Axonal conduction velocity, which ensures efficient function of the brain network, is related to axon diameter. Noninvasive, in vivo axon diameter estimates can be made with diffusion magnetic resonance imaging, but the technique requires three-dimensional (3D) validation. Here, high-resolution, 3D synchrotron X-ray nano-holotomography images of white matter samples from the corpus callosum of a monkey brain reveal that blood vessels, cells, and vacuoles affect axonal diameter and trajectory. Within single axons, we find that the variation in diameter and conduction velocity correlates with the mean diameter, contesting the value of precise diameter determination in larger axons. These complex 3D axon morphologies drive previously reported 2D trends in axon diameter and g-ratio. Furthermore, we find that these morphologies bias the estimates of axon diameter with diffusion magnetic resonance imaging and, ultimately, impact the investigation and formulation of the axon structure–function relationship.

Large ODD volume is associated with optic nerve dysfunction. The worse visual field defects associated with visible ODD should only be ascribed to larger ODD volume and not to a more superficial anatomic ODD location.

We describe an efficient algorithm that computes a segmented reconstruction directly from x-ray projection data. Our algorithm uses a parametric curve to define the segmentation. Unlike similar approaches which are based on level-sets, our method avoids a pixel or voxel grid; hence the number of unknowns is reduced to the set of points that define the curve, and attenuation coefficients of the segments. Our current implementation uses a simple closed curve and is capable of separating one object from the background. However, our basic algorithm can be applied to an arbitrary topology and multiple objects corresponding to different attenuation coefficients in the reconstruction. Through systematic tests we demonstrate a high robustness to the noise, and an excellent performance under a small number of projections.

Axonal conduction velocity, which ensures efficient function of the brain network, is related to axon diameter. Non-invasive, in vivo axon diameter estimates can be made with diffusion magnetic resonance imaging, but the technique requires 3D validation. Here, high resolution, 3D synchrotron X-ray Nano-Holotomography images of white matter samples from the corpus callosum of a monkey brain reveal that blood vessels, cells and vacuoles affect axonal diameter and trajectory. Within single axons, we find that the variance in diameter and conduction velocity correlates with the mean diameter, contesting the value of precise diameter determination in larger axons. These complex 3D axon morphologies drive previously reported 2D trends in axon diameter and g-ratio. Furthermore, we find that these morphologies bias the estimates of axon diameter with diffusion magnetic resonance imaging and, ultimately, impact the investigation and formulation of the axon structure-function relationship. 4 acquired diffusion signal 15 . However, diffusion MRI-based AD estimates 14,16,17 are larger than those obtained by histology 15,18 . A potential cause is inaccurate modeling of the WM compartments, including the century old representation of myelinated axons as cylinders. A validation of the 3D WM anatomy could thus improve diffusion MRI-based AD estimations 17 and shed light on the validity of enforcing a cylindrical geometry and constant g-ratio in axonal structure-function relations. Recent 3D electron microscopy (EM) studies on axon morphology of the mouse reveal, in high resolution, non-uniform ADs and trajectories 19,20 . However, axons are only tracked for up to 20 µm, a fraction of their length in MRI voxels. Here, we characterize the long-range micro-morphologies of axons against the backdrop of the complex 3D WM environment consisting of blood vessels, cells and vacuoles. With synchrotron X-ray Nano-Holotomography (XNH), we acquire MRI measurements of the WM from the same monkey brain as in Alexander et al. (2010) 14 and Dyrby et al. (2013) 21 , in which the MRIderived AD estimates were larger than those estimated by histology. The 3D WM environment is mapped at a voxel size of 75 nm and volume of approximately 150 ⨉ 150 ⨉ 150 µm 3 . By combining adjacent XNH volumes, we extract axons >660 µm in length and show that AD, axon trajectory and g-ratio depend on the local microstructural environment. The 3D measurements shed light on the interpretation of 2D measurements, highlighting the importance of the third dimension for a robust description of single-axon structure and function. Lastly, by performing Monte Carlo (MC) diffusion simulations on axonal substrates with morphological features deriving from the XNH-segmented axons, we show that geometrical deviations from cylinders cause an overestimation of AD with diffusion MRI.

We introduce the novel concept of a Sparse Layered Graph (SLG) for s-t graph cut segmentation of image data. The concept is based on the widely used Ishikawa layered technique for multi-object segmentation, which allows explicit object interactions, such as containment and exclusion with margins. However, the spatial complexity of the Ishikawa technique limits its use for many segmentation problems. To solve this issue, we formulate a general method for adding containment and exclusion interaction constraints to layered graphs. Given some prior knowledge, we can create a SLG, which is often orders of magnitude smaller than traditional Ishikawa graphs, with identical segmentation results. This allows us to solve many problems that could previously not be solved using general graph cut algorithms. We then propose three algorithms for further reducing the spatial complexity of SLGs, by using ordered multi-column graphs. In our experiments, we show that SLGs, and in particular ordered multi-column SLGs, can produce high-quality segmentation results using extremely simple data terms. We also show the scalability of ordered multi-column SLGs, by segmenting a highresolution volume with several hundred interacting objects.