Temporal Characteristics of NMR Signals from Spin 3/2 Nuclei of Incompletely Disordered Systems

Woessner, D. E.; Bansal, Navin

doi:10.1006/jmre.1998.1423

Cited by 26 publications

(43 citation statements)

References 25 publications

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“…Having established the Hamiltonians in the interaction representation, we are ready to discuss the spin dynamics. Spin dynamics of quadrupolar nuclei can be described by solving the Liouville equation over a range of motional regimes and following the time evolution of density operator (r) in response to RF pulses and in the presence of quadrupolar relaxation and static quadrupolar interaction (75,(81)(82)(83)(84)(93)(94)(95)(96)(97). The time evolution of density operator under a static Hamiltonian, such as the static quadrupolar Hamiltonian is given by (74):…”

Section: Sodium Nmrmentioning

confidence: 99%

Sodium and T_1ρ MRI for molecular and diagnostic imaging of articular cartilage

et al. 2006

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In this article, both sodium magnetic resonance (MR) and T 1r relaxation mapping aimed at measuring molecular changes in cartilage for the diagnostic imaging of osteoarthritis are reviewed. First, an introduction to structure of cartilage, its degeneration in osteoarthritis (OA) and an outline of diagnostic imaging methods in quantifying molecular changes and early diagnostic aspects of cartilage degeneration are described. The sodium MRI section begins with a brief overview of the theory of sodium NMR of biological tissues and is followed by a section on multiple quantum filters that can be used to quantify both bi-exponential relaxation and residual quadrupolar interaction. Specifically, (i) the rationale behind the use of sodium MRI in quantifying proteoglycan (PG) changes, (ii) validation studies using biochemical assays, (iii) studies on human OA specimens, (iv) results on animal models and (v) clinical imaging protocols are reviewed. Results demonstrating the feasibility of quantifying PG in OA patients and comparison with that in healthy subjects are also presented. The section concludes with the discussion of advantages and potential issues with sodium MRI and the impact of new technological advancements (e.g. ultra-high field scanners and parallel imaging methods). In the theory section on T 1r , a brief description of (i) principles of measuring T 1r relaxation, (ii) pulse sequences for computing T 1r relaxation maps, (iii) issues regarding radio frequency power deposition, (iv) mechanisms that contribute to T 1r in biological tissues and (v) effects of exchange and dipolar interaction on T 1r dispersion are discussed. Correlation of T 1r relaxation rate with macromolecular content and biomechanical properties in cartilage specimens subjected to trypsin and cytokineinduced glycosaminoglycan depletion and validation against biochemical assay and histopathology are presented. Experimental T 1r data from osteoarthritic specimens, animal models, healthy human subjects and as well from osteoarthritic patients are provided. The current status of T 1r relaxation mapping of cartilage and future directions is also discussed. Copyright # 2006 John Wiley & Sons, Ltd. KEYWORDS: cartilage; arthritis; spin-lock; T1rho; sodium; MRI OSTEOARTHRITIS Osteoarthritis (OA) affects more than half of the population above the age of 65 (1,2) and has a significant negative impact on the quality of life of elderly individuals (3). The economic costs in the USA from OA have been estimated to be more than 1% of the gross domestic product (4). OA is now increasingly viewed as a metabolically active joint disorder of diverse etiologies. The biochemistry of the disease is characterized by the following changes in cartilage: reduced proteoglycan (PG) concentration, possible changes in the size of collagen fibril and aggregation of PG, increased water content and increased rate of synthesis and degradation of matrix macromolecules. The earliest changes in the cartilage due to OA result in a partial breakdown in the proteoglyc...

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Section: Sodium Nmrmentioning

confidence: 99%

Sodium and T_1ρ MRI for molecular and diagnostic imaging of articular cartilage

et al. 2006

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“…However, the direct probability for the data, P(D͉␣ACI) in Eq. [5], does not include the error parameters, n i , nor does it, in any obvious way, include information about the noise characteristics. This direct probability cannot be assigned because these noise characteristics were removed by marginaliza-tion.…”

Section: Theorymentioning

confidence: 99%

“…[5] we reintroduce the standard deviation of the noise prior probability, . The joint posterior probability for the parameters, Eq.…”

Section: A the Calculationsmentioning

confidence: 99%

“…The joint posterior probability for the parameters, Eq. [5], is given by [6] where the sum rule was used to remove the standard deviation of the noise prior probability. Factoring the last term in Eq.…”

Section: A the Calculationsmentioning

confidence: 99%

“…Magnetic resonance experiments often generate data that are modeled as a sum of exponentials (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11). Experiments relying on NMR to probe reaction kinetics, diffusion, molecular dynamics, and xenobiotic metabolism are only some of the applications where parameter estimates from exponential models provide insight into chemical and biological processes.…”

Section: Introductionmentioning

confidence: 99%

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Exponential parameter estimation (in NMR) using Bayesian probability theory

Bretthorst

Hutton

Garbow

et al. 2005

Concepts Magn. Reson.

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Data modeled as sums of exponentials arise in many areas of science and are common in NMR. However, exponential parameter estimation is fundamentally a difficult problem. In this article, Bayesian probability theory is used to obtain optimal exponential parameter estimates. The calculations are implemented using Markov chain Monte Carlo with simulated annealing to draw samples from the joint posterior probability for all of the parameters appearing in the exponential model. Monte Carlo integration is then used to approximate the marginal posterior probabilities for each of the parameters. We give numerical examples taken from simulated data and NMR relaxation experiments to illustrate the calculations and the effect of prior information on the parameter estimates.

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