Stefan Heldmann

Exploring Three-Dimensional Matrix-Assisted Laser Desorption/Ionization Imaging Mass Spectrometry Data: Three-Dimensional Spatial Segmentation of Mouse Kidney

Three-dimensional (3D) imaging has a significant impact on many challenges of life sciences. Three-dimensional matrix-assisted laser desorption/ionization imaging mass spectrometry (MALDI-IMS) is an emerging label-free bioanalytical technique capturing the spatial distribution of hundreds of molecular compounds in 3D by providing a MALDI mass spectrum for each spatial point of a 3D sample. Currently, 3D MALDI-IMS cannot tap its full potential due to the lack efficient computational methods for constructing, processing, and visualizing large and complex 3D MALDI-IMS data. We present a new pipeline of efficient computational methods, which enables analysis and interpretation of a 3D MALDI-IMS data set. Construction of a MALDI-IMS data set was done according to the state-of-the-art protocols and involved sample preparation, spectra acquisition, spectra preprocessing, and registration of serial sections. For analysis and interpretation of 3D MALDI-IMS data, we applied the spatial segmentation approach which is well-accepted in analysis of two-dimensional (2D) MALDI-IMS data. In line with 2D data analysis, we used edge-preserving 3D image denoising prior to segmentation to reduce strong and chaotic spectrum-to-spectrum variation. For segmentation, we used an efficient clustering method, called bisecting k-means, which is optimized for hierarchical clustering of a large 3D MALDI-IMS data set. Using the proposed pipeline, we analyzed a central part of a mouse kidney using 33 serial sections of 3.5 μm thickness after the PAXgene tissue fixation and paraffin embedding. For each serial section, a 2D MALDI-IMS data set was acquired following the standard protocols with the high spatial resolution of 50 μm. Altogether, 512 495 mass spectra were acquired that corresponds to approximately 50 gigabytes of data. After registration of serial sections into a 3D data set, our computational pipeline allowed us to reveal the 3D kidney anatomical structure based on mass spectrometry data only. Finally, automated analysis discovered molecular masses colocalized with major anatomical regions. In the same way, the proposed pipeline can be used for analysis and interpretation of any 3D MALDI-IMS data set in particular of pathological cases.

Image Registration of Sectioned Brains

The physical (microtomy), optical (microscopy), and radiologic (tomography) sectioning of biological objects and their digitization lead to stacks of images. Due to the sectioning process and disturbances, movement of objects during imaging for example, adjacent images of the image stack are not optimally aligned to each other. Such mismatches have to be corrected automatically by suitable registration methods.Here, a whole brain of a Sprague Dawley rat was serially sectioned and stained followed by digitizing the 20 μm thin histologic sections. We describe how to prepare the images for subsequent automatic intensity based registration. Different registration schemes are presented and their results compared to each other from an anatomical and mathematical perspective. In the first part we concentrate on rigid and affine linear methods and deal only with linear mismatches of the images. Digitized images of stained histologic sections often exhibit inhomogenities of the gray level distribution coming from staining and/or sectioning variations. Therefore, a method is developed that is robust with respect to inhomogenities and artifacts. Furthermore we combined this approach by minimizing a suitable distance measure for shear and rotation mismatches of foreground objects after applying the principal axes transform. As a consequence of our investigations, we must emphasize that the combination of a robust principal axes based registration in combination with optimizing translation, rotation and shearing errors gives rise to the best reconstruction results from the mathematical and anatomical view point.Because the sectioning process introduces nonlinear deformations to the relative thin histologic sections as well, an elastic registration has to be applied to correct these deformations.In the second part of the study a detailed description of the advances of an elastic registration after affine linear registration of the rat brain is given. We found quantitative evidence that affine linear registration is a suitable starting point for the alignment of histologic sections but elastic registration must be performed to improve significantly the registration result. A strategy is presented that enables to register elastically the affine linear preregistered~ rat brain sections and the first one hundred images of serial histologic sections through both occipital lobes of a human brain (6112 images). Additionally, we will describe how a parallel implementation of the elastic registration was realized. Finally, the computed force fields have been applied here for the first time to the morphometrized data of cells determined automatically by an image analytic framework.

An octree multigrid method for quasi-static Maxwell's equations with highly discontinuous coefficients

In this paper we develop an OcTree discretization for Maxwells equations in the quasi-static regime. We then use this discretization in order to develop a multigrid method for Maxwells equations with highly discontinuous coefficients. We test our algorithms and compare it to other multilevel algorithms.

Adaptive finite volume method for distributed non-smooth parameter identification

In this paper we develop a finite volume adaptive grid refinement method for the solution of distributed parameter estimation problems with almost discontinuous coefficients. We discuss discretization on locally refined grids, as well as optimization and refinement criteria. An OcTree data structure is utilized. We show that local refinement can significantly reduce the computational effort of solving the problem, and that the resulting reconstructions can significantly improve resolution, even for noisy data and diffusive forward problems.

2D and 3D MALDI-imaging: conceptual strategies for visualization and data mining.

3D imaging has a significant impact on many challenges in life sciences, because biology is a 3-dimensional phenomenon. Current 3D imaging-technologies (various types MRI, PET, SPECT) are labeled, i.e. they trace the localization of a specific compound in the body. In contrast, 3D MALDI mass spectrometry-imaging (MALDI-MSI) is a label-free method imaging the spatial distribution of molecular compounds. It complements 3D imaging labeled methods, immunohistochemistry, and genetics-based methods. However, 3D MALDI-MSI cannot tap its full potential due to the lack of statistical methods for analysis and interpretation of large and complex 3D datasets. To overcome this, we established a complete and robust 3D MALDI-MSI pipeline combined with efficient computational data analysis methods for 3D edge preserving image denoising, 3D spatial segmentation as well as finding colocalized m/z values, which will be reviewed here in detail. Furthermore, we explain, why the integration and correlation of the MALDI imaging data with other imaging modalities allows to enhance the interpretation of the molecular data and provides visualization of molecular patterns that may otherwise not be apparent. Therefore, a 3D data acquisition workflow is described generating a set of 3 different dimensional images representing the same anatomies. First, an in-vitro MRI measurement is performed which results in a three-dimensional image modality representing the 3D structure of the measured object. After sectioning the 3D object into N consecutive slices, all N slices are scanned using an optical digital scanner, enabling for performing the MS measurements. Scanning the individual sections results into low-resolution images, which define the base coordinate system for the whole pipeline. The scanned images conclude the information from the spatial (MRI) and the mass spectrometric (MALDI-MSI) dimension and are used for the spatial three-dimensional reconstruction of the object performed by image registration techniques. Different strategies for automatic serial image registration applied to MS datasets are outlined in detail. The third image modality is histology driven, i.e. a digital scan of the histological stained slices in high-resolution. After fusion of reconstructed scan images and MRI the slice-related coordinates of the mass spectra can be propagated into 3D-space. After image registration of scan images and histological stained images, the anatomical information from histology is fused with the mass spectra from MALDI-MSI. As a result of the described pipeline we have a set of 3 dimensional images representing the same anatomies, i.e. the reconstructed slice scans, the spectral images as well as corresponding clustering results, and the acquired MRI. Great emphasis is put on the fact that the co-registered MRI providing anatomical details improves the interpretation of 3D MALDI images. The ability to relate mass spectrometry derived molecular information with in vivo and in vitro imaging has potentially important implications. This article is part of a Special Issue entitled: Computational Proteomics in the Post-Identification Era. Guest Editors: Martin Eisenacher and Christian Stephan.

MRI-compatible pipeline for three-dimensional MALDI imaging mass spectrometry using PAXgene fixation

UNLABELLED MALDI imaging mass spectrometry (MALDI-imaging) has emerged as a spatially-resolved label-free bioanalytical technique for direct analysis of biological samples and was recently introduced for analysis of 3D tissue specimens. We present a new experimental and computational pipeline for molecular analysis of tissue specimens which integrates 3D MALDI-imaging, magnetic resonance imaging (MRI), and histological staining and microscopy, and evaluate the pipeline by applying it to analysis of a mouse kidney. To ensure sample integrity and reproducible sectioning, we utilized the PAXgene fixation and paraffin embedding and proved its compatibility with MRI. Altogether, 122 serial sections of the kidney were analyzed using MALDI-imaging, resulting in a 3D dataset of 200GB comprised of 2million spectra. We show that elastic image registration better compensates for local distortions of tissue sections. The computational analysis of 3D MALDI-imaging data was performed using our spatial segmentation pipeline which determines regions of distinct molecular composition and finds m/z-values co-localized with these regions. For facilitated interpretation of 3D distribution of ions, we evaluated isosurfaces providing simplified visualization. We present the data in a multimodal fashion combining 3D MALDI-imaging with the MRI volume rendering and with light microscopic images of histologically stained sections. BIOLOGICAL SIGNIFICANCE Our novel experimental and computational pipeline for 3D MALDI-imaging can be applied to address clinical questions such as proteomic analysis of the tumor morphologic heterogeneity. Examining the protein distribution as well as the drug distribution throughout an entire tumor using our pipeline will facilitate understanding of the molecular mechanisms of carcinogenesis.

Highly accurate fast lung CT registration

Lung registration in thoracic CT scans has received much attention in the medical imaging community. Possible applications range from follow-up analysis, motion correction for radiation therapy, monitoring of air flow and pulmonary function to lung elasticity analysis. In a clinical environment, runtime is always a critical issue, ruling out quite a few excellent registration approaches. In this paper, a highly efficient variational lung registration method based on minimizing the normalized gradient fields distance measure with curvature regularization is presented. The method ensures diffeomorphic deformations by an additional volume regularization. Supplemental user knowledge, like a segmentation of the lungs, may be incorporated as well. The accuracy of our method was evaluated on 40 test cases from clinical routine. In the EMPIRE10 lung registration challenge, our scheme ranks third, with respect to various validation criteria, out of 28 algorithms with an average landmark distance of 0.72 mm. The average runtime is about 1:50 min on a standard PC, making it by far the fastest approach of the top-ranking algorithms. Additionally, the ten publicly available DIR-Lab inhale-exhale scan pairs were registered to subvoxel accuracy at computation times of only 20 seconds. Our method thus combines very attractive runtimes with state-of-the-art accuracy in a unique way.

Adaptive Mesh Refinement for Nonparametric Image Registration

Three-dimensional (3D) image registration is a computationally intensive problem which is commonly solved in medical imaging. The complexity of the problem stems from its size and nonlinearity. In this paper we present an approach that drastically reduces the problem size by using adaptive mesh refinement. Our approach requires special and careful discretization of the variational form on adaptive quad/octree grids. It further requires an appropriate refinement criterion. We show that in some cases this approach can reduce the computational time by a factor of approximately 10 or so in two dimensions and 5 in three dimensions compared to the nonadaptive approach.

An Octree Method for Parametric Image Registration

Even for reasonably sized three-dimensional (3D) images, image registration becomes a computationally intensive task. Here, we introduce and explore the concept of octrees for registration which drastically reduces the amount of processed data and thus the computational costs. We show how to map the registration problem onto an octree and present a suitable optimization technique. Furthermore, we demonstrate the performance of the new approach by academic (two-dimensional) as well as real life (3D) examples. These examples indicate that the computational time can be reduced by a factor of 3-4 compared with standard approaches.

A fully parallel algorithm for multimodal image registration using normalized gradient fields

We present a super fast variational algorithm for the challenging problem of multimodal image registration. It is capable of registering full-body CT and PET images in about a second on a standard CPU with virtually no memory requirements. The algorithm is founded on a Gauss-Newton optimization scheme with specifically tailored, mathematically optimized computations for objective function and derivatives. It is fully parallelized and perfectly scalable, thus directly suitable for usage in many-core environments. The accuracy of our method was tested on 21 PET-CT scan pairs from clinical routine. The method was able to correct random distortions in the range from -10 cm to 10 cm translation and from -15° to 15° degree rotation to subvoxel accuracy. In addition, it exhibits excellent robustness to noise.