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

Approximation Algorithms for Capacitated Location Routing

An approximation algorithm for an optimization problem runs in polynomial time for all instances and is guaranteed to deliver solutions with bounded optimality gap. We derive such algorithms for different variants of capacitated location routing, an important generalization of vehicle routing where the cost of opening the depots from which vehicles operate is taken into account. Our results originate from combining algorithms and lower bounds for different relaxations of the original problem, and besides location routing we also obtain approximation algorithms for multi-depot capacitated vehicle routing by this framework. Moreover, we extend our results to further generalizations of both problems, including a prize-collecting variant, a group version, and a variant where cross-docking is allowed. We finally present a computational study of our approximation algorithm for capacitated location routing on benchmark instances and large-scale randomly generated instances. Our study reveals that the quality of the computed solutions is much closer to optimality than the provable approximation factor

Analytical Fiber ODF Reconstruction in 3D Polarized Light Imaging: Performance Assessment

International audienceThree dimensional Polarized Light Imaging (3D-PLI) allows to map the spatial fiber structure of postmortem tissue at a sub-millimeter resolution, thanks to its birefringence property. Different methods have been recently proposed to reconstruct the fiber orientation distribution function (fODF) from high-resolution vector data provided by 3D-PLI. Here, we focus on the analytical fODF computation approach, which uses the spherical harmonics to represent the fODF and analytically computes the spherical harmonics coefficients via the spherical Fourier transform. This work deals with the assessment of the performance of this approach on rich synthetic data which simulates the geometry of the neuronal fibers and on human brain dataset. A computational complexity and robustness to noise analysis demonstrate the interest and great potential of the approach

Analytical and fast Fiber Orientation Distribution reconstruction in 3D-Polarized Light Imaging

International audienceThree dimensional Polarized Light Imaging (3D-PLI) is an optical technique which allows mapping the spatial fiber architecture of fibrous postmortem tissues, at sub-millimeter resolutions. Here, we propose an analytical and fast approach to compute the fiber orientation distribution (FOD) from high-resolution vector data provided by 3D-PLI. The FOD is modeled as a sum of K orientations/Diracs on the unit sphere, described on a spherical harmonics basis and analytically computed using the spherical Fourier transform. Experiments are performed on rich synthetic data which simulate the geometry of the neuronal fibers and on human brain data. Results indicate the analytical FOD is computationally efficient and very fast, and has high angular precision and angular resolution. Furthermore, investigations on the right occipital lobe illustrate that our strategy of FOD computation enables the bridging of spatial scales from microscopic 3D-PLI information to macro-or mesoscopic dimensions of diffusion Magnetic Resonance Imaging (MRI), while being a means to evaluate prospective resolution limits for diffusion MRI to reconstruct regionspecific white matter tracts. These results demonstrate the interest and great potential of our analytical approach

Nerve fiber modeling and 3D-PLI simulations of a tilting polarization microscope

In the Fiber Architecture group of the Institute of Neuroscience and Medicine, Structuraland Functional Organization of the Brain (INM-1), 3D Polarized Light Imaging (3D-PLI)microscopy is used to measure the orientation of nerve fibers in unstained brain sections.Interpretation of the measurement can be challenging for certain regions, for examplewhere fibers cross or are oriented perpendicular to the sectioning plane. To understandthe behavior of the measured signal of such structures without further external influences,such as non-ideal optics, simulations are used where each parameter is known. In orderto perform simulations, virtual tissue models are needed and a virtual 3D-PLI microscope,being capable of simulating the influence of the tissue on the light.In order to design realistic models of dense nerve fiber tissue, it must be ensured thatindividual nerve fibers do not overlap. This is especially difficult to design in advancefor interwoven structures, as is occurs in nerve fiber crossings. Therefore, a nerve fibermodeling specialized algorithm was designed in this thesis. The algorithm will checka given volume for overlaps of single nerve fibers, and then slowly push them apart atthe affected locations. Thus, a collision-free tissue model is created over time. Thepre-existing simulation algorithm of the 3D PLI microscope was completely redesigned aspart of this work. The algorithm is now able to run in parallel on multiple CPU cores aswell as computational clusters. Thus, a large number of simulations can be performed,allowing for greater statistics in the analyses. These two algorithms were published inthe software package fiber architecture simulation toolbox of 3D-PLI (fastPLI).Finally, in this thesis, nerve fiber models consisting of two nerve fiber populations,i. e. two densely packed crossing nerve fiber bundles, were created and subsequentlysimulated. The results show, that the orientation of the nerve fiber population, whichhas a higher proportion in the volume, can be determined. With the current resolution ofthe microscopes used, it is not possible to determine both fiber population orientationsindividual. The measured orientation seems to follow the circular mean as a functionon the proportional volume fraction of the nerve fiber populations, taking into accountthe decrease of the measured signal due to the increasing tilt angle. In summary, thedevelopment of the algorithm for modeling nerve fibers together with the simulation ina toolbox has proven to be a suitable tool to be able to investigate questions quicklythrough simulations

fastPLI: A Fiber Architecture Simulation Toolbox for 3D-PLI

fastPLI is an open source toolbox based on Python and C++ for modeling myelinated axons, i.e. nerve fibers and simulating the results of measurement of fiber orientations with a polarization microscope using 3D Polarized Light Imaging (3D-PLI). The fastPLI package includes the following modules: 1. Fiber Modelling Modules: A detailed 3D modelling of nerve fibers at the micrometer level is essential as input for the measurement simulation. In order to recreate biological tissue as a model, it is important that the nerve fibers do not spatially overlap. We have decided to implement a solver module that takes any configuration of fiber bundles as input and converts it over several iterations into a collision-free configuration. In order to generate collision free fiber arrangements, a dedicated algorithm to prohibit such overlaps has been developed. 2. Simulation Module: The 3D-PLI simulation is based on Stokes vector and Müller matrix approaches. For the simulation the polarimetric setup can be equipped with a tiltable specimen stage. By this means the brain section can be scanned from oblique views which adds important information to unambiguously analyze the 3D fiber orientation. 3. Analysis Module: The resulting simulated measurements (i.e., image stacks of a section acquired at different polarizing filter rotation angles and, optionally, at different oblique views) can be processed similarly to the real, experimental 3D-PLI

Dense Fiber Modeling for 3D-Polarized Light Imaging Simulations

3D-Polarized Light Imaging (3D-PLI) is a neuroimaging tech-nique used to study the structural connectivity of the human brain atthe meso- and microscale. In 3D-PLI, the complex nerve fiber architec-ture of the brain is characterized by 3D orientation vector fields thatare derived from birefringence measurements of unstained histologicalbrain sections by means of an effective physical model.To optimize the physical model and to better understand the under-lying microstructure, numerical simulations are essential tools to op-timize the used physical model and to understand the underlying mi-crostructure in detail. The simulations rely on predefined configurationsof nerve fiber models (e.g. crossing, kissing, or complex intermingling),their physical properties, as well as the physical properties of the em-ployed optical system to model the entire 3D-PLI measurement. Bycomparing the simulation and experimental results, possible misinter-pretations in the fiber reconstruction process of 3D-PLI can be identi-fied. Here, we focus on fiber modeling with a specific emphasize on thegeneration of dense fiber distributions as found in the human brain’swhite matter. A new algorithm will be introduced that allows to controlpossible intersections of computationally grown fiber structures

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

An integrated approach to tactical transportation planning in logistics networks

We propose a new mathematical model for transport optimization in logistics networks on the tactical level. The main features include accurately modeled tariff structures and the integration of spatial and temporal consolidation effects via a cyclic pattern expansion. Using several graph-based gadgets, we are able to formulate our problem as a capacitated network design problem. To solve the model, we propose a local search procedure that reroutes flow of multiple commodities at once. Initial solutions are generated by various heuristics, relying on shortest path augmentations and LP techniques. As an important subproblem we identify the optimization of tariff selection on individual links, which we prove to be NP-hard and for which we derive exact as well as fast greedy approaches. We complement our heuristics by lower bounds from an aggregated mixed-integer programming formulation with strengthened inequalities. In a case study from the automotive, chemical, and retail industries, we prove that most of our solutions are within a single-digit percentage of the optimum. </jats:p

MEDUSA: A GPU-based tool to create realistic phantoms of the brain microstructure using tiny spheres

A GPU-based tool to generate realistic phantoms of the brain microstructure is presented. Using a sphericalmeshing technique which decomposes each microstructural item into a set of overlapping spheres, the phantomconstruction is made very fast while reliably avoiding the collisions between items in the scene. This novelmethod is applied to the construction of human brain white matter microstructural components, namely axonalfibers, oligodendrocytes and astrocytes. The algorithm reaches high values of packing density and angulardispersion for the axonal fibers, even in the case of multiple white matter fiber populations and enables theconstruction of complex biomimicking geometries including myelinated axons, beaded axons, and glial cells. Themethod can be readily adapted to model gray matter microstructure