Fractional Diffusion Research Articles

Parsing heterogeneity in global and local white matter integrity at different stages across the psychosis continuum.

Psychosis progresses along a continuum. While heterogeneity is evident across the continuum, it remains unknown whether this is also reflected in white matter (WM) heterogeneity and whether parsing WM heterogeneity may reveal subgroups with more pronounced clinical features. This analysis included 212 participants consisting of healthy controls (HC, n = 59), individuals with high schizotypy (SPT, n = 27), at-risk mental state (ARMS, n = 35), and patients with first episode psychosis (FEP, n = 50) and schizophrenia (SZ, n = 41). Fractional anisotropy (FA) and mean diffusivity (MD) were derived from diffusion tensor imaging (DTI), and fibre density (FD), a non-tensor-derived diffusion marker, was computed. The Person-Based-Similarity Index (PBSI) and Coefficient of Variation Ratio (CVR) were computed to assess global and local heterogeneity. ANOVAs were performed to determine whether people with deviating PBSIs exhibit more pronounced clinical features. Global heterogeneity for all diffusion parameters significantly differed across groups, with greatest difference in heterogeneity between SZ and HC. Results further indicate that FA deviators exhibit lower global functioning and higher negative symptoms. Local FA heterogeneity was greater in FEP relative to ARMS and HC in almost all WM tracts, while SZ patients specifically showed greater heterogeneity in the right thalamic radiation and the left uncinate compared to HCs. Group differences in WM heterogeneity might be indicative of symptom specificity and duration. While these findings offer valuable insights into the neurobiological variability of psychosis, they are primarily hypothesis-generating. Future large-scale studies are warranted to test the robustness of diffusion markers and their clinical relevance.

Wavelet-based collocation methods for solving multi-dimensional integro-differential systems

This paper presents a comprehensive investigation of wavelet-based collocation methods for solving multi-dimensional integro-differential systems. The research addresses the challenging problem of finding numerical solutions to integro-differential equations (IDEs) that are essential in various scientific and engineering applications. We propose novel numerical approximations for infinitely dimensional problems, including fractional Cattaneo-Rayleigh waves and nonlinear diffusion problems defined on unbounded domains. The study introduces a unified computational strategy that directly applies to IDEs without discretization, particularly focusing on the integer and fractional-order Cattaneo-Rayleigh model of thermoelasticity in one-dimensional zonal regions. Through numerical experiments, we demonstrate that our wavelet collocation approach achieves high efficiency and superior accuracy compared to traditional methods. The results show particularly strong performance in handling systems with differential physical singularities, functional physical singularities, and vector-valued physical singularities. Our approach provides a valuable toolbox for addressing complex modeling challenges in biology, mechanical signal processing, and digital communications where partial integro-differential equations naturally arise.

Numerical approximation for stochastic nonlinear fractional diffusion equation driven by rough noise

In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters belonging to (0, 1/2]. We first provide the regularity of the solution. Then we employ the Wong-Zakai approximation to regularize the rough noise and discuss the convergence of the approximation. Next, the finite element and backward Euler convolution quadrature methods are used to discretize spatial and temporal operators for the obtained regularized equation, and the detailed error analyses are developed. Finally, some numerical examples are presented to confirm the theory.

Global well‐posedness of space‐time fractional diffusion equation with Rockland operator on graded lie group

In this article, we examine the general space‐time fractional diffusion equation for left‐invariant hypoelliptic homogeneous operators on graded Lie groups. Our study covers important examples such as the time fractional diffusion equation, the space‐time fractional diffusion equation when diffusion is under the influence of sub‐Laplacian on the Heisenberg group, or general stratified Lie groups. We establish the global well‐posedness of the Cauchy problem for the general space‐time fractional diffusion equation of the Rockland operator on a graded Lie group in the associated Sobolev spaces and also develop some regularity estimates for it.

Relationship between regional volume changes and water diffusion in fixed marmoset brains: an in vivo and ex vivo comparison

Ex vivo studies of the brain are often employed as experimental systems in neuroscience. In general, brains for ex vivo MRI studies are usually fixed with paraformaldehyde to preserve molecular structure and prevent tissue destruction during long-term storage. As a result, fixing brain tissue causes microstructural changes and a decrease in brain volume. Therefore, the purpose of this study was to investigate the regional effect of brain volume and microstructural changes on the restricted diffusion of water molecules in the common marmoset brain using in vivo and ex vivo brains from the same individual. We used 9.4T magnetic resonance imaging and also compared the T2-weighted images and diffusion-weighted imaging (DWI) data between in vivo and ex vivo brains to investigate changes in brain volume and diffusion of water molecules in 12 common marmosets. We compared fractional anisotropy, mean diffusivity, AD (axial diffusivity), and radial diffusivity values in white matter and gray matter between in vivo and ex vivo brains. We observed that AD showed the strongest correlation with regional volume changes in gray matter. The results showed a strong correlation between AD and changes in brain volume. By comparing the in vivo and ex vivo brains of the same individual, we identified significant correlations between the local effects of perfusion fixation on microstructural and volumetric changes of the brain and alterations in the restricted diffusion of water molecules within the brain. These findings provide valuable insights into the complex relationships between tissue fixation, brain structure, and water diffusion properties in the marmoset brain.

Magnetic resonance diffusion tensor imaging for detecting the cerebral microstructure changes in patients with CSVD -induced mild cognitive impairment.

Cerebral small vessel disease (CSVD)-induced mild cognitive impairment (MCI) has been linked to cognitive decline. Brain atrophy is considered the most common change in MCI patients, which can be measured by diffusion tensor imaging (DTI). The study aimed to explore the relationship between DTI parameters and cognitive function in CSVD patients with MCI. This retrospective analysis involved 185 patients with CSVD, comprising 87 cases with MCI and 98 cases without MCI (NMCI). Analyses of demographic and clinical characteristics were conducted. DTI-measured fractional anisotropy (FA) and mean diffusivity (MD) in the hippocampus and entorhinal cortex regions were examined. The diagnostic values were determined using receiver-operative-curve (ROC) analysis, with the Youden Index identifying optimum sensitivity and specificity. Correlations between Montreal cognitive assessment (MoCA) scores and FA or MD in MCI patients were further assessed. No significant differences were observed in demographic and clinical characteristics between MCI and NMCI groups (all p>0.05), except for diabetes prevalence (p=0.011). Notably, the ROC analysis highlighted the diagnostic potential of FA, showing the maximum area under the curve values (Hippocampus-Left: 0.76; Hippocampus-Right: 0.66; Entorhinal cortex-Left: 0.62; Entorhinal cortex-Right: 0.64). MD exhibited a significant negative correlation with MoCA scores (Hippocampus-Left: r=-0.58, p<0.001; Hippocampus-Right: r=-0.41, p<0.001; Entorhinal cortex-Left: r=-0.49, p<0.001; Entorhinal cortex-Right: r=-0.27, p<0.001), while FA showed a significant positive correlation (Hippocampus-Left: r=0.51, p<0.001; Hippocampus-Right: r=0.31, p=0.004; Entorhinal cortex-Left: r=0.35, p<0.001; Entorhinal cortex-Right: r=0.38, p<0.001). The study demonstrates the diagnostic value of DTI parameters in CSVD patients with MCI, emphasizing the associations between microstructural brain changes and cognitive function.

Diffusion-derived intravoxel-incoherent motion anisotropy relates to CSF and blood flow.

Multi-b-value diffusion MRI was acquired in 32 gradient directions for 11 healthy volunteers, and in six directions for 29 patients with cSVD and 14 controls at 3 T. A physics-informed neural network was used to estimate intravoxel incoherent motion (IVIM)-DTI model parameters, including the parenchymal slow diffusion (D-)tensor and the pseudo-diffusion (D*)-tensor, from which the fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were derived. Comparisons of D*-tensor metrics were made between lateral, third, and fourth ventricles and between the middle cerebral arteries and superior sagittal sinus. Group differences in D*-tensor metrics in normal-appearing white matter were analyzed using multivariable linear regression, correcting for age and sex. D*-anisotropy aligned well with CSF flow and arterial blood flow. FA(D*), MD(D*), AD(D*), and RD(D*) were highest in the third, moderate in the fourth, and lowest in the lateral ventricles. The arteries showed higher MD(D*), AD(D*), and RD(D*) than the sagittal sinus. Higher FA(D*) in the normal-appearing white matter was related to cSVD diagnosis and older age, suggesting microvascular architecture alterations. Multi-b-value, multi-directional diffusion analysis using the IVIM-DTI model enables assessment of the cerebral microstructure, fluid flow, and microvascular architecture, providing information on neurodegeneration, glymphatic waste clearance, and the vasculature in one measurement.

Feynman-Kac formula for tempered fractional general diffusion equations driven by TFBM

In this article, we investigate the following stochastic tempered fractional general diffusion equation driven by tempered fractional Brownian motion (TFBM) ∂ t β , η u ( t , x ) = L u ( t , x ) + u ( t , x ) B ˙ H , λ ( t ) , ( t , x ) ∈ R + × R d , where ∂ t β , η denotes the Caputo tempered fractional derivative with order β ∈ ( 0 , 1 ) and tempered parameter η > 0, 𝔏 is the infinitesimal generator of some general time-homogeneous symmetric strong Markov process { X t } t ≥ 0 with the corresponding transition semigroup { P t , t ≥ 0 } defined by P t f(x): = 𝔼 x [f(X t )], and { B H , λ ( t ) } t ≥ 0 is a TFBM with Hurst index H ∈ ( 1 2 , 1 ) and tempering parameter λ > 0 which is independent of { X t } t ≥ 0 . First of all, a novel estimate of multiple stochastic integrals with respect to the inverse tempered β-stable subordinator D β, η (t) is presented, which greatly contributes to the stochastic analysis. Then after establishing the Fubini Theorem for the stochastic integrals with respect to TFBM B H, λ (t) and the inverse tempered β-stable subordinator D β, η (t), we show that the Feynman-Kac representation u ( t , x ) = E D [ P D β , η ( t ) f ( x ) e ∫ 0 t ∫ 0 t δ ( s − r ) d D β , η ( s ) d B H , λ ( r ) ] is the weak solution of the stochastic tempered fractional general diffusion equation driven by TFBM with the initial value f by means of the techniques of Malliavin calculus and convergence analysis. From the Feynman-Kac formula, several kinds of continuity of the solutions with respect to time and tempered parameter η of tempered fractional derivative are proved by using the scaling property of the inverse tempered β-stable subordinator D β, η (t) and the novel estimate of stochastic integrals with respect to B H, λ (t) and D β, η (t). In particular for the stochastic fractional general diffusion equation driven by fractional Brownian motion (FBM) but in the time fractional derivative case, we can also obtain the sharp upper and lower bounds for the Hölder regularity and the moments of the solution.

Morphological similarity and white matter structural mapping of new daily persistent headache: a structural connectivity and tract-specific study

BackgroundNew daily persistent headache (NDPH) is a rare primary headache disorder characterized by daily and persistent sudden onset headaches. Specific abnormalities in gray matter and white matter structure are associated with pain, but have not been well studied in NDPH. The objective of this work is to explore the fiber tracts and structural connectivity, which can help reveal unique gray and white matter structural abnormalities in NDPH.MethodsThe regional radiomics similarity networks were calculated from T1 weighted (T1w) MRI to depict the gray matter structure. The fiber connectivity matrices weighted by diffusion metrics like fractional anisotropy (FA), mean diffusivity (MD) and radial diffusivity (RD) were built, meanwhile the fiber tracts were segmented by anatomically-guided superficial fiber segmentation (Anat-SFSeg) method to explore the white matter structure from diffusion MRI. The considerable different neuroimaging features between NDPH and healthy controls (HC) were extracted from the connectivity and tract-based analyses. Finally, decision tree regression was used to predict the clinical scores (i.e. pain intensity) from the above neuroimaging features.ResultsT1w and diffusion MRI data were available in 51 participants after quality control: 22 patients with NDPH and 29 HCs. Significantly decreased morphological similarity was found between the right superior frontal gyrus and right hippocampus. The superficial white matter (SWM) showed significantly decreased FA in fiber tracts including the right superficial-frontal, left superficial-occipital, bilateral superficial-occipital-temporal (Sup-OT) and right superficial-temporal, meanwhile significant increased RD was found in the left Sup-OT. For the fiber connectivity, NDPH showed significantly decreased FA in the bilateral basal ganglion and temporal lobe, increased MD in the right frontal lobe, and increased RD in the right frontal lobe and left temporal-occipital lobe. Clinical scores could be predicted dominantly by the above significantly different neuroimaging features through decision tree regression.ConclusionsOur research indicates the structural abnormalities of SWM and the neural pathways projected between regions like right hippocampus and left caudate nucleus, along with morphological similarity changes between the right superior frontal gyrus and right hippocampus, constitute the pathological features of NDPH. The decision tree regression demonstrates correlations between these structural changes and clinical scores.

White matter organization abnormalities in adults with 47,XXX: a 7 Tesla MRI study

47,XXX (Triple X syndrome) is a sex chromosome aneuploidy characterized by the presence of a supernumerary X chromosome in affected females, and has been associated with a variable cognitive, behavioral, and psychiatric phenotype. Alterations in brain gray matter structure and function have been reported, but less is known about white matter (WM) organization in 47,XXX. Therefore, we conducted 7 T diffusion tensor imaging and characterized fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity of 22 adult women with 47,XXX and 22 age-matched typically developing females using tract-based spatial statistics. Relationships between phenotypic traits and WM organization characteristics in 47,XXX were also investigated. Adults with 47,XXX showed lower axial diffusivity in the body of the corpus callosum and the right superior longitudinal fasciculus. WM organization variability was not associated with IQ and social cognition and social functioning deficits in 47,XXX. Our findings indicate an effect of a supernumerary X chromosome in adult women on axonal integrity of the body of the corpus callosum and the right superior longitudinal fasciculus. These findings provide additional insight into the role of the X chromosome on WM organization. Future research is warranted to explore the clinical significant impact of altered WM organization in 47,XXX.

Microstructural alterations of cerebellar peduncles in multiple sclerosis: a diffusion tensor imaging study.

Ataxia, tremors, dysarthria, and sometimes impaired cognition are the signs of cerebellum involvement in multiple sclerosis (MS). These symptoms affect up to 80% of patients and are usually hard to treat. To find the underlying involvement of the cerebellum in MS, we assessed the microstructural alterations with DTI in the cerebellar peduncles of the affected subjects. We included 58 relapsing-remitting MS patients and 27 healthy controls. Patients were divided into 18 patients of relapsing-remitting MS with cerebellar impairment (RRMSc) and 40 without cerebellar impairment (RRMSnc). Using Diffusion Tensor Imaging (DTI), we calculated fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), and axial diffusivity (AD) metrics in all subjects. We also checked if there were associations between DTI metrics and clinical cerebellar measures (i.e., tremor severity and the scale for the assessment and rating of ataxia). ANOVA and post-hoc results showed significant differences in DTI metrics between RRMSc and HC and between RRMSnc and HC subjects. Inferior peduncle RD remained the only metric with a significant difference across all pairwise comparisons. The general linear model assessing the effects of the three study groups on the association between DTI metrics and clinical cerebellar measures yielded no significant result. Our study showed that DTI can mainly reveal significant differences between different MS groups and HCs. Our results imply the role of cerebellar peduncles in the pathophysiology of MS and that this role does not necessarily reflect the severity of cerebellar signs of the patients.

A spline-based framework for solving the space–time fractional convection–diffusion problem

In this study we consider a spline-based collocation method to approximate the solution of fractional convection–diffusion equations which include fractional derivatives in both space and time. This kind of fractional differential equations are valuable for modeling various real-world phenomena across different scientific disciplines such as finance, physics, biology and engineering.The model includes the fractional derivatives of order between 0 and 1 in space and time, considered in the Caputo sense and the spatial fractional diffusion, represented by the Riesz-Caputo derivative (fractional order between 1 and 2). We propose and analyze a collocation method that employs a B-spline representation of the solution. This method exploits the symmetry properties of both the spline basis functions and the Riesz-Caputo operator, leading to an efficient approach for solving the fractional differential problem. We discuss the advantages of using Greville Abscissae as collocation points, and compare this choice with other possible distributions of points. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.

Grading of clear cell renal cell carcinoma by using monoexponential, biexponential, and stretched exponential diffusion-weighted MR imaging.

To evaluate the diagnostic accuracy of monoexponential, biexponential and stretched-exponential diffusion-weighted imaging (DWI) models in the grading of clear cell renal cell carcinoma (ccRCC). Fifty-one patients with pathologically proven ccRCC underwent DWI with fifteen b factors (0, 10, 30, 50, 70, 100, 150, 200, 300, 400, 600, 800, 1000, 1500, 2000 sec/mm²) on a 3.0T MR scanner. The isotropic apparent diffusion coefficient (ADC), true diffusion coefficient (ADCslow), pseudodiffusion coefficient (ADCfast), and fraction of perfusion (f) were derived from DWI using a biexponential model. The water diffusion heterogeneity index (α) and distributed diffusion coefficient (DDC) were derived from DWI using a stretched-exponential model. All values were calculated for the solid area of tumors and compared between high-grade and low-grade ccRCC. The Mann-Whitney U test and receiver operating characteristic (ROC) analysis were used for statistical analysis. The DeLong test was performed to compare the ROC curves. The mean ADC, DDC, ADCslow and α values were significantly lower in high-grade ccRCC than in low-grade ccRCC (P< 0.01). However, the ADCfast and f were not significantly different between the two groups (P > 0.05). According to the ROC analyses, the AUC for α was 0.941, which was significantly greater than those of the other parameters, with a sensitivity of 100% and a specificity of 84.2%. The DeLong test showed that there were significant differences in the ROCs among ADCfast/ADC, ADCfast/α, f/ADCslow, ADCfast/ADCslow, f/α, DDC/α, and f/ADC. Diffusion-related parameters (ADC, DDC, ADCslow and α) could be used to distinguish between low- and high-grade ccRCC. The α derived from the stretched-exponential model may be the most promising parameter for grading ccRCC.

A Novel Approach to Solving Fractional Diffusion Equations Using Fractional Beta Derivative

This paper introduces a novel application of fractional beta derivatives in solving fractional diffusion equations with an emphasis on systems exhibiting anomalous diffusion and memory effects. The work explores the fractional beta derivative as an extension of classical fractional derivatives by incorporating a parameter β (beta) that controls the system’s memory behavior. We investigate both the analytical and numerical solutions of these equations, demonstrating the superior flexibility of fractional beta derivatives in modeling complex diffusion processes. Additionally, we provide a comparison between classical fractional derivatives and the new fractional beta approach to highlight the advantages in terms of accuracy and computational efficiency. We begin by reviewing the theoretical background of fractional derivatives and proceed to introduce the beta derivative as a modification that provides additional flexibility in modeling complex systems. Applications in fields such as control theory, signal processing, and bioengineering are highlighted. Furthermore, numerical methods for solving fractional beta differential equations are discussed, along with potential areas for future research.

Segmental abnormalities of white matter microstructure in multiple sclerosis and neuromyelitis optica spectrum disorder identified by automated fiber quantification

BackgroundMultiple sclerosis (MS) and neuromyelitis optica spectrum disorders (NMOSD) are different in pathogenesis, but both could lead to white matter (WM) microstructural damage. The aim of this study was to explore the differences in the patterns of WM fiber tract damage in relapsing-remitting MS (RRMS) and NMOSD by automated fiber quantification (AFQ). Materials and MethodsForty-one RRMS patients, 30 NMOSD patients and 30 healthy controls (HC) underwent MRI examination. AFQ was applied to identify and quantify 100 equally spaced nodes of specific WM fiber tracts for each participant. Measurements of fractional anisotropy (FA), mean diffusion (MD), axial diffusivity (AD) and radial diffusivity (RD) for each segment of a specific fiber tract were compared between RRMS, NMOSD and HC. ResultsThe decrease in FA was found in 7 fiber tracts in entire tract comparison and 9 fiber tracts in pointwise comparison in RRMS patients. However, the FA in left thalamic radiation (TR) and right uncinate fasciculus showed significant differences between RRMS and HC only in the pointwise comparison, but not in the entire tract comparison. The MD, AD and RD of WM fiber tracts in RRMS patients were extensively increased both in the entire level and in the pointwise level. NMOSD patients showed significant FA decrease in left TR and callosum forceps minor (CF_minor), and significant RD increase in CF_minor in the pointwise level. In the pointwise comparison between RRMS and NMOSD, significant FA decrease was found in right inferior fronto-occipital fasciculus and bilateral inferior longitudinal fasciculus in RRMS patients, focal or widespread MD, AD and RD increase was found in multiple fiber tracts. ConclusionThe AFQ approach is a more sensitive way to reflect WM microstructural abnormalities, revealing extensive WM microstructural damage in RRMS and limited WM fiber tract damage in NMOSD.

Causal relationships between cortical brain structural alterations and migraine subtypes: a bidirectional Mendelian randomization study of 2,347 neuroimaging phenotypes

BackgroundPrevious studies have shown that migraines are associated with brain structural changes. However, the causal relationships between these changes and migraine, as well as its subtypes, migraine with aura (MA) and migraine without aura (MO), remain largely unclear.MethodsWe utilized genome-wide association study (GWAS) summary statistics from European cohorts for 2,347 cortical structural magnetic resonance imaging (MRI) phenotypes, derived from both T1-weighted and diffusion tensor imaging scans (n = 36,663), with migraine and its subtypes (n = 147,970–375,752). Cortical phenotypes included both macrostructural (e.g., cortical thickness, surface area) and microstructural (e.g., fractional anisotropy, mean diffusivity) features. Genetic correlations were first assessed to identify significant associations, followed by bidirectional Mendelian randomization (MR) analyses to determine causal relationships between these brain phenotypes and migraine, as well as its subtypes (MA and MO). Sensitivity analyses were applied to ensure the robustness of the results.ResultsGenetic correlation analysis identified 510 significant associations between cortical structural phenotypes and migraine across 401 distinct traits. Forward MR analysis revealed nine significant causal effects of cortical structural changes on migraine risk. Specifically, increased cortical thickness and local gyrification index in specific cortical regions were associated with a decreased risk of overall migraine, MA, and MO, while intracellular volume fraction and orientation diffusion index in specific regions increased the risk of MA and MO. Reverse MR analysis demonstrated that MA causally increased mean diffusivity in the insular and frontal opercular cortex. Sensitivity analyses confirmed the robustness of these findings, with no evidence of horizontal pleiotropy or heterogeneity.ConclusionThis study identifies causal relationships between cortical neuroimaging phenotypes and migraine, highlighting potential biomarkers for migraine diagnosis, treatment, and prevention.

Stimulated echo acquisition mode (STEAM) diffusion tensor imaging with different diffusion encoding times in the supraspinatus muscle: Test-retest reliability and comparison to spin echo diffusion tensor imaging.

Diffusion tensor imaging (DTI) provides insight into the skeletal muscle microstructure and can be acquired using a stimulated echo acquisition mode (STEAM)-based approach to quantify time-dependent tissue diffusion. This study examined diffusion metrics and signal-to-noise ratio (SNR) in the supraspinatus muscle obtained with a STEAM-DTI sequence with different diffusion encoding times (Δ) and compared them to measures from a spin echo (SE) sequence. Ten healthy subjects (mean age 31.5 ± 4.7years; five females) underwent 3-Tesla STEAM and SE-DTI of the shoulder in three sessions. STEAM was acquired with Δ of 100/200/400/600 ms. The diffusion encoding time in SE scans was 19ms (b = 500s/mm2). Region of interest-based measurement of fractional anisotropy (FA), mean diffusivity (MD), and SNR was performed. Intraclass correlation coefficients (ICCs) were computed to assess test-retest reliability. ANOVA with post-hoc pairwise tests was used to compare measures between different Δ of STEAM as well as STEAM and SE, respectively. FA was significantly higher (FASTEAM: 0.38-0.46 vs. FASE: 0.26) and MD significantly lower (MDSTEAM: 1.20-1.33 vs. MDSE: 1.62×10-3mm2/s) in STEAM compared to SE (p < 0.001, respectively). SNR was significantly higher for SE (72.3 ± 8.7) than for STEAM (p < 0.001). ICCs were excellent for FA in STEAM (≥0.911) and SE (0.960). For MD, ICCs were good for STEAM100ms-600ms (≥0.759) and SE (0.752). STEAM and SE exhibited excellent reliability for FA and good reliability for MD in the supraspinatus muscle. SNR was significantly higher in SE compared to STEAM.

Correlation of White Matter Microstructure MRI and Inflammatory Cytokine Alterations With Symptom Severity in Premenstrual Syndrome.

Women with premenstrual syndrome (PMS) are at increased risk for depression throughout their lives. White matter (WM) microstructure and inflammatory cytokine alterations have been proposed in its etiology. To investigate whether WM, assessed using diffusion tensor imaging (DTI), and inflammatory cytokine levels are altered in PMS, and to examine the relationships between WM microstructure, inflammatory cytokines, and symptom severity. Prospective. Forty-two PMS patients and 58 healthy controls (HCs), categorized according to the daily record of severity of problems (DRSP). 3-T, echo planar imaging DTI. Fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were measured by using tract-based spatial statistics (TBSS). Venous blood was collected to measure cytokines, including interleukin-1β (IL-1β) and tumor necrosis factor-α (TNF-α). Symptoms were assessed by using the DRSP. Two-sample t test or Mann-Whitney U test were used to compare the DRSP and cytokines. Abnormal DTI metrics in WM were extracted and the differences between groups were analyzed by using two sample t-tests. Spearman's correlation (r) was used to assess the relationship between DTI metrics, cytokines, and DRSP. A P-value <0.05 with FDR correction was considered statistically significant. Compared with HCs, PMS patients showed significantly lower FA in the corpus callosum and corona radiata, and significantly higher MD, AD, and RD in the corticospinal tract (CST), and significantly higher MD and RD in the anterior thalamic radiation (ATR). These differential metrics were significantly correlated with DRSP. Patients showed significantly higher IL-1β and TNF-α than HCs. Moreover, TNF-α correlated positively with MD, AD, and RD in both groups (r range, 0.256-0.315). Alterations of WM microstructure and IL-1β and TNF-α may be associated with PMS symptom severity, and TNF-α may correlate with DTI metrics of CST and ATR pathways. 1 TECHNICAL EFFICACY: Stage 2.

Neuroimaging Correlates with Clinical Severity in Wilson Disease: A Multiparametric Quantitative Brain MRI.

Previous studies have reported metal accumulation and microstructure changes in deep gray nuclei (DGN) in Wilson disease (WD). However, there are limited studies that investigate whether there is metal accumulation and microstructure changes in DGN of patients with WD with normal-appearing routine MRI. This study aimed to evaluate multiparametric changes in DGN of WD and whether the findings correlate with clinical severity in patients with WD. The study enrolled 28 patients with WD (19 with neurologic symptoms) and 25 controls. Fractional anisotropy (FA), mean diffusivity (MD), and magnetic susceptibility in globus pallidus, pontine tegmentum, dentate nucleus, red nucleus, head of caudate nucleus, putamen, substantia nigra, and thalamus were extracted. Correlations between imaging data and the Unified Wilson's Disease Rating Scale (UWDRS) neurologic subitems were explored. FA, MD, and susceptibility values were higher in multiple DGN of patients with WD than controls (P < .05). Patients with WD without abnormal signals in DGN on routine MRI also had higher FA, MD, and susceptibility values than controls (P < .017). We found that UWDRS neurologic subscores correlated with FA and susceptibility values of DGN (P < .05). In addition, we also found that FA and susceptibility values in specific structures correlated with specific neurologic symptoms of WD (ie, tremor, parkinsonism, dysarthria, dystonia, and ataxia) (P < .05). Patients with WD have increased FA, MD, and susceptibility values even before the lesion is morphologically apparent on routine MRI. The increased FA and susceptibility values correlate with clinical severity of WD.

Modeling Pollutant Diffusion in the Ground Using Conformable Fractional Derivative in Spherical Coordinates with Complete Symmetry

The conformal fractional derivative (CFD) has become a hot research topic since it has a physical interpretation and is easier to grasp and apply to problems compared with other fractional derivatives. Its application to heat transfer, diffusion, diffusion-advection, and wave propagation problems can be found in the literature. Fractional diffusion equations have received great attention recently due to their applicability in physical, chemical, and biological processes and engineering. The diffusion of the pollutants within the ground, which is an important environmental problem, can be modeled with a diffusion equation. Diffusion in some porous materials or soil can be modeled more accurately with fractional derivatives or the conformal fractional derivative. In this study, the diffusion problem of a spilled pollutant leaking into the ground modeled with the conformal fractional time derivative in spherical coordinates has been solved analytically using the Fourier series for a constant mass flow rate and complete symmetry under the assumptions of homogeneous and isotropic soil, constant soil temperature, and constant permeability. The solutions have been simulated spatially and in time. A parametric analysis of the problem has been performed for several values of the CFD order. The simulation results are interpreted. It has also been suggested how to find the parameters of the soil to see whether the CFD can be used to model the soil or not. The approach described here can also be used for modeling pollution problems involving different boundary conditions.