Elsevier

Medical Image Analysis

Volume 32, August 2016, Pages 18-31
Medical Image Analysis

A spherical harmonics intensity model for 3D segmentation and 3D shape analysis of heterochromatin foci

https://doi.org/10.1016/j.media.2016.03.001Get rights and content

Highlights

  • Model-based approach for automatic 3D segmentation of heterochromatin foci.

  • Novel 3D parametric intensity model based on a spherical harmonics expansion.

  • 3D shape analysis of heterochromatin by exploiting the segmentation result.

  • Quantitative evaluation based on synthetic and real confocal microscopy image data.

  • The approach copes well with high noise levels and various 3D shapes and sizes.

Abstract

The genome is partitioned into regions of euchromatin and heterochromatin. The organization of heterochromatin is important for the regulation of cellular processes such as chromosome segregation and gene silencing, and their misregulation is linked to cancer and other diseases. We present a model-based approach for automatic 3D segmentation and 3D shape analysis of heterochromatin foci from 3D confocal light microscopy images. Our approach employs a novel 3D intensity model based on spherical harmonics, which analytically describes the shape and intensities of the foci. The model parameters are determined by fitting the model to the image intensities using least-squares minimization. To characterize the 3D shape of the foci, we exploit the computed spherical harmonics coefficients and determine a shape descriptor. We applied our approach to 3D synthetic image data as well as real 3D static and real 3D time-lapse microscopy images, and compared the performance with that of previous approaches. It turned out that our approach yields accurate 3D segmentation results and performs better than previous approaches. We also show that our approach can be used for quantifying 3D shape differences of heterochromatin foci.

Introduction

The genomic DNA of eukaryotic cells is packaged into chromatin, a large protein-DNA complex located inside the cell nucleus. Transcription, DNA replication, and DNA repair are examples of vital biological processes that depend on chromatin organization (Sexton et al., 2015, Cremer et al., 2015). In a coarse-grained classification, two functional states of chromatin are distinguished: the more open euchromatin active in transcription, and the more densely packed heterochromatin that is biologically inactive. Furthermore, formation of a stable heterochromatin structure is important for proper chromosome segregation and genomic stability, and its misregulation is linked to cancer and other diseases (Hahn et al., 2010, Plass et al., 2013). The establishment of heterochromatin is controlled by DNA methylation and post-translational histone modification, as well as the recruitment of architectural protein factors that recognize these so called epigenetic signals (Saksouk et al., 2015). The quantitative analysis of the underlying regulatory epigenetic networks based on fluorescence microscopy images as well as other experimental readouts (Müller et al., 2009, Hathaway et al., 2012, Müller-Ott et al., 2014) is an emerging topic in biomedical science and medical diagnosis (Webster et al., 2013, Saab et al., 2014). A prototypic example of a transcriptionally silenced heterochromatic state is that of pericentric heterochromatin in mouse (Probst et al., 2008). It is ideally suited for a fluorescence microscopy image-based analysis. Due to their higher DNA content and enrichment of AT sequences, pericentric heterochromatic domains form condensed clusters that can be identified in mouse cells by staining with DAPI (4,6-diamidino-2-phenylindole), a fluorescent DNA-intercalating dye. Perturbances of the underlying epigenetic network are reflected in the structure and formation of pericentric heterochromatic domains. Furthermore, their shape changes during differentiation of embryonic stem cells and is functionally relevant for the pluripotent stem cell state (Meshorer et al., 2006, Mattout et al., 2015). Thus, there is a need to quantify heterochromatin and shape changes of heterochromatin domains in relation to cell differentiation, gene silencing, and chromosome segregation as well as to the misregulation of these processes in disease.

In this work, we address the task of heterochromatin quantification by introducing a novel approach for image analysis of heterochromatin domains in 3D fluorescence microscopy images. The pericentric heterochromatin regions studied here in mouse fibroblasts appear as bright fluorescent foci under the microscope (Fig. 1, left). To investigate heterochromatin formation and associated epigenetic mechanisms, these foci need to be accurately segmented and quantified. The formation process is connected with the dynamic recruitment of chromatin modifiers like the histone methyltransferases Suv39h1/h2 and Suv4-20h1/h2 or the heterochromatin protein 1 (HP1) isoforms (Hahn et al., 2013, Müller-Ott et al., 2014). To study the spatial and temporal dynamics of proteins in heterochromatin regions, multichannel 3D images showing foci of DAPI-stained DNA in one channel and foci of fluorescently labeled proteins in additional channels can be acquired (Fig. 1). Manual extraction of quantitative 3D information about foci, however, is difficult and highly time-consuming. On the other hand, computer-controlled microscopy systems enable to automate the acquisition of multichannel image data and can gather a large number of 3D images in short time (Pepperkok et al., 2006). Hence, automated image analysis approaches are required, which can extract the relevant information from multichannel 3D images by accurate 3D foci segmentation.

The automated segmentation of heterochromatin foci, however, is challenging for several reasons. In contrast to other subcellular structures (e.g., endoplasmic reticulum exit sites (Matula et al., 2010) or telomeres (Wörz et al., 2010, Osterwald et al., 2015)) the size and 3D shape of heterochromatin foci are subject to a high degree of variability. In particular, the 3D shape of foci can be highly irregular, thus standard geometric models like spheres or ellipsoids are not well suited for 3D shape representation. In addition, the appearance (intensity signal) of heterochromatin foci depends on the distribution of the staining dyes and is impaired by photon noise, non-uniform illumination, and by the blurring effect of the microscope described by the point spread function (PSF) (Waters et al., 2009). As a result, the intensity contrast of heterochromatin foci with respect to the nucleus background varies significantly and can be relatively low (Fig. 1). The latter issue is particularly relevant for the analysis of live cell microscopy images, where laser power needs to be kept to a minimum level to avoid photo damaging the cells as well as bleaching the fluorescence signal during time course experiments. Hence, automatic approaches for 3D heterochromatin foci segmentation must cope with shape variations, non-homogeneous image intensities, as well as varying and low foci contrast.

In previous work, different methods were used for segmentation of heterochromatin foci from 3D fluorescence microscopy images. Often, global intensity thresholds are applied (e.g., (Beil et al., 2002, Beil et al., 2005, Böcker et al., 2006, Jost et al., 2011, Ivashkevich et al., 2011, Cantaloube et al., 2012)), which are sensitive to intensity variations. Thus, approaches based on global thresholds are often combined with other techniques, such as the top-hat transform (Böcker et al., 2006, Ivashkevich et al., 2011, Cantaloube et al., 2012) or the H-dome transform (Ivashkevich et al., 2011) to improve the segmentation accuracy. Local thresholding within nuclei regions (Horáková et al., 2010, Eck et al., 2012) diminishes the effect of intensity variations between different nuclei, however, contrast variations between different foci in one nucleus are not addressed. In Andrey et al. (Andrey et al., 2010), Poulet et al. (Poulet et al., 2015), foci segmentation is performed by partitioning the nucleus into regions using the watershed transform and exclusion of low-contrast regions using manually defined thresholds. However, in the case of high levels of image noise or foci with low contrast, the watershed transform tends to over-segmentation. In Dzyubachyk et al. (Dzyubachyk et al., 2010), foci segmentation is performed by determining foreground voxels based on energy minimization using graph cuts within regions around the foci. However, as in the aforementioned approaches, segmentation is limited to the discrete voxel raster, and the blurring of the imaging process described by the microscope’s PSF is not incorporated. In contrast, 3D parametric intensity models describe the shape and intensities of a structure by means of an analytic function, and allow incorporation of the image blurring as well as a priori information on foci appearance to improve the segmentation accuracy. For 3D segmentation, the model function is directly fitted to the image intensities within a 3D region-of-interest (ROI). Parametric intensity models were previously used for heterochromatin analysis (Eck et al., 2012) and analysis of other subcellular structures (Thomann et al., 2002, Wörz et al., 2010). However, there only regularly shaped models (e.g., spheres and ellipsoids) were used. Furthermore, 3D shape analysis of the foci was not considered, but provides additional insights into the heterochromatin formation process.

In this paper, we present a novel approach for accurate 3D model-based segmentation and 3D shape analysis of heterochromatin foci from multichannel 3D fluorescent microscopy images. Our approach employs a new 3D parametric intensity model, which is based on a spherical harmonics (SH) shape representation. Compared to previous intensity models, the new model enables to capture and analyze highly irregular 3D foci shapes. In previous work on 3D segmentation from biomedical images, different types of deformable models based on SH parametrization were used, for example, active shape models (Székely et al., 1996, Kelemen et al., 1996), statistical shape models (Kelemen et al., 1999, Tutar et al., 2006), and models combined with level set segmentation (Baust et al., 2010). Such approaches were used, for example, for the segmentation of brain structures from MR images (Székely et al., 1996, Kelemen et al., 1999) or the segmentation of cell nuclei (Kelemen et al., 1996, Marshall et al., 1996), however, 3D intensity models were not used and segmentation of heterochromatin or associated proteins was not considered. In this work, we use SH to formulate a 3D parametric intensity model, which describes both shape and intensities of heterochromatin foci. For 3D segmentation of heterochromatin foci in microscopy images, the proposed SH intensity model is directly fitted to the image intensities by least-squares minimization. Based on the segmentation result, the determined SH expansion coefficients are exploited for analyzing the 3D shape of the foci. SH shape analysis was previously used, for example, for brain structures in Gerig et al. (Gerig et al., 2001), Styner et al. (Styner et al., 2004), for lung nodules in El-Baz et al. (El-Baz et al., 2011), for cells in Khairy et al. (Khairy et al., 2010), Ducroz et al. (Ducroz et al., 2012), Du et al. (Du et al., 2013), and for cell nuclei in Singh et al. (Singh et al., 2011), however, approaches for characterizing the 3D shape of heterochromatin foci have not yet been introduced. Furthermore, the aforementioned approaches determine a voxel-based (Styner et al., 2004, Khairy et al., 2010, Singh et al., 2011) or mesh-based (El-Baz et al., 2011, Ducroz et al., 2012) segmentation result, which is converted into a SH representation, often by employing the surface parametrization method proposed in Brechbühler et al. (Brechbühler et al., 1995). In our approach, such a conversion is not necessary since we directly obtain an analytic SH representation from segmentation by 3D model fitting. We demonstrate that 3D shape analysis based on the computed SH coefficients enables distinguishing different foci shapes and analyzing temporal shape changes. This work combines and extends our previous conference papers (Eck et al., 2013, Eck et al., 2014). Compared to that work, we have improved the automatic initialization of the model and use a Hessian-based multiscale approach for automatic estimation of a suitable 3D ROI for model fitting. Also, we describe the SH intensity model in more detail and present improvements on the computational efficiency. In addition, we have conducted a more comprehensive performance evaluation, in particular, we included a validation study based on 3D synthetic image data. We also successfully applied the approach to real 3D static and 3D dynamic image data and compared the results with previous approaches.

This paper is organized as follows. In Section 2, we introduce our 3D SH intensity model for representing the 3D shape and intensities of heterochromatin foci. Section 3 describes the approach for automatic 3D foci segmentation based on 3D model fitting. In Section 4, we present our approach for 3D shape analysis based on the SH expansion coefficients determined by model fitting. Experimental results for synthetic and real 3D image data are presented in Section 5. Finally, in Section 6 we discuss and conclude the work.

Section snippets

3D spherical harmonics intensity model

In this section, we introduce a 3D spherical harmonics (SH) intensity model for analytic representation of the shape and intensities of heterochromatin foci in 3D microscopy images. First, we describe the 3D SH shape model (Section 2.1), and then we formulate a 3D SH intensity model (Section 2.2). The 3D SH intensity model provides the basis for both automatic 3D foci segmentation (Section 3) and 3D foci shape analysis (Section 4).

Automatic 3D foci segmentation

In this section, we describe how the spherical harmonics (SH) intensity model in (11) is utilized for 3D segmentation of heterochromatin foci. The segmentation approach is fully automatic and consists of four steps detailed below. First, 3D foci detection is performed to obtain coarse foci positions. Second, the size of the foci is estimated to determine the 3D region-of-interest (ROI) for model fitting. Using the results of foci detection and ROI size determination, the 3D SH intensity model

3D foci shape analysis

In this section, we describe how the 3D shape of heterochromatin foci can be analyzed based on the 3D SH intensity model gM, SH in (11). By fitting the 3D SH intensity model to the image data, the SH coefficients alm and blm are automatically determined. Depending on the degree l, the coefficients alm and blm control the influence of the SH basis functions of different frequencies and thus contain information about the frequency components which determine the 3D shape of the fitted

Experimental results

To analyze the performance of our approach, we used 3D synthetic and 3D real static image data, as well as 3D real dynamic time-lapse images.

Conclusion

We have introduced a 3D model-based approach for automatic 3D segmentation of pericentric heterochromatin foci from 3D confocal light microscopy images. Our approach employs a novel 3D parametric intensity model based on a spherical harmonics (SH) expansion which analytically describes the 3D shape and intensities of the foci. To perform 3D foci segmentation, the 3D SH intensity model is directly fitted to the image intensities by solving a least-squares minimization problem. We have also

Acknowledgment

This work was supported by the projects EpiSys (0315502) and CancerTelSys (01ZX1302) in the SysTec and e:Med programs of the German Federal Ministry of Education and Research (BMBF). We thank Dr. Qin Zhang (DKFZ Heidelberg, BioQuant, Division of Theoretical Systems Biology) for providing ground truth segmentation results.

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