Determination of pore space shape and size in porous systems using NMR diffusometry. Beyond the short gradient pulse approximation

Price, William S.; Stilbs, Peter; Söderman, Olle

doi:10.1016/s1090-7807(02)00134-9

Cited by 39 publications

(36 citation statements)

References 13 publications

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“…As a result, diffusion propagators recovered through Eq. [2] are constrained to be symmetric, i.e., P(r ᠬ) ϭ P(Ϫr ᠬ), because the information related to asymmetric components of a microstructure is contained in the phase of the signal (18). Since this loss of information is a common limitation of all the aforementioned dMRI techniques, throughout this article we will use a simpler nomenclature-we will refer to the modulus of the complex signal simply as diffusion signal or diffusion image.…”

Section: Theory Q-space Imagingmentioning

confidence: 99%

“…Approaches that estimate diffusion propagators or quantities derived from it by means of Eq. [2] and the discrete (or fast) Fourier transform are known as q-space imaging or diffusion spectrum imaging (see Refs. 1,11).…”

Section: Theory Q-space Imagingmentioning

confidence: 99%

“…[2]. However, as we shall see later, it is convenient for computing the exact ODF in a straightforward way.…”

Section: Orientation Distribution Function (Odf)mentioning

confidence: 99%

“…[2] under the assumption that the normalized diffusion signal attenuates monoexponentially as follows (12):…”

Section: Monoexponential Eqbi (Meeqbi)mentioning

confidence: 99%

“…When the diffusion is constrained by the presence of obstacles, dMRI experiments yield information about the confining geometry (2). Recently, there has been a large amount of interest in using dMRI techniques to obtain information about the microgeometry of porous structures and biological cells, which is supported by the noninvasive nature of these measurements.…”

mentioning

confidence: 99%

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Mathematical description of q‐space in spherical coordinates: Exact q‐ball imaging

Canales-Rodríguez

Melie‐García

Iturria-Medina

2009

Magnetic Resonance in Med

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Novel methodologies have been recently developed to characterize the microgeometry of neural tissues and porous structures via diffusion MRI data. In line with these previous works, this article provides a detailed mathematical description of q-space in spherical coordinates that helps to highlight the differences and similarities between various related q-space methodologies proposed to date such as q-ball imaging (QBI), diffusion spectrum imaging (DSI), and diffusion orientation transform imaging (DOT). This formulation provides a direct relationship between the orientation distribution function (ODF) and the diffusion data without using any approximation. Under this relationship, the exact ODF can be computed by means of the Radon transform of the radial projection (in q-space) of the diffusion MRI signal. This new methodology, termed exact q-ball imaging (EQBI), was put into practice using an analytical ODF estimation in terms of spherical harmonics that allows obtaining model-free and model-based reconstructions. This work provides a new framework for combining information coming from diffusion data recorded on multiple spherical shells in q-space (hybrid diffusion imaging encoding scheme), which is capable of mapping ODF to a high accuracy. This represents a step toward a more efficient development of diffusion MRI experiments for obtaining better ODF estimates. Diffusion MRI (dMRI) data are routinely used for studying molecular diffusion in fluids (1). When the diffusion is constrained by the presence of obstacles, dMRI experiments yield information about the confining geometry (2). Recently, there has been a large amount of interest in using dMRI techniques to obtain information about the microgeometry of porous structures and biological cells, which is supported by the noninvasive nature of these measurements. Also, dMRI techniques are able to probe the pore geometry over a range of length scales not accessible to standard techniques like x-ray and small-angle neutron scattering.Diffusion tensor imaging (DTI) is the first dMRI technique that has been proposed to quantify in vivo the anisotropy of the water self-diffusion process in fibrous tissues (3). This approach allows estimating a second-order self-diffusion tensor D from a series of dMRI data without requiring exogenous contrast agents. DTI provides relevant information that is not available from other imaging modalities; however, this technique can only resolve a single fiber direction within each voxel.In the last few years a number of novel methodologies have been developed to characterize more accurately the microgeometry of neural tissues (for a partial list of such publications, see . Among these advanced methods and algorithms, q-ball imaging (QBI) (6) and diffusion spectrum imaging (DSI) (11) have generated considerable interest due to a number of benefits such as model independence, theoretical soundness, and the ability to resolve intravoxel orientational heterogeneity.In DSI the molecular displacement probability density function (also ...

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Section: Theory Q-space Imagingmentioning

confidence: 99%

Section: Theory Q-space Imagingmentioning

confidence: 99%

“…[2]. However, as we shall see later, it is convenient for computing the exact ODF in a straightforward way.…”

Section: Orientation Distribution Function (Odf)mentioning

confidence: 99%

“…[2] under the assumption that the normalized diffusion signal attenuates monoexponentially as follows (12):…”

Section: Monoexponential Eqbi (Meeqbi)mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Mathematical description of q‐space in spherical coordinates: Exact q‐ball imaging

Canales-Rodríguez

Melie‐García

Iturria-Medina

2009

Magnetic Resonance in Med

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Diffusion Measurement by Monitoring Molecular Displacement

Kärger

Ruthven

Theodorou

2012

Diffusion in Nanoporous Materials

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NMR on emulsions: characterisation of liquid dispersed systems

Bernewitz¹,

Guthausen²,

Schuchmann³

2011

Magnetic Reson in Chemistry

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Pulsed field gradient NMR (PFG-NMR) is an important method for the characterisation of emulsions. Apart from its application in quality control and process development, especially high-field NMR methods can be applied to investigate emulsions properties on the molecular level. Meanwhile, complex emulsion structures such as double emulsions have been developed and require analytical tools especially for the determination of droplet size distributions. This contribution provides an overview on the possibilities and methods of PFG-NMR referring to measurement, data processing and interpretation of droplet size distributions. Comparison of techniques and measurements on double emulsions are presented.

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Determination of pore space shape and size in porous systems using NMR diffusometry. Beyond the short gradient pulse approximation

Cited by 39 publications

References 13 publications

Mathematical description of q‐space in spherical coordinates: Exact q‐ball imaging

Mathematical description of q‐space in spherical coordinates: Exact q‐ball imaging

Diffusion Measurement by Monitoring Molecular Displacement

NMR on emulsions: characterisation of liquid dispersed systems

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