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CONTEXT: The diatomic molecules of potassium 39 K 2 a 3 ∑ u + is widely used in industrial chemicals and alternative energy. Besides that, 39 K 2 a 3 ∑ u + is very useful for researching molecular interactions and energy states, especially in the context of quantum chemistry and spectroscopy. In the present work, a newly proposed diatomic potential model within relativistic and non-relativistic quantum mechanics has been considered, to obtain corresponding energy eigenvalues and related normalized eigenfunctions. METHODS: The Dirac equation has been solved for an arbitrary spin-orbit quantum number κ using the path integral technique with the q -deformed generalized Pöschl-Teller potential ( D G P T ) . By including a Pekeris-type approximation to handle the centrifugal factor, it was possible to obtain the spin and pseudospin-symmetric solution of the relativistic energy eigenvalues and wave equation. To assess the correctness of this work, Maple software was used to present some numerical findings for various values of n and κ . With the constraint λ ~ > η ~ + 1 , it was shown that in the situation of pseudospin symmetry, only bound states exist with negative energy. In the non-relativistic limits, the non-relativistic ro-vibrational energy expression of the diatomic molecule is derived from the relativistic energy equation under spin symmetry. Under Varshni conditions, both vibrational and ro-vibrational energies of the 39 K 2 a 3 ∑ u + molecule were computed and compared with the RKR data. The average absolute percentage deviations from the RKR data obtained for the potassium molecule are 0.5018 % . This demonstrates that the ( D G P T ) model is a very consistent model to study and characterize diatomic molecules.

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Objectives: To explore the effectiveness of diffusion quantitative parameters derived from advanced diffusion models in detecting brain microstructural changes in patients with chronic kidney disease (CKD). Methods: The study comprised 44 CKD patients (eGFR<59 mL/min/1.73 m2) and 35 age-and sex-matched healthy controls. All patients underwent diffusion spectrum imaging (DSI) and conventional magnetic resonance imaging. Reconstructed to obtain diffusion MRI models, including diffusion tensor imaging (DTI), neurite orientation dispersion and density imaging (NODDI) and Mean Apparent Propagator (MAP)-MRI, were processed to obtain multi-parameter maps. The Tract-Based Spatial Statistics (TBSS) analysis was utilized for detecting microstructural differences and Pearson correlation analysis assessed the relationship between renal metabolism markers and diffusion parameters in the brain regions of CKD patients. Receiver operating characteristic (ROC) curve analysis assessed the diagnostic performance of diffusion models, with AUC comparisons made using DeLong's method. Results: Significant differences were noted in DTI, NODDI, and MAP-MRI parameters between CKD patients and controls (p < 0.05). DTI indicated a decrease in Fractional Anisotropy(FA) and an increase in Mean and Radial Diffusivity (MD and RD) in CKD patients. NODDI indicated decreased Intracellular and increased Extracellular Volume Fractions (ICVF and ECVF). MAP-MRI identified extensive microstructural changes, with elevated Mean Squared Displacement (MSD) and Q-space Inverse Variance (QIV) values, and reduced Non-Gaussianity (NG), Axial Non-Gaussianity (NGAx), Radial Non-Gaussianity (NGRad), Return-to-Origin Probability (RTOP), Return-to-Axis Probability (RTAP), and Return-to-Plane Probability (RTPP). There was a moderate correlation between serum uric acid (SUA) and diffusion parameters in six brain regions (p < 0.05). ROC analysis showed the AUC values of DTI_FA ranged from 0.70 to 0.793. MAP_NGAx in the Retrolenticular part of the internal capsule R reported a high AUC value of 0.843 (p < 0.05), which was not significantly different from other diffusion parameters (p > 0.05). Conclusion: The advanced diffusion models (DTI, NODDI, and MAP-MRI) are promising for detecting brain microstructural changes in CKD patients, offering significant insights into CKD-affected brain areas.

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Head motion correction is particularly challenging in diffusion-weighted MRI (dMRI) scans due to the dramatic changes in image contrast at different gradient strengths and directions. Head motion correction is typically performed using a Gaussian Process model implemented in FSL's Eddy. Recently, the 3dSHORE-based SHORELine method was introduced that does not require shell-based acquisitions, but it has not been previously benchmarked. Here we perform a comprehensive evaluation of both methods on realistic simulations of a software fiber phantom that provides known ground-truth head motion. We demonstrate that both methods perform remarkably well, but that performance can be impacted by sampling scheme and the extent of head motion and the denoising strategy applied before head motion correction. Furthermore, we find Eddy benefits from denoising the data first with MP-PCA. In sum, we provide the most extensive known benchmarking of dMRI head motion correction, together with extensive simulation data and a reproducible workflow. PRACTITIONER POINTS: Both Eddy and SHORELine head motion correction methods performed quite well on a large variety of simulated data. Denoising with MP-PCA can improve head motion correction performance when Eddy is used. SHORELine effectively corrects motion in non-shelled diffusion spectrum imaging data.

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Subcortical nuclei and other deep brain structures play essential roles in regulating the central and peripheral nervous systems. However, many of these nuclei and their subregions are challenging to identify and delineate in conventional MRI due to their small size, hidden location, and often subtle contrasts compared to neighboring regions. To address these limitations, we scanned the whole brain of the marmoset monkeys in ex vivo using a clinically feasible diffusion MRI method, called the mean apparent propagator (MAP)-MRI, along with T2W and MTR (T1-like contrast) images acquired at 7 Tesla. Additionally, we registered these multimodal MRI volumes to the high-resolution images of matched whole-brain histology sections with seven different stains obtained from the same brain specimens. At high spatial resolution, the microstructural parameters and fiber orientation distribution functions derived with MAP-MRI can distinguish the subregions of many subcortical and deep brain structures, including fiber tracts of different sizes and orientations. The good correlation with multiple but distinct histological stains from the same brain serves as a thorough validation of the structures identified with MAP-MRI and other MRI parameters. Moreover, the anatomical details of deep brain structures found in the volumes of MAP-MRI parameters are not visible in conventional T1W or T2W images. The high-resolution mapping using novel MRI contrasts, combined and correlated with histology, can elucidate structures that were previously invisible radiologically. Thus, this multimodal approach offers a roadmap toward identifying salient brain areas in vivo in future neuroradiological studies. It also provides a useful anatomical standard reference for the region definition of subcortical targets and the generation of a 3D digital template atlas for the marmoset brain research (Saleem et al., 2023). Additionally, we conducted a cross-species comparison between marmoset and macaque monkeys using results from our previous studies (Saleem et al., 2021). We found that the two species had distinct patterns of iron distribution in subregions of the basal ganglia, red nucleus, and deep cerebellar nuclei, confirmed with T2W MRI and histology.

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Direction of arrival (DOA) estimation for conformal arrays is challenging due to non-omnidirectional element patterns and shadow effects. Conical conformal array (CCA) can avoid the shadow effect at small elevation angles. So CCA is suitable for DOA estimation on both azimuth and elevation angles at small elevation angles. However, the element pattern in CCA cannot be obtained by conventional directional element coordinate transformation. Its local element pattern also has connection with the cone angle. The paper establishes the CCA radiation pattern in local coordinate system using 2-D coordinate transformation. In addition, in the case of large elevation angle, only half elements of the CCA can receive signal due to the shadow effect. The array degrees of freedom (DOF) are reduced by halves. We introduce the difference coarray method, which increases the DOF. Moreover, we propose a more accurate propagator method for 2-D cases. This method constructs a new propagation matrix and reduces the estimation error. In addition, this method reduces computational complexity by using linear computations instead of eigenvalue decomposition (EVD) and avoids spectral search. Simulation and experiment verify the estimation performance of the CCA. Both demonstrate the CCA model established in this paper is corresponding to the designed CCA antenna, and the proposed algorithms meet the needs of CCA angle detection. When the number of array elements is 12, the estimation accuracy is about 5 degrees.

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To better understand documented cognitive decline in hemodialysis (HD) patients, diffusion MRI (dMRI) has been used to characterize brain anatomical deficits relative to controls. Studies to this point have primarily used diffusion tensor imaging (DTI) to model the three-dimensional diffusion of water in HD patients, with DTI parameters reflecting underlying microstructural changes of brain tissue. Since DTI has some limitations in characterizing tissue microstructure, some of which may be complicated by HD, we explored the use of the mean apparent propagator (MAP) model to describe diffusion in HD patients. We collected anatomical T1 and T2 FLAIR MRIs as well as multi-shell dMRI in ten HD participants and ten age-matched controls. The T1 and T2 FLAIR MRIs were used for tissue segmentation and identification of white matter hyperintensity, respectively. Multi-shell dMRI data were used to estimate MAP and DTI diffusion models. Each model was then used to characterize the differences between the HD cohort and the age-matched controls in normal appearing white matter, subcortical gray matter, corpus callosum (CC) and bilateral radiata (Rad). As expected, parameters of both DTI and MAP models of dMRI were significantly different in HD participants compared to controls. However, some MAP parameters suggested additional tissue microstructural changes in HD participants, such as increased axonal diameter. Measurements of non-Gaussianity indicated that MAP provided better a diffusion estimate than DTI, and MAP appeared to provide a more accurate measure of anisotropy in Rad, based on measures of the Rad/CC ratio. In conclusion, parameters of the MAP and DTI models were both sensitive to changes in diffusivity in HD participants compared to controls; however, the MAP model appeared to provide additional detailed information about changes in brain tissue microstructure.

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The relationship between brain microstructure and aging has been the subject of intense study, with diffusion MRI perhaps the most effective modality for elucidating these associations. Here, we used the mean apparent propagator (MAP)-MRI framework, which is suitable to characterize complex microstructure, to investigate age-related cerebral differences in a cohort of cognitively unimpaired participants and compared the results to those derived using diffusion tensor imaging. We studied MAP-MRI metrics, among them the non-Gaussianity (NG) and propagator anisotropy (PA), and established an opposing pattern in white matter of higher NG alongside lower PA among older adults, likely indicative of axonal degradation. In gray matter, however, these two indices were consistent with one another, and exhibited regional pattern heterogeneity compared to other microstructural parameters, which could indicate fewer neuronal projections across cortical layers along with an increased glial concentration. In addition, we report regional variations in the magnitude of age-related microstructural differences consistent with the posterior-anterior shift in aging paradigm. These results encourage further investigations in cognitive impairments and neurodegeneration.

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We investigate the role of leaky guided waves in transcranial ultrasound transmission in temporal and parietal bones at large incidence angles. Our numerical and experimental results show that the dispersion characteristics of the fundamental leaky guided wave mode with longitudinal polarization can be leveraged to estimate the critical angle above which efficient shear mode conversion takes place, and below which major transmission drops can be expected. Simulations that employ a numerical propagator matrix and a Semi-Analytical approach establish the transcranial dispersion characteristics and transmission coefficients at different incident angles. Experimental transmission tests conducted at 500 kHz and radiation tests performed in the 200-800 kHz range confirm the numerical findings in terms of transmitted peak pressure and frequency-radiation angle spectra, based on which the connection between critical angles, dispersion and transmission is demonstrated. Our results support the identification of transcranial ultrasound strategies that leverage shear mode conversion, which is less sensitive to phase aberrations compared to normal incidence ultrasound. These findings can also enable higher transmission rates in cranial bones with low porosity by leveraging dispersion information extracted through signal processing, without requiring measurement of geometric and mechanical properties of the cranial bone.

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The transient resonances are a challenge to bound state quantum mechanics. These states lie in the continuum part of the spectrum of the Hamiltonian. For this, one has to treat a continuum problem due to electron-molecule scattering and the many-electron correlation problem simultaneously. Moreover, the description of a resonance requires a wavefunction that bridges the part that resembles a bound state with another that resembles a continuum state such that the continuity of the wavefunction and its first derivative with respect to the distance between the incoming projectile and the target is maintained. A review of the recent advances in the theoretical investigation of the negative-ion resonances (NIR) is presented. The NIRs are ubiquitous in nature. They result from the scattering of electrons off of an atomic or molecular target. They are important for numerous chemical processes in upper atmosphere, space and even biological systems. A contextual background of the existing theoretical methods as well as the newly-developed multiconfigurational propagator tools based on a complex absorbing potential are discussed.

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Hybrid Diffusion Imaging (HYDI) was one of the first attempts to use multi-shell samplings of the q-space to infer diffusion properties beyond Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI). HYDI was intended as a flexible protocol embedding both DTI (for lower b-values) and HARDI (for higher b-values) processing, as well as Diffusion Spectrum Imaging (DSI) when the entire data set was exploited. In the latter case, the spherical sampling of the q-space is re-gridded by interpolation to a Cartesian lattice whose extent covers the range of acquired b-values, hence being acquisition-dependent. The Discrete Fourier Transform (DFT) is afterwards used to compute the corresponding Cartesian sampling of the Ensemble Average Propagator (EAP) in an entirely non-parametric way. From this lattice, diffusion markers such as the Return To Origin Probability (RTOP) or the Mean Squared Displacement (MSD) can be numerically estimated. We aim at re-formulating this scheme by means of a Fourier Transform encoding matrix that eliminates the need for q-space re-gridding at the same time it preserves the non-parametric nature of HYDI-DSI. The encoding matrix is adaptively designed at each voxel according to the underlying DTI approximation, so that an optimal sampling of the EAP can be pursued without being conditioned by the particular acquisition protocol. The estimation of the EAP is afterwards carried out as a regularized Quadratic Programming (QP) problem, which allows to impose positivity constraints that cannot be trivially embedded within the conventional HYDI-DSI. We demonstrate that the definition of the encoding matrix in the adaptive space allows to analytically (as opposed to numerically) compute several popular descriptors of diffusion with the unique source of error being the cropping of high frequency harmonics in the Fourier analysis of the attenuation signal. They include not only RTOP and MSD, but also Return to Axis/Plane Probabilities (RTAP/RTPP), which are defined in terms of specific spatial directions and are not available with the former HYDI-DSI. We report extensive experiments that suggest the benefits of our proposal in terms of accuracy, robustness and computational efficiency, especially when only standard, non-dedicated q-space samplings are available.

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PURPOSE: We seek to reformulate the so-called Propagator Anisotropy (PA) and Non-Gaussianity (NG), originally conceived for the Mean Apparent Propagator diffusion MRI (MAP-MRI), to the Micro-Structure adaptive convolution kernels and dual Fourier Integral Transforms (MiSFIT). These measures describe relevant normalized features of the Ensemble Average Propagator (EAP). THEORY AND METHODS: First, the indices, which are defined as the EAP's dissimilarity from an isotropic (PA) or a Gaussian (NG) one, are analytically reformulated within the MiSFIT framework. Then a comparison between the resulting maps is drawn by means of a visual analysis, a quantitative assessment via numerical simulations, a test-retest study across the MICRA dataset (6 subjects scanned five times) and, finally, a computational time evaluation. RESULTS: Findings illustrate the visual similarity between the indices computed with either technique. Evaluation against synthetic ground truth data, however, demonstrates MiSFIT's improved accuracy. In addition, the test-retest study reveals MiSFIT's higher degree of reliability in most of white matter regions. Finally, the computational time evaluation shows MiSFIT's time reduction up to two orders of magnitude. CONCLUSIONS: Despite being a direct development on the MAP-MRI representation, the PA and the NG can be reliably and efficiently computed within MiSFIT's framework. This, together with the previous findings in the original MiSFIT's article, could mean the difference that definitely qualifies diffusion MRI to be incorporated into regular clinical settings.

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The variations in cellular composition and tissue architecture measured with histology provide the biological basis for partitioning the brain into distinct cytoarchitectonic areas and for characterizing neuropathological tissue alterations. Clearly, there is an urgent need to develop whole-brain neuroradiological methods that can assess cortical cyto- and myeloarchitectonic features non-invasively. Mean apparent propagator (MAP) MRI is a clinically feasible diffusion MRI method that quantifies efficiently and comprehensively the net microscopic displacements of water molecules diffusing in tissues. We investigate the sensitivity of high-resolution MAP-MRI to detecting areal and laminar variations in cortical cytoarchitecture and compare our results with observations from corresponding histological sections in the entire brain of a rhesus macaque monkey. High-resolution images of MAP-derived parameters, in particular the propagator anisotropy (PA), non-gaussianity (NG), and the return-to-axis probability (RTAP) reveal cortical area-specific lamination patterns in good agreement with the corresponding histological stained sections. In a few regions, the MAP parameters provide superior contrast to the five histological stains used in this study, delineating more clearly boundaries and transition regions between cortical areas and laminar substructures. Throughout the cortex, various MAP parameters can be used to delineate transition regions between specific cortical areas observed with histology and to refine areal boundaries estimated using atlas registration-based cortical parcellation. Using surface-based analysis of MAP parameters we quantify the cortical depth dependence of diffusion propagators in multiple regions-of-interest in a consistent and rigorous manner that is largely independent of the cortical folding geometry. The ability to assess cortical cytoarchitectonic features efficiently and non-invasively, its clinical feasibility, and translatability make high-resolution MAP-MRI a promising 3D imaging tool for studying whole-brain cortical organization, characterizing abnormal cortical development, improving early diagnosis of neurodegenerative diseases, identifying targets for biopsies, and complementing neuropathological investigations.

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Crohn's disease (CD) is a chronic and relapsing inflammatory bowel disorder that has been shown to generate neurological impairments, which has the potential to signify disease activity in an underlying neurological manner. The objective of this study was to investigate the abnormalities of brain microstructure and the corresponding functional connectivity (FC) in patients with CD, as well as their associations with disease condition. Twenty-two patients with CD and 22 age-, gender-, and education-matched healthy controls (HCs) were enrolled in this study. All subjects underwent mean apparent propagator (MAP)-MRI and resting-state functional magnetic resonance imaging (MRI) (rs-fMRI) data collection. Each patient was evaluated clinically for the condition and duration of the disease. The MAP metrics were extracted and compared between two groups. Pearson's correlation analysis was conducted to determine the relationship between disease characteristics and significantly abnormal MAP metrics in the CD group. Regions of interest (ROIs) for ROI-wise FC analysis were selected based on their correlation with MAP metrics. Results showed that multiple brain regions, including the parahippocampus and thalamus, exhibited statistically significant differences in MAP metrics between CD patients and HCs. Additionally, CD patients exhibited decreased FC between the left parahippocampus and bilateral thalamus, as well as the right parahippocampus and bilateral thalamus. The findings of this work provide preliminary evidence that structural abnormalities in the parahippocampal gyrus (PHG) and thalamus, as well as decreased FC between them, may reflect the degree of inflammatory of the disease and serve as brain biomarkers for evaluating CD activity.

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PURPOSE: Distinguishing glioblastoma (GBM) and solitary brain metastasis (SBM) is vital for determining the optimal treatment. GBM and SBM present similar imaging characteristics on conventional magnetic resonance imaging (MRI). The aim of this study was to evaluate the efficacy of quantitative analysis of mean apparent propagator (MAP)-MRI for distinguishing GBM and SBM. METHOD: Eighty-nine patients were enrolled. Regions of interest (ROIs), including the enhancing area (EA), peritumoural high signal intensity area (PHA), and maximum abnormal signal area (MASA), were manually delineated. The following MAP parameters for each region were measured: mean square displacement (MSD), non-Gaussianity (NG), NG axial (NGAx), NG vertical, Q-space inverse variance, return to origin probability (RTOP), return to axis probability (RTAP), and return to plane probability (RTPP). Normalised MAP values from each region were compared between the GBM and SBM groups, and their diagnostic efficiency was assessed. Multivariate logistic regression analysis was used to create the most accurate model. RESULTS: Compared with the SBM group, the MSD was significantly lower in the GBM group, whereas the RTAP, RTOP, and RTPP were significantly higher in each region, except for RTAPPHA (all P < 0.05). RTPPPHA, MSDEA, and RTPPMASA showed the most significant differences (all P < 0.01). The best logistic regression model combined RTPPPHA, MSDEA, and NGAxMASA (area under the curve, 0.840). CONCLUSIONS: Quantitative analysis of MAP-MRI is useful for distinguishing GBM from SBM. Multivariate analysis combined with multiple ROIs can improve diagnostic performance.

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BACKGROUND: To compare the microstructural integrity of the corticospinal tract (CST) between glioma patients with motor epilepsy and without epilepsy using mean apparent propagator magnetic resonance imaging (MAP-MRI). METHODS: A total of 26 patients with glioma adjacent to the CST pathway (10 with motor epilepsy and 16 without epilepsy) and 13 matched healthy controls underwent brain structural and diffusion MRI. The morphological characteristics of the CST (tract volume, tract number, and average length) were extracted, and diffusion parameter values including mean squared displacement (MSD), q-space inverse variance (QIV), return-to-origin probability (RTOP), return-to-axis probabilities (RTAP), return-to-plane probabilities (RTPP), fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) along the CST were evaluated. The CST features were compared between healthy and affected sides and the relative CST features were compared across the three groups of participants. A receiver operating characteristic (ROC) curve was plotted to assess the performance of each relative CST characteristic for glioma-induced CST changes. RESULTS: For patients without epilepsy, the tract number, tract volume, FA, RD, MSD, QIV, and RTAP changed significantly on the affected CST side compared with those on the healthy CST side (P=0.002, 0.002, 0.030 0.017, 0.039, 0.044, and 0.002, respectively). In contrast, for patients with motor epilepsy, no significant difference was found between the affected and healthy side in almost all CST features except RTPP (P=0.028). Compared with patients with motor epilepsy, the relative tract number, tract volume, AD, and RTAP were significantly lower (P=0.027, 0.018, 0.040, and 0.027, respectively) in patients without epilepsy, and their areas under the curve (AUCs) were 0.763, 0.781, 0.744, and 0.763, respectively. No significant difference was found between patients with motor epilepsy and matched healthy controls. CONCLUSIONS: The MAP-MRI is a promising approach for evaluating CST changes. It provides additional information reflecting the microstructural complexity of the CST and demonstrates the preserved microstructural integrity of the CST in glioma patients with motor epilepsy.

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BACKGROUND: White matter (WM) impairment is a hallmark of amyotrophic lateral sclerosis (ALS). This study evaluated the capacity of mean apparent propagator magnetic resonance imaging (MAP-MRI) for detecting ALS-related WM alterations. METHODS: Diffusion images were obtained from 52 ALS patients and 51 controls. MAP-derived indices [return-to-origin/-axis/-plane probability (RTOP/RTAP/RTPP) and non-Gaussianity (NG)/perpendicular/parallel NG (NG⊥/NG||)] were computed. Measures from diffusion tensor/kurtosis imaging (DTI/DKI) and neurite orientation dispersion and density imaging (NODDI) were also obtained. Voxel-wise analysis (VBA) was performed to determine differences in these parameters. Relationship between MAP parameters and disease severity (assessed by the revised ALS Functional Rating Scale (ALSFRS-R)) was evaluated by Pearson's correlation analysis in a voxel-wise way. ALS patients were further divided into two subgroups: 29 with limb-only involvement and 23 with both bulbar and limb involvement. Subgroup analysis was then conducted to investigate diffusion parameter differences related to bulbar impairment. RESULTS: The VBA (with threshold of P < 0.05 after family-wise error correction (FWE)) showed that ALS patients had significantly decreased RTOP/RTAP/RTPP and NG/ NG⊥/NG|| in a set of WM areas, including the bilateral precentral gyrus, corona radiata, posterior limb of internal capsule, midbrain, middle corpus callosum, anterior corpus callosum, parahippocampal gyrus, and medulla. MAP-MRI had the capacity to capture WM damage in ALS, which was higher than DTI and similar to DKI/NODDI. RTOP/RTAP/NG/NG⊥/NG|| parameters, especially in the bilateral posterior limb of internal capsule and middle corpus callosum, were significantly correlated with ALSFRS-R (with threshold of FWE-corrected P < 0.05). The VBA (with FWE-corrected P < 0.05) revealed the significant RTAP reduction in subgroup with both bulbar and limb involvement, compared with those with limb-only involvement. CONCLUSIONS: Microstructural impairments in corticospinal tract and corpus callosum represent the consistent characteristic of ALS. MAP-MRI could provide alternative measures depicting ALS-related WM alterations, complementary to the common diffusion imaging methods.

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A unified approach is presented for investigating coupled spin-orbital fluctuations within a realistic three-orbital model for strongly spin-orbit coupled systems with electron fillingsn= 3, 4, 5 in thet2gsector ofdyz,dxz,dxyorbitals. A generalized fluctuation propagator is constructed which is consistent with the generalized self-consistent Hartree-Fock approximation where all Coulomb interaction contributions involving orbital diagonal and off-diagonal spin and charge condensates are included. Besides the low-energy magnon, intermediate-energy orbiton and spin-orbiton, and high-energy spin-orbit exciton modes, the generalized spectral function also shows other high-energy excitations such as the Hund's coupling induced gapped magnon modes. We relate the characteristic features of the coupled spin-orbital excitations to the complex magnetic behavior resulting from the interplay between electronic bands, spin-orbit coupling, Coulomb interactions, and structural distortion effects, as realized in the compounds NaOsO3, Ca2RuO4, and Sr2IrO4.

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Phase-contrast magnetic resonance velocimetry (PC-MRI) has been widely used to investigate flow properties in numerous systems. In a horizontal cylindrical pipe (3 mm diameter), we investigated the accuracy of PC-MRI as the flow transitioned from laminar to turbulent flow (Reynolds number 352-2708). We focus primarily on velocimetry errors introduced by skewed intra-voxel displacement distributions, a consequence of PC-MRI theory assuming symmetric distributions. We demonstrated how rapid fluctuations in the velocity field, can produce broad asymmetric intravoxel displacement distributions near the wall. Depending on the shape of the distribution, this resulted in PC-MRI measurements under-estimating (positive skewness) or over-estimating (negative skewness) the true mean intravoxel velocity, which could have particular importance to clinical wall shear stress measurements. The magnitude of these velocity errors was shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution. These experimental results confirm our previous theoretical analysis, which gives a relationship for PC-MRI velocimetry errors, as a function of the higher moments of the intravoxel displacement distribution (skewness, variance, and kurtosis) and the experimental parameters q and Δ. This suggests that PC-MRI errors in such unsteady/turbulent flow conditions can potentially be reduced by employing lower q values or shorter observation times Δ.

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PURPOSE: The apparent propagator anisotropy (APA) is a new diffusion MRI metric that, while drawing on the benefits of the ensemble averaged propagator anisotropy (PA) compared to the fractional anisotropy (FA), can be estimated from single-shell data. THEORY AND METHODS: Computation of the full PA requires acquisition of large datasets with many diffusion directions and different b-values, and results in extremely long processing times. This has hindered adoption of the PA by the community, despite evidence that it provides meaningful information beyond the FA. Calculation of the complete propagator can be avoided under the hypothesis that a similar sensitivity/specificity may be achieved from apparent measurements at a given shell. Assuming that diffusion anisotropy (DiA) is nondependent on the b-value, a closed-form expression using information from one single shell (ie, b-value) is reported. RESULTS: Publicly available databases with healthy and diseased subjects are used to compare the APA against other anisotropy measures. The structural information provided by the APA correlates with that provided by the PA for healthy subjects, while it also reveals statistically relevant differences in white matter regions for two pathologies, with a higher reliability than the FA. Additionally, APA has a computational complexity similar to the FA, with processing-times several orders of magnitude below the PA. CONCLUSIONS: The APA can extract more relevant white matter information than the FA, without any additional demands on data acquisition. This makes APA an attractive option for adoption into existing diffusion MRI analysis pipelines.

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BACKGROUND AND PURPOSE: Mean apparent propagator (MAP) MRI is a novel diffusion imaging method to map tissue microstructure. The purpose of this study was to evaluate the diagnostic value of the MAP MRI in Parkinson's disease (PD) in comparison with conventional diffusion tensor imaging (DTI). METHODS: 23 PD patients and 22 age- and gender-matched healthy controls were included. MAP MRI and DTI were performed on a 3T MR scanner with a 20-channel head coil. The MAP metrics including mean square displacement (MSD), return to the origin probability (RTOP), return to the axis probability (RTAP), and return to the plane probability (RTPP), and DTI metrics including fractional anisotropy (FA), and mean diffusivity (MD), were measured in subcortical gray matter and compared between the two groups. The receiver operating characteristic (ROC) curve was used to analyze the diagnostic performance of all the metrics. The association between the diffusion metrics and disease severity was assessed by Pearson correlation analysis. RESULTS: For MAP MRI, the mean values of MSD in the bilateral caudate, pallidum, putamen, thalamus and substantia nigra (SN) were higher in PD patients than in healthy controls (p FDR ≤ 0.001); the mean values of the zero displacement probabilities (RTOP, RTAP, and RTPP) in the bilateral caudate, pallidum, putamen and thalamus were lower in PD patients (p FDR < 0.001). For DTI, only FA in the bilateral SN was significantly higher in PD patients than those in the controls (p FDR < 0.001). ROC analysis showed that the areas under the curves of MAP MRI metrics (MSD, RTOP, RTAP, and RTPP) in the bilateral caudate, pallidum, putamen and thalamus (range, 0.85-0.94) were greater than those of FA and MD of DTI (range, 0.55-0.69) in discriminating between PD patients and healthy controls. RTAP in the ipsilateral pallidum (r = -0.56, p FDR = 0.027), RTOP in the bilateral and contralateral putamen (r = -0.58, p FDR = 0.019; r = -0.57, p FDR = 0.024) were negatively correlated with UPDRS III motor scores. CONCLUSION: MAP MRI outperformed the conventional DTI in the diagnosis of PD and evaluation of the disease severity.