Quantitative estimation of 3-D fiber course in gross histological sections of the human brain using polarized light

Near-real-time Mueller polarimetric image processing for neurosurgical intervention

PURPOSE

Wide-field imaging Mueller polarimetry is a revolutionary, label-free, and non-invasive modality for computer-aided intervention; in neurosurgery, it aims to provide visual feedback of white matter fibre bundle orientation from derived parameters. Conventionally, robust polarimetric parameters are estimated after averaging multiple measurements of intensity for each pair of probing and detected polarised light. Long multi-shot averaging, however, is not compatible with real-time in vivo imaging, and the current performance of polarimetric data processing hinders the translation to clinical practice.

METHODS

A learning-based denoising framework is tailored for fast, single-shot, noisy acquisitions of polarimetric intensities. Also, performance-optimised image processing tools are devised for the derivation of clinically relevant parameters. The combination recovers accurate polarimetric parameters from fast acquisitions with near-real-time performance, under the assumption of pseudo-Gaussian polarimetric acquisition noise.

RESULTS

The denoising framework is trained, validated, and tested on experimental data comprising tumour-free and diseased human brain samples in different conditions. Accuracy and image quality indices showed significant ( p < 0.05 ) improvements on testing data for a fast single-pass denoising versus the state-of-the-art and high polarimetric image quality standards. The computational time is reported for the end-to-end processing.

CONCLUSION

The end-to-end image processing achieved real-time performance for a localised field of view ( ≈ 6.5 mm 2 ). The denoised polarimetric intensities produced visibly clear directional patterns of neuronal fibre tracts in line with reference polarimetric image quality standards; directional disruption was kept in case of neoplastic lesions. The presented advances pave the way towards feasible oncological neurosurgical translations of novel, label-free, interventional feedback.

Impact of corpus callosum fiber tract crossing on polarimetric images of human brain histological sections: ex vivo studies in transmission configuration

Significance

Imaging Mueller polarimetry is capable to trace in-plane orientation of brain fiber tracts by detecting the optical anisotropy of white matter of healthy brain. Brain tumor cells grow chaotically and destroy this anisotropy. Hence, the drop in scalar retardance values and randomization of the azimuth of the optical axis could serve as the optical marker for brain tumor zone delineation.

Aim

The presence of underlying crossing fibers can also affect the values of scalar retardance and the azimuth of the optical axis. We studied and analyzed the impact of fiber crossing on the polarimetric images of thin histological sections of brain corpus callosum.

Approach

We used the transmission Mueller microscope for imaging of two-layered stacks of thin sections of corpus callosum tissue to mimic the overlapping brain fiber tracts with different fiber orientations. The decomposition of the measured Mueller matrices was performed with differential and Lu-Chipman algorithms and completed by the statistical analysis of the maps of scalar retardance, azimuth of the optical axis, and depolarization.

Results

Our results indicate the sensitivity of Mueller polarimetry to different spatial arrangement of brain fiber tracts as seen in the maps of scalar retardance and azimuth of optical axis of two-layered stacks of corpus callosum sections The depolarization varies slightly (< 15 % ) with the orientation of the optical axes in both corpus callosum stripes, but its value increases by 2.5 to 3 times with the stack thickness.

Conclusions

The crossing brain fiber tracts measured in transmission induce the drop in values of scalar retardance and randomization of the azimuth of the optical axis at optical path length of 15    μ m . It suggests that the presence of nerve fibers crossing within the depth of few microns will be also detected in polarimetric maps of brain white matter measured in reflection configuration.

An open resource combining multi-contrast MRI and microscopy in the macaque brain

Understanding brain structure and function often requires combining data across different modalities and scales to link microscale cellular structures to macroscale features of whole brain organisation. Here we introduce the BigMac dataset, a resource combining in vivo MRI, extensive postmortem MRI and multi-contrast microscopy for multimodal characterisation of a single whole macaque brain. The data spans modalities (MRI and microscopy), tissue states (in vivo and postmortem), and four orders of spatial magnitude, from microscopy images with micrometre or sub-micrometre resolution, to MRI signals on the order of millimetres. Crucially, the MRI and microscopy images are carefully co-registered together to facilitate quantitative multimodal analyses. Here we detail the acquisition, curation, and first release of the data, that together make BigMac a unique, openly-disseminated resource available to researchers worldwide. Further, we demonstrate example analyses and opportunities afforded by the data, including improvement of connectivity estimates from ultra-high angular resolution diffusion MRI, neuroanatomical insight provided by polarised light imaging and myelin-stained histology, and the joint analysis of MRI and microscopy data for reconstruction of the microscopy-inspired connectome. All data and code are made openly available.

Instant polarized light microscopy pi (IPOLπ) for quantitative imaging of collagen architecture and dynamics in ocular tissues

Collagen architecture determines the biomechanical environment in the eye, and thus characterizing collagen fiber organization and biomechanics is essential to fully understand eye physiology and pathology. We recently introduced instant polarized light microscopy (IPOL) that encodes optically information about fiber orientation and retardance through a color snapshot. Although IPOL allows imaging collagen at the full acquisition speed of the camera, with excellent spatial and angular resolutions, a limitation is that the orientation-encoding color is cyclic every 90 degrees (π/2 radians). In consequence, two orthogonal fibers have the same color and therefore the same orientation when quantified by color-angle mapping. In this study, we demonstrate IPOLπ, a new variation of IPOL, in which the orientation-encoding color is cyclic every 180 degrees (π radians). Herein we present the fundamentals of IPOLπ, including a framework based on a Mueller-matrix formalism to characterize how fiber orientation and retardance determine the color. The improved quantitative capability of IPOLπ enables further study of essential biomechanical properties of collagen in ocular tissues, such as fiber anisotropy and crimp. We present a series of experimental calibrations and quantitative procedures to visualize and quantify ocular collagen orientation and microstructure in the optic nerve head, a region in the back of the eye. There are four important strengths of IPOLπ compared to IPOL. First, IPOLπ can distinguish the orientations of orthogonal collagen fibers via colors, whereas IPOL cannot. Second, IPOLπ requires a lower exposure time than IPOL, thus allowing faster imaging speed. Third, IPOLπ allows visualizing non-birefringent tissues and backgrounds from tissue absorption, whereas both appear dark in IPOL images. Fourth, IPOLπ is cheaper and less sensitive to imperfectly collimated light than IPOL. Altogether, the high spatial, angular, and temporal resolutions of IPOLπ enable a deeper insight into ocular biomechanics and eye physiology and pathology.

Instant polarized light microscopy pi (IPOLπ) for quantitative imaging of collagen architecture and dynamics in ocular tissues

Collagen architecture determines the biomechanical environment in the eye, and thus characterizing collagen fiber organization and biomechanics is essential to fully understand eye physiology and pathology. We recently introduced instant polarized light microscopy (IPOL) that encodes optically information about fiber orientation and retardance through a color snapshot. Although IPOL allows imaging collagen at the full acquisition speed of the camera, with excellent spatial and angular resolutions, a limitation is that the orientation-encoding color is cyclic every 90 degrees (π/2 radians). In consequence, two orthogonal fibers have the same color and therefore the same orientation when quantified by color-angle mapping. In this study, we demonstrate IPOLπ, a new variation of IPOL, in which the orientation-encoding color is cyclic every 180 degrees (π radians). Herein we present the fundamentals of IPOLπ, including a framework based on a Mueller-matrix formalism to characterize how fiber orientation and retardance determine the color. The improved quantitative capability of IPOLπ enables further study of essential biomechanical properties of collagen in ocular tissues, such as fiber anisotropy and crimp. We present a series of experimental calibrations and quantitative procedures to visualize and quantify ocular collagen orientation and microstructure in the optic nerve head, a region in the back of the eye. There are four important strengths of IPOLπ compared to IPOL. First, IPOLπ can distinguish the orientations of orthogonal collagen fibers via colors, whereas IPOL cannot. Second, IPOLπ requires a lower exposure time than IPOL, thus allowing faster imaging speed. Third, IPOLπ allows visualizing non-birefringent tissues and backgrounds from tissue absorption, whereas both appear dark in IPOL images. Fourth, IPOLπ is cheaper and less sensitive to imperfectly collimated light than IPOL. Altogether, the high spatial, angular, and temporal resolutions of IPOLπ enable a deeper insight into ocular biomechanics and eye physiology and pathology.

CODA: quantitative 3D reconstruction of large tissues at cellular resolution

A central challenge in biology is obtaining high-content, high-resolution information while analyzing tissue samples at volumes relevant to disease progression. We address this here with CODA, a method to reconstruct exceptionally large (up to multicentimeter cubed) tissues at subcellular resolution using serially sectioned hematoxylin and eosin-stained tissue sections. Here we demonstrate CODA's ability to reconstruct three-dimensional (3D) distinct microanatomical structures in pancreas, skin, lung and liver tissues. CODA allows creation of readily quantifiable tissue volumes amenable to biological research. As a testbed, we assess the microanatomy of the human pancreas during tumorigenesis within the branching pancreatic ductal system, labeling ten distinct structures to examine heterogeneity and structural transformation during neoplastic progression. We show that pancreatic precancerous lesions develop into distinct 3D morphological phenotypes and that pancreatic cancer tends to spread far from the bulk tumor along collagen fibers that are highly aligned to the 3D curves of ductal, lobular, vascular and neural structures. Thus, CODA establishes a means to transform broadly the structural study of human diseases through exploration of exhaustively labeled 3D microarchitecture.

Backscattering polarimetric imaging of the human brain to determine the orientation and degree of alignment of nerve fiber bundles

The nerve fiber bundles constitutive of the white matter in the brain are organized in such a way that they exhibit a certain degree of structural anisotropy and birefringence. The birefringence exhibited by such aligned fibrous tissue is known to be extremely sensitive to small pathological alterations. Indeed, highly aligned anisotropic fibers exhibit higher birefringence than structures with weaker alignment and anisotropy, such as cancerous tissue. In this study, we performed experiments on thick coronal slices of a healthy human brain to explore the possibility of (i) measuring, with a polarimetric microscope the birefringence exhibited by the white matter and (ii) relating the measured birefringence to the fiber orientation and the degree of alignment. This is done by analyzing the spatial distribution of the degree of polarization of the backscattered light and its variation with the polarization state of the probing beam. We demonstrate that polarimetry can be used to reliably distinguish between white and gray matter, which might help to intraoperatively delineate unstructured tumorous tissue and well organized healthy brain tissue. In addition, we show that our technique is able to sensitively reconstruct the local mean nerve fiber orientation in the brain, which can help to guide tumor resections by identifying vital nerve fiber trajectories thereby improving the outcome of the brain surgery.

Microscopic susceptibility anisotropy imaging

PURPOSE

The gradient-echo MR signal in brain white matter depends on the orientation of the fibers with respect to the external magnetic field. To map microstructure-specific magnetic susceptibility in orientationally heterogeneous material, it is thus imperative to regress out unwanted orientation effects.

METHODS

This work introduces a novel framework, referred to as microscopic susceptibility anisotropy imaging, that disentangles the 2 principal effects conflated in gradient-echo measurements, (a) the susceptibility properties of tissue microenvironments, especially the myelin microstructure, and (b) the axon orientation distribution relative to the magnetic field. Specifically, we utilize information about the orientational tissue structure inferred from diffusion MRI data to factor out the B 0 -direction dependence of the frequency difference signal.

RESULTS

A human pilot study at 3 T demonstrates proxy maps of microscopic susceptibility anisotropy unconfounded by fiber crossings and orientation dispersion as well as magnetic field direction. The developed technique requires only a dual-echo gradient-echo scan acquired at 1 or 2 head orientations with respect to the magnetic field and a 2-shell diffusion protocol achievable on standard scanners within practical scan times.

CONCLUSIONS

The quantitative recovery of microscopic susceptibility features in the presence of orientational heterogeneity potentially improves the assessment of microstructural tissue integrity.

Decoding the microstructural correlate of diffusion MRI

Diffusion imaging has evolved considerably over the past decade. While it provides valuable information about the structural connectivity at the macro- and mesoscopic scale, bridging the gap to the microstructure at the level of single nerve fibers poses an enormous challenge. This is particularly true for the human brain with its large size, its large white-matter volume and availability of histological techniques for studying human whole-brain sections and subsequent 3D reconstruction. Classic post-mortem techniques for studying the fiber architecture of the brain, such as myeloarchitectonic staining or dye tracing, are complemented by novel histological approaches, such as 3D polarized light imaging or optical coherence tomography, enabling unique insight into the fiber architecture from large fiber bundles within deep white matter to single nerve fibers in the cortex. The present review discusses the benefits and challenges of these latest developments in comparison with the classic techniques, with particular focus on the mutual exchange between in vivo and post-mortem diffusion imaging and post-mortem microstructural approaches for understanding the wiring of the brain across different scales.

Photogrammetry of the Human Brain: A Novel Method for Three-Dimensional Quantitative Exploration of the Structural Connectivity in Neurosurgery and Neurosciences

BACKGROUND

Anatomic awareness of the structural connectivity of the brain is mandatory for neurosurgeons, to select the most effective approaches for brain resections. Although standard microdissection is a validated technique to investigate the different white matter (WM) pathways and to verify the results of tractography, the possibility of interactive exploration of the specimens and reliable acquisition of quantitative information has not been described. Photogrammetry is a well-established technique allowing an accurate metrology on highly defined three-dimensional (3D) models. The aim of this work is to propose the application of the photogrammetric technique for supporting the 3D exploration and the quantitative analysis on the cerebral WM connectivity.

METHODS

The main perisylvian pathways, including the superior longitudinal fascicle and the arcuate fascicle were exposed using the Klingler technique. The photogrammetric acquisition followed each dissection step. The point clouds were registered to a reference magnetic resonance image of the specimen. All the acquisitions were coregistered into an open-source model.

RESULTS

We analyzed 5 steps, including the cortical surface, the short intergyral fibers, the indirect posterior and anterior superior longitudinal fascicle, and the arcuate fascicle. The coregistration between the magnetic resonance imaging mesh and the point clouds models was highly accurate. Multiple measures of distances between specific cortical landmarks and WM tracts were collected on the photogrammetric model.

CONCLUSIONS

Photogrammetry allows an accurate 3D reproduction of WM anatomy and the acquisition of unlimited quantitative data directly on the real specimen during the postdissection analysis. These results open many new promising neuroscientific and educational perspectives and also optimize the quality of neurosurgical treatments.

Microstructural parcellation of the human brain

The human cerebral cortex is composed of a mosaic of areas thought to subserve different functions. The parcellation of the cortex into areas has a long history and has been carried out using different combinations of structural, connectional, receptotopic, and functional properties. Here we give a brief overview of the history of cortical parcellation, and explore different microstructural properties and analysis techniques that can be used to define the borders between different regions. We show that accounting for the 3D geometry of the highly folded human cortex is especially critical for accurate parcellation. We close with some thoughts on future directions and best practices for combining modalities.

as-PSOCT: Volumetric microscopic imaging of human brain architecture and connectivity

Polarization sensitive optical coherence tomography (PSOCT) with serial sectioning has enabled the investigation of 3D structures in mouse and human brain tissue samples. By using intrinsic optical properties of back-scattering and birefringence, PSOCT reliably images cytoarchitecture, myeloarchitecture and fiber orientations. In this study, we developed a fully automatic serial sectioning polarization sensitive optical coherence tomography (as-PSOCT) system to enable volumetric reconstruction of human brain samples with unprecedented sample size and resolution. The 3.5 μm in-plane resolution and 50 μm through-plane voxel size allow inspection of cortical layers that are a single-cell in width, as well as small crossing fibers. We show the abilities of as-PSOCT in quantifying layer thicknesses of the cerebellar cortex and creating microscopic tractography of intricate fiber networks in the subcortical nuclei and internal capsule regions, all based on volumetric reconstructions. as-PSOCT provides a viable tool for studying quantitative cytoarchitecture and myeloarchitecture and mapping connectivity with microscopic resolution in the human brain.

Diffusion MRI microstructure models with in vivo human brain Connectome data: results from a multi-group comparison

A large number of mathematical models have been proposed to describe the measured signal in diffusion-weighted (DW) magnetic resonance imaging (MRI). However, model comparison to date focuses only on specific subclasses, e.g. compartment models or signal models, and little or no information is available in the literature on how performance varies among the different types of models. To address this deficiency, we organized the 'White Matter Modeling Challenge' during the International Symposium on Biomedical Imaging (ISBI) 2015 conference. This competition aimed to compare a range of different kinds of models in their ability to explain a large range of measurable in vivo DW human brain data. Specifically, we assessed the ability of models to predict the DW signal accurately for new diffusion gradients and b values. We did not evaluate the accuracy of estimated model parameters, as a ground truth is hard to obtain. We used the Connectome scanner at the Massachusetts General Hospital, using gradient strengths of up to 300 mT/m and a broad set of diffusion times. We focused on assessing the DW signal prediction in two regions: the genu in the corpus callosum, where the fibres are relatively straight and parallel, and the fornix, where the configuration of fibres is more complex. The challenge participants had access to three-quarters of the dataset and their models were ranked on their ability to predict the remaining unseen quarter of the data. The challenge provided a unique opportunity for a quantitative comparison of diverse methods from multiple groups worldwide. The comparison of the challenge entries reveals interesting trends that could potentially influence the next generation of diffusion-based quantitative MRI techniques. The first is that signal models do not necessarily outperform tissue models; in fact, of those tested, tissue models rank highest on average. The second is that assuming a non-Gaussian (rather than purely Gaussian) noise model provides little improvement in prediction of unseen data, although it is possible that this may still have a beneficial effect on estimated parameter values. The third is that preprocessing the training data, here by omitting signal outliers, and using signal-predicting strategies, such as bootstrapping or cross-validation, could benefit the model fitting. The analysis in this study provides a benchmark for other models and the data remain available to build up a more complete comparison in the future.

Automatic Segmentation of Human Cortical Layer-Complexes and Architectural Areas Using Ex vivo Diffusion MRI and Its Validation

Recently, several magnetic resonance imaging contrast mechanisms have been shown to distinguish cortical substructure corresponding to selected cortical layers. Here, we investigate cortical layer and area differentiation by automatized unsupervised clustering of high-resolution diffusion MRI data. Several groups of adjacent layers could be distinguished in human primary motor and premotor cortex. We then used the signature of diffusion MRI signals along cortical depth as a criterion to detect area boundaries and find borders at which the signature changes abruptly. We validate our clustering results by histological analysis of the same tissue. These results confirm earlier studies which show that diffusion MRI can probe layer-specific intracortical fiber organization and, moreover, suggests that it contains enough information to automatically classify architecturally distinct cortical areas. We discuss the strengths and weaknesses of the automatic clustering approach and its appeal for MR-based cortical histology.

Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI

The question whether our brain pathways adhere to a geometric grid structure has been a popular topic of debate in the diffusion imaging and neuroscience societies. Wedeen et al. (2012a, b) proposed that the brain's white matter is organized like parallel sheets of interwoven pathways. Catani et al. (2012) concluded that this grid pattern is most likely an artifact, resulting from methodological biases that cause the tractography pathways to cross in orthogonal angles. To date, ambiguities in the mathematical conditions for a sheet structure to exist (e.g. its relation to orthogonal angles) combined with the lack of extensive quantitative evidence have prevented wide acceptance of the hypothesis. In this work, we formalize the relevant terminology and recapitulate the condition for a sheet structure to exist. Note that this condition is not related to the presence or absence of orthogonal crossing fibers, and that sheet structure is defined formally as a surface formed by two sets of interwoven pathways intersecting at arbitrary angles within the surface. To quantify the existence of sheet structure, we present a novel framework to compute the sheet probability index (SPI), which reflects the presence of sheet structure in discrete orientation data (e.g. fiber peaks derived from diffusion MRI). With simulation experiments we investigate the effect of spatial resolution, curvature of the fiber pathways, and measurement noise on the ability to detect sheet structure. In real diffusion MRI data experiments we can identify various regions where the data supports sheet structure (high SPI values), but also areas where the data does not support sheet structure (low SPI values) or where no reliable conclusion can be drawn. Several areas with high SPI values were found to be consistent across subjects, across multiple data sets obtained with different scanners, resolutions, and degrees of diffusion weighting, and across various modeling techniques. Under the strong assumption that the diffusion MRI peaks reflect true axons, our results would therefore indicate that pathways do not form sheet structures at every crossing fiber region but instead at well-defined locations in the brain. With this framework, sheet structure location, extent, and orientation could potentially serve as new structural features of brain tissue. The proposed method can be extended to quantify sheet structure in directional data obtained with techniques other than diffusion MRI, which is essential for further validation.

Multi-compartment microscopic diffusion imaging

This paper introduces a multi-compartment model for microscopic diffusion anisotropy imaging. The aim is to estimate microscopic features specific to the intra- and extra-neurite compartments in nervous tissue unconfounded by the effects of fibre crossings and orientation dispersion, which are ubiquitous in the brain. The proposed MRI method is based on the Spherical Mean Technique (SMT), which factors out the neurite orientation distribution and thus provides direct estimates of the microscopic tissue structure. This technique can be immediately used in the clinic for the assessment of various neurological conditions, as it requires only a widely available off-the-shelf sequence with two b-shells and high-angular gradient resolution achievable within clinically feasible scan times. To demonstrate the developed method, we use high-quality diffusion data acquired with a bespoke scanner system from the Human Connectome Project. This study establishes the normative values of the new biomarkers for a large cohort of healthy young adults, which may then support clinical diagnostics in patients. Moreover, we show that the microscopic diffusion indices offer direct sensitivity to pathological tissue alterations, exemplified in a preclinical animal model of Tuberous Sclerosis Complex (TSC), a genetic multi-organ disorder which impacts brain microstructure and hence may lead to neurological manifestations such as autism, epilepsy and developmental delay.

Polychromatic polarization microscope: bringing colors to a colorless world

Interference of two combined white light beams produces Newton colors if one of the beams is retarded relative to the other by from 400 nm to 2000 nm. In this case the corresponding interfering spectral components are added as two scalars at the beam combination. If the retardance is below 400 nm the two-beam interference produces grey shades only. The interference colors are widely used for analyzing birefringent samples in mineralogy. However, many of biological structures have retardance <100 nm. Therefore, cells and tissues under a regular polarization microscope are seen as grey image, which contrast disappears at certain orientations. Here we are proposing for the first time using vector interference of polarized light in which the full spectrum colors are created at retardance of several nanometers, with the hue determined by orientation of the birefringent structure. The previously colorless birefringent images of organelles, cells, and tissues become vividly colored. This approach can open up new possibilities for the study of biological specimens with weak birefringent structures, diagnosing various diseases, imaging low birefringent crystals, and creating new methods for controlling colors of the light beam.

Unraveling the multiscale structural organization and connectivity of the human brain: the role of diffusion MRI

The structural architecture and the anatomical connectivity of the human brain show different organizational principles at distinct spatial scales. Histological staining and light microscopy techniques have been widely used in classical neuroanatomical studies to unravel brain organization. Using such techniques is a laborious task performed on 2-dimensional histological sections by skilled anatomists possibly aided by semi-automated algorithms. With the recent advent of modern magnetic resonance imaging (MRI) contrast mechanisms, cortical layers and columns can now be reliably identified and their structural properties quantified post-mortem. These developments are allowing the investigation of neuroanatomical features of the brain at a spatial resolution that could be interfaced with that of histology. Diffusion MRI and tractography techniques, in particular, have been used to probe the architecture of both white and gray matter in three dimensions. Combined with mathematical network analysis, these techniques are increasingly influential in the investigation of the macro-, meso-, and microscopic organization of brain connectivity and anatomy, both in vivo and ex vivo. Diffusion MRI-based techniques in combination with histology approaches can therefore support the endeavor of creating multimodal atlases that take into account the different spatial scales or levels on which the brain is organized. The aim of this review is to illustrate and discuss the structural architecture and the anatomical connectivity of the human brain at different spatial scales and how recently developed diffusion MRI techniques can help investigate these.

Quantitative mapping of the per-axon diffusion coefficients in brain white matter

Purpose

This article presents a simple method for estimating the effective diffusion coefficients parallel and perpendicular to the axons unconfounded by the intravoxel fiber orientation distribution. We also call these parameters the per‐axon or microscopic diffusion coefficients.

Theory and Methods

Diffusion MR imaging is used to probe the underlying tissue material. The key observation is that for a fixed b‐value the spherical mean of the diffusion signal over the gradient directions does not depend on the axon orientation distribution. By exploiting this invariance property, we propose a simple, fast, and robust estimator of the per‐axon diffusion coefficients, which we refer to as the spherical mean technique.

Results

We demonstrate quantitative maps of the axon‐scale diffusion process, which has factored out the effects due to fiber dispersion and crossing, in human brain white matter. These microscopic diffusion coefficients are estimated in vivo using a widely available off‐the‐shelf pulse sequence featuring multiple b‐shells and high‐angular gradient resolution.

Conclusion

The estimation of the per‐axon diffusion coefficients is essential for the accurate recovery of the fiber orientation distribution. In addition, the spherical mean technique enables us to discriminate microscopic tissue features from fiber dispersion, which potentially improves the sensitivity and/or specificity to various neurological conditions. Magn Reson Med, 2015. Magn Reson Med 75:1752–1763, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc.

PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study

Purpose

To identify optimal pulsed gradient spin‐echo (PGSE) and oscillating gradient spin‐echo (OGSE) sequence settings for maximizing sensitivity to axon diameter in idealized and practical conditions.

Methods

Simulations on a simple two‐compartment white matter model (with nonpermeable cylinders) are used to investigate a wide space of clinically plausible PGSE and OGSE sequence parameters with trapezoidal diffusion gradient waveforms. Signal sensitivity is measured as a derivative of the signal with respect to axon diameter. Models of parallel and dispersed fibers are investigated separately to represent idealized and practical conditions.

Results

Simulations show that, for the simple case of gradients perfectly perpendicular to straight parallel fibers, PGSE always gives maximum sensitivity. However, in real‐world scenarios where fibers have unknown and dispersed orientation, low‐frequency OGSE provides higher sensitivity. Maximum sensitivity results show that on current clinical scanners (G_max = 60 mT/m, signal to noise ratio (SNR) = 20) axon diameters below 6 µm are indistinguishable from zero. Scanners with stronger gradient systems such as the Massachusetts General Hospital (MGH) Connectom scanner (G_max = 300 mT/m) can extend this sensitivity limit down to 2–3 µm, probing a much greater proportion of the underlying axon diameter distribution.

Conclusion

Low‐frequency OGSE provides additional sensitivity to PGSE in practical situations. OGSE is particularly advantageous for systems with high performance gradients. Magn Reson Med 75:688–700, 2016. © 2015 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Understanding fiber mixture by simulation in 3D Polarized Light Imaging

3D Polarized Light Imaging (3D-PLI) is a neuroimaging technique that has opened up new avenues to study the complex architecture of nerve fibers in postmortem brains. The spatial orientations of the fibers are derived from birefringence measurements of unstained histological brain sections that are interpreted by a voxel-based analysis. This, however, implies that a single fiber orientation vector is obtained for each voxel and reflects the net effect of all comprised fibers. The mixture of various fiber orientations within an individual voxel is a priori not accessible by a standard 3D-PLI measurement. In order to better understand the effects of fiber mixture on the measured 3D-PLI signal and to improve the interpretation of real data, we have developed a simulation method referred to as SimPLI. By means of SimPLI, it is possible to reproduce the entire 3D-PLI analysis starting from synthetic fiber models in user-defined arrangements and ending with measurement-like tissue images. For the simulation, each synthetic fiber is considered as an optical retarder, i.e., multiple fibers within one voxel are described by multiple retarder elements. The investigation of different synthetic crossing fiber arrangements generated with SimPLI demonstrated that the derived fiber orientations are strongly influenced by the relative mixture of crossing fibers. In case of perpendicularly crossing fibers, for example, the derived fiber direction corresponds to the predominant fiber direction. The derived fiber inclination turned out to be not only influenced by myelin density but also systematically overestimated due to signal attenuation. Similar observations were made for synthetic models of optic chiasms of a human and a hooded seal which were opposed to experimental 3D-PLI data sets obtained from the chiasms of both species. Our study showed that SimPLI is a powerful method able to test hypotheses on the underlying fiber structure of brain tissue and, therefore, to improve the reliability of the extraction of nerve fiber orientations with 3D-PLI.

Temperature and concentration dependent fibrillogenesis for improved magnetic alignment of collagen gels

Collagen fibrils form the structural basis for a broad range of complex biological tissues and materials.

FIBRASCAN: a novel method for 3D white matter tract reconstruction in MR space from cadaveric dissection

INTRODUCTION

Diffusion tractography relies on complex mathematical models that provide anatomical information indirectly, and it needs to be validated. In humans, up to now, tractography has mainly been validated by qualitative comparison with data obtained from dissection. No quantitative comparison was possible because Magnetic Resonance Imaging (MRI) and dissection data are obtained in different reference spaces, and because fiber tracts are progressively destroyed by dissection. Here, we propose a novel method and software (FIBRASCAN) that allow accurate reconstruction of fiber tracts from dissection in MRI reference space.

METHOD

Five human hemispheres, obtained from four formalin-fixed brains were prepared for Klingler's dissection, placed on a holder with fiducial markers, MR scanned, and then dissected to expose the main association tracts. During dissection, we performed iterative acquisitions of the surface and texture of the specimens using a laser scanner and two digital cameras. Each texture was projected onto the corresponding surface and the resulting set of textured surfaces was coregistered thanks to the fiducial holders. The identified association tracts were then interactively segmented on each textured surface and reconstructed from the pile of surface segments. Finally, the reconstructed tracts were coregistered onto ex vivo MRI space thanks to the fiducials. Each critical step of the process was assessed to measure the precision of the method.

RESULTS

We reconstructed six fiber tracts (long, anterior and posterior segments of the superior longitudinal fasciculus; Inferior fronto-occipital, Inferior longitudinal and uncinate fasciculi) from cadaveric dissection and ported them into ex vivo MRI reference space. The overall accuracy of the method was of the order of 1mm: surface-to-surface registration=0.138mm (standard deviation (SD)=0.058mm), deformation of the specimen during dissection=0.356mm (SD=0.231mm), and coregistration surface-MRI=0.6mm (SD=0.274mm). The spatial resolution of the method (distance between two consecutive surface acquisitions) was 0.345mm (SD=0.115mm).

CONCLUSION

This paper presents the robustness of a novel method, FIBRASCAN, for accurate reconstruction of fiber tracts from dissection in the ex vivo MR reference space. This is a major step toward quantitative comparison of MR tractography with dissection results.

Can T2-spectroscopy resolve submicrometer axon diameters?

The microscopic geometry of white matter carries rich information about brain function in health and disease. A key challenge for medical imaging is to estimate microstructural features noninvasively. One important parameter is the axon diameter, which correlates with the conduction time delay of action potentials and is affected by various neurological disorders. Diffusion magnetic resonance (MR) experiments are the method of choice today when we aim to recover the axon diameter distribution, although the technique requires very high gradient strengths in order to assess nerve fibers with one micrometer or less in diameter. In practice in-vivo brain imaging is only sensitive to the largest axons, not least due to limitations in the human physiology which tolerates only moderate gradient strengths. This work studies, from a theoretical perspective, the feasibility of T2-spectroscopy to resolve submicrometer tissue structures. Exploiting the surface relaxation effect, we formulate a plausible biophysical model relating the axon diameter distribution to the T2-weighted signal, which is based on a surface-to-volume ratio approximation of the Bloch-Torrey equation. Under a certain regime of bulk and surface relaxation coefficients, our simulation results suggest that it might be possible to reveal axons smaller than one micrometer in diameter.

Anatomical brain networks on the prediction of abnormal brain states

Graph-based brain anatomical network analysis models the brain as a graph whose nodes represent structural/functional regions, whereas the links between them represent nervous fiber connections. Initial studies of brain anatomical networks using this approach were devoted to describe the key organizational principles of the normal brain, while current trends seem to be more focused on detecting network alterations associated to specific brain disorders. Anatomical networks reconstructed using diffusion-weighed magnetic resonance-imaging techniques can be particularly useful in predicting abnormal brain states in which the white matter structure and, subsequently, the interconnections between gray matter regions are altered (e.g., due to the presence of diseases such as schizophrenia, stroke, multiple sclerosis, and dementia). This article offers an overview from early gross connectional anatomy explorations until more recent advances on anatomical brain network reconstruction approaches, with a specific focus on how the latter move toward the prediction of abnormal brain states. While anatomical graph-based predictor approaches are still at an early stage, they bear promising implications for individualized clinical diagnosis of neurological and psychiatric disorders, as well as for neurodevelopmental evaluations and subsequent assisted creation of educational strategies related to specific cognitive disorders.

Networks of anatomical covariance

Functional imaging or diffusion-weighted imaging techniques are widely used to understand brain connectivity at the systems level and its relation to normal neurodevelopment, cognition or brain disorders. It is also possible to extract information about brain connectivity from the covariance of morphological metrics derived from anatomical MRI. These covariance patterns may arise from genetic influences on normal development and aging, from mutual trophic reinforcement as well as from experience-related plasticity. This review describes the basic methodological strategies, the biological basis of the observed covariance as well as applications in normal brain and brain disease before a final review of future prospects for the technique.

Quantitative polarized light microscopy of unstained mammalian cochlear sections

Hearing loss is the most common sensory deficit in the world, and most frequently it originates in the inner ear. Yet, the inner ear has been difficult to access for diagnosis because of its small size, delicate nature, complex three-dimensional anatomy, and encasement in the densest bone in the body. Evolving optical methods are promising to afford cellular diagnosis of pathologic changes in the inner ear. To appropriately interpret results from these emerging technologies, it is important to characterize optical properties of cochlear tissues. Here, we focus on that characterization using quantitative polarized light microscopy (qPLM) applied to unstained cochlear sections of the mouse, a common animal model of human hearing loss. We find that the most birefringent cochlear materials are collagen fibrils and myelin. Retardance of the otic capsule, the spiral ligament, and the basilar membrane are substantially higher than that of other cochlear structures. Retardance of the spiral ligament and the basilar membrane decrease from the cochlear base to the apex, compared with the more uniform retardance of other structures. The intricate structural details revealed by qPLM of unstained cochlear sections ex vivo strongly motivate future application of polarization-sensitive optical coherence tomography to human cochlea in vivo.

Layer-specific intracortical connectivity revealed with diffusion MRI

In this work, we show for the first time that the tangential diffusion component is orientationally coherent at the human cortical surface. Using diffusion magnetic resonance imaging (dMRI), we have succeeded in tracking intracortical fiber pathways running tangentially within the cortex. In contrast with histological methods, which reveal little regarding 3-dimensional organization in the human brain, dMRI delivers additional understanding of the layer dependence of the fiber orientation. A postmortem brain block was measured at very high angular and spatial resolution. The dMRI data had adequate resolution to allow analysis of the fiber orientation within 4 notional cortical laminae. We distinguished a lamina at the cortical surface where diffusion was tangential along the surface, a lamina below the surface where diffusion was mainly radial, an internal lamina covering the Stria of Gennari, where both strong radial and tangential diffusion could be observed, and a deep lamina near the white matter, which also showed mainly radial diffusion with a few tangential compartments. The measurement of the organization of the tangential diffusion component revealed a strong orientational coherence at the cortical surface.

Nonparametric Bayesian inference of the fiber orientation distribution from diffusion-weighted MR images

Diffusion MR imaging provides a unique tool to probe the microgeometry of nervous tissue and to explore the wiring diagram of the neural connections noninvasively. Generally, a forward model is established to map the intra-voxel fiber architecture onto the observable diffusion signals, which is reformulated in this article by adopting a measure-theoretic approach. However, the inverse problem, i.e., the spherical deconvolution of the fiber orientation density from noisy MR measurements, is ill-posed. We propose a nonparametric representation of the tangential distribution of the nerve fibers in terms of a Dirichlet process mixture. Given a second-order approximation of the impulse response of a fiber segment, the specified problem is solved by Bayesian statistics under a Rician noise model, using an adaptive reversible jump Markov chain Monte Carlo sampler. The density estimation framework is demonstrated by various experiments with a diffusion MR dataset featuring high angular resolution, uncovering the fiber orientation field in the cerebral white matter of the living human brain.

High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging

Functional interactions between different brain regions require connecting fiber tracts, the structural basis of the human connectome. To assemble a comprehensive structural understanding of neural network elements from the microscopic to the macroscopic dimensions, a multimodal and multiscale approach has to be envisaged. However, the integration of results from complementary neuroimaging techniques poses a particular challenge. In this paper, we describe a steadily evolving neuroimaging technique referred to as three-dimensional polarized light imaging (3D-PLI). It is based on the birefringence of the myelin sheaths surrounding axons, and enables the high-resolution analysis of myelinated axons constituting the fiber tracts. 3D-PLI provides the mapping of spatial fiber architecture in the postmortem human brain at a sub-millimeter resolution, i.e., at the mesoscale. The fundamental data structure gained by 3D-PLI is a comprehensive 3D vector field description of fibers and fiber tract orientations – the basis for subsequent tractography. To demonstrate how 3D-PLI can contribute to unravel and assemble the human connectome, a multiscale approach with the same technology was pursued. Two complementary state-of-the-art polarimeters providing different sampling grids (pixel sizes of 100 and 1.6 μm) were used. To exemplarily highlight the potential of this approach, fiber orientation maps and 3D fiber models were reconstructed in selected regions of the brain (e.g., Corpus callosum, Internal capsule, Pons). The results demonstrate that 3D-PLI is an ideal tool to serve as an interface between the microscopic and macroscopic levels of organization of the human connectome.

Microstructural analysis of human white matter architecture using polarized light imaging: views from neuroanatomy

To date, there are several methods for mapping connectivity, ranging from the macroscopic to molecular scales. However, it is difficult to integrate this multiply-scaled data into one concept. Polarized light imaging (PLI) is a method to quantify fiber orientation in gross histological brain sections based on the birefringent properties of the myelin sheaths. The method is capable of imaging fiber orientation of larger-scale architectural patterns with higher detail than diffusion MRI of the human brain. PLI analyses light transmission through a gross histological section of a human brain under rotation of a polarization filter combination. Estimates of the angle of fiber direction and the angle of fiber inclination are automatically calculated at every point of the imaged section. Multiple sections can be assembled into a 3D volume. We describe the principles of PLI and present several studies of fiber anatomy as a synopsis of PLI: six brainstems were serially sectioned, imaged with PLI, and 3D reconstructed. Pyramidal tract and lemniscus medialis were segmented in the PLI datasets. PLI data from the internal capsule was related to results from confocal laser scanning microscopy, which is a method of smaller scale fiber anatomy. PLI fiber architecture of the extreme capsule was compared to macroscopical dissection, which represents a method of larger-scale anatomy. The microstructure of the anterior human cingulum bundle was analyzed in serial sections of six human brains. PLI can generate highly resolved 3D datasets of fiber orientation of the human brain and has high comparability to diffusion MR. To get additional information regarding axon structure and density, PLI can also be combined with classical histological stains. It brings the directional aspects of diffusion MRI into the range of histology and may represent a promising tool to close the gap between larger-scale diffusion orientation and microstructural histological analysis of connectivity.

Towards ultra-high resolution fibre tract mapping of the human brain - registration of polarised light images and reorientation of fibre vectors

Polarised light imaging (PLI) utilises the birefringence of the myelin sheaths in order to visualise the orientation of nerve fibres in microtome sections of adult human post-mortem brains at ultra-high spatial resolution. The preparation of post-mortem brains for PLI involves fixation, freezing and cutting into 100-μm-thick sections. Hence, geometrical distortions of histological sections are inevitable and have to be removed for 3D reconstruction and subsequent fibre tracking. We here present a processing pipeline for 3D reconstruction of these sections using PLI derived multimodal images of post-mortem brains. Blockface images of the brains were obtained during cutting; they serve as reference data for alignment and elimination of distortion artefacts. In addition to the spatial image transformation, fibre orientation vectors were reoriented using the transformation fields, which consider both affine and subsequent non-linear registration. The application of this registration and reorientation approach results in a smooth fibre vector field, which reflects brain morphology. PLI combined with 3D reconstruction and fibre tracking is a powerful tool for human brain mapping. It can also serve as an independent method for evaluating in vivo fibre tractography.

Variational inference of the fiber orientation density using diffusion MR imaging

Diffusion MR imaging has enabled the in vivo exploration of the connectional architecture in human brain. This method particularly reveals the complex system of long-range nerve fibers that integrate the functionally distinct areas of the cerebral cortex. Since the fibers are not directly observed but the diffusion process of water molecules in the underlying material, a forward model is established that maps the microgeometry of nervous tissue onto the diffusion-weighted signals. This article proposes the spherical deconvolution of the fiber orientation density in a reproducing kernel Hilbert space, thereby generalizing previous approaches that perform a truncated Fourier analysis on the sphere. The specified inverse problem is solved within a smoothing spline framework which preserves the characteristic properties of a density function, namely its normalization and non-negativity. A Gaussian process model allows the specification of confidence bands for the estimated fiber orientation density and the rigorous selection of the hyperparameters, here the high-frequency content in the density function and the noise variance of the MR observations. In addition, we weaken the constant diffusivity assumption frequently made in the spherical convolution methodology. The novel approach, which uncovers the fiber orientation field of white matter, is demonstrated with diffusion-weighted data sets featuring high angular resolution.

Polarized light imaging of white matter architecture

Polarized light imaging (PLI) is a method to image fiber orientation in gross histological brain sections based on the birefringent properties of the myelin sheaths. The method uses the transmission of polarized light to quantitatively estimate the fiber orientation and inclination angles at every point of the imaged section. Multiple sections can be assembled into a 3D volume, from which the 3D extent of fiber tracts can be extracted. This article describes the physical principles of PLI and describes two major applications of the method: the imaging of white matter orientation of the rat brain and the generation of fiber orientation maps of the human brain in white and gray matter. The strengths and weaknesses of the method are set out.

On the Origin of the Extracellular Action Potential Waveform: A Modeling Study

Although extracellular unit recording is typically used for the detection of spike occurrences, it also has the theoretical ability to report about what are typically considered intracellular features of the action potential. We address this theoretical ability by developing a model system that captures features of experimentally recorded simultaneous intracellular and extracellular recordings of CA1 pyramidal neurons. We use the line source approximation method of Holt and Koch to model the extracellular action potential (EAP) voltage resulting from the spiking activity of individual neurons. We compare the simultaneous intracellular and extracellular recordings of CA1 pyramidal neurons recorded in vivo with model predictions for the same cells reconstructed and simulated with compartmental models. The model accurately reproduces both the waveform and the amplitude of the EAPs, although it was difficult to achieve simultaneous good matches on both the intracellular and extracellular waveforms. This suggests that accounting for the EAP waveform provides a considerable constraint on the overall model. The developed model explains how and why the waveform varies with electrode position relative to the recorded cell. Interestingly, each cell's dendritic morphology had very little impact on the EAP waveform. The model also demonstrates that the varied composition of ionic currents in different cells is reflected in the features of the EAP.

A 3D fiber model of the human brainstem

A new neuroanatomic approach to evaluate the fiber orientation in gross histological sections of the human brain was developed. Serial sections of a human brainstem were used to derive fiber orientation maps by analysis of polarized light sequences of these sections. Fiber inclination maps visualize angles of inclination, and fiber direction maps show angles of direction. These angles define vectors which can be visualized as RGB-colors. The serial sections were aligned to each other using the minimized Euclidian distance as fit criterion. In the 3D data set of the human brainstem the major fiber tracts were segmented, and three-dimensional models of these fiber tracts were generated. The presented results demonstrate that two kinds of fiber atlases are feasible: a fiber orientation atlas representing a vector in each voxel, which shows the nerve fiber orientation, and a volume-based atlas representing the major fiber tracts. These models can be used for the evaluation of diffusion tensor data as well as for neurosurgical planning.

Microwave dielectric measurements and tissue characteristics of the human brain: potential in localizing intracranial tissues

This study describes the measurements of dielectric properties in the microwave range to differentiate various human central nervous structures. Using a vector network analyser transmission and reflection coefficients were measured from 500 MHz to 18 GHz in four human formalin fixed human brains. The positions of the electrodes were marked, and the tissue was histologically stained to visualize the myelo- and the cytoarchitecture as well as the nerve fibre orientation at the electrodes. The profiles of the transmission coefficients showed a characteristic minimum peak. In order to describe this peak, a mathematical function was fitted. Parameters derived from digital image processing were used to characterize the myelo- and cytoarchitecure of the tissue at the electrodes. A multiple regression model, with the frequency at the transmission peak minimum as a dependent variable and two tissue characteristics at the two electrodes as independent variables, showed a multiple regression coefficient of 0.765. A neural network model was able to estimate the frequency at the transmission peak minimum from the tissue characteristics at the electrode. The measurements of dielectric properties are well suited to differentiate distinct intracerebral structures. The method could be used for online monitoring of the needle's position during a stereotactic intervention in neurosurgery.

In vivo 3D visualization of normal pyramidal tracts in human subjects using diffusion weighted magnetic resonance imaging and a neuronavigation system

We describe the potential of anisotropic diffusion weighted imaging to visualize the course of large cerebral fiber tracts. Five healthy volunteers were investigated at a field strength of 1.5 Tesla, employing a spin-echo diffusion weighted sequence with gradient sensitivity in six non-collinear directions to visualize the course of the pyramidal tracts. The pyramidal tracts were segmented and reconstructed for three-dimensional visualization. Reconstruction results together with a fusioned high resolution 3D T1 weighted image data set were available in a customized neuronavigation system. Origination in the primary motor cortex, convergence in the centrum semiovale, the posterior limb of the internal capsule, the cerebral peduncles, the splitting at the level of the pons, and the pyramidal decussation were identified in all subjects. Fiber tract maps might have the prospect of guiding neurosurgical interventions, especially when being linked to a neuronavigation system. Other potential applications include the demonstration of the anatomical substrate of functional connectivity in the human brain.