Imaging Multiexponential Relaxation in the (y, LogeT1) Plane, with Application to Clay Filtration in Rock Cores

Fordham, E.J.; Sezginer, A.; Hall, Luis J.

doi:10.1006/jmra.1995.1073

Cited by 80 publications

(65 citation statements)

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“…[3] is in general ill-conditioned in the sense that a small change in M may result in a large change in F. The general strategies to solve this problem have been discussed extensively in the mathematical literature (12). Numerical recipes (13) and other NMR literature (9,10,14) are a good introduction. One technique uses regularization and obtains a fit to the data through minimization of the expression…”

Section: Brief Review Of the Algorithmmentioning

confidence: 99%

“…The dimensionality of the vector space for the unconstrained optimization problem equals the size of the compressed data. In the third step, the optimal amplitude of the regularization term (α) was chosen by BRD (15) or S-curve method (10). The essence of both of these methods for choosing α is to find the most stable solution with the fit error M − K 1 F K 2 2 similar to the known noise variance.…”

Section: Brief Review Of the Algorithmmentioning

confidence: 99%

“…There are several algorithms for inverse Laplace transform in one dimension (8)(9)(10). However, the straightforward extension of such algorithms to two-dimensions makes an enormous demand on computer memory and speed and has been accomplished only on a Cray (3).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion

Song

Venkataramanan

Hürlimann

et al. 2002

Journal of Magnetic Resonance

690

546

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Section: Brief Review Of the Algorithmmentioning

confidence: 99%

Section: Brief Review Of the Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion

Song

Venkataramanan

Hürlimann

et al. 2002

Journal of Magnetic Resonance

690

546

View full text Add to dashboard Cite

“…A smoothing term is introduced in a non-negative least-squares routine method [7,26] to avoid the unstable oscillations: [23-251 J For each value of 6, a unique solution for f ( T2) exists. In this study the method proposed by Fordham et al [6] was used to choose the appropriate level of smoothing, using an optimum 6 (hOpt). To do so, an optimal regularization parameter called "slop tolerance" or "slop" will be introduced.…”

Section: Nmr Spin-spin Relaxation Time T2 Spectrummentioning

confidence: 99%

Determination of cortical bone porosity and pore size distribution using a low field pulsed NMR approach

Wang

2003

Journal Orthopaedic Research

179

190

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The objective of this study was first to prove the concept of a low field pulsed nuclear magnetic resonance (NMR) process for assessing the cortical porosity and pore size distribution of human bone in vitro, and then to apply the technique to detect age-related changes of bone in these parameters. The Carr-~Purcell--Meiboom-Gill NMR spin echo train method is used to determine the porosity, and an inversion NMR spin-spin relaxation (T2) spectrum is used to assess the pore size distribution in cortical bone. Using these techniques, cortical porosity and pore size distribution of 19 specimens of human cadaveric bone, ranging from 16 to 89 years of age, were assessed. The NMR results were compared with the histomorphometric data of the same bone samples to verify the efficacy of the NMR approach. Moreover, a coefficient (surface relaxivity) relating the pore size to the T2 relaxation time was determined empirically for the Haversian canals and the osteocytic lacunae. The results of this study demonstrate that the in vitro NMR approach using T2 relaxation techniques can directly assess the porosity and pore size distribution (Haversian canals and osteocytic lacunae) in human cortical bone. In addition, this study indicates that the age-related changes in cortical porosity relate predominantly to Haversian canals, whereas the porosity of osteocytic lacunae appears to be independent of age.

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“…Commonly used methods include Tikonov regularization 88 and the maximum entropy method 89 to handle this and other types of inversion. 90 Several NMR papers [91][92][93] use regularization and they are a good introduction to this problem.…”

Section: Laplace Inversionmentioning

confidence: 99%

Magnetic resonance in porous media: Recent progress

Song

Cho²,

Hopper³

et al. 2008

The Journal of Chemical Physics

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The anomalous adsorbate dynamics at surfaces in porous media studied by nuclear magnetic resonance methods. The orientational structure factor and Lévy walks J. Chem. Phys. 109, 6929 (1998) Recent years have seen significant progress in the NMR study of porous media from natural and industrial sources and of cultural significance such as paintings. This paper provides a brief outline of the recent technical development of NMR in this area. These advances are relevant for broad NMR applications in material characterization.

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Imaging Multiexponential Relaxation in the (y, LogeT1) Plane, with Application to Clay Filtration in Rock Cores

Cited by 80 publications

References 0 publications

T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion

T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion

Determination of cortical bone porosity and pore size distribution using a low field pulsed NMR approach

Magnetic resonance in porous media: Recent progress

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