## What is/are Diffusion Coefficient?

Diffusion Coefficient - The framework has higher Li+ diffusion coefficient, lower chemical reactivity, and better lithiophilicity than pure Li.^{[1]}By utilizing Lyapunov direct method, sufficient conditions of Mittag-Leffler (M-L) stability for FRDEs are derived in the form of linear matrix inequalities (LMIs), and the robustness analysis of the controllers to the reaction coefficient and diffusion coefficient of the system is given.

^{[2]}045, RMA4 model with diffusion coefficient of 1 and NH3-N degradation coefficient of 0.

^{[3]}The techniques reveal the trajectories of individual particles, with a resolution well below the diffraction limit of light, and from them the parameters defining the motion model, such as diffusion coefficients and confinement lengths.

^{[4]}The key factor responsible for the change in the characteristics of the oxygen reaction in TTG is the decrease in the electrical conductivity and diffusion coefficients of O2 and Li+ with increasing concentration, due to the viscosity of the solution and low dielectric constant.

^{[5]}Besides, the limited current density and diffusion coefficient were calculated.

^{[6]}When the temperature was between 510 K and 530 K, the diffusion coefficient of Fe2+ and OH− could reach the minimum value of 2.

^{[7]}Studies of Diffusion coefficient, swelling, porosity, loading and drug release at various pH medium, mucoadhesive strength and impact on Caco-2 cell viability were conducted.

^{[8]}The Li+ diffusion coefficient calculated from the CV tests showed that both K+/Cl− and K+/F− co-doping facilitated Li+ diffusion in the LNMO.

^{[9]}The diffusion coefficient, absorption coefficient and permeability coefficient of the composites for each fibre treatment was used to study the absorption kinetics.

^{[10]}Among these parameters, inputs are the diffusion coefficient and inlet flow rate, while outputs are velocity, pressure, and concentration.

^{[11]}The available experimental self-diffusion coefficients of twenty-two liquid elements near their melting temperatures are compared with the calculated data by the first-principal dynamics simulation.

^{[12]}The high spatial resolution available from the high static field gradients of our setup allows the observation of the lithium ion diffusion inside the small (<100 nm) LATP crystallites, yielding a high self-diffusion coefficient of D = 2 × 10−12 m2/s at room temperature.

^{[13]}Taking into account the ionic strength of the solution, the diffusion coefficient of the reducing anion Cr(VI) was calculated, which allowed to move to the criterion equations of the form Nu = f (Pr, Re).

^{[14]}To better understand the diffusion behaviors of Tc(IV)-L complexes in the water-rock system, the diffusion coefficients (Dw) of VO2+ [as a surrogate to 99Tc(IV)] and their complexes with ligands (Oxalate, NTA and EDTA) in water were studied by a capillary method.

^{[15]}Then, the mean drift and diffusion coefficients of the two kinds of motion are calculated with the stochastic averaging methodology for energy envelope under the assumed condition that the impact vibration system is quasi-conservative.

^{[16]}The effects of anisotropy on the drag and diffusion coefficients may have a visible impact on the measured observables associated with heavy quarks, such as the nuclear suppression factor and flow coefficients in high-energetic heavy-ion collisions at the RHIC and LHC.

^{[17]}Through the calculations of the adsorption energy, diffusion energy, diffusion coefficient, and theoretical voltage, we find that with the increasing diameter of the AlN nanotube (AlNNT), the adsorption energy for Mg shows a decreasing trend, while the adsorption energy for Mg2+ shows a contrary trend.

^{[18]}A dissolution model for such bulk carbides is established using thermodynamic and kinetic methods, where the diffusion coefficients for carbon and chromium in austenite and the solute concentrations at the phase interface are calculated assuming local equilibrium conditions.

^{[19]}It leads to the diffusion coefficient to be independent of the spatial position; the volume of the reactor is constant, and the number density of the fuel atoms is also relatively constant.

^{[20]}The comparison of the adsorption properties of the three zeolites shows a particular behavior of the 3A, which is characterized by both the higher water uptake and the specific affinity reflected by the initial adsorption rate and the diffusion coefficient.

^{[21]}The aim of this work was to use the diffusion coefficient ration (Dm/Dline) as a parameter to characterize the stability of protein at high concentration, to compare the effects of ArgHCl and NaCl on the interaction of highly concentrated proteins under different pH conditions, and to explore the correlation with protein stability.

^{[22]}In this model, the feature details of the data are preserved by a diffusion coefficient based on the gradient information.

^{[23]}The diffusion coefficient of a solute as small as argon is much greater than that obtained from the hydrodynamic-based Stokes-Einstein (SE) relation, as was reported experimentally.

^{[24]}The interdiffusion coefficient (DAlCu) was measured by applying Fick's second law.

^{[25]}The MLP inputs were three values of logarithm of normalized signal decays, that is, we assume The output is single for diffusion coefficient 𝐷 or diffusional kurtosis 𝐾.

^{[26]}In the first stage, the recovery of vanadium was possible in its V4+ state at low reduction potentials, whereas for the second stage, cyclic voltammetry was used to calculate the diffusion coefficient and the heterogeneous velocity coefficient of the V5+/V4+ redox pair.

^{[27]}The thicknesses of the sublayers tend to zero with different rates and the diffusion coefficients scale suitably.

^{[28]}Furthermore, extensive numerical evaluation of the system is carried out under different networks, whose results show that the diffusion coefficient can change the patterns significantly.

^{[29]}We collected experimental data on chemical migration from different products into saliva for multiple substance groups and materials, identifying chemical concentration and diffusion coefficient as main properties of influence.

^{[30]}The diffusion coefficient of the curing agent in the course of heating was newly calculated by the initial increase in the absorbance and our model based on Fickian diffusion.

^{[31]}Secondly, the least-squares method for a multivariate polynomial is utilized to functionalize the relation of the thermal group PDF and the core parameters, including diffusion coefficient, removal cross-section, neutron source, and normalized surface flux.

^{[32]}The interdiffusion coefficients were extracted using Sauer–Freise integral.

^{[33]}Kinetic parameters such as the diffusion coefficient D, electron transfer number and the transfer coefficients β at 298 K were 8.

^{[34]}Diffusion coefficients for Na+ was measured in low-permeability samples (diameter of 3 cm and average length of 7 cm) from the deep disposal site of the Siberian Chemical Combine (SCC) using the end-diffusion technique.

^{[35]}Results from CV and SWV measurements show that the redox reaction of Mn(II) on a tungsten working electrode is a diffusion controlled quasi-reversible reaction with two electrons transferred, and the diffusion coefficient is determined as 1.

^{[36]}The cathode process was a quasi-reversible process controlled by diffusion, and the diffusion coefficient was calculated to be 0.

^{[37]}Second, linear sweep voltammetry reveals that the diffusion coefficient is 2.

^{[38]}Diffusion coefficients estimated are of ~10−7cm2/s order.

^{[39]}Here, we report measurements of the molecular self-diffusion coefficient of dense supercritical CH4 reaching the freezing pressure.

^{[40]}Here, we study two-step Fds by considering the magnetic turbulence and background magnetic field in the sheath–MC structure with diffusion coefficients calculated using theoretical models, to reproduce the Fd associated with the ground-level enhancement event on 2000 July 14 by solving the focused transport equation.

^{[41]}In this paper, a theoretical derivation of the diffusion coefficient in the case of a purely turbulent magnetic field is presented.

^{[42]}We use an approximation method to prove the existence of nontrivial weak solutions for two nonlocal inhomogeneous elliptic problems in a bounded domain $$\Omega $$ of $${\mathbb {R}}^n \, (n\ge 1)$$ under weak conditions on the diffusion coefficients M, $$N: (0,+\infty )\rightarrow {\mathbb {R}}$$ and some hypotheses on the $$n\times n$$ matrix function a and the functions f, $$g: \Omega \times {\mathbb {R}}\rightarrow {\mathbb {R}}$$ that we will give below.

^{[43]}The diffusion coefficients of ZnMb in the particle for the distribution (Ddis) and release (Dre) processes are determined from the rate constants, e.

^{[44]}We derive in closed form the dynamics of the optimal Pigouvian tax, that is, its drift and diffusion coefficients.

^{[45]}Finally, the self-diffusion coefficient of [BMIM][BDP] and HAc is 0.

^{[46]}Such surprising observations are rationalized by a simple model highlighting the often overlooked role of the diffusion coefficient ratio of the two vapours in conjunction with the non-ideality of the mixture.

^{[47]}In the present work, an analytical solution is derived for the diffusion equation as applicable to a multicomponent diffusion couple with a constant set of interdiffusion coefficients.

^{[48]}The diffusion coefficients (cm2 s−1) of O2− increase from 7.

^{[49]}Through dimension analysis, the correlation between the collapse coefficient n and the melt surface tension σ, zero-shear melt viscosity η0, diffusion coefficient D, maximum bubble diameter dmax, melt density ρ, initial bubble number density Nini were established and the variation of D with temperature could be predicted as an exponential correlation.

^{[50]}

## diffusion weighted imaging

Diffusion-weighted imaging (DWI) and relative apparent diffusion coefficient (rADC) can be used to predict the upgrade risks of the lesions, and the ADC of upgraded lesions is lower than that of non-upgraded lesions.^{[1]}Diffusion-weighted imaging (A,a) shows cortical hyperintensity in the left temporal, parietal, and occipital lobes with cortical restricted diffusion on apparent diffusion coefficient map (B,b).

^{[2]}The diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC) sequences were normal.

^{[3]}The acute response of malignant glioma to PDT can be detected as linear transient hyperintense signal on diffusion-weighted imaging (DWI) and a decline in apparent diffusion coefficient (ADC) values without symptoms.

^{[4]}These abnormalities showed as a hyperintense signal on diffusion-weighted imaging and a hypointense signal on apparent-diffusion coefficient maps.

^{[5]}MRI showed a 51 × 52 × 65 mm tumor occupying almost the whole prostate gland and invading the seminal vesicle and rectum as moderately heterogeneous hypointensity on T2-weighted image, restricted diffusion on apparent diffusion coefficient map and diffusion-weighted imaging, and heterogeneous enhancement on Gd-enhanced T1-weighted image.

^{[6]}STUDY DESIGN This retrospective study included 98 neonates (35-41 weeks of gestation) with neonatal encephalopathy, who underwent therapeutic hypothermia; diffusion-weighted imaging and proton MR spectroscopy were performed at 24-96 hours (n =56) and 7-14 days (n = 92) after birth, respectively, to estimate apparent diffusion coefficient (ADC) values, N-acetylaspartate and N-acetylaspartylglutamate (tNAA), lactate, and choline concentrations, and lactate/tNAA, tNAA/choline ratios in the deep gray matter.

^{[7]}In this study, we develop a radiomic model for predicting csPCa based solely on native b2000 diffusion weighted imaging (DWIb2000) and debate the effectiveness of apparent diffusion coefficient (ADC) in the same task.

^{[8]}Aim: The study goal is to detect if apparent diffusion coefficient (ADC), a quantitative parameter of diffusion-weighted imaging (DWI), can recognize HCC post TACE residuals.

^{[9]}Diffusion weighted imaging (DWI) and apparent diffusion coefficient (ADC) can be used to reflect tumor microstructure.

^{[10]}The lesions showed high or slightly higher signal on diffusion-weighted imaging and decreased apparent diffusion coefficient (ADC) values, which differed between the two groups (p=0.

^{[11]}Background: The diffusion-weighted imaging (DWI) with apparent diffusion coefficient (ADC) map and the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) constitute the functional MRI technique with many oncological applications as it can define tissue microstructure and characterize the post-treatment changes from a recurrent tumor in treated head and neck squamous cell carcinoma (HNSCC).

^{[12]}His brain MRI showed multifocal lesions with restriction on diffusion-weighted imaging and apparent diffusion coefficient with a hyperintense Video 1.

^{[13]}The acute response of malignant glioma to PDT can be detected as linear transient hyperintense signal on diffusion-weighted imaging (DWI) and a decline in apparent diffusion coefficient values without symptoms.

^{[14]}METHODOLOGICAL INNOVATIONS Current studies of diffusion-weighted imaging (DWI)-MRI with analysis of the apparent diffusion coefficient (ADC) histogram indicate the potential to differentiate blastemal or anaplastic high-risk histology nephroblatoma subtypes.

^{[15]}For MRI, volumetry from T2-weighted images and change in apparent diffusion coefficient (ADC) from diffusion-weighted imaging was used.

^{[16]}Blinded interpretation of MRI for diffusion-weighted imaging and hemorrhage was conducted, with subsequent quantification of apparent diffusion coefficient (ADC) values.

^{[17]}Patients and methods We investigated contrast-enhanced MRI, apparent diffusion coefficient (ADC) in diffusion-weighted imaging and 1H-magnetic resonance spectroscopy (1H-MRS) in detecting early morphologic and metabolic changes in borderline or resectable liver metastases, as a response to first-line neoadjuvant or conversion therapy in a prospective substudy of the RAXO trial (NCT01531621, EudraCT2011-003158-24).

^{[18]}OBJECTIVE To evaluate the feasibility, image quality, and apparent diffusion coefficient (ADC) values of diffusion-weighted imaging (DWI) using echo planar imaging (EPI) with Compressed SENSE (EPICS-DWI) of the abdomen and to compare them with conventional single-shot EPI with parallel imaging (PI) technique (PI-DWI).

^{[19]}Background: To determine whether diffusion-weighted imaging (DWI) with measurement of apparent diffusion coefficient (ADC) will help in differentiating endometrial cancer from normal endometrium and to determine whether the grades of endometrial cancer will show significant difference in ADC values.

^{[20]}Four data sets were independently analyzed by two readers: (1) 3D fat-suppressed T2-weighted imaging (FS-T2WI) alone; (2) the combination of 3D FS-T2WI and T2FFE imaging in the HBP of Gd-EOB-MRI; (3) the combination of 3D FS-T2WI, diffusion-weighted imaging (DWI) with the b-value of 1000 s/mm2 and the apparent diffusion coefficient (ADC); and (4) a dynamic study of Gd-EOB-MRI.

^{[21]}This meta-analysis was performed to evaluate whether apparent diffusion coefficient (ADC) from diffusion-weighted imaging (DWI) can predict treatment response of patients with nasopharyngeal carcinoma.

^{[22]}PURPOSE The purpose of this study was to investigate the age-related changes in apparent diffusion coefficient (ADC) values of the mandibular bone marrow using diffusion-weighted imaging (DWI).

^{[23]}This study was designed to assess the reliability of MRI in diagnostic evaluation of renal masses, specifically characterising lesions with diffusion weighted imaging (DWI) and apparent diffusion coefficient (ADC) values.

^{[24]}Objective The A6702 multisite trial confirmed that apparent diffusion coefficient (ADC) measures can improve breast MRI accuracy and reduce unnecessary biopsies, but also found that technical issues rendered many lesions non-evaluable on diffusion-weighted imaging (DWI).

^{[25]}Editorial for “Apparent Diffusion Coefficient of Brain Abscesses Predicts Microbial Culture Yields” While diffusion-weighted imaging (DWI) was previously used widely in the diagnosis of cerebral ischemia, more recently, it has shown considerable potential for better identification of ring-enhancing mass lesions.

^{[26]}SCBF as a marker of severity was compared to T1 mapping and to spinal cord-optimized diffusion weighted imaging (DWI) with filtered parallel apparent diffusion coefficient.

^{[27]}Ill defined tumor showed moderately heterogeneous hypointensity on T2-weighted image, hypointensity on T1-weighted image, restricted diffusion on diffusion weighted imaging (DWI) and apparent diffusion coefficient map, and heterogeneous enhancement following IV administration of gadolinium diethylenetriaminepentaacetic acid (Gd-DTPA).

^{[28]}To investigate the effect of b value and size of region of interest (ROI) on apparent diffusion coefficient (ADC) measurement and its reproducibility in liver diffusion-weighted imaging (DWI).

^{[29]}OBJECTIVE High b-value diffusion-weighted imaging (hDWI) with a b-value of 2000 s/mm2 provides insufficient image contrast between benign and malignant tissues and an overlap of apparent diffusion coefficient (ADC) between Gleason grades (GG) in prostate cancer (PC).

^{[30]}Radiomics features were extracted from T2 weighted imaging (T2WI), diffusion-weighted imaging (DWI), and apparent diffusion coefficient (ADC); radiomics signatures were built using the least absolute shrinkage and selection operator (LASSO) and logistic regression.

^{[31]}The aim of the study was to analyze computed tomography (CT) perfusion parameters and diffusion-weighted imaging apparent diffusion coefficient (ADC) values in pancreatic ductal adenocarcinoma (PDAC) and to establish the diagnostic value of these modalities determining the tumor grade.

^{[32]}Objective: To research the first-order features of magnetic resonance (MR) diffusion-weighted imaging (DWI)-apparent diffusion coefficient (ADC) in maxillofacial malignant mesenchymal tumours.

^{[33]}Based on the results of the present study, quantifications of the 18F-FDG PET uptake provide useful prognostic data for the evaluation of histopathological response to neoadjuvant treatment as well as the aggressiveness of high-risk sarcomas, whereas no correlation between the different outcome variables and the results for tumor size and diffusion-weighted imaging-derived apparent diffusion coefficient values was found.

^{[34]}This study aimed to establish and validate a radiomics nomogram using the radiomics score (rad-score) based on multiregional diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC) features combined with clinical factors for evaluating HER-2 2+ status of breast cancer.

^{[35]}As the cell density increased, a lower apparent diffusion coefficient (ADC) value was found with the diffusion-weighted imaging (DWI) sequence.

^{[36]}The manual annotations of pelvic bony structures (which included lumbar vertebra, sacrococcyx, ilium, acetabulum, femoral head, femoral neck, ischium, and pubis) on diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC) images were used to create reference standards.

^{[37]}The solid component exhibits slightly higher signal on T2-weighted imaging with fat suppression, restricted diffusion on diffusion weighted imaging (DWI) and apparent diffusion coefficient (ADC) maps, and honeycomb-like persistent enhancement.

^{[38]}Most of the lesions (9/11) exhibited isointensity or slight hyperintensity on diffusion-weighted imaging and hyperintensity on apparent diffusion coefficient maps.

^{[39]}Diffusion weighted imaging (DWI)-derived parameters including the diffusion coefficient (D), fractional order parameter (β) and microstructural quantity (μ) sourced from FROC-DWI, and apparent diffusion coefficient (ADC) derived from mono-exponential DWI, as well as the aspartate aminotransferase-to-platelet ratio index (APRI) and fibrosis-4 (FIB-4) were calculated.

^{[40]}Diffusion-weighted imaging is a non-invasive functional imaging modality for breast tumor characterization through apparent diffusion coefficients.

^{[41]}Diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC) sequences revealed restricted diffusion compatible with cytotoxic edema, whereas single-photon emission computed tomography (SPECT) indicated hyperperfusion in the same region, leading to the conclusion that he was having possible nonconvulsive status epilepticus (NCSE).

^{[42]}A total of 4,424 radiomic features were obtained from contrast-enhanced T1-weighted imaging (CE-T1WI) with the contrast-enhancing and peri-enhancing edema region, T2-weighted imaging (T2WI), diffusion-weighted imaging (DWI)-derived apparent diffusion coefficient (ADC), and 18F-fluorodeoxyglucose positron emission tomography (18F-FDG PET) images.

^{[43]}According to European Society of Breast Radiology diffusion-weighted imaging consensus, mean apparent diffusion coefficient value obtained by drawing a small region of interest on the lesion apparent diffusion coefficient map showed a low diffusion level.

^{[44]}MRI modalities, such as T1, T2, diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC), were used for simulation comparisons.

^{[45]}BACKGROUND Diffusion-weighted imaging (DWI) is an important method for clinically significant prostate cancer (csPCa) diagnosis; however, the Prostate Imaging-Reporting and Data System (PI-RADS) requires the subjective assessment of "markedly hypointense or not" on apparent diffusion coefficient (ADC) map.