure 5 shows example results obtained when two
separate surfaces present in the same data set are reconstructed simultaneously. If regions
exist where the distance between the surfaces is equal to or smaller than the reconstruction
mesh spacing the separate surfaces might merge/attach to each other. This problem can be
solved by increasing the mesh resolution or processing the surfaces separately. Exemplary
results of the cell tracking analysis can be found in the supplementary material section ‘cell
track analysis’, Figure 7 Supplementary Figure 6.
Supplementary Material
Refer to Web version on PubMed Central for supplementary material.
Acknowledgments
This research was supported by the Intramural Research Program of NIAID, NIH.
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Figure 1.
Iterative Voronoi mesh optimization illustrated in 2D plane. Voronoi cells are depicted by
center point (blue) and cell border (magenta). A: Initial random distribution of vertices. B,
C, D: optimized mesh after 1, 10 and 500 iterations. E: Movement of Voronoi cell centroids
during optimization process indicated by grey trajectory. F: Average movement of centroids
during the optimization process. The linear plot shows the relatively fast convergence after
~30 iterations. The logarithmic plot shows local maxima prominent between 200 and 400
iterations, which indicate that the final neighborhood configuration has not been reached. At
more than 400 iterations the optimum hexagonal structure is accomplished and the average
centroid movement falls strictly monotonously.
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Figure 2.
Binary image generation from fluorescence microscopy data. A: Original confocal image
(example zslice of 3D stack data) of a T cell; B: binary segmentation result used as input
for surface reconstruction (image size: 500×500 pixel).
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Figure 3.
Illustration of Voronoi surface elements. Reconstruction result after optimization (20
iterations) with adaptive vertex insertion (using T cell data shown in Figure 2). Because
surfaces that are not perfect spheres cannot be approximated by 2D planar polygonal
Voronoi elements that have continuous transitions between neighboring cells. To achieve
continuity at the element boundaries Voronoi elements are used that correspond to
projections of the 2D planar elements onto the voxel surface. These elements still fulfill the
Voronoi criteria and are bended along the connections of neighboring Voronoi center points
that form the edges of the dual surface triangulation. The Voronoi center points are located
directly on the surface given by the voxel image data.
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Figure 4.
Optimizing surface reconstruction for a given number of vertices/elements (n=500) for the T
cell shown in Figure 2. Blue: Lines connecting the Voronoi cell centers. A, initial arbitrary
vertex distribution. B, C and D after 2, 10 and 100 optimization iterations.
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Figure 5.
Automatic adaptive surface reconstruction of the T cell microscopy data shown in Figure 1,
minimizing the required number of vertices/elements for a given reconstruction accuracy
(ratio outofplane/inplane resolution 9:1, average cell radius ~4.5μm, compare scale in Fig.
1). Blue lines: Voronoi mesh; Grey lines: Corresponding ‘dual’ triangular mesh connecting
the Voronoi cell centers. A: Initial surface approximation with a small number of vertices
(n=20). B, C: Optimization results after 11 (B) and 26 (C) iterations based on acute angle
refinement criterion: Adaptive vertex insertion if angles between adjacent triangles are
smaller than 135 degrees allows for accurately resolving morphological features while
minimizing the number of surface vertices (n(final)=289) (C, D: rotation and magnification
of C).
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Figure 6.
Surface reconstruction of cell conjugates. A: Confocal microscopy data of a cognate T cell
(green) forming a synapse with an antigenpresenting cell (blue). B: Surface reconstruction
result (ratio outofplane/inplane resolution 9:1).
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