<title>Anisotropic diffusion driven by diffusion tensors</title>

AbstractDiffusion is a major molecular transport mechanism in biological systems. Quantifying direction-dependent (i.e., anisotropic) diffusion is vitally important to depicting how the three-dimensional (3D) tissue structure and composition affect the biochemical environment, and thus define tissue functions. However, a tool for noninvasively measuring the 3D anisotropic extracellular diffusion of biorelevant molecules is not yet available. Here, we present light-sheet imaging-based Fourier transform fluorescence recovery after photobleaching (LiFT-FRAP), which noninvasively determines 3D diffusion tensors of various biomolecules with diffusivities up to 51 µm2 s−1, reaching the physiological diffusivity range in most biological systems. Using cornea as an example, LiFT-FRAP reveals fundamental limitations of current invasive two-dimensional diffusion measurements, which have drawn controversial conclusions on extracellular diffusion in healthy and clinically treated tissues. Moreover, LiFT-FRAP demonstrates that tissue structural or compositional changes caused by diseases or scaffold fabrication yield direction-dependent diffusion changes. These results demonstrate LiFT-FRAP as a powerful platform technology for studying disease mechanisms, advancing clinical outcomes, and improving tissue engineering.

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Anisotropic diffusion for image denoising based on diffusion tensors

Journal of Visual Communication and Image Representation ◽

10.1016/j.jvcir.2012.01.012 ◽

2012 ◽

Vol 23 (3) ◽

pp. 516-521 ◽

Cited By ~ 17

Author(s):

Feng Liu ◽

Jingbo Liu

Keyword(s):

Image Denoising ◽

Anisotropic Diffusion ◽

Diffusion Tensors

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Histopathological correlation of diffusion basis spectrum imaging metrics of a biopsy-proven inflammatory demyelinating brain lesion: A brief report

Multiple Sclerosis Journal ◽

10.1177/1352458518786072 ◽

2018 ◽

Vol 25 (14) ◽

pp. 1937-1941 ◽

Cited By ~ 9

Author(s):

Afsaneh Shirani ◽

Peng Sun ◽

Robert E Schmidt ◽

Kathryn Trinkaus ◽

Robert T Naismith ◽

...

Keyword(s):

Anisotropic Diffusion ◽

Vasogenic Edema ◽

Brain Lesion ◽

Resonance Imaging ◽

Histopathological Correlation ◽

Weighted Magnetic Resonance Imaging ◽

Spectrum Imaging ◽

Magnetic Resonance Imaging Mri ◽

Axonal Density ◽

Diffusion Tensors

Diffusion basis spectrum imaging (DBSI) models diffusion-weighted magnetic resonance imaging (MRI) signals as a combination of discrete anisotropic diffusion tensors and a spectrum of isotropic diffusion tensors. Here, we report the histopathological correlates of DBSI in the biopsied brain tissue of a patient with an inflammatory demyelinating lesion typical of multiple sclerosis (MS). Increased radial diffusivity (marker of demyelination), decreased fiber fraction (apparent axonal density), elevated nonrestricted isotropic fraction (marker of vasogenic edema), but unchanged axial diffusivity (marker of integrity of residual axons) seen in the lesion appeared consistent with histopathological findings of inflammatory demyelination with relative axonal sparing. Our report supports the application of DBSI as a biomarker in human studies of MS.

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A generalised complete flux scheme for anisotropic advection-diffusion equations

Advances in Computational Mathematics ◽

10.1007/s10444-021-09846-x ◽

2021 ◽

Vol 47 (2) ◽

Author(s):

Hanz Martin Cheng ◽

Jan ten Thije Boonkkamp

Keyword(s):

Anisotropic Diffusion ◽

Second Order ◽

Diffusion Equations ◽

Order Method ◽

Advection Diffusion ◽

Diffusion Tensors

AbstractIn this paper, we consider separating the discretisation of the diffusive and advective fluxes in the complete flux scheme. This allows the combination of several discretisation methods for the homogeneous flux with the complete flux (CF) method. In particular, we explore the combination of the hybrid mimetic mixed (HMM) method and the CF method, in order to utilise the advantages of each of these methods. The usage of HMM allows us to handle anisotropic diffusion tensors on generic polygonal (polytopal) grids, whereas the CF method provides a framework for the construction of a uniformly second-order method, even when the problem is advection dominated.

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Anisotropic Diffusion in ITK

The Insight Journal ◽

10.54294/en3833 ◽

2014 ◽

Author(s):

Jean-marie Mirebeau ◽

Jérôme Fehrenbach ◽

Laurent Risser ◽

Shaza Tobji

Keyword(s):

Anisotropic Diffusion ◽

Three Dimensional ◽

Processing Technique ◽

Image Features ◽

Image Processing Technique ◽

Linear Diffusion ◽

Diffusion Technique ◽

Non Linear ◽

Diffusion Tensors ◽

Scalar Diffusion

Anisotropic Non-Linear Diffusion is a powerful image processing technique, which allows to simultaneously remove the noise and enhance sharp features in two or three dimensional images. Anisotropic Diffusion is understood here in the sense of Weickert, meaning that diffusion tensors are anisotropic and reflect the local orientation of image features. This is in contrast with the non-linear diffusion filter of Perona and Malik, which only involves scalar diffusion coefficients, in other words isotropic diffusion tensors. In this paper, we present an anisotropic non-linear diffusion technique we implemented in ITK. This technique is based on a recent adaptive scheme making the diffusion stable and requiring limited numerical resources.

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An Evaluation of Colour-to-Greyscale Image Conversion by Linear Anisotropic Diffusion and Manual Colour Grading

Color and Imaging Conference ◽

10.2352/issn.2169-2629.2019.27.13 ◽

2019 ◽

Vol 2019 (1) ◽

pp. 69-74

Author(s):

Aldo Barba ◽

Ivar Farup ◽

Marius Pedersen

Keyword(s):

Anisotropic Diffusion ◽

Motion Pictures ◽

Current Paper ◽

Original Image ◽

Colour Image ◽

Image Conversion ◽

Significant Difference ◽

Greyscale Image

In the paper "Colour-to-Greyscale Image Conversion by Linear Anisotropic Diffusion of Perceptual Colour Metrics", Farup et al. presented an algorithm to convert colour images to greyscale. The algorithm produces greyscale reproductions that preserve detail derived from local colour differences in the original colour image. Such detail is extracted by using linear anisotropic diffusion to build a greyscale reproduction from a gradient of the original image that is in turn calculated using Riemannised colour metrics. The purpose of the current paper is to re-evaluate one of the psychometric experiments for these two methods (CIELAB L* and anisotropic Δ99) by using a flipping method to compare their resulting images instead of the side by side method used in the original evaluation. In addition to testing the two selected algorithms, a third greyscale reproduction was manually created (colour graded) using a colour correction software commonly used to process motion pictures. Results of the psychometric experiment found that when comparing images using the flipping method, there was a statistically significant difference between the anisotropic Δ99 and CIELAB L* conversions that favored the anisotropic method. The comparison between Δ99 conversion and the manually colour graded image also showed a statistically significant difference between them, in this case favoring the colour graded version.

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