arXiv subjects

Markus Axer

Publications and source records attributed to Markus Axer.

18 recordsLinked to original sources

arXiv2026

3D scattered light imaging: extracting 3D fiber orientations from 1D line profiles in brain imaging

Understanding the 3D fiber architecture of the brain at the microscopic scale is essential for revealing its structural connectivity and function. Polarization-based optical imaging (3D-PLI) techniques enable high-fidelity reconstruction of single nerve fiber orientations but struggle to resolve fiber crossings, which are critical for recovering the full connectome. Scattering-based imaging provides access to the structure factor of three-dimensionally oriented fibers. By probing a fixed scattering angle under multiple azimuthal illumination angles, in-plane fiber orientations and crossings can be recovered using computational scattered light imaging (SLI). However, despite containing 3D information, a theoretical framework to extract full 3D orientations has been lacking. In this talk, a simple analogical approximation of Rayleigh-Gans scattering theory is introduced to extract the 3D orientation of nerve fibers from one-dimensional SLI measurements. The theory is validated using tilted microscopic glass phantoms consisting of 2 um-thick rod lattices fabricated by two-photon lithography. Finally, the method is applied to brain tissue samples and compared with 3D-PLI.

physics.optics↗

arXiv2025

From Fibers to Cells: Fourier-Based Registration Enables Virtual Cresyl Violet Staining From 3D Polarized Light Imaging

Comprehensive assessment of the various aspects of the brain's microstructure requires the use of complementary imaging techniques. This includes measuring the spatial distribution of cell bodies (cytoarchitecture) and nerve fibers (myeloarchitecture). The gold standard for cytoarchitectonic analysis is light microscopic imaging of cell-body stained tissue sections. To reveal the 3D orientations of nerve fibers, 3D Polarized Light Imaging (3D-PLI) has been introduced, a method that is label-free and allows subsequent staining of sections after 3D-PLI measurement. By post-staining for cell bodies, a direct link between fiber- and cytoarchitecture can potentially be established in the same section. However, inevitable distortions introduced during the staining process make a costly nonlinear and cross-modal registration necessary in order to study the detailed relationships between cells and fibers in the images. In addition, the complexity of processing histological sections for post-staining only allows for a limited number of such samples. In this work, we take advantage of deep learning methods for image-to-image translation to generate a virtual staining of 3D-PLI that is spatially aligned at the cellular level. We use a supervised setting, building on a unique dataset of brain sections, to which Cresyl violet staining has been applied after 3D-PLI measurement. To ensure high correspondence between both modalities, we address the misalignment of training data using Fourier-based registration. In this way, registration can be efficiently calculated during training for local image patches of target and predicted staining. We demonstrate that the proposed method can predict a Cresyl violet staining from 3D-PLI, resulting in a virtual staining that exhibits plausible patterns of cell organization in gray matter, with larger cell bodies being localized at their expected positions.

eess.IV↗

arXiv2024

Scattering polarimetry enables correlative nerve fiber imaging and multimodal analysis

Mapping the intricate network of nerve fibers is crucial for understanding brain function. Three-Dimensional Polarized Light Imaging (3D-PLI) and Computational Scattered Light Imaging (ComSLI) map dense nerve fibers in brain sections with micrometer resolution using visible light. 3D-PLI reconstructs 3D-fiber orientations, while ComSLI disentangles multiple directions per pixel. So far, these imaging techniques have been realized in separate setups. A combination within a single device would facilitate faster measurements, pixelwise mapping, cross-validation of fiber orientations, and leverage the advantages of each technique while mitigating their limitations. Here, we introduce the Scattering Polarimeter, a microscope that facilitates correlative large-area scans by integrating 3D-PLI and ComSLI measurements into a single system. Based on a Mueller polarimeter, it incorporates variable retarders and a large-area light source for direct and oblique illumination, enabling combined 3D-PLI and ComSLI measurements. Applied to human and vervet monkey brain sections, the Scattering Polarimeter generates results comparable to state-of-the-art 3D-PLI and ComSLI setups and creates a multimodal fiber direction map, integrating the robust fiber orientations obtained from 3D-PLI with fiber crossings from ComSLI. Furthermore, we discuss applications of the Scattering Polarimeter for unprecedented correlative and multimodal brain imaging.

physics.med-ph↗

arXiv2024

Analyzing Regional Organization of the Human Hippocampus in 3D-PLI Using Contrastive Learning and Geometric Unfolding

Understanding the cortical organization of the human brain requires interpretable descriptors for distinct structural and functional imaging data. 3D polarized light imaging (3D-PLI) is an imaging modality for visualizing fiber architecture in postmortem brains with high resolution that also captures the presence of cell bodies, for example, to identify hippocampal subfields. The rich texture in 3D-PLI images, however, makes this modality particularly difficult to analyze and best practices for characterizing architectonic patterns still need to be established. In this work, we demonstrate a novel method to analyze the regional organization of the human hippocampus in 3D-PLI by combining recent advances in unfolding methods with deep texture features obtained using a self-supervised contrastive learning approach. We identify clusters in the representations that correspond well with classical descriptions of hippocampal subfields, lending validity to the developed methodology.

cs.CV↗

arXiv2024

Self-Supervised Representation Learning for Nerve Fiber Distribution Patterns in 3D-PLI

A comprehensive understanding of the organizational principles in the human brain requires, among other factors, well-quantifiable descriptors of nerve fiber architecture. Three-dimensional polarized light imaging (3D-PLI) is a microscopic imaging technique that enables insights into the fine-grained organization of myelinated nerve fibers with high resolution. Descriptors characterizing the fiber architecture observed in 3D-PLI would enable downstream analysis tasks such as multimodal correlation studies, clustering, and mapping. However, best practices for observer-independent characterization of fiber architecture in 3D-PLI are not yet available. To this end, we propose the application of a fully data-driven approach to characterize nerve fiber architecture in 3D-PLI images using self-supervised representation learning. We introduce a 3D-Context Contrastive Learning (CL-3D) objective that utilizes the spatial neighborhood of texture examples across histological brain sections of a 3D reconstructed volume to sample positive pairs for contrastive learning. We combine this sampling strategy with specifically designed image augmentations to gain robustness to typical variations in 3D-PLI parameter maps. The approach is demonstrated for the 3D reconstructed occipital lobe of a vervet monkey brain. We show that extracted features are highly sensitive to different configurations of nerve fibers, yet robust to variations between consecutive brain sections arising from histological processing. We demonstrate their practical applicability for retrieving clusters of homogeneous fiber architecture, performing classification with minimal annotations, and query-based retrieval of characteristic components of fiber architecture such as U-fibers.

cs.CV↗

arXiv2022

GORDA: Graph-based ORientation Distribution Analysis of SLI scatterometry Patterns of Nerve Fibres

Scattered Light Imaging (SLI) is a novel approach for microscopically revealing the fibre architecture of unstained brain sections. The measurements are obtained by illuminating brain sections from different angles and measuring the transmitted (scattered) light under normal incidence. The evaluation of scattering profiles commonly relies on a peak picking technique and feature extraction from the peaks, which allows quantitative determination of parallel and crossing in-plane nerve fibre directions for each image pixel. However, the estimation of the 3D orientation of the fibres cannot be assessed with the traditional methodology. We propose an unsupervised learning approach using spherical convolutions for estimating the 3D orientation of neural fibres, resulting in a more detailed interpretation of the fibre orientation distributions in the brain.

eess.IV↗

arXiv2021

Automated computation of nerve fibre inclinations from 3D polarised light imaging measurements of brain tissue

The method 3D polarised light imaging (3D-PLI) measures the birefringence of histological brain sections to determine the spatial course of nerve fibres (myelinated axons). While the in-plane fibre directions can be determined with high accuracy, the computation of the out-of-plane fibre inclinations is more challenging because they are derived from the strength of the birefringence signals (retardation), which depends e.g. on the amount of nerve fibres. One possibility to improve the accuracy is to consider the average transmitted light intensity (transmittance weighting). The current procedure requires effortful manual adjustment of parameters and anatomical knowledge. Here, we introduce an automated, optimised computation of the fibre inclinations, allowing for a much faster, reproducible determination of fibre orientations in 3D-PLI. Depending on the degree of myelination, the algorithm uses different models (transmittance-weighted, unweighted, or a linear combination), allowing to go beyond traditional definitions of white and grey matter and account for regionally specific behaviour. As the algorithm is parallelised and GPU optimised, and uses images from standard 3D-PLI (retardation and transmittance), it can be applied to large data sets, also from previous measurements. The functionality is demonstrated on unstained coronal and sagittal histological sections of vervet monkey and rat brains.

physics.bio-ph↗

arXiv2021

Scatterometry Measurements with Scattered Light Imaging Enable New Insights into the Nerve Fiber Architecture of the Brain

The correct reconstruction of individual (crossing) nerve fibers is a prerequisite when constructing a detailed network model of the brain. The recently developed technique Scattered Light Imaging (SLI) allows the reconstruction of crossing nerve fiber pathways in whole brain tissue samples with micrometer resolution: The individual fiber orientations are determined by illuminating unstained histological brain sections from different directions, measuring the transmitted scattered light under normal incidence, and studying the light intensity profiles of each pixel in the resulting image series. So far, SLI measurements were performed with a fixed polar angle of illumination and a small number of illumination directions, providing only an estimate of the nerve fiber directions and limited information about the underlying tissue structure. Here, we use an LED display with individually controllable light-emitting diodes to measure the full distribution of scattered light behind the sample (scattering pattern) for each image pixel at once, enabling scatterometry measurements of whole brain tissue samples. We compare our results to coherent Fourier scatterometry (raster-scanning the sample with a non-focused laser beam) and previous SLI measurements with fixed polar angle of illumination, using sections from a vervet monkey brain and human optic tracts. Finally, we present SLI scatterometry measurements of a human brain section with 3 $\mu$m in-plane resolution, demonstrating that the technique is a powerful approach to gain new insights into the nerve fiber architecture of the human brain.

physics.bio-ph↗

arXiv2020

Independent Component Analysis for noise and artifact removal in Three-dimensional Polarized Light Imaging

In recent years, Independent Component Analysis (ICA) has successfully been applied to remove noise and artifacts in images obtained from Three-dimensional Polarized Light Imaging (3D-PLI) at the mesoscale (i.e., 64 $\mu$m). Here, we present an automatic denoising procedure for gray matter regions that allows to apply the ICA also to microscopic images, with reasonable computational effort. Apart from an automatic segmentation of gray matter regions, we applied the denoising procedure to several 3D-PLI images from a rat and a vervet monkey brain section.

physics.med-ph↗

arXiv2020

Scattered Light Imaging: Resolving the substructure of nerve fiber crossings in whole brain sections with micrometer resolution

For developing a detailed network model of the brain based on image reconstructions, it is necessary to spatially resolve crossing nerve fibers. The accuracy hereby depends on many factors, including the spatial resolution of the imaging technique. 3D Polarized Light Imaging (3D-PLI) allows the three-dimensional reconstruction of nerve fiber tracts in whole brain sections with micrometer in-plane resolution, but leaves uncertainties in pixels containing crossing fibers. Here we introduce Scattered Light Imaging (SLI) to resolve the substructure of nerve fiber crossings. The measurement is performed on the same unstained histological brain sections as in 3D-PLI. By illuminating the brain sections from different angles and measuring the transmitted (scattered) light under normal incidence, SLI provides information about the underlying nerve fiber structure. A fully automated evaluation of the resulting light intensity profiles has been developed, allowing the user to extract various characteristics, like the individual directions of in-plane crossing nerve fibers, for each image pixel at once. We validate the reconstructed nerve fiber directions against results from previous simulation studies, scatterometry measurements, and fiber directions obtained from 3D-PLI. We demonstrate in different brain samples (human optic tracts, vervet monkey brain, rat brain) that the 2D fiber directions can be reliably reconstructed for up to three crossing nerve fiber bundles in each image pixel with an in-plane resolution of up to 6.5 $\mu$m. We show that SLI also yields reliable fiber directions in brain regions with low 3D-PLI signals coming from regions with a low density of myelinated nerve fibers or out-of-plane fibers. In combination with 3D-PLI, the technique can be used for a full reconstruction of the three-dimensional nerve fiber architecture in the brain.

physics.med-ph↗

arXiv2019

Dense Fiber Modeling for 3D-Polarized Light Imaging Simulations

3D-Polarized Light Imaging (3D-PLI) is a neuroimaging technique used to study the structural connectivity of the human brain at the meso- and microscale. In 3D-PLI, the complex nerve fiber architecture of the brain is characterized by 3D orientation vector fields that are derived from birefringence measurements of unstained histological brain sections by means of an effective physical model. To optimize the physical model and to better understand the underlying microstructure, numerical simulations are essential tools to optimize the used physical model and to understand the underlying microstructure in detail. The simulations rely on predefined configurations of nerve fiber models (e.g. crossing, kissing, or complex intermingling), their physical properties, as well as the physical properties of the employed optical system to model the entire 3D-PLI measurement. By comparing the simulation and experimental results, possible misinterpretations in the fiber reconstruction process of 3D-PLI can be identified. Here, we focus on fiber modeling with a specific emphasize on the generation of dense fiber distributions as found in the human brain's white matter. A new algorithm will be introduced that allows to control possible intersections of computationally grown fiber structures.

physics.comp-ph↗

arXiv2018

Towards ultra-high resolution 3D reconstruction of a whole rat brain from 3D-PLI data

3D reconstruction of the fiber connectivity of the rat brain at microscopic scale enables gaining detailed insight about the complex structural organization of the brain. We introduce a new method for registration and 3D reconstruction of high- and ultra-high resolution (64 $\mu$m and 1.3 $\mu$m pixel size) histological images of a Wistar rat brain acquired by 3D polarized light imaging (3D-PLI). Our method exploits multi-scale and multi-modal 3D-PLI data up to cellular resolution. We propose a new feature transform-based similarity measure and a weighted regularization scheme for accurate and robust non-rigid registration. To transform the 1.3 $\mu$m ultra-high resolution data to the reference blockface images a feature-based registration method followed by a non-rigid registration is proposed. Our approach has been successfully applied to 278 histological sections of a rat brain and the performance has been quantitatively evaluated using manually placed landmarks by an expert.

cs.CV↗

arXiv2018

Diattenuation Imaging reveals different brain tissue properties

When transmitting polarised light through histological brain sections, different types of diattenuation (polarisation-dependent attenuation of light) can be observed: In some brain regions, the light is minimally attenuated when it is polarised parallel to the nerve fibres (referred to as D+), in others, it is maximally attenuated (referred to as D-). The underlying mechanisms of these effects and their relationship to tissue properties were so far unknown. Here, we demonstrate in experimental studies that diattenuation of both types D+ and D- can be observed in brain tissue samples from different species (rodent, monkey, and human) and that the strength and type of diattenuation depend on the nerve fibre orientations. By combining finite-difference time-domain simulations and analytical modelling, we explain the observed diattenuation effects and show that they are caused both by anisotropic absorption (dichroism) and by anisotropic light scattering. Our studies demonstrate that the diattenuation signal depends not only on the nerve fibre orientations but also on other brain tissue properties like tissue homogeneity, fibre size, and myelin sheath thickness. This allows to use the diattenuation signal to distinguish between brain regions with different tissue properties and establishes Diattenuation Imaging as a valuable imaging technique.

physics.med-ph↗

arXiv2018

Finite-Difference Time-Domain simulations of transmission microscopy enable a better interpretation of 3D nerve fiber architectures in the brain

In many laboratories, conventional bright-field transmission microscopes are available to study the structure and organization principles of fibrous tissue samples, but they usually provide only 2D information. To access the third (out-of-plane) dimension, more advanced techniques are employed. An example is 3D Polarized Light Imaging (3D-PLI), which measures the birefringence of histological brain sections to derive the spatial nerve fiber orientations. Here, we show how light scattering in transmission microscopy measurements can be leveraged to gain 3D structural information about fibrous tissue samples like brain tissue. For this purpose, we developed a simulation framework using finite-difference time-domain (FDTD) simulations and high performance computing, which can easily be adapted to other microscopy techniques and tissue types with comparable fibrous structures (e.g., muscle fibers, collagen, or artificial fibers). As conventional bright-field transmission microscopy provides usually only 2D information about tissue structures, a three-dimensional reconstruction of fibers across several sections is difficult. By combining our simulations with experimental studies, we show that the polarization-independent transmitted light intensity (transmittance) contains 3D information: We demonstrate in several experimental studies on brain sections from different species (rodent, monkey, human) that the transmittance decreases significantly (by more than 50%) with the increasing out-of-plane angle of the nerve fibers. Our FDTD simulations show that this decrease is mainly caused by polarization-independent light scattering in combination with the finite numerical aperture of the imaging system. This allows to use standard transmission microscopy techniques to obtain 3D information about the fiber inclination and to detect steep fibers, without need for additional measurements.

physics.med-ph↗

arXiv2017

Diattenuation of Brain Tissue and its Impact on 3D Polarized Light Imaging

3D-Polarized Light Imaging (3D-PLI) reconstructs nerve fibers in histological brain sections by measuring their birefringence. This study investigates another effect caused by the optical anisotropy of brain tissue - diattenuation. Based on numerical and experimental studies and a complete analytical description of the optical system, the diattenuation was determined to be below 4 % in rat brain tissue. It was demonstrated that the diattenuation effect has negligible impact on the fiber orientations derived by 3D-PLI. The diattenuation signal, however, was found to highlight different anatomical structures that cannot be distinguished with current imaging techniques, which makes Diattenuation Imaging a promising extension to 3D-PLI.

physics.med-ph↗

arXiv2016

Finite-Difference Time-Domain Simulation for Three-dimensional Polarized Light Imaging

Three-dimensional Polarized Light Imaging (3D-PLI) is a promising technique to reconstruct the nerve fiber architecture of human post-mortem brains from birefringence measurements of histological brain sections with micrometer resolution. To better understand how the reconstructed fiber orientations are related to the underlying fiber structure, numerical simulations are employed. Here, we present two complementary simulation approaches that reproduce the entire 3D-PLI analysis: First, we give a short review on a simulation approach that uses the Jones matrix calculus to model the birefringent myelin sheaths. Afterwards, we introduce a more sophisticated simulation tool: a 3D Maxwell solver based on a Finite-Difference Time-Domain algorithm that simulates the propagation of the electromagnetic light wave through the brain tissue. We demonstrate that the Maxwell solver is a valuable tool to better understand the interaction of polarized light with brain tissue and to enhance the accuracy of the fiber orientations extracted by 3D-PLI.

physics.med-ph↗

arXiv2015

A Jones matrix formalism for simulating three-dimensional polarized light imaging of brain tissue

The neuroimaging technique three-dimensional polarized light imaging (3D-PLI) provides a high-resolution reconstruction of nerve fibres in human post-mortem brains. The orientations of the fibres are derived from birefringence measurements of histological brain sections assuming that the nerve fibres - consisting of an axon and a surrounding myelin sheath - are uniaxial birefringent and that the measured optic axis is oriented in direction of the nerve fibres (macroscopic model). Although experimental studies support this assumption, the molecular structure of the myelin sheath suggests that the birefringence of a nerve fibre can be described more precisely by multiple optic axes oriented radially around the fibre axis (microscopic model). In this paper, we compare the use of the macroscopic and the microscopic model for simulating 3D-PLI by means of the Jones matrix formalism. The simulations show that the macroscopic model ensures a reliable estimation of the fibre orientations as long as the polarimeter does not resolve structures smaller than the diameter of single fibres. In the case of fibre bundles, polarimeters with even higher resolutions can be used without losing reliability. When taking the myelin density into account, the derived fibre orientations are considerably improved.

physics.med-ph↗

arXiv2005

Maximizing the Bandwidth Efficiency of the CMS Tracker Analog Optical Links

The feasibility of achieving faster data transmission using advanced digital modulation techniques over the current CMS Tracker analog optical link is explored. The spectral efficiency of Quadrature Amplitude Modulation -Orthogonal Frequency Division Multiplexing (QAM-OFDM) makes it an attractive option for a future implementation of the readout link. An analytical method for estimating the data-rate that can be achieved using OFDM over the current optical links is described and the first theoretical results are presented.

physics.ins-det↗