Estimation Of Apparent Diffusion Coefficient Research Articles

Electrocatalytic oxidation of methanol to soluble products on polycrystalline platinum: Application of convolution potential sweep voltammetry in the estimation of kinetic parameters

Irreversible oxidation of methanol on polycrystalline platinum leading to soluble products has been carried out by fast scan voltammetry, and the reaction has been studied under diffusion controlled process. The conventional analysis of current–potential data, viz. dependence of peak potential on scan rate and peak width measurements, resulted in the estimation of apparent diffusion coefficient of methanol and the anodic transfer coefficient of the electrode reaction. However, from the convolution potential sweep voltammetry, a more accurate and reliable kinetic data were obtained. Under the above conditions, methanol oxidation follows Butler–Volmer rate law with a linear variation of logarithmic heterogeneous rate constant with electrode potential. A constant apparent anodic transfer coefficient independent of electrode potential was observed pointing to the fact that the standard potential of the reaction cannot be determined from the voltammetric experiments. The experimental current–potential curve was compared with a theoretical voltammogram and further oxidation of products at the electrode surface has also been analyzed using limiting convolution current.

Improving apparent diffusion coefficient estimates and elucidating tumor heterogeneity using Bayesian adaptive smoothing

The spatial distribution of apparent diffusion coefficient (ADC) estimates in tumors is typically heterogeneous, although this observed variability is composed of both true regional differences and random measurement uncertainty. In this study, an adaptive Bayesian adaptive smoothing (BAS) model for estimating ADC values is developed and applied to data acquired in two murine tumor models in vivo. BAS models have previously been shown to reduce parameter uncertainty through the use of a Markov random field. Here, diffusion data acquired with four averages was used as an empirical gold standard for evaluating the BAS model. ADC estimates using BAS displayed a significantly closer accordance with the gold standard data and, following analysis of uncertainty estimates, appeared to even outperform the gold standard. These observations were also reflected in simulations. These results have strong implications for clinical studies, as it suggests that the BAS postprocessing technique can be used to improve ADC estimates without the need to compromise on spatial resolution or signal-to-noise or for the adaptation of acquisition hardware. A novel measure of tumor ADC heterogeneity was also defined, which identified differences between tumors derived from different cell lines, which were reflected in histological variations within the tissue microenvironment.

Evaluating segmentation algorithms for diffusion-weighted MR images: a task-based approach.

Apparent Diffusion Coefficient (ADC) of lesions obtained from Diffusion Weighted Magnetic Resonance Imaging is an emerging biomarker for evaluating anti-cancer therapy response. To compute the lesion's ADC, accurate lesion segmentation must be performed. To quantitatively compare these lesion segmentation algorithms, standard methods are used currently. However, the end task from these images is accurate ADC estimation, and these standard methods don't evaluate the segmentation algorithms on this task-based measure. Moreover, standard methods rely on the highly unlikely scenario of there being perfectly manually segmented lesions. In this paper, we present two methods for quantitatively comparing segmentation algorithms on the above task-based measure; the first method compares them given good manual segmentations from a radiologist, the second compares them even in absence of good manual segmentations.

Heterogeneity of White Matter Hyperintensities in Alzheimer's Disease: Post-Mortem Quantitative MRI and Neuropathology

White matter hyperintensities (WMH) are frequently seen on T2-weighted MRI scans of elderly subjects with and without Alzheimer's disease. WMH are only weakly and inconsistently associated with cognitive decline, which may be explained by heterogeneity of the underlying neuropathological substrates. The use of quantitative MRI could increase specificity for these neuropathological changes. We assessed whether post-mortem quantitative MRI is able to reflect differences in neuropathological correlates of WMH in tissue samples obtained post-mortem from Alzheimer's disease patients and from non-demented elderly. Thirty-three formalin-fixed, coronal brain slices from II Alzheimer's disease patients (mean age: 83 ± 10 years, eight females) and 15 slices from seven non-demented controls (mean age: 78 ± 10 years, four females) with WMH were scanned at 1.5 T using qualitative (fluid-attenuated inversion recovery, FLAIR) and quantitative MRI [diffusion tensor imaging (DTI) including estimation of apparent diffusion coefficient (ADC) and fractional anisotropy (FA), and T1-relaxation time mapping based on flip-angle array). A total of 104 regions of interest were defined on FLAIR images in WMH and normal appearing white matter (NAWM). Neuropathological examination included (semiquantitative assessment of axonal density (Bodian), myelin density (LFB), astrogliosis (GFAP) and microglial activation (HLA-DR). Patient groups (Alzheimer's disease versus controls) and tissue types (WMH versus NAWM) were compared with respect to QMRI and neuropathological measures. Overall, Alzheimer's disease patients had significantly lower FA ( P < 0.01) and higher T1-values than controls ( P = 0.04). WMH showed lower FA ( P < 0.01) and higher T1-values ( P < 0.001) than NAWM in both patient groups. A significant interaction between patient group and tissue type was found for the T1 measurements, indicating that the difference in T1-relaxation time between NAWM and WMH was larger in Alzheimer's disease patients than in non-demented controls. All neuropathological measures showed differences between WMH and NAWM, although the difference in microglial activation was specific for Alzheimer's disease. Multivariate regression models revealed that in Alzheimer's disease, axonal density was an independent determinant of FA, whereas T1 was independently determined by axonal and myelin density and microglial activation. Quantitative MRI techniques reveal differences in WMH between Alzheimer's disease and non-demented elderly, and are able to reflect the severity of the neuropathological changes involved.

Robust estimation of the apparent diffusion coefficient (ADC) in heterogeneous solid tumors

The least-squares algorithm is known to bias apparent diffusion coefficient (ADC) values estimated from magnitude MR data, although this effect is commonly assumed to be negligible. In this study the effect of this bias on tumor ADC estimates was evaluated in vivo and was shown to introduce a consistent and significant underestimation of ADC, relative to those given by a robust maximum likelihood approach (on average, a 23.4 +/- 12% underestimation). Monte Carlo simulations revealed that the magnitude of the bias increased with ADC and decreasing signal-to-noise ratio (SNR). In vivo, this resulted in a much-reduced ability to resolve necrotic regions from surrounding viable tumor tissue compared with a maximum likelihood approach. This has significant implications for the evaluation of diffusion MR data in vivo, in particular in heterogeneous tumor tissue, when evaluating bi- and multiexponential tumor diffusion models for the modeling of data acquired with larger b-values (b > 1000 s/mm(2)) and for data with modest SNR. Use of a robust approach to modeling magnitude MR data from tumors is therefore recommended over the least-squares approach when evaluating data from heterogeneous tumors.

Heterogeneity of white matter hyperintensities in Alzheimer's disease: post-mortem quantitative MRI and neuropathology

White matter hyperintensities (WMH) are frequently seen on T(2)-weighted MRI scans of elderly subjects with and without Alzheimer's disease. WMH are only weakly and inconsistently associated with cognitive decline, which may be explained by heterogeneity of the underlying neuropathological substrates. The use of quantitative MRI could increase specificity for these neuropathological changes. We assessed whether post-mortem quantitative MRI is able to reflect differences in neuropathological correlates of WMH in tissue samples obtained post-mortem from Alzheimer's disease patients and from non-demented elderly. Thirty-three formalin-fixed, coronal brain slices from 11 Alzheimer's disease patients (mean age: 83 +/- 10 years, eight females) and 15 slices from seven non-demented controls (mean age: 78 +/- 10 years, four females) with WMH were scanned at 1.5 T using qualitative (fluid-attenuated inversion recovery, FLAIR) and quantitative MRI [diffusion tensor imaging (DTI) including estimation of apparent diffusion coefficient (ADC) and fractional anisotropy (FA), and T(1)-relaxation time mapping based on flip-angle array). A total of 104 regions of interest were defined on FLAIR images in WMH and normal appearing white matter (NAWM). Neuropathological examination included (semi-)quantitative assessment of axonal density (Bodian), myelin density (LFB), astrogliosis (GFAP) and microglial activation (HLA-DR). Patient groups (Alzheimer's disease versus controls) and tissue types (WMH versus NAWM) were compared with respect to QMRI and neuropathological measures. Overall, Alzheimer's disease patients had significantly lower FA (P < 0.01) and higher T(1)-values than controls (P = 0.04). WMH showed lower FA (P < 0.01) and higher T(1)-values (P < 0.001) than NAWM in both patient groups. A significant interaction between patient group and tissue type was found for the T(1) measurements, indicating that the difference in T(1)-relaxation time between NAWM and WMH was larger in Alzheimer's disease patients than in non-demented controls. All neuropathological measures showed differences between WMH and NAWM, although the difference in microglial activation was specific for Alzheimer's disease. Multivariate regression models revealed that in Alzheimer's disease, axonal density was an independent determinant of FA, whereas T(1) was independently determined by axonal and myelin density and microglial activation. Quantitative MRI techniques reveal differences in WMH between Alzheimer's disease and non-demented elderly, and are able to reflect the severity of the neuropathological changes involved.

A nonstandard smoothing in reconstruction of apparent diffusion coefficient profiles from diffusion weighted images

We present a new variational framework for simultaneous smoothing and estimation of apparent diffusion coefficient (ADC) profiles from High Angular Resolution Diffusion-weighted MRI. The model approximates the ADC profiles at each voxel by a 4th order spherical harmonic series (SHS). The coefficients in SHS are obtained by solving a constrained minimization problem. The smoothing with feature preserved is achieved by minimizing a variable exponent, linear growth functional, and the data constraint is determined by the original Stejskal-Tanner equation. The antipodal symmetry and positiveness of the ADC are accommodated in the model. We use these coefficients and variance of the ADC profiles from its mean to classify the diffusion in each voxel as isotropic, anisotropic with single fiber orientation, or two fiber orientations. The proposed model has been applied to both simulated data and HARD MRI human brain data . The experiments demonstrated the effectiveness of our method in estimation and smoothing of ADC profiles and in enhancement of diffusion anisotropy. Further characterization of non-Gaussian diffusion based on the proposed model showed a consistency between our results and known neuroanatomy.

Apparent diffusion coefficients from high angular resolution diffusion imaging: Estimation and applications

High angular resolution diffusion imaging has recently been of great interest in characterizing non-Gaussian diffusion processes. One important goal is to obtain more accurate fits of the apparent diffusion processes in these non-Gaussian regions, thus overcoming the limitations of classical diffusion tensor imaging. This paper presents an extensive study of high-order models for apparent diffusion coefficient estimation and illustrates some of their applications. Using a meaningful modified spherical harmonics basis to capture the physical constraints of the problem, a new regularization algorithm is proposed. The new smoothing term is based on the Laplace-Beltrami operator and its closed form implementation is used in the fitting procedure. Next, the linear transformation between the coefficients of a spherical harmonic series of order l and independent elements of a rank-l high-order diffusion tensor is explicitly derived. This relation allows comparison of the state-of-the-art anisotropy measures computed from spherical harmonics and tensor coefficients. Published results are reproduced accurately and it is also possible to recover voxels with isotropic, single fiber anisotropic, and multiple fiber anisotropic diffusion. Validation is performed on apparent diffusion coefficients from synthetic data, from a biological phantom, and from a human brain dataset.

Magnetic resonance measurement of tetramethylammonium diffusion in rat brain: Comparison of magnetic resonance and ionophoresis in vivo diffusion measurements

Magnetic resonance (MR) and ionophoresis are two experimental methods that provide measurements of molecular diffusion in living tissue. Typical experimental settings yield MR studies that are sensitive to mean molecular displacements of approximately 5 microm, and ionophoresis experiments to displacements of > or =100 microm. An assessment of the correspondence between the methods is hampered by the fact that no common probe molecule has been used. One of the most frequently utilized probe molecules in ionophoresis measurements is the tetramethylammonium (TMA) ion. In the current work the diffusion properties of TMA were studied in rat brain in vivo with localized (1)H MR spectroscopy (MRS). Standard treatment of the MR data yielded a 3.6-fold lower apparent diffusion coefficient (ADC) compared to ionophoresis. To explore the source of this discrepancy, a separate data processing scheme was applied to the MR data to monitor individual elapsed displacement-distance subpopulations of TMA molecules. This analysis revealed a dependence of the ADC estimation on a given subpopulation's elapsed displacement distance. The MR-derived ADC approached the ionophoresis-derived value as the elapsed displacement distance increased to 15 microm. These observations demonstrate that MR and ionophoresis studies provide complementary information, and that ADC estimates obtained from the two techniques are sensitive to different biophysical determinants.