Estimation Of Diffusion Parameters Research Articles

Removal of olefinic fat chemical shift artifact in diffusion MRI

Diffusion-weighted (DW) MRI has emerged as a key tool for assessing the microstructure of tissues in healthy and diseased states. Because of its rapid acquisition speed and insensitivity to motion, single-shot echo-planar imaging is the most common DW imaging technique. However, the presence of fat signal can severely affect DW-echo planar imaging acquisitions because of the chemical shift artifact. Fat suppression is usually achieved through some form of chemical shift-based fat saturation. Such methods effectively suppress the signal originating from aliphatic fat protons, but fail to suppress the signal from olefinic protons. Olefinic fat signal may result in significant distortions in the DW images, which bias the subsequently estimated diffusion parameters. This article introduces a method for removing olefinic fat signal from DW images, based on an echo time-shifted acquisition. The method is developed and analyzed specifically in the context of single-shot DW-echo-planar imaging, where image phase is generally unreliable. The proposed method is tested with phantom and in vivo datasets, and compared with a standard acquisition to demonstrate its performance.

More accurate estimation of diffusion tensor parameters using diffusion kurtosis imaging

With diffusion tensor imaging, the diffusion of water molecules through brain structures is quantified by parameters, which are estimated assuming monoexponential diffusion-weighted signal attenuation. The estimated diffusion parameters, however, depend on the diffusion weighting strength, the b-value, which hampers the interpretation and comparison of various diffusion tensor imaging studies. In this study, a likelihood ratio test is used to show that the diffusion kurtosis imaging model provides a more accurate parameterization of both the Gaussian and non-Gaussian diffusion component compared with diffusion tensor imaging. As a result, the diffusion kurtosis imaging model provides a b-value-independent estimation of the widely used diffusion tensor parameters as demonstrated with diffusion-weighted rat data, which was acquired with eight different b-values, uniformly distributed in a range of [0,2800 sec/mm(2)]. In addition, the diffusion parameter values are significantly increased in comparison to the values estimated with the diffusion tensor imaging model in all major rat brain structures. As incorrectly assuming additive Gaussian noise on the diffusion-weighted data will result in an overestimated degree of non-Gaussian diffusion and a b-value-dependent underestimation of diffusivity measures, a Rician noise model was used in this study.

Cholesterol Depletion Mimics the Effect of Cytoskeletal Destabilization on Membrane Dynamics of the Serotonin1A Receptor: A zFCS Study

Single-point fluorescence correlation spectroscopy (FCS) of membrane-bound molecules suffers from a number of limitations leading to inaccurate estimation of diffusion parameters. To overcome such problems and with the overall goal of addressing membrane heterogeneities, we performed z-scan FCS (zFCS) of the serotonin1A receptor. We analyzed the results according to FCS diffusion laws that provide information on the organization of the diffusing species. Analysis of our results shows that the diffusion coefficients of the receptor and a fluorescently labeled phospholipid are similar when probed at length scales ∼210 nm. We discuss the significance of the spatiotemporal evolution of dynamics of membrane-bound molecules in the overall context of membrane domains and heterogeneity. Importantly, our results show that the serotonin1A receptor exhibits confinement in cell membranes, possibly due to interaction with the actin cytoskeleton. Surprisingly, depletion of membrane cholesterol appears to reduce receptor confinement in a manner similar to that observed in the case of cytoskeletal destabilization, implying possible changes in the actin cytoskeleton induced upon cholesterol depletion. These results constitute the first report on G-protein-coupled receptor dynamics utilizing a combination of zFCS and the FCS diffusion laws, and present a convenient approach to explore cell membrane heterogeneity at the submicron level.

Piecewise linear regression: A statistical method for the analysis of experimental adsorption data by the intraparticle-diffusion models

The film-diffusion and the intraparticle-diffusion models are widely used to analyze the mechanism of adsorption. The plots of these models often have a multi-linear nature, and in general, the graphical method is employed to analyze the data in which the linear segments are determined visually. This method suffers from subjectivity and therefore its estimated diffusion parameters are not very reliable. An alternative statistical method, piecewise linear regression (PLR) is presented and applied to experimental data. The results demonstrate that the use of PLR is practical and leads to diffusion estimates that may be quite different from the graphical method. PLR also determined the exact time periods for each diffusion regime, which opens new possibilities for analyzing and understanding the mechanism of diffusion. In order to encourage the testing and application of PLR, an easy to use Microsoft ® Excel™ spreadsheet is made available.

A simple method for rectified noise floor suppression: Phase‐corrected real data reconstruction with application to diffusion‐weighted imaging

Diffusion-weighted MRI is an intrinsically low signal-to-noise ratio application due to the application of diffusion-weighting gradients and the consequent longer echo times. The signal-to-noise ratio worsens with increasing image resolution and diffusion imaging methods that use multiple and higher b-values. At low signal-to-noise ratios, standard magnitude reconstructed diffusion-weighted images are confounded by the existence of a rectified noise floor, producing poor estimates of diffusion metrics. Herein, we present a simple method of rectified noise floor suppression that involves phase correction of the real data. This approach was evaluated for diffusion-weighted imaging data, obtained from ethanol and water phantoms and the brain of a healthy volunteer. The parameter fits from monoexponential, biexponential, and stretched-exponential diffusion models were computed using phase-corrected real data and magnitude data. The results demonstrate that this newly developed simple approach of using phase-corrected real images acts to reduce or even suppress the confounding effects of a rectified noise floor, thereby producing more accurate estimates of diffusion parameters.

Stimulated echo induced misestimates on diffusion tensor indices and its remedy

To report possible erroneous estimates of diffusion parameters in the twice-refocused spin-echo (TRSE) technique, proposed to eliminate eddy-current-induced geometric distortions in diffusion-weighted echo-planar imaging, when stimulated echo signals are inappropriately included. Eleven subjects were included for imaging experiments on two 1.5 Tesla systems using the TRSE sequence. Three versions, two with unbalanced crusher gradients inserted to dephase the stimulated echo from the b = 0 images and one with balanced crusher gradients, were implemented. The apparent diffusion coefficients (ADC) and fractional anisotropy (FA) were derived and compared. The ADCs obtained with unbalanced crusher gradients were closer to values reported in the literature. Stimulated echo led to ADC over-estimations by 34.2%, 50.4%, 54.0%, 51.5%, 24.0%, and 41.9% in the genu of corpus callosum, splenium of corpus callosum, bilateral corona radiata, internal capsule, mediofrontal gyrus, and the cuneus, respectively (P < 0.01), with concomitant reduction in FA in highly anisotropic regions. Over-estimations of diffusion coefficients were found to be roughly equal along all directions. Formation of stimulated echo in the TRSE technique can lead to erroneous estimations of the diffusion parameters, even if no prominent morphological artifacts are seen.

Comparison of physiological triggering schemes for diffusion‐weighted magnetic resonance imaging in kidneys

To determine the potential benefit of combined respiratory-cardiac triggering for diffusion-weighted imaging (DWI) of kidneys compared to respiratory triggering alone (RT). Renal DWI was performed in 17 volunteers comparing RT, combined respiratory-cardiac triggering (RCT), and combined respiratory-cardiac triggering with slice position correction (RCTF). Data were analyzed in three ways: A1) Model-free analysis of the signal stability over repeated measurements; A2) Analysis of the deviation from diffusion-model fitting comparing the root mean squared error (RMSE), assessing within-subject variabilities; and A3) Analysis of diffusion indices comparing between-subject variabilities. Combined respiratory-cardiac triggering yielded lower signal fluctuations and more reliable diffusion parameter estimation than respiratory triggering alone in all three analysis methods: A1) The mean coefficient of variation (CV) for all subjects was 4.2 +/- 1.1% and 4.3 +/- 0.9% for RCT and RCTF, respectively, which was significantly lower compared to RT (5.3 +/- 0.9%, P < 0.005); A2) RT yielded significantly higher RMSEs than RCT and RCTF; A3) The between-subject variations of diffusion indices tended toward higher values for RT. The results were independent of perfusion contributions to the DWI data. No difference was determined between RCT and RCTF. Total acquisition time was only slightly prolonged for respiratory-cardiac double-triggering. Respiratory-cardiac double-triggering seems advantageous for renal DWI.

Parametrix Approximation of Diffusion Transition Densities

A new analytical approximation tool, derived from the classical PDE theory, is introduced in order to build approximate transition densities of diffusions. The tool is useful for approximate pricing and hedging of financial derivatives and for maximum likelihood and method of moments estimates of diffusion parameters. The approximation is uniform with respect to time and space variables. Moreover, easily computable error bounds are available in any dimension.

Maximum a posteriori estimation of diffusion tensor parameters using a Rician noise model: Why, how and but

The diffusion tensor is a commonly used model for diffusion-weighted MR image data. The parameters are typically estimated by ordinary or weighted least squares on log-transformed data, assuming normal or log-normal distribution of measurement errors respectively. This may not be adequate when using high b-values and or performing high-resolution scans, resulting in poor SNR, in which case the difference between the assumed and the true (Rician) noise model becomes important. As a consequence the estimated diffusion parameters will be biased, underestimating the true diffusion. In this paper a computational framework is presented where parameters pertaining to a spectral decomposition of the diffusion tensor are estimated using a Rician noise model. The parameters are estimated using a Fisher-scoring scheme which gives robust and rapid convergence. It is demonstrated how the Fisher-information matrix can be used as a generic tool for designing optimal experiments. It is shown that the Rician noise model leads to significantly less biased estimates for a large range of b-values and SNR, but that the Rician estimates have a poorer precision compared to the Gaussian model for very low SNR. By pooling the Rician estimates of uncertainty over neighbouring voxel estimates with higher precision, but still not as high as with a Gaussian model, can be obtained. We suggest the use of a Rician estimator when it is important with truly quantitative values and when comparing different predictive models. The higher precision of the Gaussian estimates may be more important when the objective is to compare diffusion related parameters over time or across groups.

Feasibility study for the development of certified reference materials for specific migration testing. Part 2: Estimation of diffusion parameters and comparison of experimental and predicted data

This paper describes the second part of a project whose main objective was to develop the know-how to produce certified reference materials (CRMs) for specific migration testing. Certification parameters discussed are the diffusion coefficient, D P , the respective polymer-specific coefficient, A P , of the migrant polymer combinations and the partitioning coefficient, K P, , F , describing the partitioning of the migrant between the polymer and a food simulant. The parameters were determined for 16 preliminary candidate CRMs. Each parameter was determined by one laboratory. The six materials most suitable as reference materials were selected and the parameters then determined by four laboratories. The coefficients resulting from this small-scale interlaboratory comparison study can be regarded as the most reliable values available to date. These coefficients were applied for a comparison of experimental and predicted migration data. The experimental migration data arose from the same project and were determined by one laboratory for the first 16 materials and subsequently by four laboratories for the six materials selected in the second phase. Overall, experimental and predicted migration data fit together quite well. Roughly half of the predicted data were within ±10%; almost all predicted data were within ±40% compared with the experimental data.

Phase states of methane in fossil coals

NMR measurements have revealed that methane can exist in coal samples in the state of solid solution rather than only adsorbed gas, opening new ways to prevention of gas dynamic accidents in underground coal mines and true estimation of coalbed methane resources. Understanding molecular structure of coal constituents and forms of methane occurrence in coal is the only way of extracting safely either coal or methane. We had studied nuclear magnetic resonance lines in various coals at room or low temperatures and have found that there exist three species of methane molecules differing in molecular mobility. Based on estimated diffusion parameters, these species were attributed to free methane, adsorbed methane, and solid solution of methane in crystalline coal substance. While first two phases are well known and can be analyzed by many different techniques, the last one hardly can be studied by methods other than NMR, resulting in inadequate estimations of methane resources.

A 40Ar/39Ar laser probe study of micas from the Sesia Zone, Italian Alps: implications for metamorphic and deformation histories

Two samples from the Eclogite Micaschist Complex (EMC) and the Seconda Zona Diorito–Kinzigitica (IIDK) of the Sesia Zone have been studied using a high‐spatial resolution laser probe 40Ar/39Ar technique with the aim of investigating the complexities of argon behaviour in metamorphic rocks and comparing their thermal histories. Data from a single large phengite grain from the EMC show a range of ages from mid‐Jurassic to Upper Cretaceous. These ‘apparent age’ variations are spatially related to both locationwithin the grain and to intragrain microstructure. Modelling of the data shows that the profile formedby the diffusion of an excess argon component into the grain, parallel to the mica cleavage. Profileasymmetry is explained by temporal variations in microstructural development enabling excess argon toenter the grain at different times in different places. The temperatures of the initiation of deformationand the possible time‐scales for the deformation can be calculated as a function of cooling rate. Allestimates suggest deformation at greenschist facies, in accord with the observed retrograde mineral assemblage. Absolute temperature estimates for deformation vary by less than 22 °C for different cooling ratesof 10 and 30 °C Ma−1 but vary by 80 °C with different estimates of diffusion parameters. The durationof deformation was for at least 2 Ma at 10 °C Ma−1 or 0.7 Ma at 30 °C Ma−1. Biotites from the IIDKsample record a Permian to Upper Cretaceous age range that correlates with grain size, the smallestgrain sizes yielding the youngest ages. This relationship is best explained by a partial resetting of biotitesduring an Alpine thermal event initiated not more than 70 Ma ago. Modelling of these data suggest thatthe sample never exceeded 300 °C during the Alpine. The profoundly different thermal histories of thetwo units—the EMC recrystallized at 550 °C whilst the IIDK remained below 300 °C—suggests thatthey may not have been juxtaposed until much later than the eclogite facies metamorphism.

Diffusion of silicon and gallium (as an analogue for aluminum) network-forming cations and their relationship to viscosity in albite melt

Self-diffusion of Si and tracer diffusion of Ga have been measured in an albitic melt, Na0.97Al0.99Si3.02O8, at 1 atmosphere between 1160 and 1558°C. Diffusion of these network-forming elements was studied for comparison with viscous transport and Nuclear Magnetic Resonance (NMR) relaxation parameters measured in albite melts and glasses. Gallium was used as an analogue for Al and estimated diffusion parameters for both Ga and Al are presumed to be equivalent. Diffusion can be described by Arrhenius lines for both Si and Ga (with 1-standard errors): +6.58 × 10−3Dsi = 1.37 × 10−4exp(−337.4 ± 52.6/RT)−1.35 × 10−4 +7.97 DAl ∼ DGa = 3.55 × 10−1 exp (−424.6 ± 42.5 /RT)−3.39 × 10−1, where diffusivities are in m2s−1 and activation energies are in kJ/mol. Comparison of Si and Ga diffusivities with Si/Al diffusivities in crystalline albite indicates relatively small differences between activation energies for diffusion of 3+ and 4+ network-forming cations in crystalline and in molten albite. Apparently, the energy barrier to diffusion of these network-forming cations is influenced significantly only by nearest neighbours, and is not strongly affected by changing the dominant structure from four-membered rings of (Si, Al)O4 tetrahedra in crystalline albite to three-, four-, and six-membered rings of tetrahedra in molten albite. Comparison of Na diffusion in albite crystals and glass demonstrates significant differences in activation energies for diffusion. The behaviour of oxygen diffusion appears to be intermediate between Na and network-forming cations, however, this observation is based upon limited oxygen diffusion data for rhyolitic, not albitic, melts. Activation energies for Ga diffusion in albite melt are similar to those measured in rhyolite melt at 1.0 GPa. The silicon activation energy for diffusion is three times higher in albite melt than in rhyolite melt at 1.0 GPa and does not correlate with the activation energy for the inverse of the NMR spin-lattice relaxation. The differences between Si activation energies in albite and rhyolite melts are suggested to be due to the presence of a mixed alkali-like effect in the latter melt. Calculated diffusivities based upon measured viscosities for albite melt and the Eyring equation agree almost within error with Ga diffusivities, but are typically 3–10 times greater than Si diffusivities. This correlation suggests that diffusion of Al in albite melt controls viscous transport. The activation energy for oxygen diffusion in crystalline albite and the estimated activation energy for oxygen diffusion in the melt are much lower than the activation energy for viscous transport and argue against a relationship between oxygen diffusion and viscous transport in this aluminosilicate melt. The more rapid diffusion of Ga and A1 compared to Si in albite melt is proposed to be due to the more frequent formation of five- or six-coordinated Ga-O and Al-O transition state complexes than similar Si-O complexes. The previously observed relationship between viscosity and chemical diffusivities during interdiffusion (Baker, 1992b) suggests that diffusion of Al also controls chemical diffusion in basaltic to rhyolitic melts.

Estimate of diffusion parameters of aircraft exhaust plumes near the tropopause from nitric oxide and turbulence measurements

Horizontal and vertical plume scales and respective diffusivities for dispersion of exhaust plumes from airliners at cruising altitudes are determined from nitric oxide (NO) and turbulence data measured with the DLR Falcon research aircraft flying through the plumes. Ten plumes of known source aircraft were encountered about 5 to 100 min after emission at about 9.4 to 11.3 km altitude near the tropopause in the North Atlantic flight corridor at 8°W on three days in October 1993. The ambient atmosphere was stably stratified with bulk Richardson numbers greater than 10. The measured NO peaks had half widths of 500 to 2000 m with maximum concentrations up to 2.4 parts per billion by volume (ppbv), clearly exceeding the background values between 0.13 and 0.5 ppbv. For analysis the measured plumes are approximated by an analytical Gaussian plume model which accounts for anisotropic diffusion in the stably stratified atmosphere and for shear. Two methods are given to obtain diffusivity parameters from either the individual plume data or the set of all plume measurements. Using estimates of the emitted mass of NO per unit length, the vertical plume width is found to be 140 m on average. This width is related to mixing in the initial trailing vortex pair of the aircraft. The range of the plume data suggests vertical diffusivity values between 0 and 0.6 m2 s−1. The turbulence data exhibit strong anisotropic air motions with practically zero turbulent dissipation and weak vertical velocity fluctuations. This implies very small vertical diffusivities. The horizontal diffusivity is estimated as between 5 and 20 m2 s−1 from the increase of horizontal plume scales with time. For constant diffusivities, shear dominates the lateral dispersion after a time of about 1 hour even for the cases with only a weak mean shear of 0.002 s−1.

AES depth profiling of a new type of multilayer structure composed of Cr/Ni layers of various thicknesses

A new multilayer structure for the systematic study of sputter depth profiling and interdiffusion was designed and sputter-deposited on a smooth silicon substrate. It is composed of alternating chromium and nickel thin films with a thickness increasing from 15 nm to 200 nm in the direction from the multilayer surface to the silicon substrate and with a total thickness of 1.1 microm. The advantages of this structure are: (1) determination of the depth resolution in sputter profiling in the wide range 15 nm-1.1 microm, (2) prompt and precise ion gun calibration at low and high sputtering rates, (3) possibilities of extracting interdiffusion parameters by different methods. AES sputter depth profiles obtained for as-deposited Cr/Ni multilayers and after annealing at 400°C, 500°C and 800°C are presented and discussed. Numerical evaluations of interface width data allow an estimation of diffusion parameters.

Monte Carlo analysis of experiments on individual adatoms

Quantitative studies of individual adatom motion using the field ion microscope are difficult in as much as the number of observations is limited. However, simulations by Monte Carlo techniques make it possible to maximize the information obtained from small statistical samples. Questions encountered in studying the diffusion and interaction of adatoms have therefore been examined by simulation, and results are presented for the following topics: (1) Corrections for the finite size of planes on which atomic diffusion is observed. (2) Statistical scatter in the estimation of diffusion parameters from the temperature dependence of the mean-square displacement. (3) Conditions for measuring rates of single- and double-length jumps in atomic diffusion. (4) Uncertainties in the estimation of interaction energies from pair distribution measurements.