Field-Cycling NMR Relaxometry

Kimmich, Rainer; Anoardo, Esteban

doi:10.1007/978-3-642-60582-6_15

Cited by 74 publications

(105 citation statements)

References 228 publications

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“…Since the order of the fractional operator can be connected with the fractal features of the tissue, the fractional model also provides a representation of a complex tissue not as a series of compartments and relaxation times, but as a single generalized exponential function in terms of α and T 2 or β and T 1 . Such models have been recently applied to the attenuation of acoustic waves in random multi-scale media [37, 38] viscoelasticity [39, 40] and to NMR analysis of diffusion in porous media [41-46]. …”

Section: Discussionmentioning

confidence: 99%

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

Magin

Velasco

et al. 2011

Journal of Magnetic Resonance

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We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues.

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Section: Discussionmentioning

confidence: 99%

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

Magin

Velasco

et al. 2011

Journal of Magnetic Resonance

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“…A PGStE method (consisting of: p/2 pulse -t 1 -p/2 pulse -t 2 -p/2 pulse -t 1 -echo) was employed for the diffusion-coefficient measurements, as reported previously. [8][9][10][11][12] Typical experimental conditions for the PGStE 7 Li and 19 F NMR measurements were as follows: The echo signal intensity was measured by changing the gradient strength G from 0 to 11 T m…”

Section: Methodsmentioning

confidence: 99%

Dynamic Transport in Li‐Conductive Polymer Electrolytes Plasticized with Poly(ethylene glycol)–Borate/Aluminate Ester

et al. 2009

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The addition of plasticizers into Li(+)-conductive solid polymer electrolytes (SPEs) is a commonly known technique to enhance the ionic conductivity. Among the used plasticizers, alkoxides of group-13 elements [such as poly(ethylene glycol) (PEG)-borate ester] are promising candidates due to the Lewis acidity of the elements of this group (i.e. B, Al, and so on), which interact with the anions and may increase the degree of dissociation of the salts and the transport number of the SPEs. By means of pulsed-gradient stimulated-echo NMR (PGStE-NMR) and AC impedance measurements, we investigate the effect of Lewis acidity originated from group-13 elements on the transport number and the dissociation rate of SPEs containing various plasticizers. Our results show that the degree of salt dissociation is significantly enhanced by the addition of plasticizers including group-13 elements, whereas only a small or negligible increase of the transport number is observed for these SPEs. We infer that the plasticizers exhibiting Lewis acidity associate with the anions, and that the associated pairs can migrate in the SPEs as fast as free anions, which results in a lower transport number than expected.

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“…The time evolving magnetization can be calculated from the C i coefficients of Eq. [4], as m͑t͒ ϭ ␥ប Tr͕I ⅐ ͑t͖͒.…”

Section: The Nmr Signalmentioning

confidence: 98%

Nuclear Magnetic Resonance in Inhomogeneous Magnetic Fields

Balibanu

Hailu

Eymael

et al. 2000

Journal of Magnetic Resonance

123

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Field-Cycling NMR Relaxometry

Cited by 74 publications

References 228 publications

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

Dynamic Transport in Li‐Conductive Polymer Electrolytes Plasticized with Poly(ethylene glycol)–Borate/Aluminate Ester

Nuclear Magnetic Resonance in Inhomogeneous Magnetic Fields

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