Nuclear-Magnetic-Resonance Study of Self-Diffusion in a Bounded Medium

Wayne, R. C.; Cotts, R. M.

doi:10.1103/physrev.151.264

Cited by 175 publications

(45 citation statements)

References 12 publications

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“…Analytical solutions to this equation followed for freely diffusing species during a spin echo experiment 15 and, later, for diffusion in restricted geometries. [16][17][18] About a decade after its introduction, Stejskal and Tanner solved the Bloch-Torrey equation 19 for the case of free, anisotropic diffusion in the principal frame of reference. However, the Stejskal-Tanner formula is not generally useable to measure an effective diffusion tensor using NMR or MRI methods for several reasons.…”

Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review

2002

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This article treats the theoretical underpinnings of diffusion-tensor magnetic resonance imaging (DT-MRI), as well as experimental design and data analysis issues. We review the mathematical model underlying DT-MRI, discuss the quantitative parameters that are derived from the measured effective diffusion tensor, and describe artifacts thet arise in typical DT-MRI acquisitions. We also discuss difficulties in identifying appropriate models to describe water diffusion in heterogeneous tissues, as well as in interpreting experimental data obtained in such issues. Finally, we describe new statistical methods that have been developed to analyse DT-MRI data, and their potential uses in clinical and multi-site studies.

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Section: Characterizing Diffusion In Biological Systemsmentioning

confidence: 99%

Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review

2002

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“…Both MR parameters are known to be sensitive to the state of water. 2,[12][13][14] Here, the basic states of water are known as free and bound water. They differ in terms of molecular mobility.…”

Section: Resultsmentioning

confidence: 99%

Self-organizing Map Analysis for Understanding Comprehensive Relationships between Formulation Variables, State of Water, and the Physical Stability of Pharmaceutical Emulsions

Onuki

Hasegawa

Horita³

et al. 2015

CHEMICAL & PHARMACEUTICAL BULLETIN

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The physical stability of pharmaceutical emulsions is an important quality attribute to be considered. To obtain a better understanding of this issue, this study investigated the contribution of the state of water to the physical stability of pharmaceutical emulsions. The key technology to evaluate the state of water was magnetic resonance imaging (MRI). For sample preparation, model emulsions with different formulation variables (surfactant content, water content, and hydrophilic-lipophilic balance) were prepared. The T 1 relaxation time, diffusion coefficient, and viscosity were measured as physical properties. The physical stability of the samples was evaluated using apparent diffusion coefficient maps acquired by MRI. Data analysis of the observed data was performed using the nonlinear response surface method and Kohonen's self-organizing map (SOM). It was determined that, depending on the formulation variables, the state of water was substantially changed and it played a significant role in the physical stability. SOM analysis successfully classified the conditions of formulation variables into four distinct clusters in terms of the similarity of the physical properties of the resultant emulsions, and then clarified the characteristics of the stable emulsions. This study provided us with a comprehensive understanding of the formulation variables, physical properties, and stability concerning the preparation of the model emulsion.Key words pharmaceutical emulsion; magnetic resonance imaging; physical stability; T 1 relaxation time; diffusion coefficient Oil-in-water type emulsions are widely used for various semisolid topical dosage forms. Pharmaceutical emulsions are less greasy than ointments, they are easier to apply and can be easily washed off from the skin surface; thus, they are highly acceptable to patients. 1) For the development of pharmaceutical emulsions, physical stability is a very important quality attribute to be considered. This is because emulsions are thermodynamically unstable by nature. In general, the destabilization processes of emulsions are classified into four distinct processes: creaming, flocculation, coalescence, and Ostwald ripening.1) Coalescence and Ostwald ripening are the most serious types of destabilization, whereas creaming and flocculation are subtle destabilization processes.We have been investigating the physical stability of pharmaceutical emulsions using magnetic resonance imaging (MRI).2-4) MRI is one of the most popular molecular imaging methods; it permits the nondestructive monitoring of a sample using the principle of nuclear magnetic resonance (NMR). In addition, MRI can visualize the state of water in a sample by using magnetic resonance (MR) parameters. In a previous study, we established a new method to monitor destabilization processes of pharmaceutical emulsions.4) The key technology is the visualization of the state of water. Water in pharmaceutical emulsions can exist in various states depending on its particular location and microenvironment.2) Once cre...

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“…4 This approach gives a good idea about the phase accumulation of a diffusing spin in the motional averaging regime. Although the applied magnetic field is static, a diffusing spin experiences a time-dependent magnetic field.…”

Section: Motional Averaging Scalingmentioning

confidence: 99%

“…The dephasing in a porous material was first described by Wayne and Cotts. 4 Robertson 5 provided the necessary theory to explain the experimental data. Recently, Hürlimann 6 gave an overview of all possible spin-echo decay mechanisms due to dephasing in a single pore in the presence of a uniform magnetic-field gradient.…”

Section: Introductionmentioning

confidence: 99%

Nuclear magnetic resonance dephasing effects in a spherical pore with a magnetic dipolar field

Valckenborg

Huinink

Kopinga

2003

The Journal of Chemical Physics

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The NMR dephasing behavior of the nuclear spins of a fluid confined in a porous material can be investigated by Hahn spin echoes. Previous experimental results on water in a magnetically doped clay have shown a nonmonoexponentially decaying magnetization, which can be understood neither by the known dephasing rate of freely diffusing spins in a uniform gradient nor by spins diffusing in a restricted geometry. For a better understanding of NMR measurements on these systems, a systematic survey was performed of the various length scales that are involved. The standard length scales for the situation of a uniform gradient are diffusing length, structure length, and dephasing length. We show that for a nonuniform gradient, a new length scale has to be introduced: the magnetic-field curvature length. When a particle diffuses less than this length scale, it experiences a local uniform gradient. In that case the spin-echo decay can be described by the so-called local gradient approximation ͑LGA͒. When a particle diffuses over a longer distance than the structure length, the spin-echo decay can be described by the motional averaging regime. For both regimes, scaling laws are derived. In this paper, a random-walk model is used to simulate the dephasing effect of diffusing spins in a spherical pore in the presence of a magnetic dipole field. By varying the dipole magnitude, situations can be created in which the dephasing behavior scales according to the motional averaging regime or according to the LGA regime, for certain ranges of echo times. Two model systems are investigated: a spherical pore in the vicinity of a magnetic point dipole and a spherical pore adjacent to a magnetic dipolar grain of the same size as the pore. The simulated magnetization decay curves of both model systems confirm the scaling laws. The LGA, characterized by a nonmonoexponential magnetization decay, is also investigated by calculating the spatially resolved magnetization in the pore. For this regime, the magnetization is found to be inhomogeneously distributed within the pore, whereas it is homogeneously distributed in the motional averaging regime.

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Nuclear-Magnetic-Resonance Study of Self-Diffusion in a Bounded Medium

Cited by 175 publications

References 12 publications

Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review

Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review

Self-organizing Map Analysis for Understanding Comprehensive Relationships between Formulation Variables, State of Water, and the Physical Stability of Pharmaceutical Emulsions

Nuclear magnetic resonance dephasing effects in a spherical pore with a magnetic dipolar field

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