Automatic phasing of MR images. Part I: Linearly varying phase

Bretthorst, G. Larry

doi:10.1016/j.jmr.2007.12.010

Cited by 18 publications

(28 citation statements)

References 19 publications

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“…Fig. 1 illustrates what happens when the linear phasing algorithm, described in [1], is applied to a gradient-echo image. A strong signal persists in the imaginary image, Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Panel b is an absorption-mode image before any phasing parameters were applied. Panels c and d are the real and imaginary images after applying the linear phasing algorithm [1]. Note that the image intensity oscillates between positive and negative values in both the real and imaginary images.…”

Section: The Model Equationmentioning

confidence: 99%

“…As described in [1], absorption-mode images have significant advantages over absolute value images; these advantages include: eliminating correlations between the signal and the noise, eliminating constant offsets, eliminating absolute values and increasing the signal-to-noise ratio. Part of the problem of producing absorption-mode images was solved by the algorithm presented in [1], an algorithm that can produce an absorption-mode image from any 2D magnetic resonance data sets in which the phase varies linearly as a function of position in both phase-encode and readout directions. Linearly varying, positionally dependent phases are common in spin-echo experiments because the acquisition method tends to remove phase artifacts arising from inhomogeneous magnetic fields.…”

Section: Introductionmentioning

confidence: 99%

“…The high frequency oscillations apparent in this panel are largely caused by the origin of time in the discrete Fourier transform. Panels c and d are the real and imaginary images that result from applying the linear phasing algorithm described in [1]. The linear phasing algorithm has removed the high frequency oscillations, but it has left behind a slowly varying, positionally dependent phase variation that causes the signal intensity to oscillate between the real and imaginary parts of the image.…”

Section: Introductionmentioning

confidence: 99%

“…The calculations presented in [1] were for the first-order phase parameters. A point estimate for the zero-order or constant phase was given in that paper, but it was not derived.…”

Section: Introductionmentioning

confidence: 99%

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Automatic phasing of MR images. Part II: Voxel-wise phase estimation

Bretthorst

2008

Journal of Magnetic Resonance

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“…Fig. 1 illustrates what happens when the linear phasing algorithm, described in [1], is applied to a gradient-echo image. A strong signal persists in the imaginary image, Fig.…”

Section: Resultsmentioning

confidence: 99%

Section: The Model Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The calculations presented in [1] were for the first-order phase parameters. A point estimate for the zero-order or constant phase was given in that paper, but it was not derived.…”

Section: Introductionmentioning

confidence: 99%

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Automatic phasing of MR images. Part II: Voxel-wise phase estimation

Bretthorst

2008

Journal of Magnetic Resonance

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Magnetic resonance data modeling: The Bayesian analysis toolbox

Quirk¹,

Bretthorst²,

Garbow³

et al. 2018

Concepts Magnetic Resonance

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Bayesian probability theory provides optimal parameter estimates and robust model selection from a family of competing data models. However, widespread adoption of the Bayesian approach to the analysis of magnetic resonance and other data types has been hindered by its perceived complexity and heavy computational burden. This manuscript describes the Bayesian Analysis Toolbox, a computationally efficient, robust, and highly optimized suite of data modeling software packages based upon the precepts of Bayesian probability theory. The Toolbox is downloadable at no cost for noncommercial applications from http://bayesiananalysis.wustl.edu. The Toolbox extends Bayesian‐based data analysis to a variety of real‐world data analysis problems commonly encountered in spectroscopy and imaging, with a focus on magnetic resonance‐derived data, making the power of this approach available to the non‐expert user.

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Magnetization transfer induced biexponential longitudinal relaxation

Prantner

Bretthorst

Neil

et al. 2008

Magnetic Resonance in Med

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Longitudinal relaxation of brain water 1 H magnetization in mammalian brain in vivo is typically analyzed on a per-voxel basis using a monoexponential model, thereby assigning a single relaxation time constant to all 1 H magnetization within a given voxel. This approach was tested by obtaining inversion recovery (IR) data from gray matter of rats at 64 exponentially spaced recovery times. Using Bayesian probability for model selection, brain water data were best represented by a biexponential function characterized by fast and slow relaxation components. At 4.7T, the amplitude fraction of the rapidly relaxing component is 3.4% ؎ 0.7% with a rate constant of 44 ؎ 12 s -1 (mean ؎ SD; 174 voxels from four rats). The rate constant of the slow relaxing component is 0.66 ؎ 0. Longitudinal relaxation rate constant (R 1 ϭ 1/T 1 ) measurements of tissue water are key to a variety of MR methods, including dynamic contrast-enhanced techniques (1) and assessment of multiple sclerosis patients for damage to normal-appearing white matter (2). Data from such measurements in brain are typically modeled as a monoexponential magnetization recovery, assuming that the longitudinal relaxation of all water can be represented by a single R 1 . However, in vivo voxel resolution is coarse on the scale of tissue microstructure and water exists in a variety of magnetic environments ("compartments") within a single in vivo voxel. Each compartment potentially provides a unique relaxation environment for water. Consistent with this concept, a variety of tissues display multiexponential T 2 relaxation and each exponential component can be assigned to a unique anatomical compartment (3,4). Further, multiple R 1 components have been described for peripheral nerve (4,5), though not for brain gray matter.Non-monoexponential in vivo relaxation data are generally analyzed by one of two methods. The first method models relaxation data as the sum of a small number of discrete exponential functions, with each exponential component having a unique amplitude and R 1 . In this case, the implicit biophysical picture is that water within a given voxel can be approximated as residing in a few separate magnetic environments that are not in fast exchange. In the limit of slow exchange this would enable measurement of compartment-specific R 1 values. The second method models relaxation data with a continuous distribution of exponential functions. Here the implicit biophysical picture is that water within a given voxel should be approximated as residing in a large number of separate magnetic environments that are not in fast exchange (6,7).Taking advantage of high-field magnets equipped with high-performance gradients, the study reported herein was done using highly time-resolved inversion recovery (IR) spin-echo echo-planar imaging (SEPI) to acquire data sets with 64 to 128 exponentially spaced inversion time (TI) values. Bayesian probability theory (8,9) was employed to select among models composed of sums of from one to four exponentials. The relaxation data...

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Automatic phasing of MR images. Part I: Linearly varying phase

Cited by 18 publications

References 19 publications

Automatic phasing of MR images. Part II: Voxel-wise phase estimation

Automatic phasing of MR images. Part II: Voxel-wise phase estimation

Magnetic resonance data modeling: The Bayesian analysis toolbox

Magnetization transfer induced biexponential longitudinal relaxation

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